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+Project Gutenberg's The Concept of Nature, by Alfred North Whitehead
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: The Concept of Nature
+       The Tarner Lectures Delivered in Trinity College, November 1919
+
+Author: Alfred North Whitehead
+
+Release Date: July 16, 2006 [EBook #18835]
+
+Language: English
+
+Character set encoding: UTF-8
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+*** START OF THIS PROJECT GUTENBERG EBOOK THE CONCEPT OF NATURE ***
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+  |                                                                  |
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+  |                                                                  |
+  | "...relating the entity discriminated by sight with that         |
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+  | suggested by the sense.                                          |
+  |                                                                  |
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+  | to inversely.                                                    |
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+
+                            The Concept of
+
+
+                                NATURE
+
+
+                         THE TARNER LECTURES
+                     DELIVERED IN TRINITY COLLEGE
+                            NOVEMBER 1919
+
+
+                        Alfred North Whitehead
+
+
+
+
+PREFACE
+
+
+The contents of this book were originally delivered at Trinity College
+in the autumn of 1919 as the inaugural course of Tarner lectures. The
+Tarner lectureship is an occasional office founded by the liberality of
+Mr Edward Tarner. The duty of each of the successive holders of the post
+will be to deliver a course on 'the Philosophy of the Sciences and the
+Relations or Want of Relations between the different Departments of
+Knowledge.' The present book embodies the endeavour of the first
+lecturer of the series to fulfil his task.
+
+The chapters retain their original lecture form and remain as delivered
+with the exception of minor changes designed to remove obscurities of
+expression. The lecture form has the advantage of suggesting an audience
+with a definite mental background which it is the purpose of the lecture
+to modify in a specific way. In the presentation of a novel outlook with
+wide ramifications a single line of communications from premises to
+conclusions is not sufficient for intelligibility. Your audience will
+construe whatever you say into conformity with their pre-existing
+outlook. For this reason the first two chapters and the last two
+chapters are essential for intelligibility though they hardly add to the
+formal completeness of the exposition. Their function is to prevent the
+reader from bolting up side tracks in pursuit of misunderstandings. The
+same reason dictates my avoidance of the existing technical terminology
+of philosophy. The modern natural philosophy is shot through and
+through with the fallacy of bifurcation which is discussed in the second
+chapter of this work. Accordingly all its technical terms in some subtle
+way presuppose a misunderstanding of my thesis. It is perhaps as well to
+state explicitly that if the reader indulges in the facile vice of
+bifurcation not a word of what I have here written will be intelligible.
+
+The last two chapters do not properly belong to the special course.
+Chapter VIII is a lecture delivered in the spring of 1920 before the
+Chemical Society of the students of the Imperial College of Science and
+Technology. It has been appended here as conveniently summing up and
+applying the doctrine of the book for an audience with one definite type
+of outlook.
+
+This volume on 'the Concept of Nature' forms a companion book to my
+previous work _An Enquiry concerning the Principles of Natural
+Knowledge_. Either book can be read independently, but they supplement
+each other. In part the present book supplies points of view which were
+omitted from its predecessor; in part it traverses the same ground with
+an alternative exposition. For one thing, mathematical notation has been
+carefully avoided, and the results of mathematical deductions are
+assumed. Some of the explanations have been improved and others have
+been set in a new light. On the other hand important points of the
+previous work have been omitted where I have had nothing fresh to say
+about them. On the whole, whereas the former work based itself chiefly
+on ideas directly drawn from mathematical physics, the present book
+keeps closer to certain fields of philosophy and physics to the
+exclusion of mathematics. The two works meet in their discussions of
+some details of space and time.
+
+I am not conscious that I have in any way altered my views. Some
+developments have been made. Those that are capable of a
+non-mathematical exposition have been incorporated in the text. The
+mathematical developments are alluded to in the last two chapters. They
+concern the adaptation of the principles of mathematical physics to the
+form of the relativity principle which is here maintained. Einstein's
+method of using the theory of tensors is adopted, but the application is
+worked out on different lines and from different assumptions. Those of
+his results which have been verified by experience are obtained also by
+my methods. The divergence chiefly arises from the fact that I do not
+accept his theory of non-uniform space or his assumption as to the
+peculiar fundamental character of light-signals. I would not however be
+misunderstood to be lacking in appreciation of the value of his recent
+work on general relativity which has the high merit of first disclosing
+the way in which mathematical physics should proceed in the light of the
+principle of relativity. But in my judgment he has cramped the
+development of his brilliant mathematical method in the narrow bounds of
+a very doubtful philosophy.
+
+The object of the present volume and of its predecessor is to lay the
+basis of a natural philosophy which is the necessary presupposition of a
+reorganised speculative physics. The general assimilation of space and
+time which dominates the constructive thought can claim the independent
+support of Minkowski from the side of science and also of succeeding
+relativists, while on the side of philosophers it was, I believe, one
+theme of Prof. Alexander's Gifford lectures delivered some few years ago
+but not yet published. He also summarised his conclusions on this
+question in a lecture to the Aristotelian Society in the July of 1918.
+Since the publication of _An Enquiry concerning the Principles of
+Natural Knowledge_ I have had the advantage of reading Mr C. D. Broad's
+_Perception, Physics, and Reality_ [Camb. Univ. Press, 1914]. This
+valuable book has assisted me in my discussion in Chapter II, though I
+am unaware as to how far Mr Broad would assent to any of my arguments as
+there stated.
+
+It remains for me to thank the staff of the University Press, its
+compositors, its proof-readers, its clerks, and its managing officials,
+not only for the technical excellence of their work, but for the way
+they have co-operated so as to secure my convenience.
+
+A. N. W.
+
+    IMPERIAL COLLEGE OF SCIENCE
+        AND TECHNOLOGY.
+            _April_, 1920.
+
+
+
+
+CONTENTS
+
+
+   CHAP.                                                  PAGE
+
+       I NATURE AND THOUGHT                                  1
+
+      II THEORIES OF THE BIFURCATION OF NATURE              26
+
+     III TIME                                               49
+
+      IV THE METHOD OF EXTENSIVE ABSTRACTION                74
+
+       V SPACE AND MOTION                                   99
+
+      VI CONGRUENCE                                        120
+
+     VII OBJECTS                                           143
+
+    VIII SUMMARY                                           164
+
+      IX THE ULTIMATE PHYSICAL CONCEPTS                    185
+
+         NOTE: ON THE GREEK CONCEPT OF A POINT             197
+
+         NOTE: ON SIGNIFICANCE AND INFINITE EVENTS         197
+
+         INDEX                                             199
+
+
+
+
+THE CONCEPT OF NATURE
+
+
+
+
+CHAPTER I
+
+NATURE AND THOUGHT
+
+
+The subject-matter of the Tarner lectures is defined by the founder to
+be 'the Philosophy of the Sciences and the Relations or Want of
+Relations between the different Departments of Knowledge.' It is fitting
+at the first lecture of this new foundation to dwell for a few moments
+on the intentions of the donor as expressed in this definition; and I do
+so the more willingly as I shall thereby be enabled to introduce the
+topics to which the present course is to be devoted.
+
+We are justified, I think, in taking the second clause of the definition
+as in part explanatory of the earlier clause. What is the philosophy of
+the sciences? It is not a bad answer to say that it is the study of the
+relations between the different departments of knowledge. Then with
+admirable solicitude for the freedom of learning there is inserted in
+the definition after the word 'relations' the phrase 'or want of
+relations.' A disproof of relations between sciences would in itself
+constitute a philosophy of the sciences. But we could not dispense
+either with the earlier or the later clause. It is not every relation
+between sciences which enters into their philosophy. For example biology
+and physics are connected by the use of the microscope. Still, I may
+safely assert that a technical description of the uses of the microscope
+in biology is not part of the philosophy of the sciences. Again, you
+cannot abandon the later clause of the definition; namely that
+referring to the relations between the sciences, without abandoning the
+explicit reference to an ideal in the absence of which philosophy must
+languish from lack of intrinsic interest. That ideal is the attainment
+of some unifying concept which will set in assigned relationships within
+itself all that there is for knowledge, for feeling, and for emotion.
+That far off ideal is the motive power of philosophic research; and
+claims allegiance even as you expel it. The philosophic pluralist is a
+strict logician; the Hegelian thrives on contradictions by the help of
+his absolute; the Mohammedan divine bows before the creative will of
+Allah; and the pragmatist will swallow anything so long as it 'works.'
+
+The mention of these vast systems and of the age-long controversies from
+which they spring, warns us to concentrate. Our task is the simpler one
+of the philosophy of the sciences. Now a science has already a certain
+unity which is the very reason why that body of knowledge has been
+instinctively recognised as forming a science. The philosophy of a
+science is the endeavour to express explicitly those unifying
+characteristics which pervade that complex of thoughts and make it to be
+a science. The philosophy of the sciences--conceived as one subject--is
+the endeavour to exhibit all sciences as one science, or--in case of
+defeat--the disproof of such a possibility.
+
+Again I will make a further simplification, and confine attention to the
+natural sciences, that is, to the sciences whose subject-matter is
+nature. By postulating a common subject-matter for this group of
+sciences a unifying philosophy of natural science has been thereby
+presupposed.
+
+What do we mean by nature? We have to discuss the philosophy of natural
+science. Natural science is the science of nature. But--What is nature?
+
+Nature is that which we observe in perception through the senses. In
+this sense-perception we are aware of something which is not thought and
+which is self-contained for thought. This property of being
+self-contained for thought lies at the base of natural science. It means
+that nature can be thought of as a closed system whose mutual relations
+do not require the expression of the fact that they are thought about.
+
+Thus in a sense nature is independent of thought. By this statement no
+metaphysical pronouncement is intended. What I mean is that we can think
+about nature without thinking about thought. I shall say that then we
+are thinking 'homogeneously' about nature.
+
+Of course it is possible to think of nature in conjunction with thought
+about the fact that nature is thought about. In such a case I shall say
+that we are thinking 'heterogeneously' about nature. In fact during the
+last few minutes we have been thinking heterogeneously about nature.
+Natural science is exclusively concerned with homogeneous thoughts about
+nature.
+
+But sense-perception has in it an element which is not thought. It is a
+difficult psychological question whether sense-perception involves
+thought; and if it does involve thought, what is the kind of thought
+which it necessarily involves. Note that it has been stated above that
+sense-perception is an awareness of something which is not thought.
+Namely, nature is not thought. But this is a different question, namely
+that the fact of sense-perception has a factor which is not thought. I
+call this factor 'sense-awareness.' Accordingly the doctrine that
+natural science is exclusively concerned with homogeneous thoughts about
+nature does not immediately carry with it the conclusion that natural
+science is not concerned with sense-awareness.
+
+However, I do assert this further statement; namely, that though natural
+science is concerned with nature which is the terminus of
+sense-perception, it is not concerned with the sense-awareness itself.
+
+I repeat the main line of this argument, and expand it in certain
+directions.
+
+Thought about nature is different from the sense-perception of nature.
+Hence the fact of sense-perception has an ingredient or factor which is
+not thought. I call this ingredient sense-awareness. It is indifferent
+to my argument whether sense-perception has or has not thought as
+another ingredient. If sense-perception does not involve thought, then
+sense-awareness and sense-perception are identical. But the something
+perceived is perceived as an entity which is the terminus of the
+sense-awareness, something which for thought is beyond the fact of that
+sense-awareness. Also the something perceived certainly does not contain
+other sense-awarenesses which are different from the sense-awareness
+which is an ingredient in that perception. Accordingly nature as
+disclosed in sense-perception is self-contained as against
+sense-awareness, in addition to being self-contained as against thought.
+I will also express this self-containedness of nature by saying that
+nature is closed to mind.
+
+This closure of nature does not carry with it any metaphysical doctrine
+of the disjunction of nature and mind. It means that in sense-perception
+nature is disclosed as a complex of entities whose mutual relations are
+expressible in thought without reference to mind, that is, without
+reference either to sense-awareness or to thought. Furthermore, I do not
+wish to be understood as implying that sense-awareness and thought are
+the only activities which are to be ascribed to mind. Also I am not
+denying that there are relations of natural entities to mind or minds
+other than being the termini of the sense-awarenesses of minds.
+Accordingly I will extend the meaning of the terms 'homogeneous
+thoughts' and 'heterogeneous thoughts' which have already been
+introduced. We are thinking 'homogeneously' about nature when we are
+thinking about it without thinking about thought or about
+sense-awareness, and we are thinking 'heterogeneously' about nature when
+we are thinking about it in conjunction with thinking either about
+thought or about sense-awareness or about both.
+
+I also take the homogeneity of thought about nature as excluding any
+reference to moral or aesthetic values whose apprehension is vivid in
+proportion to self-conscious activity. The values of nature are perhaps
+the key to the metaphysical synthesis of existence. But such a synthesis
+is exactly what I am not attempting. I am concerned exclusively with the
+generalisations of widest scope which can be effected respecting that
+which is known to us as the direct deliverance of sense-awareness.
+
+I have said that nature is disclosed in sense-perception as a complex of
+entities. It is worth considering what we mean by an entity in this
+connexion. 'Entity' is simply the Latin equivalent for 'thing' unless
+some arbitrary distinction is drawn between the words for technical
+purposes. All thought has to be about things. We can gain some idea of
+this necessity of things for thought by examination of the structure of
+a proposition.
+
+Let us suppose that a proposition is being communicated by an expositor
+to a recipient. Such a proposition is composed of phrases; some of these
+phrases may be demonstrative and others may be descriptive.
+
+By a demonstrative phrase I mean a phrase which makes the recipient
+aware of an entity in a way which is independent of the particular
+demonstrative phrase. You will understand that I am here using
+'demonstration' in the non-logical sense, namely in the sense in which a
+lecturer demonstrates by the aid of a frog and a microscope the
+circulation of the blood for an elementary class of medical students. I
+will call such demonstration 'speculative' demonstration, remembering
+Hamlet's use of the word 'speculation' when he says,
+
+    There is no speculation in those eyes.
+
+Thus a demonstrative phrase demonstrates an entity speculatively. It may
+happen that the expositor has meant some other entity--namely, the
+phrase demonstrates to him an entity which is diverse from the entity
+which it demonstrates to the recipient. In that case there is confusion;
+for there are two diverse propositions, namely the proposition for the
+expositor and the proposition for the recipient. I put this possibility
+aside as irrelevant for our discussion, though in practice it may be
+difficult for two persons to concur in the consideration of exactly the
+same proposition, or even for one person to have determined exactly the
+proposition which he is considering.
+
+Again the demonstrative phrase may fail to demonstrate any entity. In
+that case there is no proposition for the recipient. I think that we
+may assume (perhaps rashly) that the expositor knows what he means.
+
+A demonstrative phrase is a gesture. It is not itself a constituent of
+the proposition, but the entity which it demonstrates is such a
+constituent. You may quarrel with a demonstrative phrase as in some way
+obnoxious to you; but if it demonstrates the right entity, the
+proposition is unaffected though your taste may be offended. This
+suggestiveness of the phraseology is part of the literary quality of the
+sentence which conveys the proposition. This is because a sentence
+directly conveys one proposition, while in its phraseology it suggests a
+penumbra of other propositions charged with emotional value. We are now
+talking of the one proposition directly conveyed in any phraseology.
+
+This doctrine is obscured by the fact that in most cases what is in form
+a mere part of the demonstrative gesture is in fact a part of the
+proposition which it is desired directly to convey. In such a case we
+will call the phraseology of the proposition elliptical. In ordinary
+intercourse the phraseology of nearly all propositions is elliptical.
+
+Let us take some examples. Suppose that the expositor is in London, say
+in Regent's Park and in Bedford College, the great women's college which
+is situated in that park. He is speaking in the college hall and he
+says,
+
+    'This college building is commodious.'
+
+The phrase 'this college building' is a demonstrative phrase. Now
+suppose the recipient answers,
+
+    'This is not a college building, it is the lion-house in the Zoo.'
+
+Then, provided that the expositor's original proposition has not been
+couched in elliptical phraseology, the expositor sticks to his original
+proposition when he replies,
+
+    'Anyhow, _it_ is commodious.'
+
+Note that the recipient's answer accepts the speculative demonstration
+of the phrase 'This college building.' He does not say, 'What do you
+mean?' He accepts the phrase as demonstrating an entity, but declares
+that same entity to be the lion-house in the Zoo. In his reply, the
+expositor in his turn recognises the success of his original gesture as
+a speculative demonstration, and waives the question of the suitability
+of its mode of suggestiveness with an 'anyhow.' But he is now in a
+position to repeat the original proposition with the aid of a
+demonstrative gesture robbed of any suggestiveness, suitable or
+unsuitable, by saying,
+
+    '_It_ is commodious.'
+
+The '_it_' of this final statement presupposes that thought has seized
+on the entity as a bare objective for consideration.
+
+We confine ourselves to entities disclosed in sense-awareness. The
+entity is so disclosed as a relatum in the complex which is nature. It
+dawns on an observer because of its relations; but it is an objective
+for thought in its own bare individuality. Thought cannot proceed
+otherwise; namely, it cannot proceed without the ideal bare 'it' which
+is speculatively demonstrated. This setting up of the entity as a bare
+objective does not ascribe to it an existence apart from the complex in
+which it has been found by sense-perception. The 'it' for thought is
+essentially a relatum for sense-awareness.
+
+The chances are that the dialogue as to the college building takes
+another form. Whatever the expositor originally meant, he almost
+certainly now takes his former statement as couched in elliptical
+phraseology, and assumes that he was meaning,
+
+    'This is a college building and is commodious.'
+
+Here the demonstrative phrase or the gesture, which demonstrates the
+'it' which is commodious, has now been reduced to 'this'; and the
+attenuated phrase, under the circumstances in which it is uttered, is
+sufficient for the purpose of correct demonstration. This brings out the
+point that the verbal form is never the whole phraseology of the
+proposition; this phraseology also includes the general circumstances of
+its production. Thus the aim of a demonstrative phrase is to exhibit a
+definite 'it' as a bare objective for thought; but the _modus operandi_
+of a demonstrative phrase is to produce an awareness of the entity as a
+particular relatum in an auxiliary complex, chosen merely for the sake
+of the speculative demonstration and irrelevant to the proposition. For
+example, in the above dialogue, colleges and buildings, as related to
+the 'it' speculatively demonstrated by the phrase 'this college
+building,' set that 'it' in an auxiliary complex which is irrelevant to
+the proposition
+
+    'It is commodious.'
+
+Of course in language every phrase is invariably highly elliptical.
+Accordingly the sentence
+
+    'This college building is commodious'
+
+means probably
+
+    'This college building is commodious as a college building.'
+
+But it will be found that in the above discussion we can replace
+'commodious' by 'commodious as a college building' without altering our
+conclusion; though we can guess that the recipient, who thought he was
+in the lion-house of the Zoo, would be less likely to assent to.
+
+    'Anyhow, it is commodious as a college building.'
+
+A more obvious instance of elliptical phraseology arises if the
+expositor should address the recipient with the remark,
+
+    'That criminal is your friend.'
+
+The recipient might answer,
+
+    'He is my friend and you are insulting.'
+
+Here the recipient assumes that the phrase 'That criminal' is elliptical
+and not merely demonstrative. In fact, pure demonstration is impossible
+though it is the ideal of thought. This practical impossibility of pure
+demonstration is a difficulty which arises in the communication of
+thought and in the retention of thought. Namely, a proposition about a
+particular factor in nature can neither be expressed to others nor
+retained for repeated consideration without the aid of auxiliary
+complexes which are irrelevant to it.
+
+I now pass to descriptive phrases. The expositor says,
+
+    'A college in Regent's Park is commodious.'
+
+The recipient knows Regent's Park well. The phrase 'A college in
+Regent's Park' is descriptive for him. If its phraseology is not
+elliptical, which in ordinary life it certainly will be in some way or
+other, this proposition simply means,
+
+    'There is an entity which is a college building in Regent's Park
+    and is commodious.'
+
+If the recipient rejoins,
+
+    'The lion-house in the Zoo is the only commodious building in
+    Regent's Park,'
+
+he now contradicts the expositor, on the assumption that a lion-house in
+a Zoo is not a college building.
+
+Thus whereas in the first dialogue the recipient merely quarrelled with
+the expositor without contradicting him, in this dialogue he contradicts
+him. Thus a descriptive phrase is part of the proposition which it helps
+to express, whereas a demonstrative phrase is not part of the
+proposition which it helps to express.
+
+Again the expositor might be standing in Green Park--where there are no
+college buildings--and say,
+
+    'This college building is commodious.'
+
+Probably no proposition will be received by the recipient because the
+demonstrative phrase,
+
+    'This college building'
+
+has failed to demonstrate owing to the absence of the background of
+sense-awareness which it presupposes.
+
+But if the expositor had said,
+
+    'A college building in Green Park is commodious,'
+
+the recipient would have received a proposition, but a false one.
+
+Language is usually ambiguous and it is rash to make general assertions
+as to its meanings. But phrases which commence with 'this' or 'that' are
+usually demonstrative, whereas phrases which commence with 'the' or 'a'
+are often descriptive. In studying the theory of propositional
+expression it is important to remember the wide difference between the
+analogous modest words 'this' and 'that' on the one hand and 'a' and
+'the' on the other hand. The sentence
+
+    'The college building in Regent's Park is commodious'
+
+means, according to the analysis first made by Bertrand Russell, the
+proposition,
+
+   'There is an entity which (i) is a college building in Regent's
+   Park and (ii) is commodious and (iii) is such that any college
+   building in Regent's Park is identical with it.'
+
+The descriptive character of the phrase 'The college building in
+Regent's Park' is thus evident. Also the proposition is denied by the
+denial of any one of its three component clauses or by the denial of any
+combination of the component clauses. If we had substituted 'Green Park'
+for 'Regent's Park' a false proposition would have resulted. Also the
+erection of a second college in Regent's Park would make the proposition
+false, though in ordinary life common sense would politely treat it as
+merely ambiguous.
+
+'The Iliad' for a classical scholar is usually a demonstrative phrase;
+for it demonstrates to him a well-known poem. But for the majority of
+mankind the phrase is descriptive, namely, it is synonymous with 'The
+poem named "the Iliad".'
+
+Names may be either demonstrative or descriptive phrases. For example
+'Homer' is for us a descriptive phrase, namely, the word with some
+slight difference in suggestiveness means 'The man who wrote the Iliad.'
+
+This discussion illustrates that thought places before itself bare
+objectives, entities as we call them, which the thinking clothes by
+expressing their mutual relations. Sense-awareness discloses fact with
+factors which are the entities for thought. The separate distinction of
+an entity in thought is not a metaphysical assertion, but a method of
+procedure necessary for the finite expression of individual
+propositions. Apart from entities there could be no finite truths; they
+are the means by which the infinitude of irrelevance is kept out of
+thought.
+
+To sum up: the termini for thought are entities, primarily with bare
+individuality, secondarily with properties and relations ascribed to
+them in the procedure of thought; the termini for sense-awareness are
+factors in the fact of nature, primarily relata and only secondarily
+discriminated as distinct individualities.
+
+No characteristic of nature which is immediately posited for knowledge
+by sense-awareness can be explained. It is impenetrable by thought, in
+the sense that its peculiar essential character which enters into
+experience by sense-awareness is for thought merely the guardian of its
+individuality as a bare entity. Thus for thought 'red' is merely a
+definite entity, though for awareness 'red' has the content of its
+individuality. The transition from the 'red' of awareness to the 'red'
+of thought is accompanied by a definite loss of content, namely by the
+transition from the factor 'red' to the entity 'red.' This loss in the
+transition to thought is compensated by the fact that thought is
+communicable whereas sense-awareness is incommunicable.
+
+Thus there are three components in our knowledge of nature, namely,
+fact, factors, and entities. Fact is the undifferentiated terminus of
+sense-awareness; factors are termini of sense-awareness, differentiated
+as elements of fact; entities are factors in their function as the
+termini of thought. The entities thus spoken of are natural entities.
+Thought is wider than nature, so that there are entities for thought
+which are not natural entities.
+
+When we speak of nature as a complex of related entities, the 'complex'
+is fact as an entity for thought, to whose bare individuality is
+ascribed the property of embracing in its complexity the natural
+entities. It is our business to analyse this conception and in the
+course of the analysis space and time should appear. Evidently the
+relations holding between natural entities are themselves natural
+entities, namely they are also factors of fact, there for
+sense-awareness. Accordingly the structure of the natural complex can
+never be completed in thought, just as the factors of fact can never be
+exhausted in sense-awareness. Unexhaustiveness is an essential character
+of our knowledge of nature. Also nature does not exhaust the matter for
+thought, namely there are thoughts which would not occur in any
+homogeneous thinking about nature.
+
+The question as to whether sense-perception involves thought is largely
+verbal. If sense-perception involves a cognition of individuality
+abstracted from the actual position of the entity as a factor in fact,
+then it undoubtedly does involve thought. But if it is conceived as
+sense-awareness of a factor in fact competent to evoke emotion and
+purposeful action without further cognition, then it does not involve
+thought. In such a case the terminus of the sense-awareness is something
+for mind, but nothing for thought. The sense-perception of some lower
+forms of life may be conjectured to approximate to this character
+habitually. Also occasionally our own sense-perception in moments when
+thought-activity has been lulled to quiescence is not far off the
+attainment of this ideal limit.
+
+The process of discrimination in sense-awareness has two distinct sides.
+There is the discrimination of fact into parts, and the discrimination
+of any part of fact as exhibiting relations to entities which are not
+parts of fact though they are ingredients in it. Namely the immediate
+fact for awareness is the whole occurrence of nature. It is nature as an
+event present for sense-awareness, and essentially passing. There is no
+holding nature still and looking at it. We cannot redouble our efforts
+to improve our knowledge of the terminus of our present sense-awareness;
+it is our subsequent opportunity in subsequent sense-awareness which
+gains the benefit of our good resolution. Thus the ultimate fact for
+sense-awareness is an event. This whole event is discriminated by us
+into partial events. We are aware of an event which is our bodily life,
+of an event which is the course of nature within this room, and of a
+vaguely perceived aggregate of other partial events. This is the
+discrimination in sense-awareness of fact into parts.
+
+I shall use the term 'part' in the arbitrarily limited sense of an event
+which is part of the whole fact disclosed in awareness.
+
+Sense-awareness also yields to us other factors in nature which are not
+events. For example, sky-blue is seen as situated in a certain event.
+This relation of situation requires further discussion which is
+postponed to a later lecture. My present point is that sky-blue is found
+in nature with a definite implication in events, but is not an event
+itself. Accordingly in addition to events, there are other factors in
+nature directly disclosed to us in sense-awareness. The conception in
+thought of all the factors in nature as distinct entities with definite
+natural relations is what I have in another place[1] called the
+'diversification of nature.'
+
+[1] Cf. _Enquiry_.
+
+There is one general conclusion to be drawn from the foregoing
+discussion. It is that the first task of a philosophy of science should
+be some general classification of the entities disclosed to us in
+sense-perception.
+
+Among the examples of entities in addition to 'events' which we have
+used for the purpose of illustration are the buildings of Bedford
+College, Homer, and sky-blue. Evidently these are very different sorts
+of things; and it is likely that statements which are made about one
+kind of entity will not be true about other kinds. If human thought
+proceeded with the orderly method which abstract logic would suggest to
+it, we might go further and say that a classification of natural
+entities should be the first step in science itself. Perhaps you will be
+inclined to reply that this classification has already been effected,
+and that science is concerned with the adventures of material entities
+in space and time.
+
+The history of the doctrine of matter has yet to be written. It is the
+history of the influence of Greek philosophy on science. That influence
+has issued in one long misconception of the metaphysical status of
+natural entities. The entity has been separated from the factor which is
+the terminus of sense-awareness. It has become the substratum for that
+factor, and the factor has been degraded into an attribute of the
+entity. In this way a distinction has been imported into nature which is
+in truth no distinction at all. A natural entity is merely a factor of
+fact, considered in itself. Its disconnexion from the complex of fact is
+a mere abstraction. It is not the substratum of the factor, but the very
+factor itself as bared in thought. Thus what is a mere procedure of mind
+in the translation of sense-awareness into discursive knowledge has been
+transmuted into a fundamental character of nature. In this way matter
+has emerged as being the metaphysical substratum of its properties, and
+the course of nature is interpreted as the history of matter.
+
+Plato and Aristotle found Greek thought preoccupied with the quest for
+the simple substances in terms of which the course of events could be
+expressed. We may formulate this state of mind in the question, What is
+nature made of? The answers which their genius gave to this question,
+and more particularly the concepts which underlay the terms in which
+they framed their answers, have determined the unquestioned
+presuppositions as to time, space and matter which have reigned in
+science.
+
+In Plato the forms of thought are more fluid than in Aristotle, and
+therefore, as I venture to think, the more valuable. Their importance
+consists in the evidence they yield of cultivated thought about nature
+before it had been forced into a uniform mould by the long tradition of
+scientific philosophy. For example in the _Timaeus_ there is a
+presupposition, somewhat vaguely expressed, of a distinction between the
+general becoming of nature and the measurable time of nature. In a later
+lecture I have to distinguish between what I call the passage of nature
+and particular time-systems which exhibit certain characteristics of
+that passage. I will not go so far as to claim Plato in direct support
+of this doctrine, but I do think that the sections of the _Timaeus_
+which deal with time become clearer if my distinction is admitted.
+
+This is however a digression. I am now concerned with the origin of the
+scientific doctrine of matter in Greek thought. In the _Timaeus_ Plato
+asserts that nature is made of fire and earth with air and water as
+intermediate between them, so that 'as fire is to air so is air to
+water, and as air is to water so is water to earth.' He also suggests a
+molecular hypothesis for these four elements. In this hypothesis
+everything depends on the shape of the atoms; for earth it is cubical
+and for fire it is pyramidal. To-day physicists are again discussing
+the structure of the atom, and its shape is no slight factor in that
+structure. Plato's guesses read much more fantastically than does
+Aristotle's systematic analysis; but in some ways they are more
+valuable. The main outline of his ideas is comparable with that of
+modern science. It embodies concepts which any theory of natural
+philosophy must retain and in some sense must explain. Aristotle asked
+the fundamental question, What do we mean by 'substance'? Here the
+reaction between his philosophy and his logic worked very unfortunately.
+In his logic, the fundamental type of affirmative proposition is the
+attribution of a predicate to a subject. Accordingly, amid the many
+current uses of the term 'substance' which he analyses, he emphasises
+its meaning as 'the ultimate substratum which is no longer predicated of
+anything else.'
+
+The unquestioned acceptance of the Aristotelian logic has led to an
+ingrained tendency to postulate a substratum for whatever is disclosed
+in sense-awareness, namely, to look below what we are aware of for the
+substance in the sense of the 'concrete thing.' This is the origin of
+the modern scientific concept of matter and of ether, namely they are
+the outcome of this insistent habit of postulation.
+
+Accordingly ether has been invented by modern science as the substratum
+of the events which are spread through space and time beyond the reach
+of ordinary ponderable matter. Personally, I think that predication is a
+muddled notion confusing many different relations under a convenient
+common form of speech. For example, I hold that the relation of green to
+a blade of grass is entirely different from the relation of green to
+the event which is the life history of that blade for some short period,
+and is different from the relation of the blade to that event. In a
+sense I call the event the situation of the green, and in another sense
+it is the situation of the blade. Thus in one sense the blade is a
+character or property which can be predicated of the situation, and in
+another sense the green is a character or property of the same event
+which is also its situation. In this way the predication of properties
+veils radically different relations between entities.
+
+Accordingly 'substance,' which is a correlative term to 'predication,'
+shares in the ambiguity. If we are to look for substance anywhere, I
+should find it in events which are in some sense the ultimate substance
+of nature.
+
+Matter, in its modern scientific sense, is a return to the Ionian effort
+to find in space and time some stuff which composes nature. It has a
+more refined signification than the early guesses at earth and water by
+reason of a certain vague association with the Aristotelian idea of
+substance.
+
+Earth, water, air, fire, and matter, and finally ether are related in
+direct succession so far as concerns their postulated characters of
+ultimate substrata of nature. They bear witness to the undying vitality
+of Greek philosophy in its search for the ultimate entities which are
+the factors of the fact disclosed in sense-awareness. This search is the
+origin of science.
+
+The succession of ideas starting from the crude guesses of the early
+Ionian thinkers and ending in the nineteenth century ether reminds us
+that the scientific doctrine of matter is really a hybrid through which
+philosophy passed on its way to the refined Aristotelian concept of
+substance and to which science returned as it reacted against
+philosophic abstractions. Earth, fire, and water in the Ionic philosophy
+and the shaped elements in the _Timaeus_ are comparable to the matter
+and ether of modern scientific doctrine. But substance represents the
+final philosophic concept of the substratum which underlies any
+attribute. Matter (in the scientific sense) is already in space and
+time. Thus matter represents the refusal to think away spatial and
+temporal characteristics and to arrive at the bare concept of an
+individual entity. It is this refusal which has caused the muddle of
+importing the mere procedure of thought into the fact of nature. The
+entity, bared of all characteristics except those of space and time, has
+acquired a physical status as the ultimate texture of nature; so that
+the course of nature is conceived as being merely the fortunes of matter
+in its adventure through space.
+
+Thus the origin of the doctrine of matter is the outcome of uncritical
+acceptance of space and time as external conditions for natural
+existence. By this I do not mean that any doubt should be thrown on
+facts of space and time as ingredients in nature. What I do mean is 'the
+unconscious presupposition of space and time as being that within which
+nature is set.' This is exactly the sort of presupposition which tinges
+thought in any reaction against the subtlety of philosophical criticism.
+My theory of the formation of the scientific doctrine of matter is that
+first philosophy illegitimately transformed the bare entity, which is
+simply an abstraction necessary for the method of thought, into the
+metaphysical substratum of these factors in nature which in various
+senses are assigned to entities as their attributes; and that, as a
+second step, scientists (including philosophers who were scientists) in
+conscious or unconscious ignoration of philosophy presupposed this
+substratum, _qua_ substratum for attributes, as nevertheless in time and
+space.
+
+This is surely a muddle. The whole being of substance is as a substratum
+for attributes. Thus time and space should be attributes of the
+substance. This they palpably are not, if the matter be the substance of
+nature, since it is impossible to express spatio-temporal truths without
+having recourse to relations involving relata other than bits of matter.
+I waive this point however, and come to another. It is not the substance
+which is in space, but the attributes. What we find in space are the red
+of the rose and the smell of the jasmine and the noise of cannon. We
+have all told our dentists where our toothache is. Thus space is not a
+relation between substances, but between attributes.
+
+Thus even if you admit that the adherents of substance can be allowed to
+conceive substance as matter, it is a fraud to slip substance into space
+on the plea that space expresses relations between substances. On the
+face of it space has nothing to do with substances, but only with their
+attributes. What I mean is, that if you choose--as I think wrongly--to
+construe our experience of nature as an awareness of the attributes of
+substances, we are by this theory precluded from finding any analogous
+direct relations between substances as disclosed in our experience. What
+we do find are relations between the attributes of substances. Thus if
+matter is looked on as substance in space, the space in which it finds
+itself has very little to do with the space of our experience.
+
+The above argument has been expressed in terms of the relational theory
+of space. But if space be absolute--namely, if it have a being
+independent of things in it--the course of the argument is hardly
+changed. For things in space must have a certain fundamental relation to
+space which we will call occupation. Thus the objection that it is the
+attributes which are observed as related to space, still holds.
+
+The scientific doctrine of matter is held in conjunction with an
+absolute theory of time. The same arguments apply to the relations
+between matter and time as apply to the relations between space and
+matter. There is however (in the current philosophy) a difference in the
+connexions of space with matter from those of time with matter, which I
+will proceed to explain.
+
+Space is not merely an ordering of material entities so that any one
+entity bears certain relations to other material entities. The
+occupation of space impresses a certain character on each material
+entity in itself. By reason of its occupation of space matter has
+extension. By reason of its extension each bit of matter is divisible
+into parts, and each part is a numerically distinct entity from every
+other such part. Accordingly it would seem that every material entity is
+not really one entity. It is an essential multiplicity of entities.
+There seems to be no stopping this dissociation of matter into
+multiplicities short of finding each ultimate entity occupying one
+individual point. This essential multiplicity of material entities is
+certainly not what is meant by science, nor does it correspond to
+anything disclosed in sense-awareness. It is absolutely necessary that
+at a certain stage in this dissociation of matter a halt should be
+called, and that the material entities thus obtained should be treated
+as units. The stage of arrest may be arbitrary or may be set by the
+characteristics of nature; but all reasoning in science ultimately drops
+its space-analysis and poses to itself the problem, 'Here is one
+material entity, what is happening to it as a unit entity?' Yet this
+material entity is still retaining its extension, and as thus extended
+is a mere multiplicity. Thus there is an essential atomic property in
+nature which is independent of the dissociation of extension. There is
+something which in itself is one, and which is more than the logical
+aggregate of entities occupying points within the volume which the unit
+occupies. Indeed we may well be sceptical as to these ultimate entities
+at points, and doubt whether there are any such entities at all. They
+have the suspicious character that we are driven to accept them by
+abstract logic and not by observed fact.
+
+Time (in the current philosophy) does not exert the same disintegrating
+effect on matter which occupies it. If matter occupies a duration of
+time, the whole matter occupies every part of that duration. Thus the
+connexion between matter and time differs from the connexion between
+matter and space as expressed in current scientific philosophy. There is
+obviously a greater difficulty in conceiving time as the outcome of
+relations between different bits of matter than there is in the
+analogous conception of space. At an instant distinct volumes of space
+are occupied by distinct bits of matter. Accordingly there is so far no
+intrinsic difficulty in conceiving that space is merely the resultant of
+relations between the bits of matter. But in the one-dimensional time
+the same bit of matter occupies different portions of time. Accordingly
+time would have to be expressible in terms of the relations of a bit of
+matter with itself. My own view is a belief in the relational theory
+both of space and of time, and of disbelief in the current form of the
+relational theory of space which exhibits bits of matter as the relata
+for spatial relations. The true relata are events. The distinction which
+I have just pointed out between time and space in their connexion with
+matter makes it evident that any assimilation of time and space cannot
+proceed along the traditional line of taking matter as a fundamental
+element in space-formation.
+
+The philosophy of nature took a wrong turn during its development by
+Greek thought. This erroneous presupposition is vague and fluid in
+Plato's _Timaeus_. The general groundwork of the thought is still
+uncommitted and can be construed as merely lacking due explanation and
+the guarding emphasis. But in Aristotle's exposition the current
+conceptions were hardened and made definite so as to produce a faulty
+analysis of the relation between the matter and the form of nature as
+disclosed in sense-awareness. In this phrase the term 'matter' is not
+used in its scientific sense.
+
+I will conclude by guarding myself against a misapprehension. It is
+evident that the current doctrine of matter enshrines some fundamental
+law of nature. Any simple illustration will exemplify what I mean. For
+example, in a museum some specimen is locked securely in a glass case.
+It stays there for years: it loses its colour, and perhaps falls to
+pieces. But it is the same specimen; and the same chemical elements and
+the same quantities of those elements are present within the case at the
+end as were present at the beginning. Again the engineer and the
+astronomer deal with the motions of real permanences in nature. Any
+theory of nature which for one moment loses sight of these great basic
+facts of experience is simply silly. But it is permissible to point out
+that the scientific expression of these facts has become entangled in a
+maze of doubtful metaphysics; and that, when we remove the metaphysics
+and start afresh on an unprejudiced survey of nature, a new light is
+thrown on many fundamental concepts which dominate science and guide the
+progress of research.
+
+
+
+
+CHAPTER II
+
+THEORIES OF THE BIFURCATION OF NATURE
+
+
+In my previous lecture I criticised the concept of matter as the
+substance whose attributes we perceive. This way of thinking of matter
+is, I think, the historical reason for its introduction into science,
+and is still the vague view of it at the background of our thoughts
+which makes the current scientific doctrine appear so obvious. Namely we
+conceive ourselves as perceiving attributes of things, and bits of
+matter are the things whose attributes we perceive.
+
+In the seventeenth century the sweet simplicity of this aspect of matter
+received a rude shock. The transmission doctrines of science were then
+in process of elaboration and by the end of the century were
+unquestioned, though their particular forms have since been modified.
+The establishment of these transmission theories marks a turning point
+in the relation between science and philosophy. The doctrines to which I
+am especially alluding are the theories of light and sound. I have no
+doubt that the theories had been vaguely floating about before as
+obvious suggestions of common sense; for nothing in thought is ever
+completely new. But at that epoch they were systematised and made exact,
+and their complete consequences were ruthlessly deduced. It is the
+establishment of this procedure of taking the consequences seriously
+which marks the real discovery of a theory. Systematic doctrines of
+light and sound as being something proceeding from the emitting bodies
+were definitely established, and in particular the connexion of light
+with colour was laid bare by Newton.
+
+The result completely destroyed the simplicity of the 'substance and
+attribute' theory of perception. What we see depends on the light
+entering the eye. Furthermore we do not even perceive what enters the
+eye. The things transmitted are waves or--as Newton thought--minute
+particles, and the things seen are colours. Locke met this difficulty by
+a theory of primary and secondary qualities. Namely, there are some
+attributes of the matter which we do perceive. These are the primary
+qualities, and there are other things which we perceive, such as
+colours, which are not attributes of matter, but are perceived by us as
+if they were such attributes. These are the secondary qualities of
+matter.
+
+Why should we perceive secondary qualities? It seems an extremely
+unfortunate arrangement that we should perceive a lot of things that are
+not there. Yet this is what the theory of secondary qualities in fact
+comes to. There is now reigning in philosophy and in science an
+apathetic acquiescence in the conclusion that no coherent account can be
+given of nature as it is disclosed to us in sense-awareness, without
+dragging in its relations to mind. The modern account of nature is not,
+as it should be, merely an account of what the mind knows of nature; but
+it is also confused with an account of what nature does to the mind. The
+result has been disastrous both to science and to philosophy, but
+chiefly to philosophy. It has transformed the grand question of the
+relations between nature and mind into the petty form of the interaction
+between the human body and mind.
+
+Berkeley's polemic against matter was based on this confusion introduced
+by the transmission theory of light. He advocated, rightly as I think,
+the abandonment of the doctrine of matter in its present form. He had
+however nothing to put in its place except a theory of the relation of
+finite minds to the divine mind.
+
+But we are endeavouring in these lectures to limit ourselves to nature
+itself and not to travel beyond entities which are disclosed in
+sense-awareness.
+
+Percipience in itself is taken for granted. We consider indeed
+conditions for percipience, but only so far as those conditions are
+among the disclosures of perception. We leave to metaphysics the
+synthesis of the knower and the known. Some further explanation and
+defence of this position is necessary, if the line of argument of these
+lectures is to be comprehensible.
+
+The immediate thesis for discussion is that any metaphysical
+interpretation is an illegitimate importation into the philosophy of
+natural science. By a metaphysical interpretation I mean any discussion
+of the how (beyond nature) and of the why (beyond nature) of thought and
+sense-awareness. In the philosophy of science we seek the general
+notions which apply to nature, namely, to what we are aware of in
+perception. It is the philosophy of the thing perceived, and it should
+not be confused with the metaphysics of reality of which the scope
+embraces both perceiver and perceived. No perplexity concerning the
+object of knowledge can be solved by saying that there is a mind knowing
+it[2].
+
+[2] Cf. _Enquiry_, preface.
+
+In other words, the ground taken is this: sense-awareness is an
+awareness of something. What then is the general character of that
+something of which we are aware? We do not ask about the percipient or
+about the process, but about the perceived. I emphasise this point
+because discussions on the philosophy of science are usually extremely
+metaphysical--in my opinion, to the great detriment of the subject.
+
+The recourse to metaphysics is like throwing a match into the powder
+magazine. It blows up the whole arena. This is exactly what scientific
+philosophers do when they are driven into a corner and convicted of
+incoherence. They at once drag in the mind and talk of entities in the
+mind or out of the mind as the case may be. For natural philosophy
+everything perceived is in nature. We may not pick and choose. For us
+the red glow of the sunset should be as much part of nature as are the
+molecules and electric waves by which men of science would explain the
+phenomenon. It is for natural philosophy to analyse how these various
+elements of nature are connected.
+
+In making this demand I conceive myself as adopting our immediate
+instinctive attitude towards perceptual knowledge which is only
+abandoned under the influence of theory. We are instinctively willing to
+believe that by due attention, more can be found in nature than that
+which is observed at first sight. But we will not be content with less.
+What we ask from the philosophy of science is some account of the
+coherence of things perceptively known.
+
+This means a refusal to countenance any theory of psychic additions to
+the object known in perception. For example, what is given in perception
+is the green grass. This is an object which we know as an ingredient in
+nature. The theory of psychic additions would treat the greenness as a
+psychic addition furnished by the perceiving mind, and would leave to
+nature merely the molecules and the radiant energy which influence the
+mind towards that perception. My argument is that this dragging in of
+the mind as making additions of its own to the thing posited for
+knowledge by sense-awareness is merely a way of shirking the problem of
+natural philosophy. That problem is to discuss the relations _inter se_
+of things known, abstracted from the bare fact that they are known.
+Natural philosophy should never ask, what is in the mind and what is in
+nature. To do so is a confession that it has failed to express relations
+between things perceptively known, namely to express those natural
+relations whose expression is natural philosophy. It may be that the
+task is too hard for us, that the relations are too complex and too
+various for our apprehension, or are too trivial to be worth the trouble
+of exposition. It is indeed true that we have gone but a very small way
+in the adequate formulation of such relations. But at least do not let
+us endeavour to conceal failure under a theory of the byplay of the
+perceiving mind.
+
+What I am essentially protesting against is the bifurcation of nature
+into two systems of reality, which, in so far as they are real, are real
+in different senses. One reality would be the entities such as electrons
+which are the study of speculative physics. This would be the reality
+which is there for knowledge; although on this theory it is never known.
+For what is known is the other sort of reality, which is the byplay of
+the mind. Thus there would be two natures, one is the conjecture and the
+other is the dream.
+
+Another way of phrasing this theory which I am arguing against is to
+bifurcate nature into two divisions, namely into the nature apprehended
+in awareness and the nature which is the cause of awareness. The nature
+which is the fact apprehended in awareness holds within it the greenness
+of the trees, the song of the birds, the warmth of the sun, the hardness
+of the chairs, and the feel of the velvet. The nature which is the cause
+of awareness is the conjectured system of molecules and electrons which
+so affects the mind as to produce the awareness of apparent nature. The
+meeting point of these two natures is the mind, the causal nature being
+influent and the apparent nature being effluent.
+
+There are four questions which at once suggest themselves for discussion
+in connexion with this bifurcation theory of nature. They concern (i)
+causality, (ii) time, (iii) space, and (iv) delusions. These questions
+are not really separable. They merely constitute four distinct starting
+points from which to enter upon the discussion of the theory.
+
+Causal nature is the influence on the mind which is the cause of the
+effluence of apparent nature from the mind. This conception of causal
+nature is not to be confused with the distinct conception of one part of
+nature as being the cause of another part. For example, the burning of
+the fire and the passage of heat from it through intervening space is
+the cause of the body, its nerves and its brain, functioning in certain
+ways. But this is not an action of nature on the mind. It is an
+interaction within nature. The causation involved in this interaction is
+causation in a different sense from the influence of this system of
+bodily interactions within nature on the alien mind which thereupon
+perceives redness and warmth.
+
+The bifurcation theory is an attempt to exhibit natural science as an
+investigation of the cause of the fact of knowledge. Namely, it is an
+attempt to exhibit apparent nature as an effluent from the mind because
+of causal nature. The whole notion is partly based on the implicit
+assumption that the mind can only know that which it has itself produced
+and retains in some sense within itself, though it requires an exterior
+reason both as originating and as determining the character of its
+activity. But in considering knowledge we should wipe out all these
+spatial metaphors, such as 'within the mind' and 'without the mind.'
+Knowledge is ultimate. There can be no explanation of the 'why' of
+knowledge; we can only describe the 'what' of knowledge. Namely we can
+analyse the content and its internal relations, but we cannot explain
+why there is knowledge. Thus causal nature is a metaphysical chimera;
+though there is need of a metaphysics whose scope transcends the
+limitation to nature. The object of such a metaphysical science is not
+to explain knowledge, but exhibit in its utmost completeness our concept
+of reality.
+
+However, we must admit that the causality theory of nature has its
+strong suit. The reason why the bifurcation of nature is always creeping
+back into scientific philosophy is the extreme difficulty of exhibiting
+the perceived redness and warmth of the fire in one system of relations
+with the agitated molecules of carbon and oxygen, with the radiant
+energy from them, and with the various functionings of the material
+body. Unless we produce the all-embracing relations, we are faced with a
+bifurcated nature; namely, warmth and redness on one side, and
+molecules, electrons and ether on the other side. Then the two factors
+are explained as being respectively the cause and the mind's reaction to
+the cause.
+
+Time and space would appear to provide these all-embracing relations
+which the advocates of the philosophy of the unity of nature require.
+The perceived redness of the fire and the warmth are definitely related
+in time and in space to the molecules of the fire and the molecules of
+the body.
+
+It is hardly more than a pardonable exaggeration to say that the
+determination of the meaning of nature reduces itself principally to the
+discussion of the character of time and the character of space. In
+succeeding lectures I shall explain my own view of time and space. I
+shall endeavour to show that they are abstractions from more concrete
+elements of nature, namely, from events. The discussion of the details
+of the process of abstraction will exhibit time and space as
+interconnected, and will finally lead us to the sort of connexions
+between their measurements which occur in the modern theory of
+electromagnetic relativity. But this is anticipating our subsequent line
+of development. At present I wish to consider how the ordinary views of
+time and space help, or fail to help, in unifying our conception of
+nature.
+
+First, consider the absolute theories of time and space. We are to
+consider each, namely both time and space, to be a separate and
+independent system of entities, each system known to us in itself and
+for itself concurrently with our knowledge of the events of nature. Time
+is the ordered succession of durationless instants; and these instants
+are known to us merely as the relata in the serial relation which is the
+time-ordering relation, and the time-ordering relation is merely known
+to us as relating the instants. Namely, the relation and the instants
+are jointly known to us in our apprehension of time, each implying the
+other.
+
+This is the absolute theory of time. Frankly, I confess that it seems to
+me to be very unplausible. I cannot in my own knowledge find anything
+corresponding to the bare time of the absolute theory. Time is known to
+me as an abstraction from the passage of events. The fundamental fact
+which renders this abstraction possible is the passing of nature, its
+development, its creative advance, and combined with this fact is
+another characteristic of nature, namely the extensive relation between
+events. These two facts, namely the passage of events and the extension
+of events over each other, are in my opinion the qualities from which
+time and space originate as abstractions. But this is anticipating my
+own later speculations.
+
+Meanwhile, returning to the absolute theory, we are to suppose that time
+is known to us independently of any events in time. What happens in time
+occupies time. This relation of events to the time occupied, namely this
+relation of occupation, is a fundamental relation of nature to time.
+Thus the theory requires that we are aware of two fundamental relations,
+the time-ordering relation between instants, and the time-occupation
+relation between instants of time and states of nature which happen at
+those instants.
+
+There are two considerations which lend powerful support to the reigning
+theory of absolute time. In the first place time extends beyond nature.
+Our thoughts are in time. Accordingly it seems impossible to derive time
+merely from relations between elements of nature. For in that case
+temporal relations could not relate thoughts. Thus, to use a metaphor,
+time would apparently have deeper roots in reality than has nature. For
+we can imagine thoughts related in time without any perception of
+nature. For example we can imagine one of Milton's angels with thoughts
+succeeding each other in time, who does not happen to have noticed that
+the Almighty has created space and set therein a material universe. As a
+matter of fact I think that Milton set space on the same absolute level
+as time. But that need not disturb the illustration. In the second place
+it is difficult to derive the true serial character of time from the
+relative theory. Each instant is irrevocable. It can never recur by the
+very character of time. But if on the relative theory an instant of time
+is simply the state of nature at that time, and the time-ordering
+relation is simply the relation between such states, then the
+irrevocableness of time would seem to mean that an actual state of all
+nature can never return. I admit it seems unlikely that there should
+ever be such a recurrence down to the smallest particular. But extreme
+unlikeliness is not the point. Our ignorance is so abysmal that our
+judgments of likeliness and unlikeliness of future events hardly count.
+The real point is that the exact recurrence of a state of nature seems
+merely unlikely, while the recurrence of an instant of time violates our
+whole concept of time-order. The instants of time which have passed, are
+passed, and can never be again.
+
+Any alternative theory of time must reckon with these two considerations
+which are buttresses of the absolute theory. But I will not now continue
+their discussion.
+
+The absolute theory of space is analogous to the corresponding theory of
+time, but the reasons for its maintenance are weaker. Space, on this
+theory, is a system of extensionless points which are the relata in
+space-ordering relations which can technically be combined into one
+relation. This relation does not arrange the points in one linear series
+analogously to the simple method of the time-ordering relation for
+instants. The essential logical characteristics of this relation from
+which all the properties of space spring are expressed by mathematicians
+in the axioms of geometry. From these axioms[3] as framed by modern
+mathematicians the whole science of geometry can be deduced by the
+strictest logical reasoning. The details of these axioms do not now
+concern us. The points and the relations are jointly known to us in our
+apprehension of space, each implying the other. What happens in space,
+occupies space. This relation of occupation is not usually stated for
+events but for objects. For example, Pompey's statue would be said to
+occupy space, but not the event which was the assassination of Julius
+Caesar. In this I think that ordinary usage is unfortunate, and I hold
+that the relations of events to space and to time are in all respects
+analogous. But here I am intruding my own opinions which are to be
+discussed in subsequent lectures. Thus the theory of absolute space
+requires that we are aware of two fundamental relations, the
+space-ordering relation, which holds between points, and the
+space-occupation relation between points of space and material objects.
+
+[3] Cf. (for example) _Projective Geometry_ by Veblen and Young, vol. i.
+1910, vol. ii. 1917, Ginn and Company, Boston, U.S.A.
+
+This theory lacks the two main supports of the corresponding theory of
+absolute time. In the first place space does not extend beyond nature in
+the sense that time seems to do. Our thoughts do not seem to occupy
+space in quite the same intimate way in which they occupy time. For
+example, I have been thinking in a room, and to that extent my thoughts
+are in space. But it seems nonsense to ask how much volume of the room
+they occupied, whether it was a cubic foot or a cubic inch; whereas the
+same thoughts occupy a determinate duration of time, say, from eleven to
+twelve on a certain date.
+
+Thus whereas the relations of a relative theory of time are required to
+relate thoughts, it does not seem so obvious that the relations of a
+relative theory of space are required to relate them. The connexion of
+thought with space seems to have a certain character of indirectness
+which appears to be lacking in the connexion of thought with time.
+
+Again the irrevocableness of time does not seem to have any parallel for
+space. Space, on the relative theory, is the outcome of certain
+relations between objects commonly said to be in space; and whenever
+there are the objects, so related, there is the space. No difficulty
+seems to arise like that of the inconvenient instants of time which
+might conceivably turn up again when we thought that we had done with
+them.
+
+The absolute theory of space is not now generally popular. The knowledge
+of bare space, as a system of entities known to us in itself and for
+itself independently of our knowledge of the events in nature, does not
+seem to correspond to anything in our experience. Space, like time,
+would appear to be an abstraction from events. According to my own
+theory it only differentiates itself from time at a somewhat developed
+stage of the abstractive process. The more usual way of expressing the
+relational theory of space would be to consider space as an abstraction
+from the relations between material objects.
+
+Suppose now we assume absolute time and absolute space. What bearing
+has this assumption on the concept of nature as bifurcated into causal
+nature and apparent nature? Undoubtedly the separation between the two
+natures is now greatly mitigated. We can provide them with two systems
+of relations in common; for both natures can be presumed to occupy the
+same space and the same time. The theory now is this: Causal events
+occupy certain periods of the absolute time and occupy certain positions
+of the absolute space. These events influence a mind which thereupon
+perceives certain apparent events which occupy certain periods in the
+absolute time and occupy certain positions of the absolute space; and
+the periods and positions occupied by the apparent events bear a
+determinate relation to the periods and positions occupied by the causal
+events.
+
+Furthermore definite causal events produce for the mind definite
+apparent events. Delusions are apparent events which appear in temporal
+periods and spatial positions without the intervention of these causal
+events which are proper for influencing of the mind to their perception.
+
+The whole theory is perfectly logical. In these discussions we cannot
+hope to drive an unsound theory to a logical contradiction. A reasoner,
+apart from mere slips, only involves himself in a contradiction when he
+is shying at a _reductio ad absurdum_. The substantial reason for
+rejecting a philosophical theory is the 'absurdum' to which it reduces
+us. In the case of the philosophy of natural science the 'absurdum' can
+only be that our perceptual knowledge has not the character assigned to
+it by the theory. If our opponent affirms that his knowledge has that
+character, we can only--after making doubly sure that we understand
+each other--agree to differ. Accordingly the first duty of an expositor
+in stating a theory in which he disbelieves is to exhibit it as logical.
+It is not there where his trouble lies.
+
+Let me summarise the previously stated objections to this theory of
+nature. In the first place it seeks for the cause of the knowledge of
+the thing known instead of seeking for the character of the thing known:
+secondly it assumes a knowledge of time in itself apart from events
+related in time: thirdly it assumes a knowledge of space in itself apart
+from events related in space. There are in addition to these objections
+other flaws in the theory.
+
+Some light is thrown on the artificial status of causal nature in this
+theory by asking, why causal nature is presumed to occupy time and
+space. This really raises the fundamental question as to what
+characteristics causal nature should have in common with apparent
+nature. Why--on this theory--should the cause which influences the mind
+to perception have any characteristics in common with the effluent
+apparent nature? In particular, why should it be in space? Why should it
+be in time? And more generally, What do we know about mind which would
+allow us to infer any particular characteristics of a cause which should
+influence mind to particular effects?
+
+The transcendence of time beyond nature gives some slight reason for
+presuming that causal nature should occupy time. For if the mind
+occupies periods of time, there would seem to be some vague reason for
+assuming that influencing causes occupy the same periods of time, or at
+least, occupy periods which are strictly related to the mental periods.
+But if the mind does not occupy volumes of space, there seems to be no
+reason why causal nature should occupy any volumes of space. Thus space
+would seem to be merely apparent in the same sense as apparent nature is
+merely apparent. Accordingly if science is really investigating causes
+which operate on the mind, it would seem to be entirely on the wrong
+tack in presuming that the causes which it is seeking for have spatial
+relations. Furthermore there is nothing else in our knowledge analogous
+to these causes which influence the mind to perception. Accordingly,
+beyond the rashly presumed fact that they occupy time, there is really
+no ground by which we can determine any point of their character. They
+must remain for ever unknown.
+
+Now I assume as an axiom that science is not a fairy tale. It is not
+engaged in decking out unknowable entities with arbitrary and fantastic
+properties. What then is it that science is doing, granting that it is
+effecting something of importance? My answer is that it is determining
+the character of things known, namely the character of apparent nature.
+But we may drop the term 'apparent'; for there is but one nature, namely
+the nature which is before us in perceptual knowledge. The characters
+which science discerns in nature are subtle characters, not obvious at
+first sight. They are relations of relations and characters of
+characters. But for all their subtlety they are stamped with a certain
+simplicity which makes their consideration essential in unravelling the
+complex relations between characters of more perceptive insistence.
+
+The fact that the bifurcation of nature into causal and apparent
+components does not express what we mean by our knowledge is brought
+before us when we realise our thoughts in any discussion of the causes
+of our perceptions. For example, the fire is burning and we see a red
+coal. This is explained in science by radiant energy from the coal
+entering our eyes. But in seeking for such an explanation we are not
+asking what are the sort of occurrences which are fitted to cause a mind
+to see red. The chain of causation is entirely different. The mind is
+cut out altogether. The real question is, When red is found in nature,
+what else is found there also? Namely we are asking for an analysis of
+the accompaniments in nature of the discovery of red in nature. In a
+subsequent lecture I shall expand this line of thought. I simply draw
+attention to it here in order to point out that the wave-theory of light
+has not been adopted because waves are just the sort of things which
+ought to make a mind perceive colours. This is no part of the evidence
+which has ever been adduced for the wave-theory, yet on the causal
+theory of perception, it is really the only relevant part. In other
+words, science is not discussing the causes of knowledge, but the
+coherence of knowledge. The understanding which is sought by science is
+an understanding of relations within nature.
+
+So far I have discussed the bifurcation of nature in connexion with the
+theories of absolute time and of absolute space. My reason has been that
+the introduction of the relational theories only weakens the case for
+bifurcation, and I wished to discuss this case on its strongest grounds.
+
+For instance, suppose we adopt the relational theory of space. Then the
+space in which apparent nature is set is the expression of certain
+relations between the apparent objects. It is a set of apparent
+relations between apparent relata. Apparent nature is the dream, and
+the apparent relations of space are dream relations, and the space is
+the dream space. Similarly the space in which causal nature is set is
+the expression of certain relations between the causal objects. It is
+the expression of certain facts about the causal activity which is going
+on behind the scenes. Accordingly causal space belongs to a different
+order of reality to apparent space. Hence there is no pointwise
+connexion between the two and it is meaningless to say that the
+molecules of the grass are in any place which has a determinate spatial
+relation to the place occupied by the grass which we see. This
+conclusion is very paradoxical and makes nonsense of all scientific
+phraseology. The case is even worse if we admit the relativity of time.
+For the same arguments apply, and break up time into the dream time and
+causal time which belong to different orders of reality.
+
+I have however been discussing an extreme form of the bifurcation
+theory. It is, as I think, the most defensible form. But its very
+definiteness makes it the more evidently obnoxious to criticism. The
+intermediate form allows that the nature we are discussing is always the
+nature directly known, and so far it rejects the bifurcation theory. But
+it holds that there are psychic additions to nature as thus known, and
+that these additions are in no proper sense part of nature. For example,
+we perceive the red billiard ball at its proper time, in its proper
+place, with its proper motion, with its proper hardness, and with its
+proper inertia. But its redness and its warmth, and the sound of the
+click as a cannon is made off it are psychic additions, namely,
+secondary qualities which are only the mind's way of perceiving nature.
+This is not only the vaguely prevalent theory, but is, I believe, the
+historical form of the bifurcation theory in so far as it is derived
+from philosophy. I shall call it the theory of psychic additions.
+
+This theory of psychic additions is a sound common-sense theory which
+lays immense stress on the obvious reality of time, space, solidity and
+inertia, but distrusts the minor artistic additions of colour, warmth
+and sound.
+
+The theory is the outcome of common-sense in retreat. It arose in an
+epoch when the transmission theories of science were being elaborated.
+For example, colour is the result of a transmission from the material
+object to the perceiver's eye; and what is thus transmitted is not
+colour. Thus colour is not part of the reality of the material object.
+Similarly for the same reason sounds evaporate from nature. Also warmth
+is due to the transfer of something which is not temperature. Thus we
+are left with spatio-temporal positions, and what I may term the
+'pushiness' of the body. This lands us to eighteenth and nineteenth
+century materialism, namely, the belief that what is real in nature is
+matter, in time and in space and with inertia.
+
+Evidently a distinction in quality has been presupposed separating off
+some perceptions due to touch from other perceptions. These
+touch-perceptions are perceptions of the real inertia, whereas the other
+perceptions are psychic additions which must be explained on the causal
+theory. This distinction is the product of an epoch in which physical
+science has got ahead of medical pathology and of physiology.
+Perceptions of push are just as much the outcome of transmission as are
+perceptions of colour. When colour is perceived the nerves of the body
+are excited in one way and transmit their message towards the brain, and
+when push is perceived other nerves of the body are excited in another
+way and transmit their message towards the brain. The message of the one
+set is not the conveyance of colour, and the message of the other set is
+not the conveyance of push. But in one case colour is perceived and in
+the other case the push due to the object. If you snip certain nerves,
+there is an end to the perception of colour; and if you snip certain
+other nerves, there is an end to the perception of push. It would appear
+therefore that any reasons which should remove colour from the reality
+of nature should also operate to remove inertia.
+
+Thus the attempted bifurcation of apparent nature into two parts of
+which one part is both causal for its own appearance and for the
+appearance of the other part, which is purely apparent, fails owing to
+the failure to establish any fundamental distinction between our ways of
+knowing about the two parts of nature as thus partitioned. I am not
+denying that the feeling of muscular effort historically led to the
+formulation of the concept of force. But this historical fact does not
+warrant us in assigning a superior reality in nature to material inertia
+over colour or sound. So far as reality is concerned all our
+sense-perceptions are in the same boat, and must be treated on the same
+principle. The evenness of treatment is exactly what this compromise
+theory fails to achieve.
+
+The bifurcation theory however dies hard. The reason is that there
+really is a difficulty to be faced in relating within the same system of
+entities the redness of the fire with the agitation of the molecules. In
+another lecture I will give my own explanation of the origin of the
+difficulty and of its solution.
+
+Another favourite solution, the most attenuated form which the
+bifurcation theory assumes, is to maintain that the molecules and ether
+of science are purely conceptual. Thus there is but one nature, namely
+apparent nature, and atoms and ether are merely names for logical terms
+in conceptual formulae of calculation.
+
+But what is a formula of calculation? It is presumably a statement that
+something or other is true for natural occurrences. Take the simplest of
+all formulae, Two and two make four. This--so far as it applies to
+nature--asserts that if you take two natural entities, and then again
+two other natural entities, the combined class contains four natural
+entities. Such formulae which are true for any entities cannot result in
+the production of the concepts of atoms. Then again there are formulae
+which assert that there are entities in nature with such and such
+special properties, say, for example, with the properties of the atoms
+of hydrogen. Now if there are no such entities, I fail to see how any
+statements about them can apply to nature. For example, the assertion
+that there is green cheese in the moon cannot be a premiss in any
+deduction of scientific importance, unless indeed the presence of green
+cheese in the moon has been verified by experiment. The current answer
+to these objections is that, though atoms are merely conceptual, yet
+they are an interesting and picturesque way of saying something else
+which is true of nature. But surely if it is something else that you
+mean, for heaven's sake say it. Do away with this elaborate machinery of
+a conceptual nature which consists of assertions about things which
+don't exist in order to convey truths about things which do exist. I am
+maintaining the obvious position that scientific laws, if they are true,
+are statements about entities which we obtain knowledge of as being in
+nature; and that, if the entities to which the statements refer are not
+to be found in nature, the statements about them have no relevance to
+any purely natural occurrence. Thus the molecules and electrons of
+scientific theory are, so far as science has correctly formulated its
+laws, each of them factors to be found in nature. The electrons are only
+hypothetical in so far as we are not quite certain that the electron
+theory is true. But their hypothetical character does not arise from the
+essential nature of the theory in itself after its truth has been
+granted.
+
+Thus at the end of this somewhat complex discussion, we return to the
+position which was affirmed at its beginning. The primary task of a
+philosophy of natural science is to elucidate the concept of nature,
+considered as one complex fact for knowledge, to exhibit the fundamental
+entities and the fundamental relations between entities in terms of
+which all laws of nature have to be stated, and to secure that the
+entities and relations thus exhibited are adequate for the expression of
+all the relations between entities which occur in nature.
+
+The third requisite, namely that of adequacy, is the one over which all
+the difficulty occurs. The ultimate data of science are commonly assumed
+to be time, space, material, qualities of material, and relations
+between material objects. But data as they occur in the scientific laws
+do not relate all the entities which present themselves in our
+perception of nature. For example, the wave-theory of light is an
+excellent well-established theory; but unfortunately it leaves out
+colour as perceived. Thus the perceived redness--or, other colour--has
+to be cut out of nature and made into the reaction of the mind under the
+impulse of the actual events of nature. In other words this concept of
+the fundamental relations within nature is inadequate. Thus we have to
+bend our energies to the enunciation of adequate concepts.
+
+But in so doing, are we not in fact endeavouring to solve a metaphysical
+problem? I do not think so. We are merely endeavouring to exhibit the
+type of relations which hold between the entities which we in fact
+perceive as in nature. We are not called on to make any pronouncement as
+to the psychological relation of subjects to objects or as to the status
+of either in the realm of reality. It is true that the issue of our
+endeavour may provide material which is relevant evidence for a
+discussion on that question. It can hardly fail to do so. But it is only
+evidence, and is not itself the metaphysical discussion. In order to
+make clear the character of this further discussion which is out of our
+ken, I will set before you two quotations. One is from Schelling and I
+extract the quotation from the work of the Russian philosopher Lossky
+which has recently been so excellently translated into English[4]--'In
+the "Philosophy of Nature" I considered the subject-object called nature
+in its activity of self-constructing. In order to understand it, we must
+rise to an intellectual intuition of nature. The empiricist does not
+rise thereto, and for this reason in all his explanations it is always
+_he himself_ that proves to be constructing nature. It is no wonder,
+then, that his construction and that which was to be constructed so
+seldom coincide. A _Natur-philosoph_ raises nature to independence, and
+makes it construct itself, and he never feels, therefore, the necessity
+of opposing nature as constructed (_i.e._ as experience) to real
+nature, or of correcting the one by means of the other.'
+
+[4] _The Intuitive Basis of Knowledge_, by N. O. Lossky, transl. by Mrs
+Duddington, Macmillan and Co., 1919.
+
+The other quotation is from a paper read by the Dean of St Paul's before
+the Aristotelian Society in May of 1919. Dr Inge's paper is entitled
+'Platonism and Human Immortality,' and in it there occurs the following
+statement: 'To sum up. The Platonic doctrine of immortality rests on the
+_independence_ of the spiritual world. The spiritual world is not a
+world of unrealised ideals, over against a real world of unspiritual
+fact. It is, on the contrary, the real world, of which we have a true
+though very incomplete knowledge, over against a world of common
+experience which, as a complete whole, is not real, since it is
+compacted out of miscellaneous data, not all on the same level, by the
+help of the imagination. There is no world corresponding to the world of
+our common experience. Nature makes abstractions for us, deciding what
+range of vibrations we are to see and hear, what things we are to notice
+and remember.'
+
+I have cited these statements because both of them deal with topics
+which, though they lie outside the range of our discussion, are always
+being confused with it. The reason is that they lie proximate to our
+field of thought, and are topics which are of burning interest to the
+metaphysically minded. It is difficult for a philosopher to realise that
+anyone really is confining his discussion within the limits that I have
+set before you. The boundary is set up just where he is beginning to get
+excited. But I submit to you that among the necessary prolegomena for
+philosophy and for natural science is a thorough understanding of the
+types of entities, and types of relations among those entities, which
+are disclosed to us in our perceptions of nature.
+
+
+
+
+CHAPTER III
+
+TIME
+
+
+The two previous lectures of this course have been mainly critical. In
+the present lecture I propose to enter upon a survey of the kinds of
+entities which are posited for knowledge in sense-awareness. My purpose
+is to investigate the sorts of relations which these entities of various
+kinds can bear to each other. A classification of natural entities is
+the beginning of natural philosophy. To-day we commence with the
+consideration of Time.
+
+In the first place there is posited for us a general fact: namely,
+something is going on; there is an occurrence for definition.
+
+This general fact at once yields for our apprehension two factors, which
+I will name, the 'discerned' and the 'discernible.' The discerned is
+comprised of those elements of the general fact which are discriminated
+with their own individual peculiarities. It is the field directly
+perceived. But the entities of this field have relations to other
+entities which are not particularly discriminated in this individual
+way. These other entities are known merely as the relata in relation to
+the entities of the discerned field. Such an entity is merely a
+'something' which has such-and-such definite relations to some definite
+entity or entities in the discerned field. As being thus related, they
+are--owing to the particular character of these relations--known as
+elements of the general fact which is going on. But we are not aware of
+them except as entities fulfilling the functions of relata in these
+relations.
+
+Thus the complete general fact, posited as occurring, comprises both
+sets of entities, namely the entities perceived in their own
+individuality and other entities merely apprehended as relata without
+further definition. This complete general fact is the discernible and it
+comprises the discerned. The discernible is all nature as disclosed in
+that sense-awareness, and extends beyond and comprises all of nature as
+actually discriminated or discerned in that sense-awareness. The
+discerning or discrimination of nature is a peculiar awareness of
+special factors in nature in respect to their peculiar characters. But
+the factors in nature of which we have this peculiar sense-awareness are
+known as not comprising all the factors which together form the whole
+complex of related entities within the general fact there for
+discernment. This peculiarity of knowledge is what I call its
+unexhaustive character. This character may be metaphorically described
+by the statement that nature as perceived always has a ragged edge. For
+example, there is a world beyond the room to which our sight is confined
+known to us as completing the space-relations of the entities discerned
+within the room. The junction of the interior world of the room with the
+exterior world beyond is never sharp. Sounds and subtler factors
+disclosed in sense-awareness float in from the outside. Every type of
+sense has its own set of discriminated entities which are known to be
+relata in relation with entities not discriminated by that sense. For
+example we see something which we do not touch and we touch something
+which we do not see, and we have a general sense of the space-relations
+between the entity disclosed in sight and the entity disclosed in touch.
+Thus in the first place each of these two entities is known as a relatum
+in a general system of space-relations and in the second place the
+particular mutual relation of these two entities as related to each
+other in this general system is determined. But the general system of
+space-relations relating the entity discriminated by sight with that
+discriminated by sight is not dependent on the peculiar character of the
+other entity as reported by the alternative sense. For example, the
+space-relations of the thing seen would have necessitated an entity as a
+relatum in the place of the thing touched even although certain elements
+of its character had not been disclosed by touch. Thus apart from the
+touch an entity with a certain specific relation to the thing seen would
+have been disclosed by sense-awareness but not otherwise discriminated
+in respect to its individual character. An entity merely known as
+spatially related to some discerned entity is what we mean by the bare
+idea of 'place.' The concept of place marks the disclosure in
+sense-awareness of entities in nature known merely by their spatial
+relations to discerned entities. It is the disclosure of the discernible
+by means of its relations to the discerned.
+
+This disclosure of an entity as a relatum without further specific
+discrimination of quality is the basis of our concept of significance.
+In the above example the thing seen was significant, in that it
+disclosed its spatial relations to other entities not necessarily
+otherwise entering into consciousness. Thus significance is relatedness,
+but it is relatedness with the emphasis on one end only of the relation.
+
+For the sake of simplicity I have confined the argument to spatial
+relations; but the same considerations apply to temporal relations. The
+concept of 'period of time' marks the disclosure in sense-awareness of
+entities in nature known merely by their temporal relations to
+discerned entities. Still further, this separation of the ideas of space
+and time has merely been adopted for the sake of gaining simplicity of
+exposition by conformity to current language. What we discern is the
+specific character of a place through a period of time. This is what I
+mean by an 'event.' We discern some specific character of an event. But
+in discerning an event we are also aware of its significance as a
+relatum in the structure of events. This structure of events is the
+complex of events as related by the two relations of extension and
+cogredience. The most simple expression of the properties of this
+structure are to be found in our spatial and temporal relations. A
+discerned event is known as related in this structure to other events
+whose specific characters are otherwise not disclosed in that immediate
+awareness except so far as that they are relata within the structure.
+
+The disclosure in sense-awareness of the structure of events classifies
+events into those which are discerned in respect to some further
+individual character and those which are not otherwise disclosed except
+as elements of the structure. These signified events must include events
+in the remote past as well as events in the future. We are aware of
+these as the far off periods of unbounded time. But there is another
+classification of events which is also inherent in sense-awareness.
+These are the events which share the immediacy of the immediately
+present discerned events. These are the events whose characters together
+with those of the discerned events comprise all nature present for
+discernment. They form the complete general fact which is all nature now
+present as disclosed in that sense-awareness. It is in this second
+classification of events that the differentiation of space from time
+takes its origin. The germ of space is to be found in the mutual
+relations of events within the immediate general fact which is all
+nature now discernible, namely within the one event which is the
+totality of present nature. The relations of other events to this
+totality of nature form the texture of time.
+
+The unity of this general present fact is expressed by the concept of
+simultaneity. The general fact is the whole simultaneous occurrence of
+nature which is now for sense-awareness. This general fact is what I
+have called the discernible. But in future I will call it a 'duration,'
+meaning thereby a certain whole of nature which is limited only by the
+property of being a simultaneity. Further in obedience to the principle
+of comprising within nature the whole terminus of sense-awareness,
+simultaneity must not be conceived as an irrelevant mental concept
+imposed upon nature. Our sense-awareness posits for immediate
+discernment a certain whole, here called a 'duration'; thus a duration
+is a definite natural entity. A duration is discriminated as a complex
+of partial events, and the natural entities which are components of this
+complex are thereby said to be 'simultaneous with this duration.' Also
+in a derivative sense they are simultaneous with each other in respect
+to this duration. Thus simultaneity is a definite natural relation. The
+word 'duration' is perhaps unfortunate in so far as it suggests a mere
+abstract stretch of time. This is not what I mean. A duration is a
+concrete slab of nature limited by simultaneity which is an essential
+factor disclosed in sense-awareness.
+
+Nature is a process. As in the case of everything directly exhibited in
+sense-awareness, there can be no explanation of this characteristic of
+nature. All that can be done is to use language which may speculatively
+demonstrate it, and also to express the relation of this factor in
+nature to other factors.
+
+It is an exhibition of the process of nature that each duration happens
+and passes. The process of nature can also be termed the passage of
+nature. I definitely refrain at this stage from using the word 'time,'
+since the measurable time of science and of civilised life generally
+merely exhibits some aspects of the more fundamental fact of the passage
+of nature. I believe that in this doctrine I am in full accord with
+Bergson, though he uses 'time' for the fundamental fact which I call the
+'passage of nature.' Also the passage of nature is exhibited equally in
+spatial transition as well as in temporal transition. It is in virtue of
+its passage that nature is always moving on. It is involved in the
+meaning of this property of 'moving on' that not only is any act of
+sense-awareness just that act and no other, but the terminus of each act
+is also unique and is the terminus of no other act. Sense-awareness
+seizes its only chance and presents for knowledge something which is for
+it alone.
+
+There are two senses in which the terminus of sense-awareness is unique.
+It is unique for the sense-awareness of an individual mind and it is
+unique for the sense-awareness of all minds which are operating under
+natural conditions. There is an important distinction between the two
+cases. (i) For one mind not only is the discerned component of the
+general fact exhibited in any act of sense-awareness distinct from the
+discerned component of the general fact exhibited in any other act of
+sense-awareness of that mind, but the two corresponding durations which
+are respectively related by simultaneity to the two discerned components
+are necessarily distinct. This is an exhibition of the temporal passage
+of nature; namely, one duration has passed into the other. Thus not only
+is the passage of nature an essential character of nature in its _rôle_
+of the terminus of sense-awareness, but it is also essential for
+sense-awareness in itself. It is this truth which makes time appear to
+extend beyond nature. But what extends beyond nature to mind is not the
+serial and measurable time, which exhibits merely the character of
+passage in nature, but the quality of passage itself which is in no way
+measurable except so far as it obtains in nature. That is to say,
+'passage' is not measurable except as it occurs in nature in connexion
+with extension. In passage we reach a connexion of nature with the
+ultimate metaphysical reality. The quality of passage in durations is a
+particular exhibition in nature of a quality which extends beyond
+nature. For example passage is a quality not only of nature, which is
+the thing known, but also of sense-awareness which is the procedure of
+knowing. Durations have all the reality that nature has, though what
+that may be we need not now determine. The measurableness of time is
+derivative from the properties of durations. So also is the serial
+character of time. We shall find that there are in nature competing
+serial time-systems derived from different families of durations. These
+are a peculiarity of the character of passage as it is found in nature.
+This character has the reality of nature, but we must not necessarily
+transfer natural time to extra-natural entities. (ii) For two minds, the
+discerned components of the general facts exhibited in their respective
+acts of sense-awareness must be different. For each mind, in its
+awareness of nature is aware of a certain complex of related natural
+entities in their relations to the living body as a focus. But the
+associated durations may be identical. Here we are touching on that
+character of the passage nature which issues in the spatial relations of
+simultaneous bodies. This possible identity of the durations in the case
+of the sense-awareness of distinct minds is what binds into one nature
+the private experiences of sentient beings. We are here considering the
+spatial side of the passage of nature. Passage in this aspect of it also
+seems to extend beyond nature to mind.
+
+It is important to distinguish simultaneity from instantaneousness. I
+lay no stress on the mere current usage of the two terms. There are two
+concepts which I want to distinguish, and one I call simultaneity and
+the other instantaneousness. I hope that the words are judiciously
+chosen; but it really does not matter so long as I succeed in explaining
+my meaning. Simultaneity is the property of a group of natural elements
+which in some sense are components of a duration. A duration can be all
+nature present as the immediate fact posited by sense-awareness. A
+duration retains within itself the passage of nature. There are within
+it antecedents and consequents which are also durations which may be the
+complete specious presents of quicker consciousnesses. In other words a
+duration retains temporal thickness. Any concept of all nature as
+immediately known is always a concept of some duration though it may be
+enlarged in its temporal thickness beyond the possible specious present
+of any being known to us as existing within nature. Thus simultaneity is
+an ultimate factor in nature, immediate for sense-awareness.
+
+Instantaneousness is a complex logical concept of a procedure in thought
+by which constructed logical entities are produced for the sake of the
+simple expression in thought of properties of nature. Instantaneousness
+is the concept of all nature at an instant, where an instant is
+conceived as deprived of all temporal extension. For example we conceive
+of the distribution of matter in space at an instant. This is a very
+useful concept in science especially in applied mathematics; but it is a
+very complex idea so far as concerns its connexions with the immediate
+facts of sense-awareness. There is no such thing as nature at an instant
+posited by sense-awareness. What sense-awareness delivers over for
+knowledge is nature through a period. Accordingly nature at an instant,
+since it is not itself a natural entity, must be defined in terms of
+genuine natural entities. Unless we do so, our science, which employs
+the concept of instantaneous nature, must abandon all claim to be
+founded upon observation.
+
+I will use the term 'moment' to mean 'all nature at an instant.' A
+moment, in the sense in which the term is here used, has no temporal
+extension, and is in this respect to be contrasted with a duration which
+has such extension. What is directly yielded to our knowledge by
+sense-awareness is a duration. Accordingly we have now to explain how
+moments are derived from durations, and also to explain the purpose
+served by their introduction.
+
+A moment is a limit to which we approach as we confine attention to
+durations of minimum extension. Natural relations among the ingredients
+of a duration gain in complexity as we consider durations of increasing
+temporal extension. Accordingly there is an approach to ideal simplicity
+as we approach an ideal diminution of extension.
+
+The word 'limit' has a precise signification in the logic of number and
+even in the logic of non-numerical one-dimensional series. As used here
+it is so far a mere metaphor, and it is necessary to explain directly
+the concept which it is meant to indicate.
+
+Durations can have the two-termed relational property of extending one
+over the other. Thus the duration which is all nature during a certain
+minute extends over the duration which is all nature during the
+30th second of that minute. This relation of 'extending
+over'--'extension' as I shall call it--is a fundamental natural relation
+whose field comprises more than durations. It is a relation which two
+limited events can have to each other. Furthermore as holding between
+durations the relation appears to refer to the purely temporal
+extension. I shall however maintain that the same relation of extension
+lies at the base both of temporal and spatial extension. This discussion
+can be postponed; and for the present we are simply concerned with the
+relation of extension as it occurs in its temporal aspect for the
+limited field of durations.
+
+The concept of extension exhibits in thought one side of the ultimate
+passage of nature. This relation holds because of the special character
+which passage assumes in nature; it is the relation which in the case of
+durations expresses the properties of 'passing over.' Thus the duration
+which was one definite minute passed over the duration which was its
+30th second. The duration of the 30th second was part of the duration of
+the minute. I shall use the terms 'whole' and 'part' exclusively in this
+sense, that the 'part' is an event which is extended over by the other
+event which is the 'whole.' Thus in my nomenclature 'whole' and 'part'
+refer exclusively to this fundamental relation of extension; and
+accordingly in this technical usage only events can be either wholes or
+parts.
+
+The continuity of nature arises from extension. Every event extends over
+other events, and every event is extended over by other events. Thus in
+the special case of durations which are now the only events directly
+under consideration, every duration is part of other durations; and
+every duration has other durations which are parts of it. Accordingly
+there are no maximum durations and no minimum durations. Thus there is
+no atomic structure of durations, and the perfect definition of a
+duration, so as to mark out its individuality and distinguish it from
+highly analogous durations over which it is passing, or which are
+passing over it, is an arbitrary postulate of thought. Sense-awareness
+posits durations as factors in nature but does not clearly enable
+thought to use it as distinguishing the separate individualities of the
+entities of an allied group of slightly differing durations. This is one
+instance of the indeterminateness of sense-awareness. Exactness is an
+ideal of thought, and is only realised in experience by the selection of
+a route of approximation.
+
+The absence of maximum and minimum durations does not exhaust the
+properties of nature which make up its continuity. The passage of nature
+involves the existence of a family of durations. When two durations
+belong to the same family either one contains the other, or they overlap
+each other in a subordinate duration without either containing the
+other; or they are completely separate. The excluded case is that of
+durations overlapping in finite events but not containing a third
+duration as a common part.
+
+It is evident that the relation of extension is transitive; namely as
+applied to durations, if duration A is part of duration B, and
+duration B is part of duration C, then A is part of C. Thus the
+first two cases may be combined into one and we can say that two
+durations which belong to the same family _either_ are such that there
+are durations which are parts of both _or_ are completely separate.
+
+Furthermore the converse of this proposition holds; namely, if two
+durations have other durations which are parts of both _or_ if the two
+durations are completely separate, then they belong to the same family.
+
+The further characteristics of the continuity of nature--so far as
+durations are concerned--which has not yet been formulated arises in
+connexion with a family of durations. It can be stated in this way:
+There are durations which contain as parts any two durations of the same
+family. For example a week contains as parts any two of its days. It is
+evident that a containing duration satisfies the conditions for
+belonging to the same family as the two contained durations.
+
+We are now prepared to proceed to the definition of a moment of time.
+Consider a set of durations all taken from the same family. Let it have
+the following properties: (i) of any two members of the set one contains
+the other as a part, and (ii) there is no duration which is a common
+part of every member of the set.
+
+Now the relation of whole and part is asymmetrical; and by this I mean
+that if A is part of B, then B is not part of A. Also we have
+already noted that the relation is transitive. Accordingly we can easily
+see that the durations of any set with the properties just enumerated
+must be arranged in a one-dimensional serial order in which as we
+descend the series we progressively reach durations of smaller and
+smaller temporal extension. The series may start with any arbitrarily
+assumed duration of any temporal extension, but in descending the
+series the temporal extension progressively contracts and the successive
+durations are packed one within the other like the nest of boxes of a
+Chinese toy. But the set differs from the toy in this particular: the
+toy has a smallest box which forms the end box of its series; but the
+set of durations can have no smallest duration nor can it converge
+towards a duration as its limit. For the parts either of the end
+duration or of the limit would be parts of all the durations of the set
+and thus the second condition for the set would be violated.
+
+I will call such a set of durations an 'abstractive set' of durations.
+It is evident that an abstractive set as we pass along it converges to
+the ideal of all nature with no temporal extension, namely, to the ideal
+of all nature at an instant. But this ideal is in fact the ideal of a
+nonentity. What the abstractive set is in fact doing is to guide thought
+to the consideration of the progressive simplicity of natural relations
+as we progressively diminish the temporal extension of the duration
+considered. Now the whole point of the procedure is that the
+quantitative expressions of these natural properties do converge to
+limits though the abstractive set does not converge to any limiting
+duration. The laws relating these quantitative limits are the laws of
+nature 'at an instant,' although in truth there is no nature at an
+instant and there is only the abstractive set. Thus an abstractive set
+is effectively the entity meant when we consider an instant of time
+without temporal extension. It subserves all the necessary purposes of
+giving a definite meaning to the concept of the properties of nature at
+an instant. I fully agree that this concept is fundamental in the
+expression of physical science. The difficulty is to express our
+meaning in terms of the immediate deliverances of sense-awareness, and I
+offer the above explanation as a complete solution of the problem.
+
+In this explanation a moment is the set of natural properties reached by
+a route of approximation. An abstractive series is a route of
+approximation. There are different routes of approximation to the same
+limiting set of the properties of nature. In other words there are
+different abstractive sets which are to be regarded as routes of
+approximation to the same moment. Accordingly there is a certain amount
+of technical detail necessary in explaining the relations of such
+abstractive sets with the same convergence and in guarding against
+possible exceptional cases. Such details are not suitable for exposition
+in these lectures, and I have dealt with them fully elsewhere[5].
+
+[5] Cf. _An Enquiry concerning the Principles of Natural Knowledge_,
+Cambridge University Press, 1919.
+
+It is more convenient for technical purposes to look on a moment as
+being the class of all abstractive sets of durations with the same
+convergence. With this definition (provided that we can successfully
+explain what we mean by the 'same convergence' apart from a detailed
+knowledge of the set of natural properties arrived at by approximation)
+a moment is merely a class of sets of durations whose relations of
+extension in respect to each other have certain definite peculiarities.
+We may term these connexions of the component durations the 'extrinsic'
+properties of a moment; the 'intrinsic' properties of the moment are the
+properties of nature arrived at as a limit as we proceed along any one
+of its abstractive sets. These are the properties of nature 'at that
+moment,' or 'at that instant.'
+
+The durations which enter into the composition of a moment all belong to
+one family. Thus there is one family of moments corresponding to one
+family of durations. Also if we take two moments of the same family,
+among the durations which enter into the composition of one moment the
+smaller durations are completely separated from the smaller durations
+which enter into the composition of the other moment. Thus the two
+moments in their intrinsic properties must exhibit the limits of
+completely different states of nature. In this sense the two moments are
+completely separated. I will call two moments of the same family
+'parallel.'
+
+Corresponding to each duration there are two moments of the associated
+family of moments which are the boundary moments of that duration. A
+'boundary moment' of a duration can be defined in this way. There are
+durations of the same family as the given duration which overlap it but
+are not contained in it. Consider an abstractive set of such durations.
+Such a set defines a moment which is just as much without the duration
+as within it. Such a moment is a boundary moment of the duration. Also
+we call upon our sense-awareness of the passage of nature to inform us
+that there are two such boundary moments, namely the earlier one and the
+later one. We will call them the initial and the final boundaries.
+
+There are also moments of the same family such that the shorter
+durations in their composition are entirely separated from the given
+duration. Such moments will be said to lie 'outside' the given duration.
+Again other moments of the family are such that the shorter durations in
+their composition are parts of the given duration. Such moments are said
+to lie 'within' the given duration or to 'inhere' in it. The whole
+family of parallel moments is accounted for in this way by reference to
+any given duration of the associated family of durations. Namely, there
+are moments of the family which lie without the given duration, there
+are the two moments which are the boundary moments of the given
+duration, and the moments which lie within the given duration.
+Furthermore any two moments of the same family are the boundary moments
+of some one duration of the associated family of durations.
+
+It is now possible to define the serial relation of temporal order among
+the moments of a family. For let A and C be any two moments of the
+family, these moments are the boundary moments of one duration d of
+the associated family, and any moment B which lies within the duration
+d will be said to lie between the moments A and C. Thus the
+three-termed relation of 'lying-between' as relating three moments A,
+B, and C is completely defined. Also our knowledge of the passage of
+nature assures us that this relation distributes the moments of the
+family into a serial order. I abstain from enumerating the definite
+properties which secure this result, I have enumerated them in my
+recently published book[6] to which I have already referred. Furthermore
+the passage of nature enables us to know that one direction along the
+series corresponds to passage into the future and the other direction
+corresponds to retrogression towards the past.
+
+[6] Cf. _Enquiry_.
+
+Such an ordered series of moments is what we mean by time defined as a
+series. Each element of the series exhibits an instantaneous state of
+nature. Evidently this serial time is the result of an intellectual
+process of abstraction. What I have done is to give precise definitions
+of the procedure by which the abstraction is effected. This procedure is
+merely a particular case of the general method which in my book I name
+the 'method of extensive abstraction.' This serial time is evidently not
+the very passage of nature itself. It exhibits some of the natural
+properties which flow from it. The state of nature 'at a moment' has
+evidently lost this ultimate quality of passage. Also the temporal
+series of moments only retains it as an extrinsic relation of entities
+and not as the outcome of the essential being of the terms of the
+series.
+
+Nothing has yet been said as to the measurement of time. Such
+measurement does not follow from the mere serial property of time; it
+requires a theory of congruence which will be considered in a later
+lecture.
+
+In estimating the adequacy of this definition of the temporal series as
+a formulation of experience it is necessary to discriminate between the
+crude deliverance of sense-awareness and our intellectual theories. The
+lapse of time is a measurable serial quantity. The whole of scientific
+theory depends on this assumption and any theory of time which fails to
+provide such a measurable series stands self-condemned as unable to
+account for the most salient fact in experience. Our difficulties only
+begin when we ask what it is that is measured. It is evidently something
+so fundamental in experience that we can hardly stand back from it and
+hold it apart so as to view it in its own proportions.
+
+We have first to make up our minds whether time is to be found in nature
+or nature is to be found in time. The difficulty of the latter
+alternative--namely of making time prior to nature--is that time then
+becomes a metaphysical enigma. What sort of entities are its instants
+or its periods? The dissociation of time from events discloses to our
+immediate inspection that the attempt to set up time as an independent
+terminus for knowledge is like the effort to find substance in a shadow.
+There is time because there are happenings, and apart from happenings
+there is nothing.
+
+It is necessary however to make a distinction. In some sense time
+extends beyond nature. It is not true that a timeless sense-awareness
+and a timeless thought combine to contemplate a timeful nature.
+Sense-awareness and thought are themselves processes as well as their
+termini in nature. In other words there is a passage of sense-awareness
+and a passage of thought. Thus the reign of the quality of passage
+extends beyond nature. But now the distinction arises between passage
+which is fundamental and the temporal series which is a logical
+abstraction representing some of the properties of nature. A temporal
+series, as we have defined it, represents merely certain properties of a
+family of durations--properties indeed which durations only possess
+because of their partaking of the character of passage, but on the other
+hand properties which only durations do possess. Accordingly time in the
+sense of a measurable temporal series is a character of nature only, and
+does not extend to the processes of thought and of sense-awareness
+except by a correlation of these processes with the temporal series
+implicated in their procedures.
+
+So far the passage of nature has been considered in connexion with the
+passage of durations; and in this connexion it is peculiarly associated
+with temporal series. We must remember however that the character of
+passage is peculiarly associated with the extension of events, and that
+from this extension spatial transition arises just as much as temporal
+transition. The discussion of this point is reserved for a later lecture
+but it is necessary to remember it now that we are proceeding to discuss
+the application of the concept of passage beyond nature, otherwise we
+shall have too narrow an idea of the essence of passage.
+
+It is necessary to dwell on the subject of sense-awareness in this
+connexion as an example of the way in which time concerns mind, although
+measurable time is a mere abstract from nature and nature is closed to
+mind.
+
+Consider sense-awareness--not its terminus which is nature, but
+sense-awareness in itself as a procedure of mind. Sense-awareness is a
+relation of mind to nature. Accordingly we are now considering mind as a
+relatum in sense-awareness. For mind there is the immediate
+sense-awareness and there is memory. The distinction between memory and
+the present immediacy has a double bearing. On the one hand it discloses
+that mind is not impartially aware of all those natural durations to
+which it is related by awareness. Its awareness shares in the passage of
+nature. We can imagine a being whose awareness, conceived as his private
+possession, suffers no transition, although the terminus of his
+awareness is our own transient nature. There is no essential reason why
+memory should not be raised to the vividness of the present fact; and
+then from the side of mind, What is the difference between the present
+and the past? Yet with this hypothesis we can also suppose that the
+vivid remembrance and the present fact are posited in awareness as in
+their temporal serial order. Accordingly we must admit that though we
+can imagine that mind in the operation of sense-awareness might be free
+from any character of passage, yet in point of fact our experience of
+sense-awareness exhibits our minds as partaking in this character.
+
+On the other hand the mere fact of memory is an escape from transience.
+In memory the past is present. It is not present as overleaping the
+temporal succession of nature, but it is present as an immediate fact
+for the mind. Accordingly memory is a disengagement of the mind from the
+mere passage of nature; for what has passed for nature has not passed
+for mind.
+
+Furthermore the distinction between memory and the immediate present is
+not so clear as it is conventional to suppose. There is an intellectual
+theory of time as a moving knife-edge, exhibiting a present fact without
+temporal extension. This theory arises from the concept of an ideal
+exactitude of observation. Astronomical observations are successively
+refined to be exact to tenths, to hundredths, and to thousandths of
+seconds. But the final refinements are arrived at by a system of
+averaging, and even then present us with a stretch of time as a margin
+of error. Here error is merely a conventional term to express the fact
+that the character of experience does not accord with the ideal of
+thought. I have already explained how the concept of a moment
+conciliates the observed fact with this ideal; namely, there is a
+limiting simplicity in the quantitative expression of the properties of
+durations, which is arrived at by considering any one of the abstractive
+sets included in the moment. In other words the extrinsic character of
+the moment as an aggregate of durations has associated with it the
+intrinsic character of the moment which is the limiting expression of
+natural properties.
+
+Thus the character of a moment and the ideal of exactness which it
+enshrines do not in any way weaken the position that the ultimate
+terminus of awareness is a duration with temporal thickness. This
+immediate duration is not clearly marked out for our apprehension. Its
+earlier boundary is blurred by a fading into memory, and its later
+boundary is blurred by an emergence from anticipation. There is no sharp
+distinction either between memory and the present immediacy or between
+the present immediacy and anticipation. The present is a wavering
+breadth of boundary between the two extremes. Thus our own
+sense-awareness with its extended present has some of the character of
+the sense-awareness of the imaginary being whose mind was free from
+passage and who contemplated all nature as an immediate fact. Our own
+present has its antecedents and its consequents, and for the imaginary
+being all nature has its antecedent and its consequent durations. Thus
+the only difference in this respect between us and the imaginary being
+is that for him all nature shares in the immediacy of our present
+duration.
+
+The conclusion of this discussion is that so far as sense-awareness is
+concerned there is a passage of mind which is distinguishable from the
+passage of nature though closely allied with it. We may speculate, if we
+like, that this alliance of the passage of mind with the passage of
+nature arises from their both sharing in some ultimate character of
+passage which dominates all being. But this is a speculation in which we
+have no concern. The immediate deduction which is sufficient for us is
+that--so far as sense-awareness is concerned--mind is not in time or in
+space in the same sense in which the events of nature are in time, but
+that it is derivatively in time and in space by reason of the peculiar
+alliance of its passage with the passage of nature. Thus mind is in time
+and in space in a sense peculiar to itself. This has been a long
+discussion to arrive at a very simple and obvious conclusion. We all
+feel that in some sense our minds are here in this room and at this
+time. But it is not quite in the same sense as that in which the events
+of nature which are the existences of our brains have their spatial and
+temporal positions. The fundamental distinction to remember is that
+immediacy for sense-awareness is not the same as instantaneousness for
+nature. This last conclusion bears on the next discussion with which I
+will terminate this lecture. This question can be formulated thus, Can
+alternative temporal series be found in nature?
+
+A few years ago such a suggestion would have been put aside as being
+fantastically impossible. It would have had no bearing on the science
+then current, and was akin to no ideas which had ever entered into the
+dreams of philosophy. The eighteenth and nineteenth centuries accepted
+as their natural philosophy a certain circle of concepts which were as
+rigid and definite as those of the philosophy of the middle ages, and
+were accepted with as little critical research. I will call this natural
+philosophy 'materialism.' Not only were men of science materialists, but
+also adherents of all schools of philosophy. The idealists only differed
+from the philosophic materialists on question of the alignment of nature
+in reference to mind. But no one had any doubt that the philosophy of
+nature considered in itself was of the type which I have called
+materialism. It is the philosophy which I have already examined in my
+two lectures of this course preceding the present one. It can be
+summarised as the belief that nature is an aggregate of material and
+that this material exists in some sense _at_ each successive member of a
+one-dimensional series of extensionless instants of time. Furthermore
+the mutual relations of the material entities at each instant formed
+these entities into a spatial configuration in an unbounded space. It
+would seem that space--on this theory--would be as instantaneous as the
+instants, and that some explanation is required of the relations between
+the successive instantaneous spaces. The materialistic theory is however
+silent on this point; and the succession of instantaneous spaces is
+tacitly combined into one persistent space. This theory is a purely
+intellectual rendering of experience which has had the luck to get
+itself formulated at the dawn of scientific thought. It has dominated
+the language and the imagination of science since science flourished in
+Alexandria, with the result that it is now hardly possible to speak
+without appearing to assume its immediate obviousness.
+
+But when it is distinctly formulated in the abstract terms in which I
+have just stated it, the theory is very far from obvious. The passing
+complex of factors which compose the fact which is the terminus of
+sense-awareness places before us nothing corresponding to the trinity of
+this natural materialism. This trinity is composed (i) of the temporal
+series of extensionless instants, (ii) of the aggregate of material
+entities, and (iii) of space which is the outcome of relations of
+matter.
+
+There is a wide gap between these presuppositions of the intellectual
+theory of materialism and the immediate deliverances of sense-awareness.
+I do not question that this materialistic trinity embodies important
+characters of nature. But it is necessary to express these characters in
+terms of the facts of experience. This is exactly what in this lecture I
+have been endeavouring to do so far as time is concerned; and we have
+now come up against the question, Is there only one temporal series? The
+uniqueness of the temporal series is presupposed in the materialist
+philosophy of nature. But that philosophy is merely a theory, like the
+Aristotelian scientific theories so firmly believed in the middle ages.
+If in this lecture I have in any way succeeded in getting behind the
+theory to the immediate facts, the answer is not nearly so certain. The
+question can be transformed into this alternative form, Is there only
+one family of durations? In this question the meaning of a 'family of
+durations' has been defined earlier in this lecture. The answer is now
+not at all obvious. On the materialistic theory the instantaneous
+present is the only field for the creative activity of nature. The past
+is gone and the future is not yet. Thus (on this theory) the immediacy
+of perception is of an instantaneous present, and this unique present is
+the outcome of the past and the promise of the future. But we deny this
+immediately given instantaneous present. There is no such thing to be
+found in nature. As an ultimate fact it is a nonentity. What is
+immediate for sense-awareness is a duration. Now a duration has within
+itself a past and a future; and the temporal breadths of the immediate
+durations of sense-awareness are very indeterminate and dependent on the
+individual percipient. Accordingly there is no unique factor in nature
+which for every percipient is pre-eminently and necessarily the present.
+The passage of nature leaves nothing between the past and the future.
+What we perceive as present is the vivid fringe of memory tinged with
+anticipation. This vividness lights up the discriminated field within a
+duration. But no assurance can thereby be given that the happenings of
+nature cannot be assorted into other durations of alternative families.
+We cannot even know that the series of immediate durations posited by
+the sense-awareness of one individual mind all necessarily belong to the
+same family of durations. There is not the slightest reason to believe
+that this is so. Indeed if my theory of nature be correct, it will not
+be the case.
+
+The materialistic theory has all the completeness of the thought of the
+middle ages, which had a complete answer to everything, be it in heaven
+or in hell or in nature. There is a trimness about it, with its
+instantaneous present, its vanished past, its non-existent future, and
+its inert matter. This trimness is very medieval and ill accords with
+brute fact.
+
+The theory which I am urging admits a greater ultimate mystery and a
+deeper ignorance. The past and the future meet and mingle in the
+ill-defined present. The passage of nature which is only another name
+for the creative force of existence has no narrow ledge of definite
+instantaneous present within which to operate. Its operative presence
+which is now urging nature forward must be sought for throughout the
+whole, in the remotest past as well as in the narrowest breadth of any
+present duration. Perhaps also in the unrealised future. Perhaps also in
+the future which might be as well as the actual future which will be. It
+is impossible to meditate on time and the mystery of the creative
+passage of nature without an overwhelming emotion at the limitations of
+human intelligence.
+
+
+
+
+CHAPTER IV
+
+THE METHOD OF EXTENSIVE ABSTRACTION
+
+
+To-day's lecture must commence with the consideration of limited events.
+We shall then be in a position to enter upon an investigation of the
+factors in nature which are represented by our conception of space.
+
+The duration which is the immediate disclosure of our sense-awareness is
+discriminated into parts. There is the part which is the life of all
+nature within a room, and there is the part which is the life of all
+nature within a table in the room. These parts are limited events. They
+have the endurance of the present duration, and they are parts of it.
+But whereas a duration is an unlimited whole and in a certain limited
+sense is all that there is, a limited event possesses a completely
+defined limitation of extent which is expressed for us in
+spatio-temporal terms.
+
+We are accustomed to associate an event with a certain melodramatic
+quality. If a man is run over, that is an event comprised within certain
+spatio-temporal limits. We are not accustomed to consider the endurance
+of the Great Pyramid throughout any definite day as an event. But the
+natural fact which is the Great Pyramid throughout a day, meaning
+thereby all nature within it, is an event of the same character as the
+man's accident, meaning thereby all nature with spatio-temporal
+limitations so as to include the man and the motor during the period
+when they were in contact.
+
+We are accustomed to analyse these events into three factors, time,
+space, and material. In fact, we at once apply to them the concepts of
+the materialistic theory of nature. I do not deny the utility of this
+analysis for the purpose of expressing important laws of nature. What I
+am denying is that anyone of these factors is posited for us in
+sense-awareness in concrete independence. We perceive one unit factor in
+nature; and this factor is that something is going on then--there. For
+example, we perceive the going-on of the Great Pyramid in its relations
+to the goings-on of the surrounding Egyptian events. We are so trained,
+both by language and by formal teaching and by the resulting
+convenience, to express our thoughts in terms of this materialistic
+analysis that intellectually we tend to ignore the true unity of the
+factor really exhibited in sense-awareness. It is this unit factor,
+retaining in itself the passage of nature, which is the primary concrete
+element discriminated in nature. These primary factors are what I mean
+by events.
+
+Events are the field of a two-termed relation, namely the relation of
+extension which was considered in the last lecture. Events are the
+things related by the relation of extension. If an event A extends
+over an event B, then B is 'part of' A, and A is a 'whole' of
+which B is a part. Whole and part are invariably used in these
+lectures in this definite sense. It follows that in reference to this
+relation any two events A and B may have any one of four relations
+to each other, namely (i) A may extend over B, or (ii) B may
+extend over A, or (iii) A and B may both extend over some third
+event C, but neither over the other, or (iv) A and B may be
+entirely separate. These alternatives can obviously be illustrated by
+Euler's diagrams as they appear in logical textbooks.
+
+The continuity of nature is the continuity of events. This continuity is
+merely the name for the aggregate of a variety of properties of events
+in connexion with the relation of extension.
+
+In the first place, this relation is transitive; secondly, every event
+contains other events as parts of itself; thirdly every event is a part
+of other events; fourthly given any two finite events there are events
+each of which contains both of them as parts; and fifthly there is a
+special relation between events which I term 'junction.'
+
+Two events have junction when there is a third event of which both
+events are parts, and which is such that no part of it is separated from
+both of the two given events. Thus two events with junction make up
+exactly one event which is in a sense their sum.
+
+Only certain pairs of events have this property. In general any event
+containing two events also contains parts which are separated from both
+events.
+
+There is an alternative definition of the junction of two events which I
+have adopted in my recent book[7]. Two events have junction when there
+is a third event such that (i) it overlaps both events and (ii) it has
+no part which is separated from both the given events. If either of
+these alternative definitions is adopted as the definition of junction,
+the other definition appears as an axiom respecting the character of
+junction as we know it in nature. But we are not thinking of logical
+definition so much as the formulation of the results of direct
+observation. There is a certain continuity inherent in the observed
+unity of an event, and these two definitions of junction are really
+axioms based on observation respecting the character of this continuity.
+
+[7] Cf. _Enquiry_.
+
+The relations of whole and part and of overlapping are particular cases
+of the junction of events. But it is possible for events to have
+junction when they are separate from each other; for example, the upper
+and the lower part of the Great Pyramid are divided by some imaginary
+horizontal plane.
+
+The continuity which nature derives from events has been obscured by the
+illustrations which I have been obliged to give. For example I have
+taken the existence of the Great Pyramid as a fairly well-known fact to
+which I could safely appeal as an illustration. This is a type of event
+which exhibits itself to us as the situation of a recognisable object;
+and in the example chosen the object is so widely recognised that it has
+received a name. An object is an entity of a different type from an
+event. For example, the event which is the life of nature within the
+Great Pyramid yesterday and to-day is divisible into two parts, namely
+the Great Pyramid yesterday and the Great Pyramid to-day. But the
+recognisable object which is also called the Great Pyramid is the same
+object to-day as it was yesterday. I shall have to consider the theory
+of objects in another lecture.
+
+The whole subject is invested with an unmerited air of subtlety by the
+fact that when the event is the situation of a well-marked object, we
+have no language to distinguish the event from the object. In the case
+of the Great Pyramid, the object is the perceived unit entity which as
+perceived remains self-identical throughout the ages; while the whole
+dance of molecules and the shifting play of the electromagnetic field
+are ingredients of the event. An object is in a sense out of time. It is
+only derivatively in time by reason of its having the relation to events
+which I term 'situation.' This relation of situation will require
+discussion in a subsequent lecture.
+
+The point which I want to make now is that being the situation of a
+well-marked object is not an inherent necessity for an event. Wherever
+and whenever something is going on, there is an event. Furthermore
+'wherever and whenever' in themselves presuppose an event, for space and
+time in themselves are abstractions from events. It is therefore a
+consequence of this doctrine that something is always going on
+everywhere, even in so-called empty space. This conclusion is in accord
+with modern physical science which presupposes the play of an
+electromagnetic field throughout space and time. This doctrine of
+science has been thrown into the materialistic form of an all-pervading
+ether. But the ether is evidently a mere idle concept--in the
+phraseology which Bacon applied to the doctrine of final causes, it is a
+barren virgin. Nothing is deduced from it; and the ether merely
+subserves the purpose of satisfying the demands of the materialistic
+theory. The important concept is that of the shifting facts of the
+fields of force. This is the concept of an ether of events which should
+be substituted for that of a material ether.
+
+It requires no illustration to assure you that an event is a complex
+fact, and the relations between two events form an almost impenetrable
+maze. The clue discovered by the common sense of mankind and
+systematically utilised in science is what I have elsewhere[8] called
+the law of convergence to simplicity by diminution of extent.
+
+[8] Cf. _Organisation of Thought_, pp. 146 et seq. Williams and Norgate,
+1917.
+
+If A and B are two events, and A′ is part of A and B′ is part
+of B, then in many respects the relations between the parts A′ and
+B′ will be simpler than the relations between A and B. This is the
+principle which presides over all attempts at exact observation.
+
+The first outcome of the systematic use of this law has been the
+formulation of the abstract concepts of Time and Space. In the previous
+lecture I sketched how the principle was applied to obtain the
+time-series. I now proceed to consider how the spatial entities are
+obtained by the same method. The systematic procedure is identical in
+principle in both cases, and I have called the general type of procedure
+the 'method of extensive abstraction.'
+
+You will remember that in my last lecture I defined the concept of an
+abstractive set of durations. This definition can be extended so as to
+apply to any events, limited events as well as durations. The only
+change that is required is the substitution of the word 'event' for the
+word 'duration.' Accordingly an abstractive set of events is any set of
+events which possesses the two properties, (i) of any two members of the
+set one contains the other as a part, and (ii) there is no event which
+is a common part of every member of the set. Such a set, as you will
+remember, has the properties of the Chinese toy which is a nest of
+boxes, one within the other, with the difference that the toy has a
+smallest box, while the abstractive class has neither a smallest event
+nor does it converge to a limiting event which is not a member of the
+set.
+
+Thus, so far as the abstractive sets of events are concerned, an
+abstractive set converges to nothing. There is the set with its members
+growing indefinitely smaller and smaller as we proceed in thought
+towards the smaller end of the series; but there is no absolute minimum
+of any sort which is finally reached. In fact the set is just itself and
+indicates nothing else in the way of events, except itself. But each
+event has an intrinsic character in the way of being a situation of
+objects and of having parts which are situations of objects and--to
+state the matter more generally--in the way of being a field of the life
+of nature. This character can be defined by quantitative expressions
+expressing relations between various quantities intrinsic to the event
+or between such quantities and other quantities intrinsic to other
+events. In the case of events of considerable spatio-temporal extension
+this set of quantitative expressions is of bewildering complexity. If
+e be an event, let us denote by q(e) the set of quantitative expressions
+defining its character including its connexions with the rest of nature.
+Let e₁, e₂, e₃, etc. be an abstractive set, the members being so
+arranged that each member such as e_{n} extends over all the succeeding
+members such as e_{n+1}, e_{n+2} and so on. Then corresponding to the
+series
+
+    e₁, e₂, e₃, ..., e_{n}, e_{n+1}, ...,
+
+there is the series
+
+    q(e₁), q(e₂), q(e₃), ..., q(e_{n}), q(e_{n+1}), ....
+
+Call the series of events s and the series of quantitative expressions
+q(s). The series s has no last term and no events which are contained
+in every member of the series. Accordingly the series of events
+converges to nothing. It is just itself. Also the series q(s) has no
+last term. But the sets of homologous quantities running through the
+various terms of the series do converge to definite limits. For example
+if Q₁ be a quantitative measurement found in q(e₁), and Q₂ the homologue
+to Q₁ to be found in q(e₂), and Q₃ the homologue to Q₁ and Q₂ to be
+found in q(e₃), and so on, then the series
+
+    Q₁, Q₂, Q₃, ..., Q_{n}, Q_{n+1}, ...,
+
+though it has no last term, does in general converge to a definite
+limit. Accordingly there is a class of limits l(s) which is the
+class of the limits of those members of q(e_{n}) which have
+homologues throughout the series q(s) as n indefinitely increases.
+We can represent this statement diagrammatically by using an arrow (➝)
+to mean 'converges to.' Then
+
+    e₁, e₂, e₃, ..., e_{n}, e_{n+1}, ... ➝ nothing,
+
+and
+
+    q(e₁), q(e₂), q(e₃), ..., q(e_{n}), q(e_{n+1}), ... ➝ l(s).
+
+The mutual relations between the limits in the set l(s), and also
+between these limits and the limits in other sets l(s′), l(s″), ...,
+which arise from other abstractive sets s′, s″, etc., have a peculiar
+simplicity.
+
+Thus the set s does indicate an ideal simplicity of natural relations,
+though this simplicity is not the character of any actual event in s.
+We can make an approximation to such a simplicity which, as estimated
+numerically, is as close as we like by considering an event which is far
+enough down the series towards the small end. It will be noted that it
+is the infinite series, as it stretches away in unending succession
+towards the small end, which is of importance. The arbitrarily large
+event with which the series starts has no importance at all. We can
+arbitrarily exclude any set of events at the big end of an abstractive
+set without the loss of any important property to the set as thus
+modified.
+
+I call the limiting character of natural relations which is indicated by
+an abstractive set, the 'intrinsic character' of the set; also the
+properties, connected with the relation of whole and part as concerning
+its members, by which an abstractive set is defined together form what I
+call its 'extrinsic character.' The fact that the extrinsic character of
+an abstractive set determines a definite intrinsic character is the
+reason of the importance of the precise concepts of space and time. This
+emergence of a definite intrinsic character from an abstractive set is
+the precise meaning of the law of convergence.
+
+For example, we see a train approaching during a minute. The event which
+is the life of nature within that train during the minute is of great
+complexity and the expression of its relations and of the ingredients of
+its character baffles us. If we take one second of that minute, the more
+limited event which is thus obtained is simpler in respect to its
+ingredients, and shorter and shorter times such as a tenth of that
+second, or a hundredth, or a thousandth--so long as we have a definite
+rule giving a definite succession of diminishing events--give events
+whose ingredient characters converge to the ideal simplicity of the
+character of the train at a definite instant. Furthermore there are
+different types of such convergence to simplicity. For example, we can
+converge as above to the limiting character expressing nature at an
+instant within the whole volume of the train at that instant, or to
+nature at an instant within some portion of that volume--for example
+within the boiler of the engine--or to nature at an instant on some area
+of surface, or to nature at an instant on some line within the train, or
+to nature at an instant at some point of the train. In the last case the
+simple limiting characters arrived at will be expressed as densities,
+specific gravities, and types of material. Furthermore we need not
+necessarily converge to an abstraction which involves nature at an
+instant. We may converge to the physical ingredients of a certain point
+track throughout the whole minute. Accordingly there are different types
+of extrinsic character of convergence which lead to the approximation to
+different types of intrinsic characters as limits.
+
+We now pass to the investigation of possible connexions between
+abstractive sets. One set may 'cover' another. I define 'covering' as
+follows: An abstractive set p covers an abstractive set q when every
+member of p contains as its parts some members of q. It is evident
+that if any event e contains as a part any member of the set q, then
+owing to the transitive property of extension every succeeding member of
+the small end of q is part of e. In such a case I will say that the
+abstractive set q 'inheres in' the event e. Thus when an abstractive
+set p covers an abstractive set q, the abstractive set q inheres
+in every member of p.
+
+Two abstractive sets may each cover the other. When this is the case I
+shall call the two sets 'equal in abstractive force.' When there is no
+danger of misunderstanding I shall shorten this phrase by simply saying
+that the two abstractive sets are 'equal.' The possibility of this
+equality of abstractive sets arises from the fact that both sets, p
+and q, are infinite series towards their small ends. Thus the equality
+means, that given any event x belonging to p, we can always by
+proceeding far enough towards the small end of q find an event y
+which is part of x, and that then by proceeding far enough towards the
+small end of p we can find an event z which is part of y, and so
+on indefinitely.
+
+The importance of the equality of abstractive sets arises from the
+assumption that the intrinsic characters of the two sets are identical.
+If this were not the case exact observation would be at an end.
+
+It is evident that any two abstractive sets which are equal to a third
+abstractive set are equal to each other. An 'abstractive element' is the
+whole group of abstractive sets which are equal to any one of
+themselves. Thus all abstractive sets belonging to the same element are
+equal and converge to the same intrinsic character. Thus an abstractive
+element is the group of routes of approximation to a definite intrinsic
+character of ideal simplicity to be found as a limit among natural
+facts.
+
+If an abstractive set p covers an abstractive set q, then any
+abstractive set belonging to the abstractive element of which p is a
+member will cover any abstractive set belonging to the element of which
+q is a member. Accordingly it is useful to stretch the meaning of the
+term 'covering,' and to speak of one abstractive element 'covering'
+another abstractive element. If we attempt in like manner to stretch the
+term 'equal' in the sense of 'equal in abstractive force,' it is obvious
+that an abstractive element can only be equal to itself. Thus an
+abstractive element has a unique abstractive force and is the construct
+from events which represents one definite intrinsic character which is
+arrived at as a limit by the use of the principle of convergence to
+simplicity by diminution of extent.
+
+When an abstractive element A covers an abstractive element B, the
+intrinsic character of A in a sense includes the intrinsic character
+of B. It results that statements about the intrinsic character of B
+are in a sense statements about the intrinsic character of A; but the
+intrinsic character of A is more complex than that of B.
+
+The abstractive elements form the fundamental elements of space and
+time, and we now turn to the consideration of the properties involved in
+the formation of special classes of such elements. In my last lecture I
+have already investigated one class of abstractive elements, namely
+moments. Each moment is a group of abstractive sets, and the events
+which are members of these sets are all members of one family of
+durations. The moments of one family form a temporal series; and,
+allowing the existence of different families of moments, there will be
+alternative temporal series in nature. Thus the method of extensive
+abstraction explains the origin of temporal series in terms of the
+immediate facts of experience and at the same time allows for the
+existence of the alternative temporal series which are demanded by the
+modern theory of electromagnetic relativity.
+
+We now turn to space. The first thing to do is to get hold of the class
+of abstractive elements which are in some sense the points of space.
+Such an abstractive element must in some sense exhibit a convergence to
+an absolute minimum of intrinsic character. Euclid has expressed for all
+time the general idea of a point, as being without parts and without
+magnitude. It is this character of being an absolute minimum which we
+want to get at and to express in terms of the extrinsic characters of
+the abstractive sets which make up a point. Furthermore, points which
+are thus arrived at represent the ideal of events without any extension,
+though there are in fact no such entities as these ideal events. These
+points will not be the points of an external timeless space but of
+instantaneous spaces. We ultimately want to arrive at the timeless space
+of physical science, and also of common thought which is now tinged with
+the concepts of science. It will be convenient to reserve the term
+'point' for these spaces when we get to them. I will therefore use the
+name 'event-particles' for the ideal minimum limits to events. Thus an
+event-particle is an abstractive element and as such is a group of
+abstractive sets; and a point--namely a point of timeless space--will be
+a class of event-particles.
+
+Furthermore there is a separate timeless space corresponding to each
+separate temporal series, that is to each separate family of durations.
+We will come back to points in timeless spaces later. I merely mention
+them now that we may understand the stages of our investigation. The
+totality of event-particles will form a four-dimensional manifold, the
+extra dimension arising from time--in other words--arising from the
+points of a timeless space being each a class of event-particles.
+
+The required character of the abstractive sets which form
+event-particles would be secured if we could define them as having the
+property of being covered by any abstractive set which they cover. For
+then any other abstractive set which an abstractive set of an
+event-particle covered, would be equal to it, and would therefore be a
+member of the same event-particle. Accordingly an event-particle could
+cover no other abstractive element. This is the definition which I
+originally proposed at a congress in Paris in 1914[9]. There is however
+a difficulty involved in this definition if adopted without some further
+addition, and I am now not satisfied with the way in which I attempted
+to get over that difficulty in the paper referred to.
+
+[9] Cf. 'La Théorie Relationniste de l'Espace,' _Rev. de Métaphysique et
+de Morale_, vol. XXIII, 1916.
+
+The difficulty is this: When event-particles have once been defined it
+is easy to define the aggregate of event-particles forming the boundary
+of an event; and thence to define the point-contact at their boundaries
+possible for a pair of events of which one is part of the other. We can
+then conceive all the intricacies of tangency. In particular we can
+conceive an abstractive set of which all the members have point-contact
+at the same event-particle. It is then easy to prove that there will be
+no abstractive set with the property of being covered by every
+abstractive set which it covers. I state this difficulty at some length
+because its existence guides the development of our line of argument. We
+have got to annex some condition to the root property of being covered
+by any abstractive set which it covers. When we look into this question
+of suitable conditions we find that in addition to event-particles all
+the other relevant spatial and spatio-temporal abstractive elements can
+be defined in the same way by suitably varying the conditions.
+Accordingly we proceed in a general way suitable for employment beyond
+event-particles.
+
+Let σ be the name of any condition which some abstractive sets fulfil. I
+say that an abstractive set is 'σ-prime' when it has the two
+properties, (i) that it satisfies the condition σ and (ii) that it is
+covered by every abstractive set which both is covered by it and
+satisfies the condition σ.
+
+In other words you cannot get any abstractive set satisfying the
+condition σ which exhibits intrinsic character more simple than that of
+a σ-prime.
+
+There are also the correlative abstractive sets which I call the sets of
+σ-antiprimes. An abstractive set is a σ-antiprime when it has the two
+properties, (i) that it satisfies the condition σ and (ii) that it
+covers every abstractive set which both covers it and satisfies the
+condition σ. In other words you cannot get any abstractive set
+satisfying the condition σ which exhibits an intrinsic character more
+complex than that of a σ-antiprime.
+
+The intrinsic character of a σ-prime has a certain minimum of fullness
+among those abstractive sets which are subject to the condition of
+satisfying σ; whereas the intrinsic character of a σ-antiprime has a
+corresponding maximum of fullness, and includes all it can in the
+circumstances.
+
+Let us first consider what help the notion of antiprimes could give us
+in the definition of moments which we gave in the last lecture. Let the
+condition σ be the property of being a class whose members are all
+durations. An abstractive set which satisfies this condition is thus an
+abstractive set composed wholly of durations. It is convenient then to
+define a moment as the group of abstractive sets which are equal to some
+σ-antiprime, where the condition σ has this special meaning. It will be
+found on consideration (i) that each abstractive set forming a moment is
+a σ-antiprime, where σ has this special meaning, and (ii) that we have
+excluded from membership of moments abstractive sets of durations which
+all have one common boundary, either the initial boundary or the final
+boundary. We thus exclude special cases which are apt to confuse general
+reasoning. The new definition of a moment, which supersedes our previous
+definition, is (by the aid of the notion of antiprimes) the more
+precisely drawn of the two, and the more useful.
+
+The particular condition which 'σ' stood for in the definition of
+moments included something additional to anything which can be derived
+from the bare notion of extension. A duration exhibits for thought a
+totality. The notion of totality is something beyond that of extension,
+though the two are interwoven in the notion of a duration.
+
+In the same way the particular condition 'σ' required for the definition
+of an event-particle must be looked for beyond the mere notion of
+extension. The same remark is also true of the particular conditions
+requisite for the other spatial elements. This additional notion is
+obtained by distinguishing between the notion of 'position' and the
+notion of convergence to an ideal zero of extension as exhibited by an
+abstractive set of events.
+
+In order to understand this distinction consider a point of the
+instantaneous space which we conceive as apparent to us in an almost
+instantaneous glance. This point is an event-particle. It has two
+aspects. In one aspect it is there, where it is. This is its position in
+the space. In another aspect it is got at by ignoring the circumambient
+space, and by concentrating attention on the smaller and smaller set of
+events which approximate to it. This is its extrinsic character. Thus a
+point has three characters, namely, its position in the whole
+instantaneous space, its extrinsic character, and its intrinsic
+character. The same is true of any other spatial element. For example an
+instantaneous volume in instantaneous space has three characters,
+namely, its position, its extrinsic character as a group of abstractive
+sets, and its intrinsic character which is the limit of natural
+properties which is indicated by any one of these abstractive sets.
+
+Before we can talk about position in instantaneous space, we must
+evidently be quite clear as to what we mean by instantaneous space in
+itself. Instantaneous space must be looked for as a character of a
+moment. For a moment is all nature at an instant. It cannot be the
+intrinsic character of the moment. For the intrinsic character tells us
+the limiting character of nature in space at that instant. Instantaneous
+space must be an assemblage of abstractive elements considered in their
+mutual relations. Thus an instantaneous space is the assemblage of
+abstractive elements covered by some one moment, and it is the
+instantaneous space of that moment.
+
+We have now to ask what character we have found in nature which is
+capable of according to the elements of an instantaneous space different
+qualities of position. This question at once brings us to the
+intersection of moments, which is a topic not as yet considered in these
+lectures.
+
+The locus of intersection of two moments is the assemblage of
+abstractive elements covered by both of them. Now two moments of the
+same temporal series cannot intersect. Two moments respectively of
+different families necessarily intersect. Accordingly in the
+instantaneous space of a moment we should expect the fundamental
+properties to be marked by the intersections with moments of other
+families. If M be a given moment, the intersection of M with another
+moment A is an instantaneous plane in the instantaneous space of M; and
+if B be a third moment intersecting both M and A, the intersection of M
+and B is another plane in the space M. Also the common intersection of
+A, B, and M is the intersection of the two planes in the space M, namely
+it is a straight line in the space M. An exceptional case arises if B
+and M intersect in the same plane as A and M. Furthermore if C be a
+fourth moment, then apart from special cases which we need not consider,
+it intersects M in a plane which the straight line (A, B, M) meets. Thus
+there is in general a common intersection of four moments of different
+families. This common intersection is an assemblage of abstractive
+elements which are each covered (or 'lie in') all four moments. The
+three-dimensional property of instantaneous space comes to this, that
+(apart from special relations between the four moments) any fifth moment
+either contains the whole of their common intersection or none of it. No
+further subdivision of the common intersection is possible by means of
+moments. The 'all or none' principle holds. This is not an _à priori_
+truth but an empirical fact of nature.
+
+It will be convenient to reserve the ordinary spatial terms 'plane,'
+'straight line,' 'point' for the elements of the timeless space of a
+time-system. Accordingly an instantaneous plane in the instantaneous
+space of a moment will be called a 'level,' an instantaneous straight
+line will be called a 'rect,' and an instantaneous point will be called
+a 'punct.' Thus a punct is the assemblage of abstractive elements which
+lie in each of four moments whose families have no special relations to
+each other. Also if P be any moment, either every abstractive element
+belonging to a given punct lies in P, or no abstractive element of
+that punct lies in P.
+
+Position is the quality which an abstractive element possesses in virtue
+of the moments in which it lies. The abstractive elements which lie in
+the instantaneous space of a given moment M are differentiated from
+each other by the various other moments which intersect M so as to
+contain various selections of these abstractive elements. It is this
+differentiation of the elements which constitutes their differentiation
+of position. An abstractive element which belongs to a punct has the
+simplest type of position in M, an abstractive element which belongs
+to a rect but not to a punct has a more complex quality of position, an
+abstractive element which belongs to a level and not to a rect has a
+still more complex quality of position, and finally the most complex
+quality of position belongs to an abstractive element which belongs to a
+volume and not to a level. A volume however has not yet been defined.
+This definition will be given in the next lecture.
+
+Evidently levels, rects, and puncts in their capacity as infinite
+aggregates cannot be the termini of sense-awareness, nor can they be
+limits which are approximated to in sense-awareness. Any one member of a
+level has a certain quality arising from its character as also belonging
+to a certain set of moments, but the level as a whole is a mere logical
+notion without any route of approximation along entities posited in
+sense-awareness.
+
+On the other hand an event-particle is defined so as to exhibit this
+character of being a route of approximation marked out by entities
+posited in sense-awareness. A definite event-particle is defined in
+reference to a definite punct in the following manner: Let the condition
+σ mean the property of covering all the abstractive elements which are
+members of that punct; so that an abstractive set which satisfies the
+condition σ is an abstractive set which covers every abstractive element
+belonging to the punct. Then the definition of the event-particle
+associated with the punct is that it is the group of all the σ-primes,
+where σ has this particular meaning.
+
+It is evident that--with this meaning of σ--every abstractive set equal
+to a σ-prime is itself a σ-prime. Accordingly an event-particle as thus
+defined is an abstractive element, namely it is the group of those
+abstractive sets which are each equal to some given abstractive set. If
+we write out the definition of the event-particle associated with some
+given punct, which we will call π, it is as follows: The event-particle
+associated with π is the group of abstractive classes each of which has
+the two properties (i) that it covers every abstractive set in π and
+(ii) that all the abstractive sets which also satisfy the former
+condition as to π and which it covers, also cover it.
+
+An event-particle has position by reason of its association with a
+punct, and conversely the punct gains its derived character as a route
+of approximation from its association with the event-particle. These two
+characters of a point are always recurring in any treatment of the
+derivation of a point from the observed facts of nature, but in general
+there is no clear recognition of their distinction.
+
+The peculiar simplicity of an instantaneous point has a twofold origin,
+one connected with position, that is to say with its character as a
+punct, and the other connected with its character as an event-particle.
+The simplicity of the punct arises from its indivisibility by a moment.
+
+The simplicity of an event-particle arises from the indivisibility of
+its intrinsic character. The intrinsic character of an event-particle is
+indivisible in the sense that every abstractive set covered by it
+exhibits the same intrinsic character. It follows that, though there are
+diverse abstractive elements covered by event-particles, there is no
+advantage to be gained by considering them since we gain no additional
+simplicity in the expression of natural properties.
+
+These two characters of simplicity enjoyed respectively by
+event-particles and puncts define a meaning for Euclid's phrase,
+'without parts and without magnitude.'
+
+It is obviously convenient to sweep away out of our thoughts all these
+stray abstractive sets which are covered by event-particles without
+themselves being members of them. They give us nothing new in the way of
+intrinsic character. Accordingly we can think of rects and levels as
+merely loci of event-particles. In so doing we are also cutting out
+those abstractive elements which cover sets of event-particles, without
+these elements being event-particles themselves. There are classes of
+these abstractive elements which are of great importance. I will
+consider them later on in this and in other lectures. Meanwhile we will
+ignore them. Also I will always speak of 'event-particles' in preference
+to 'puncts,' the latter being an artificial word for which I have no
+great affection.
+
+Parallelism among rects and levels is now explicable.
+
+Consider the instantaneous space belonging to a moment A, and let A
+belong to the temporal series of moments which I will call α. Consider
+any other temporal series of moments which I will call β. The moments of
+β do not intersect each other and they intersect the moment A in a
+family of levels. None of these levels can intersect, and they form a
+family of parallel instantaneous planes in the instantaneous space of
+moment A. Thus the parallelism of moments in a temporal series begets
+the parallelism of levels in an instantaneous space, and thence--as it
+is easy to see--the parallelism of rects. Accordingly the Euclidean
+property of space arises from the parabolic property of time. It may be
+that there is reason to adopt a hyperbolic theory of time and a
+corresponding hyperbolic theory of space. Such a theory has not been
+worked out, so it is not possible to judge as to the character of the
+evidence which could be brought forward in its favour.
+
+The theory of order in an instantaneous space is immediately derived
+from time-order. For consider the space of a moment M. Let α be the name
+of a time-system to which M does not belong. Let A₁, A₂, A₃ etc. be
+moments of α in the order of their occurrences. Then A₁, A₂, A₃, etc.
+intersect M in parallel levels l₁, l₂, l₃, etc. Then the relative order
+of the parallel levels in the space of M is the same as the relative
+order of the corresponding moments in the time-system α. Any rect in M
+which intersects all these levels in its set of puncts, thereby receives
+for its puncts an order of position on it. So spatial order is
+derivative from temporal order. Furthermore there are alternative
+time-systems, but there is only one definite spatial order in each
+instantaneous space. Accordingly the various modes of deriving spatial
+order from diverse time-systems must harmonise with one spatial order in
+each instantaneous space. In this way also diverse time-orders are
+comparable.
+
+We have two great questions still on hand to be settled before our
+theory of space is fully adjusted. One of these is the question of the
+determination of the methods of measurement within the space, in other
+words, the congruence-theory of the space. The measurement of space will
+be found to be closely connected with the measurement of time, with
+respect to which no principles have as yet been determined. Thus our
+congruence-theory will be a theory both for space and for time. Secondly
+there is the determination of the timeless space which corresponds to
+any particular time-system with its infinite set of instantaneous spaces
+in its successive moments. This is the space--or rather, these are the
+spaces--of physical science. It is very usual to dismiss this space by
+saying that this is conceptual. I do not understand the virtue of these
+phrases. I suppose that it is meant that the space is the conception of
+something in nature. Accordingly if the space of physical science is to
+be called conceptual, I ask, What in nature is it the conception of? For
+example, when we speak of a point in the timeless space of physical
+science, I suppose that we are speaking of something in nature. If we
+are not so speaking, our scientists are exercising their wits in the
+realms of pure fantasy, and this is palpably not the case. This demand
+for a definite Habeas Corpus Act for the production of the relevant
+entities in nature applies whether space be relative or absolute. On the
+theory of relative space, it may perhaps be argued that there is no
+timeless space for physical science, and that there is only the
+momentary series of instantaneous spaces.
+
+An explanation must then be asked for the meaning of the very common
+statement that such and such a man walked four miles in some definite
+hour. How can you measure distance from one space into another space? I
+understand walking out of the sheet of an ordnance map. But the meaning
+of saying that Cambridge at 10 o'clock this morning in the appropriate
+instantaneous space for that instant is 52 miles from London at
+11 o'clock this morning in the appropriate instantaneous space for that
+instant beats me entirely. I think that, by the time a meaning has been
+produced for this statement, you will find that you have constructed
+what is in fact a timeless space. What I cannot understand is how to
+produce an explanation of meaning without in effect making some such
+construction. Also I may add that I do not know how the instantaneous
+spaces are thus correlated into one space by any method which is
+available on the current theories of space.
+
+You will have noticed that by the aid of the assumption of alternative
+time-systems, we are arriving at an explanation of the character of
+space. In natural science 'to explain' means merely to discover
+'interconnexions.' For example, in one sense there is no explanation of
+the red which you see. It is red, and there is nothing else to be said
+about it. Either it is posited before you in sense-awareness or you are
+ignorant of the entity red. But science has explained red. Namely it has
+discovered interconnexions between red as a factor in nature and other
+factors in nature, for example waves of light which are waves of
+electromagnetic disturbances. There are also various pathological
+states of the body which lead to the seeing of red without the
+occurrence of light waves. Thus connexions have been discovered between
+red as posited in sense-awareness and various other factors in nature.
+The discovery of these connexions constitutes the scientific explanation
+of our vision of colour. In like manner the dependence of the character
+of space on the character of time constitutes an explanation in the
+sense in which science seeks to explain. The systematising intellect
+abhors bare facts. The character of space has hitherto been presented as
+a collection of bare facts, ultimate and disconnected. The theory which
+I am expounding sweeps away this disconnexion of the facts of space.
+
+
+
+
+CHAPTER V
+
+SPACE AND MOTION
+
+
+The topic for this lecture is the continuation of the task of explaining
+the construction of spaces as abstracts from the facts of nature. It was
+noted at the close of the previous lecture that the question of
+congruence had not been considered, nor had the construction of a
+timeless space which should correlate the successive momentary spaces of
+a given time-system. Furthermore it was also noted that there were many
+spatial abstractive elements which we had not yet defined. We will first
+consider the definition of some of these abstractive elements, namely
+the definitions of solids, of areas, and of routes. By a 'route' I mean
+a linear segment, whether straight or curved. The exposition of these
+definitions and the preliminary explanations necessary will, I hope,
+serve as a general explanation of the function of event-particles in the
+analysis of nature.
+
+We note that event-particles have 'position' in respect to each other.
+In the last lecture I explained that 'position' was quality gained by a
+spatial element in virtue of the intersecting moments which covered it.
+Thus each event-particle has position in this sense. The simplest mode
+of expressing the position in nature of an event-particle is by first
+fixing on any definite time-system. Call it α. There will be one moment
+of the temporal series of α which covers the given event-particle. Thus
+the position of the event-particle in the temporal series α is defined
+by this moment, which we will call M. The position of the particle in
+the space of M is then fixed in the ordinary way by three levels which
+intersect in it and in it only. This procedure of fixing the position of
+an event-particle shows that the aggregate of event-particles forms a
+four-dimensional manifold. A finite event occupies a limited chunk of
+this manifold in a sense which I now proceed to explain.
+
+Let e be any given event. The manifold of event-particles falls into
+three sets in reference to e. Each event-particle is a group of equal
+abstractive sets and each abstractive set towards its small-end is
+composed of smaller and smaller finite events. When we select from these
+finite events which enter into the make-up of a given event-particle
+those which are small enough, one of three cases must occur. Either (i)
+all of these small events are entirely separate from the given event
+e, or (ii) all of these small events are parts of the event e, or
+(iii) all of these small events overlap the event e but are not parts
+of it. In the first case the event-particle will be said to 'lie
+outside' the event e, in the second case the event-particle will be
+said to 'lie inside' the event e, and in the third case the
+event-particle will be said to be a 'boundary-particle' of the event
+e. Thus there are three sets of particles, namely the set of those
+which lie outside the event e, the set of those which lie inside the
+event e, and the boundary of the event e which is the set of
+boundary-particles of e. Since an event is four-dimensional, the
+boundary of an event is a three-dimensional manifold. For a finite event
+there is a continuity of boundary; for a duration the boundary consists
+of those event-particles which are covered by either of the two bounding
+moments. Thus the boundary of a duration consists of two momentary
+three-dimensional spaces. An event will be said to 'occupy' the
+aggregate of event-particles which lie within it.
+
+Two events which have 'junction' in the sense in which junction was
+described in my last lecture, and yet are separated so that neither
+event either overlaps or is part of the other event, are said to be
+'adjoined.'
+
+This relation of adjunction issues in a peculiar relation between the
+boundaries of the two events. The two boundaries must have a common
+portion which is in fact a continuous three-dimensional locus of
+event-particles in the four-dimensional manifold.
+
+A three-dimensional locus of event-particles which is the common portion
+of the boundary of two adjoined events will be called a 'solid.' A solid
+may or may not lie completely in one moment. A solid which does not lie
+in one moment will be called 'vagrant.' A solid which does lie in one
+moment will be called a volume. A volume may be defined as the locus of
+the event-particles in which a moment intersects an event, provided that
+the two do intersect. The intersection of a moment and an event will
+evidently consist of those event-particles which are covered by the
+moment and lie in the event. The identity of the two definitions of a
+volume is evident when we remember that an intersecting moment divides
+the event into two adjoined events.
+
+A solid as thus defined, whether it be vagrant or be a volume, is a mere
+aggregate of event-particles illustrating a certain quality of position.
+We can also define a solid as an abstractive element. In order to do so
+we recur to the theory of primes explained in the preceding lecture. Let
+the condition named σ stand for the fact that each of the events of any
+abstractive set satisfying it has all the event-particles of some
+particular solid lying in it. Then the group of all the σ-primes is the
+abstractive element which is associated with the given solid. I will
+call this abstractive element the solid as an abstractive element, and I
+will call the aggregate of event-particles the solid as a locus. The
+instantaneous volumes in instantaneous space which are the ideals of our
+sense-perception are volumes as abstractive elements. What we really
+perceive with all our efforts after exactness are small events far
+enough down some abstractive set belonging to the volume as an
+abstractive element.
+
+It is difficult to know how far we approximate to any perception of
+vagrant solids. We certainly do not think that we make any such
+approximation. But then our thoughts--in the case of people who do think
+about such topics--are so much under the control of the materialistic
+theory of nature that they hardly count for evidence. If Einstein's
+theory of gravitation has any truth in it, vagrant solids are of great
+importance in science. The whole boundary of a finite event may be
+looked on as a particular example of a vagrant solid as a locus. Its
+particular property of being closed prevents it from being definable as
+an abstractive element.
+
+When a moment intersects an event, it also intersects the boundary of
+that event. This locus, which is the portion of the boundary contained
+in the moment, is the bounding surface of the corresponding volume of
+that event contained in the moment. It is a two-dimensional locus.
+
+The fact that every volume has a bounding surface is the origin of the
+Dedekindian continuity of space.
+
+Another event may be cut by the same moment in another volume and this
+volume will also have its boundary. These two volumes in the
+instantaneous space of one moment may mutually overlap in the familiar
+way which I need not describe in detail and thus cut off portions from
+each other's surfaces. These portions of surfaces are 'momental areas.'
+
+It is unnecessary at this stage to enter into the complexity of a
+definition of vagrant areas. Their definition is simple enough when the
+four-dimensional manifold of event-particles has been more fully
+explored as to its properties.
+
+Momental areas can evidently be defined as abstractive elements by
+exactly the same method as applied to solids. We have merely to
+substitute 'area' for a 'solid' in the words of the definition already
+given. Also, exactly as in the analogous case of a solid, what we
+perceive as an approximation to our ideal of an area is a small event
+far enough down towards the small end of one of the equal abstractive
+sets which belongs to the area as an abstractive element.
+
+Two momental areas lying in the same moment can cut each other in a
+momental segment which is not necessarily rectilinear. Such a segment
+can also be defined as an abstractive element. It is then called a
+'momental route.' We will not delay over any general consideration of
+these momental routes, nor is it important for us to proceed to the
+still wider investigation of vagrant routes in general. There are
+however two simple sets of routes which are of vital importance. One is
+a set of momental routes and the other of vagrant routes. Both sets can
+be classed together as straight routes. We proceed to define them
+without any reference to the definitions of volumes and surfaces.
+
+The two types of straight routes will be called rectilinear routes and
+stations. Rectilinear routes are momental routes and stations are
+vagrant routes. Rectilinear routes are routes which in a sense lie in
+rects. Any two event-particles on a rect define the set of
+event-particles which lie between them on that rect. Let the
+satisfaction of the condition σ by an abstractive set mean that the two
+given event-particles and the event-particles lying between them on the
+rect all lie in every event belonging to the abstractive set. The group
+of σ-primes, where σ has this meaning, form an abstractive element. Such
+abstractive elements are rectilinear routes. They are the segments of
+instantaneous straight lines which are the ideals of exact perception.
+Our actual perception, however exact, will be the perception of a small
+event sufficiently far down one of the abstractive sets of the
+abstractive element.
+
+A station is a vagrant route and no moment can intersect any station in
+more than one event-particle. Thus a station carries with it a
+comparison of the positions in their respective moments of the
+event-particles covered by it. Rects arise from the intersection of
+moments. But as yet no properties of events have been mentioned by which
+any analogous vagrant loci can be found out.
+
+The general problem for our investigation is to determine a method of
+comparison of position in one instantaneous space with positions in
+other instantaneous spaces. We may limit ourselves to the spaces of the
+parallel moments of one time-system. How are positions in these various
+spaces to be compared? In other words, What do we mean by motion? It is
+the fundamental question to be asked of any theory of relative space,
+and like many other fundamental questions it is apt to be left
+unanswered. It is not an answer to reply, that we all know what we mean
+by motion. Of course we do, so far as sense-awareness is concerned. I am
+asking that your theory of space should provide nature with something to
+be observed. You have not settled the question by bringing forward a
+theory according to which there is nothing to be observed, and by then
+reiterating that nevertheless we do observe this non-existent fact.
+Unless motion is something as a fact in nature, kinetic energy and
+momentum and all that depends on these physical concepts evaporate from
+our list of physical realities. Even in this revolutionary age my
+conservatism resolutely opposes the identification of momentum and
+moonshine.
+
+Accordingly I assume it as an axiom, that motion is a physical fact. It
+is something that we perceive as in nature. Motion presupposes rest.
+Until theory arose to vitiate immediate intuition, that is to say to
+vitiate the uncriticised judgments which immediately arise from
+sense-awareness, no one doubted that in motion you leave behind that
+which is at rest. Abraham in his wanderings left his birthplace where it
+had ever been. A theory of motion and a theory of rest are the same
+thing viewed from different aspects with altered emphasis.
+
+Now you cannot have a theory of rest without in some sense admitting a
+theory of absolute position. It is usually assumed that relative space
+implies that there is no absolute position. This is, according to my
+creed, a mistake. The assumption arises from the failure to make another
+distinction; namely, that there may be alternative definitions of
+absolute position. This possibility enters with the admission of
+alternative time-systems. Thus the series of spaces in the parallel
+moments of one temporal series may have their own definition of absolute
+position correlating sets of event-particles in these successive spaces,
+so that each set consists of event-particles, one from each space, all
+with the property of possessing the same absolute position in that
+series of spaces. Such a set of event-particles will form a point in the
+timeless space of that time-system. Thus a point is really an absolute
+position in the timeless space of a given time-system.
+
+But there are alternative time-systems, and each time-system has its own
+peculiar group of points--that is to say, its own peculiar definition of
+absolute position. This is exactly the theory which I will elaborate.
+
+In looking to nature for evidence of absolute position it is of no use
+to recur to the four-dimensional manifold of event-particles. This
+manifold has been obtained by the extension of thought beyond the
+immediacy of observation. We shall find nothing in it except what we
+have put there to represent the ideas in thought which arise from our
+direct sense-awareness of nature. To find evidence of the properties
+which are to be found in the manifold of event-particles we must always
+recur to the observation of relations between events. Our problem is to
+determine those relations between events which issue in the property of
+absolute position in a timeless space. This is in fact the problem of
+the determination of the very meaning of the timeless spaces of
+physical science.
+
+In reviewing the factors of nature as immediately disclosed in
+sense-awareness, we should note the fundamental character of the percept
+of 'being here.' We discern an event merely as a factor in a determinate
+complex in which each factor has its own peculiar share.
+
+There are two factors which are always ingredient in this complex, one
+is the duration which is represented in thought by the concept of all
+nature that is present now, and the other is the peculiar _locus standi_
+for mind involved in the sense-awareness. This _locus standi_ in nature
+is what is represented in thought by the concept of 'here,' namely of an
+'event here.'
+
+This is the concept of a definite factor in nature. This factor is an
+event in nature which is the focus in nature for that act of awareness,
+and the other events are perceived as referred to it. This event is part
+of the associated duration. I call it the 'percipient event.' This event
+is not the mind, that is to say, not the percipient. It is that in
+nature from which the mind perceives. The complete foothold of the mind
+in nature is represented by the pair of events, namely, the present
+duration which marks the 'when' of awareness and the percipient event
+which marks the 'where' of awareness and the 'how' of awareness. This
+percipient event is roughly speaking the bodily life of the incarnate
+mind. But this identification is only a rough one. For the functions of
+the body shade off into those of other events in nature; so that for
+some purposes the percipient event is to be reckoned as merely part of
+the bodily life and for other purposes it may even be reckoned as more
+than the bodily life. In many respects the demarcation is purely
+arbitrary, depending upon where in a sliding scale you choose to draw
+the line.
+
+I have already in my previous lecture on Time discussed the association
+of mind with nature. The difficulty of the discussion lies in the
+liability of constant factors to be overlooked. We never note them by
+contrast with their absences. The purpose of a discussion of such
+factors may be described as being to make obvious things look odd. We
+cannot envisage them unless we manage to invest them with some of the
+freshness which is due to strangeness.
+
+It is because of this habit of letting constant factors slip from
+consciousness that we constantly fall into the error of thinking of the
+sense-awareness of a particular factor in nature as being a two-termed
+relation between the mind and the factor. For example, I perceive a
+green leaf. Language in this statement suppresses all reference to any
+factors other than the percipient mind and the green leaf and the
+relation of sense-awareness. It discards the obvious inevitable factors
+which are essential elements in the perception. I am here, the leaf is
+there; and the event here and the event which is the life of the leaf
+there are both embedded in a totality of nature which is now, and within
+this totality there are other discriminated factors which it is
+irrelevant to mention. Thus language habitually sets before the mind a
+misleading abstract of the indefinite complexity of the fact of
+sense-awareness.
+
+What I now want to discuss is the special relation of the percipient
+event which is 'here' to the duration which is 'now.' This relation is a
+fact in nature, namely the mind is aware of nature as being with these
+two factors in this relation.
+
+Within the short present duration the 'here' of the percipient event has
+a definite meaning of some sort. This meaning of 'here' is the content
+of the special relation of the percipient event to its associated
+duration. I will call this relation 'cogredience.' Accordingly I ask for
+a description of the character of the relation of cogredience. The
+present snaps into a past and a present when the 'here' of cogredience
+loses its single determinate meaning. There has been a passage of nature
+from the 'here' of perception within the past duration to the different
+'here' of perception within the present duration. But the two 'heres' of
+sense-awareness within neighbouring durations may be indistinguishable.
+In this case there has been a passage from the past to the present, but
+a more retentive perceptive force might have retained the passing nature
+as one complete present instead of letting the earlier duration slip
+into the past. Namely, the sense of rest helps the integration of
+durations into a prolonged present, and the sense of motion
+differentiates nature into a succession of shortened durations. As we
+look out of a railway carriage in an express train, the present is past
+before reflexion can seize it. We live in snippits too quick for
+thought. On the other hand the immediate present is prolonged according
+as nature presents itself to us in an aspect of unbroken rest. Any
+change in nature provides ground for a differentiation among durations
+so as to shorten the present. But there is a great distinction between
+self-change in nature and change in external nature. Self-change in
+nature is change in the quality of the standpoint of the percipient
+event. It is the break up of the 'here' which necessitates the break up
+of the present duration. Change in external nature is compatible with a
+prolongation of the present of contemplation rooted in a given
+standpoint. What I want to bring out is that the preservation of a
+peculiar relation to a duration is a necessary condition for the
+function of that duration as a present duration for sense-awareness.
+This peculiar relation is the relation of cogredience between the
+percipient event and the duration. Cogredience is the preservation of
+unbroken quality of standpoint within the duration. It is the
+continuance of identity of station within the whole of nature which is
+the terminus of sense-awareness. The duration may comprise change within
+itself, but cannot--so far as it is one present duration--comprise
+change in the quality of its peculiar relation to the contained
+percipient event.
+
+In other words, perception is always 'here,' and a duration can only be
+posited as present for sense-awareness on condition that it affords one
+unbroken meaning of 'here' in its relation to the percipient event. It
+is only in the past that you can have been 'there' with a standpoint
+distinct from your present 'here.'
+
+Events there and events here are facts of nature, and the qualities of
+being 'there' and 'here' are not merely qualities of awareness as a
+relation between nature and mind. The quality of determinate station in
+the duration which belongs to an event which is 'here' in one
+determinate sense of 'here' is the same kind of quality of station which
+belongs to an event which is 'there' in one determinate sense of
+'there.' Thus cogredience has nothing to do with any biological
+character of the event which is related by it to the associated
+duration. This biological character is apparently a further condition
+for the peculiar connexion of a percipient event with the percipience of
+mind; but it has nothing to do with the relation of the percipient event
+to the duration which is the present whole of nature posited as the
+disclosure of the percipience.
+
+Given the requisite biological character, the event in its character of
+a percipient event selects that duration with which the operative past
+of the event is practically cogredient within the limits of the
+exactitude of observation. Namely, amid the alternative time-systems
+which nature offers there will be one with a duration giving the best
+average of cogredience for all the subordinate parts of the percipient
+event. This duration will be the whole of nature which is the terminus
+posited by sense-awareness. Thus the character of the percipient event
+determines the time-system immediately evident in nature. As the
+character of the percipient event changes with the passage of
+nature--or, in other words, as the percipient mind in its passage
+correlates itself with the passage of the percipient event into another
+percipient event--the time-system correlated with the percipience of
+that mind may change. When the bulk of the events perceived are
+cogredient in a duration other than that of the percipient event, the
+percipience may include a double consciousness of cogredience, namely
+the consciousness of the whole within which the observer in the train is
+'here,' and the consciousness of the whole within which the trees and
+bridges and telegraph posts are definitely 'there.' Thus in perceptions
+under certain circumstances the events discriminated assert their own
+relations of cogredience. This assertion of cogredience is peculiarly
+evident when the duration to which the perceived event is cogredient is
+the same as the duration which is the present whole of nature--in other
+words, when the event and the percipient event are both cogredient to
+the same duration.
+
+We are now prepared to consider the meaning of stations in a duration,
+where stations are a peculiar kind of routes, which define absolute
+position in the associated timeless space.
+
+There are however some preliminary explanations. A finite event will be
+said to extend throughout a duration when it is part of the duration
+and is intersected by any moment which lies in the duration. Such an
+event begins with the duration and ends with it. Furthermore every event
+which begins with the duration and ends with it, extends throughout the
+duration. This is an axiom based on the continuity of events. By
+beginning with a duration and ending with it, I mean (i) that the event
+is part of the duration, and (ii) that both the initial and final
+boundary moments of the duration cover some event-particles on the
+boundary of the event.
+
+Every event which is cogredient with a duration extends throughout that
+duration.
+
+It is not true that all the parts of an event cogredient with a duration
+are also cogredient with the duration. The relation of cogredience may
+fail in either of two ways. One reason for failure may be that the part
+does not extend throughout the duration. In this case the part may be
+cogredient with another duration which is part of the given duration,
+though it is not cogredient with the given duration itself. Such a part
+would be cogredient if its existence were sufficiently prolonged in that
+time-system. The other reason for failure arises from the
+four-dimensional extension of events so that there is no determinate
+route of transition of events in linear series. For example, the tunnel
+of a tube railway is an event at rest in a certain time-system, that is
+to say, it is cogredient with a certain duration. A train travelling in
+it is part of that tunnel, but is not itself at rest.
+
+If an event e be cogredient with a duration d, and d′ be any
+duration which is part of d. Then d′ belongs to the same time-system
+as d. Also d′ intersects e in an event e′ which is part of e
+and is cogredient with d′.
+
+Let P be any event-particle lying in a given duration d. Consider
+the aggregate of events in which P lies and which are also cogredient
+with d. Each of these events occupies its own aggregate of
+event-particles. These aggregates will have a common portion, namely the
+class of event-particle lying in all of them. This class of
+event-particles is what I call the 'station' of the event-particle P
+in the duration d. This is the station in the character of a locus. A
+station can also be defined in the character of an abstractive element.
+Let the property σ be the name of the property which an abstractive set
+possesses when (i) each of its events is cogredient with the duration
+d and (ii) the event-particle P lies in each of its events. Then the
+group of σ-primes, where σ has this meaning, is an abstractive element
+and is the station of P in d as an abstractive element. The locus of
+event-particles covered by the station of P in d as an abstractive
+element is the station of P in d as a locus. A station has
+accordingly the usual three characters, namely, its character of
+position, its extrinsic character as an abstractive element, and its
+intrinsic character.
+
+It follows from the peculiar properties of rest that two stations
+belonging to the same duration cannot intersect. Accordingly every
+event-particle on a station of a duration has that station as its
+station in the duration. Also every duration which is part of a given
+duration intersects the stations of the given duration in loci which are
+its own stations. By means of these properties we can utilise the
+overlappings of the durations of one family--that is, of one
+time-system--to prolong stations indefinitely backwards and forwards.
+Such a prolonged station will be called a point-track. A point-track is
+a locus of event-particles. It is defined by reference to one
+particular time-system, α say. Corresponding to any other time-system
+these will be a different group of point-tracks. Every event-particle
+will lie on one and only one point-track of the group belonging to any
+one time-system. The group of point-tracks of the time-system α is the
+group of points of the timeless space of α. Each such point indicates a
+certain quality of absolute position in reference to the durations of
+the family associated with α, and thence in reference to the successive
+instantaneous spaces lying in the successive moments of α. Each moment
+of α will intersect a point-track in one and only one event-particle.
+
+This property of the unique intersection of a moment and a point-track
+is not confined to the case when the moment and the point-track belong
+to the same time-system. Any two event-particles on a point-track are
+sequential, so that they cannot lie in the same moment. Accordingly no
+moment can intersect a point-track more than once, and every moment
+intersects a point-track in one event-particle.
+
+Anyone who at the successive moments of α should be at the
+event-particles where those moments intersect a given point of α will be
+at rest in the timeless space of time-system α. But in any other
+timeless space belonging to another time-system he will be at a
+different point at each succeeding moment of that time-system. In other
+words he will be moving. He will be moving in a straight line with
+uniform velocity. We might take this as the definition of a straight
+line. Namely, a straight line in the space of time-system β is the locus
+of those points of β which all intersect some one point-track which is a
+point in the space of some other time-system. Thus each point in the
+space of a time-system α is associated with one and only one straight
+line of the space of any other time-system β. Furthermore the set of
+straight lines in space β which are thus associated with points in space
+α form a complete family of parallel straight lines in space β. Thus
+there is a one-to-one correlation of points in space α with the straight
+lines of a certain definite family of parallel straight lines in space
+β. Conversely there is an analogous one-to-one correlation of the points
+in space β with the straight lines of a certain family of parallel
+straight lines in space α. These families will be called respectively
+the family of parallels in β associated with α, and the family of
+parallels in α associated with β. The direction in the space of β
+indicated by the family of parallels in β will be called the direction
+of α in space β, and the family of parallels in α is the direction of β
+in space α. Thus a being at rest at a point of space α will be moving
+uniformly along a line in space β which is in the direction of α in
+space β, and a being at rest at a point of space β will be moving
+uniformly along a line in space α which is in the direction of β in
+space α.
+
+I have been speaking of the timeless spaces which are associated with
+time-systems. These are the spaces of physical science and of any
+concept of space as eternal and unchanging. But what we actually
+perceive is an approximation to the instantaneous space indicated by
+event-particles which lie within some moment of the time-system
+associated with our awareness. The points of such an instantaneous space
+are event-particles and the straight lines are rects. Let the
+time-system be named α, and let the moment of time-system α to which our
+quick perception of nature approximates be called M. Any straight line
+r in space α is a locus of points and each point is a point-track which
+is a locus of event-particles. Thus in the four-dimensional geometry of
+all event-particles there is a two-dimensional locus which is the locus
+of all event-particles on points lying on the straight line r. I will
+call this locus of event-particles the matrix of the straight line r. A
+matrix intersects any moment in a rect. Thus the matrix of r intersects
+the moment M in a rect ρ. Thus ρ is the instantaneous rect in M which
+occupies at the moment M the straight line r in the space of α.
+Accordingly when one sees instantaneously a moving being and its path
+ahead of it, what one really sees is the being at some event-particle A
+lying in the rect ρ which is the apparent path on the assumption of
+uniform motion. But the actual rect ρ which is a locus of
+event-particles is never traversed by the being. These event-particles
+are the instantaneous facts which pass with the instantaneous moment.
+What is really traversed are other event-particles which at succeeding
+instants occupy the same points of space α as those occupied by the
+event-particles of the rect ρ. For example, we see a stretch of road and
+a lorry moving along it. The instantaneously seen road is a portion of
+the rect ρ--of course only an approximation to it. The lorry is the
+moving object. But the road as seen is never traversed. It is thought of
+as being traversed because the intrinsic characters of the later events
+are in general so similar to those of the instantaneous road that we do
+not trouble to discriminate. But suppose a land mine under the road has
+been exploded before the lorry gets there. Then it is fairly obvious
+that the lorry does not traverse what we saw at first. Suppose the lorry
+is at rest in space β. Then the straight line r of space α is in the
+direction of β in space α, and the rect ρ is the representative in the
+moment M of the line r of space α. The direction of ρ in the
+instantaneous space of the moment M is the direction of β in M, where M
+is a moment of time-system α. Again the matrix of the line r of space α
+will also be the matrix of some line s of space β which will be in the
+direction of α in space β. Thus if the lorry halts at some point P of
+space α which lies on the line r, it is now moving along the line s of
+space β. This is the theory of relative motion; the common matrix is the
+bond which connects the motion of β in space α with the motions of α in
+space β.
+
+Motion is essentially a relation between some object of nature and the
+one timeless space of a time-system. An instantaneous space is static,
+being related to the static nature at an instant. In perception when we
+see things moving in an approximation to an instantaneous space, the
+future lines of motion as immediately perceived are rects which are
+never traversed. These approximate rects are composed of small events,
+namely approximate routes and event-particles, which are passed away
+before the moving objects reach them. Assuming that our forecasts of
+rectilinear motion are correct, these rects occupy the straight lines in
+timeless space which are traversed. Thus the rects are symbols in
+immediate sense-awareness of a future which can only be expressed in
+terms of timeless space.
+
+We are now in a position to explore the fundamental character of
+perpendicularity. Consider the two time-systems α and β, each with its
+own timeless space and its own family of instantaneous moments with
+their instantaneous spaces. Let M and N be respectively a moment of
+α and a moment of β. In M there is the direction of β and in N there
+is the direction of α. But M and N, being moments of different
+time-systems, intersect in a level. Call this level λ. Then λ is an
+instantaneous plane in the instantaneous space of M and also in the
+instantaneous space of N. It is the locus of all the event-particles
+which lie both in M and in N.
+
+In the instantaneous space of M the level λ is perpendicular to the
+direction of β in M, and in the instantaneous space of N the level λ
+is perpendicular to the direction of α in N. This is the fundamental
+property which forms the definition of perpendicularity. The symmetry of
+perpendicularity is a particular instance of the symmetry of the mutual
+relations between two time-systems. We shall find in the next lecture
+that it is from this symmetry that the theory of congruence is deduced.
+
+The theory of perpendicularity in the timeless space of any time-system
+α follows immediately from this theory of perpendicularity in each of
+its instantaneous spaces. Let ρ be any rect in the moment M of α and
+let λ be a level in M which is perpendicular to ρ. The locus of those
+points of the space of α which intersect M in event-particles on ρ is
+the straight line r of space α, and the locus of those points of the
+space of α which intersect M in event-particles on λ is the plane l
+of space α. Then the plane l is perpendicular to the line r.
+
+In this way we have pointed out unique and definite properties in nature
+which correspond to perpendicularity. We shall find that this discovery
+of definite unique properties defining perpendicularity is of critical
+importance in the theory of congruence which is the topic for the next
+lecture.
+
+I regret that it has been necessary for me in this lecture to administer
+such a large dose of four-dimensional geometry. I do not apologise,
+because I am really not responsible for the fact that nature in its most
+fundamental aspect is four-dimensional. Things are what they are; and it
+is useless to disguise the fact that 'what things are' is often very
+difficult for our intellects to follow. It is a mere evasion of the
+ultimate problems to shirk such obstacles.
+
+
+
+
+CHAPTER VI
+
+CONGRUENCE
+
+
+The aim of this lecture is to establish a theory of congruence. You must
+understand at once that congruence is a controversial question. It is
+the theory of measurement in space and in time. The question seems
+simple. In fact it is simple enough for a standard procedure to have
+been settled by act of parliament; and devotion to metaphysical
+subtleties is almost the only crime which has never been imputed to any
+English parliament. But the procedure is one thing and its meaning is
+another.
+
+First let us fix attention on the purely mathematical question. When the
+segment between two points A and B is congruent to that between the
+two points C and D, the quantitative measurements of the two
+segments are equal. The equality of the numerical measures and the
+congruence of the two segments are not always clearly discriminated, and
+are lumped together under the term equality. But the procedure of
+measurement presupposes congruence. For example, a yard measure is
+applied successively to measure two distances between two pairs of
+points on the floor of a room. It is of the essence of the procedure of
+measurement that the yard measure remains unaltered as it is transferred
+from one position to another. Some objects can palpably alter as they
+move--for example, an elastic thread; but a yard measure does not alter
+if made of the proper material. What is this but a judgment of
+congruence applied to the train of successive positions of the yard
+measure? We know that it does not alter because we judge it to be
+congruent to itself in various positions. In the case of the thread we
+can observe the loss of self-congruence. Thus immediate judgments of
+congruence are presupposed in measurement, and the process of
+measurement is merely a procedure to extend the recognition of
+congruence to cases where these immediate judgments are not available.
+Thus we cannot define congruence by measurement.
+
+In modern expositions of the axioms of geometry certain conditions are
+laid down which the relation of congruence between segments is to
+satisfy. It is supposed that we have a complete theory of points,
+straight lines, planes, and the order of points on planes--in fact, a
+complete theory of non-metrical geometry. We then enquire about
+congruence and lay down the set of conditions--or axioms as they are
+called--which this relation satisfies. It has then been proved that
+there are alternative relations which satisfy these conditions equally
+well and that there is nothing intrinsic in the theory of space to lead
+us to adopt any one of these relations in preference to any other as the
+relation of congruence which we adopt. In other words there are
+alternative metrical geometries which all exist by an equal right so far
+as the intrinsic theory of space is concerned.
+
+Poincaré, the great French mathematician, held that our actual choice
+among these geometries is guided purely by convention, and that the
+effect of a change of choice would be simply to alter our expression of
+the physical laws of nature. By 'convention' I understand Poincaré to
+mean that there is nothing inherent in nature itself giving any peculiar
+_rôle_ to one of these congruence relations, and that the choice of one
+particular relation is guided by the volitions of the mind at the other
+end of the sense-awareness. The principle of guidance is intellectual
+convenience and not natural fact.
+
+This position has been misunderstood by many of Poincaré's expositors.
+They have muddled it up with another question, namely that owing to the
+inexactitude of observation it is impossible to make an exact statement
+in the comparison of measures. It follows that a certain subset of
+closely allied congruence relations can be assigned of which each member
+equally well agrees with that statement of observed congruence when the
+statement is properly qualified with its limits of error.
+
+This is an entirely different question and it presupposes a rejection of
+Poincaré's position. The absolute indetermination of nature in respect
+of all the relations of congruence is replaced by the indetermination of
+observation with respect to a small subgroup of these relations.
+
+Poincaré's position is a strong one. He in effect challenges anyone to
+point out any factor in nature which gives a preeminent status to the
+congruence relation which mankind has actually adopted. But undeniably
+the position is very paradoxical. Bertrand Russell had a controversy
+with him on this question, and pointed out that on Poincaré's principles
+there was nothing in nature to determine whether the earth is larger or
+smaller than some assigned billiard ball. Poincaré replied that the
+attempt to find reasons in nature for the selection of a definite
+congruence relation in space is like trying to determine the position of
+a ship in the ocean by counting the crew and observing the colour of
+the captain's eyes.
+
+In my opinion both disputants were right, assuming the grounds on which
+the discussion was based. Russell in effect pointed out that apart from
+minor inexactitudes a determinate congruence relation is among the
+factors in nature which our sense-awareness posits for us. Poincaré asks
+for information as to the factor in nature which might lead any
+particular congruence relation to play a preeminent _rôle_ among the
+factors posited in sense-awareness. I cannot see the answer to either of
+these contentions provided that you admit the materialistic theory of
+nature. With this theory nature at an instant in space is an independent
+fact. Thus we have to look for our preeminent congruence relation amid
+nature in instantaneous space; and Poincaré is undoubtedly right in
+saying that nature on this hypothesis gives us no help in finding it.
+
+On the other hand Russell is in an equally strong position when he
+asserts that, as a fact of observation, we do find it, and what is more
+agree in finding the same congruence relation. On this basis it is one
+of the most extraordinary facts of human experience that all mankind
+without any assignable reason should agree in fixing attention on just
+one congruence relation amid the indefinite number of indistinguishable
+competitors for notice. One would have expected disagreement on this
+fundamental choice to have divided nations and to have rent families.
+But the difficulty was not even discovered till the close of the
+nineteenth century by a few mathematical philosophers and philosophic
+mathematicians. The case is not like that of our agreement on some
+fundamental fact of nature such as the three dimensions of space. If
+space has only three dimensions we should expect all mankind to be aware
+of the fact, as they are aware of it. But in the case of congruence,
+mankind agree in an arbitrary interpretation of sense-awareness when
+there is nothing in nature to guide it.
+
+I look on it as no slight recommendation of the theory of nature which I
+am expounding to you that it gives a solution of this difficulty by
+pointing out the factor in nature which issues in the preeminence of one
+congruence relation over the indefinite herd of other such relations.
+
+The reason for this result is that nature is no longer confined within
+space at an instant. Space and time are now interconnected; and this
+peculiar factor of time which is so immediately distinguished among the
+deliverances of our sense-awareness, relates itself to one particular
+congruence relation in space.
+
+Congruence is a particular example of the fundamental fact of
+recognition. In perception we recognise. This recognition does not
+merely concern the comparison of a factor of nature posited by memory
+with a factor posited by immediate sense-awareness. Recognition takes
+place within the present without any intervention of pure memory. For
+the present fact is a duration with its antecedent and consequent
+durations which are parts of itself. The discrimination in
+sense-awareness of a finite event with its quality of passage is also
+accompanied by the discrimination of other factors of nature which do
+not share in the passage of events. Whatever passes is an event. But we
+find entities in nature which do not pass; namely we recognise
+samenesses in nature. Recognition is not primarily an intellectual act
+of comparison; it is in its essence merely sense-awareness in its
+capacity of positing before us factors in nature which do not pass. For
+example, green is perceived as situated in a certain finite event within
+the present duration. This green preserves its self-identity throughout,
+whereas the event passes and thereby obtains the property of breaking
+into parts. The green patch has parts. But in talking of the green patch
+we are speaking of the event in its sole capacity of being for us the
+situation of green. The green itself is numerically one self-identical
+entity, without parts because it is without passage.
+
+Factors in nature which are without passage will be called objects.
+There are radically different kinds of objects which will be considered
+in the succeeding lecture.
+
+Recognition is reflected into the intellect as comparison. The
+recognised objects of one event are compared with the recognised objects
+of another event. The comparison may be between two events in the
+present, or it may be between two events of which one is posited by
+memory-awareness and the other by immediate sense-awareness. But it is
+not the events which are compared. For each event is essentially unique
+and incomparable. What are compared are the objects and relations of
+objects situated in events. The event considered as a relation between
+objects has lost its passage and in this aspect is itself an object.
+This object is not the event but only an intellectual abstraction. The
+same object can be situated in many events; and in this sense even the
+whole event, viewed as an object, can recur, though not the very event
+itself with its passage and its relations to other events.
+
+Objects which are not posited by sense-awareness may be known to the
+intellect. For example, relations between objects and relations between
+relations may be factors in nature not disclosed in sense-awareness but
+known by logical inference as necessarily in being. Thus objects for our
+knowledge may be merely logical abstractions. For example, a complete
+event is never disclosed in sense-awareness, and thus the object which
+is the sum total of objects situated in an event as thus inter-related
+is a mere abstract concept. Again a right-angle is a perceived object
+which can be situated in many events; but, though rectangularity is
+posited by sense-awareness, the majority of geometrical relations are
+not so posited. Also rectangularity is in fact often not perceived when
+it can be proved to have been there for perception. Thus an object is
+often known merely as an abstract relation not directly posited in
+sense-awareness although it is there in nature.
+
+The identity of quality between congruent segments is generally of this
+character. In certain special cases this identity of quality can be
+directly perceived. But in general it is inferred by a process of
+measurement depending on our direct sense-awareness of selected cases
+and a logical inference from the transitive character of congruence.
+
+Congruence depends on motion, and thereby is generated the connexion
+between spatial congruence and temporal congruence. Motion along a
+straight line has a symmetry round that line. This symmetry is expressed
+by the symmetrical geometrical relations of the line to the family of
+planes normal to it.
+
+Also another symmetry in the theory of motion arises from the fact that
+rest in the points of β corresponds to uniform motion along a definite
+family of parallel straight lines in the space of α. We must note the
+three characteristics, (i) of the uniformity of the motion
+corresponding to any point of β along its correlated straight line in α,
+and (ii) of the equality in magnitude of the velocities along the
+various lines of α correlated to rest in the various points of β, and
+(iii) of the parallelism of the lines of this family.
+
+We are now in possession of a theory of parallels and a theory of
+perpendiculars and a theory of motion, and from these theories the
+theory of congruence can be constructed. It will be remembered that a
+family of parallel levels in any moment is the family of levels in which
+that moment is intersected by the family of moments of some other
+time-system. Also a family of parallel moments is the family of moments
+of some one time-system. Thus we can enlarge our concept of a family of
+parallel levels so as to include levels in different moments of one
+time-system. With this enlarged concept we say that a complete family of
+parallel levels in a time-system α is the complete family of levels in
+which the moments of α intersect the moments of β. This complete family
+of parallel levels is also evidently a family lying in the moments of
+the time-system β. By introducing a third time-system γ, parallel rects
+are obtained. Also all the points of any one time-system form a family
+of parallel point-tracks. Thus there are three types of parallelograms
+in the four-dimensional manifold of event-particles.
+
+In parallelograms of the first type the two pairs of parallel sides are
+both of them pairs of rects. In parallelograms of the second type one
+pair of parallel sides is a pair of rects and the other pair is a pair
+of point-tracks. In parallelograms of the third type the two pairs of
+parallel sides are both of them pairs of point-tracks.
+
+The first axiom of congruence is that the opposite sides of any
+parallelogram are congruent. This axiom enables us to compare the
+lengths of any two segments either respectively on parallel rects or on
+the same rect. Also it enables us to compare the lengths of any two
+segments either respectively on parallel point-tracks or on the same
+point-track. It follows from this axiom that two objects at rest in any
+two points of a time-system β are moving with equal velocities in any
+other time-system α along parallel lines. Thus we can speak of the
+velocity in α due to the time-system β without specifying any particular
+point in β. The axiom also enables us to measure time in any
+time-system; but does not enable us to compare times in different
+time-systems.
+
+The second axiom of congruence concerns parallelograms on congruent
+bases and between the same parallels, which have also their other pairs
+of sides parallel. The axiom asserts that the rect joining the two
+event-particles of intersection of the diagonals is parallel to the rect
+on which the bases lie. By the aid of this axiom it easily follows that
+the diagonals of a parallelogram bisect each other.
+
+Congruence is extended in any space beyond parallel rects to all rects
+by two axioms depending on perpendicularity. The first of these axioms,
+which is the third axiom of congruence, is that if ABC is a triangle
+of rects in any moment and D is the middle event-particle of the base
+BC, then the level through D perpendicular to BC contains A when
+and only when AB is congruent to AC. This axiom evidently expresses
+the symmetry of perpendicularity, and is the essence of the famous pons
+asinorum expressed as an axiom.
+
+The second axiom depending on perpendicularity, and the fourth axiom of
+congruence, is that if r and A be a rect and an event-particle in the
+same moment and AB and AC be a pair of rectangular rects intersecting r
+in B and C, and AD and AE be another pair of rectangular rects
+intersecting r in D and E, then either D or E lies in the segment BC and
+the other one of the two does not lie in this segment. Also as a
+particular case of this axiom, if AB be perpendicular to r and in
+consequence AC be parallel to r, then D and E lie on opposite sides of B
+respectively. By the aid of these two axioms the theory of congruence
+can be extended so as to compare lengths of segments on any two rects.
+Accordingly Euclidean metrical geometry in space is completely
+established and lengths in the spaces of different time-systems are
+comparable as the result of definite properties of nature which indicate
+just that particular method of comparison.
+
+The comparison of time-measurements in diverse time-systems requires two
+other axioms. The first of these axioms, forming the fifth axiom of
+congruence, will be called the axiom of 'kinetic symmetry.' It expresses
+the symmetry of the quantitative relations between two time-systems when
+the times and lengths in the two systems are measured in congruent
+units.
+
+The axiom can be explained as follows: Let α and β be the names of two
+time-systems. The directions of motion in the space of α due to rest in
+a point of β is called the 'β-direction in α' and the direction of
+motion in the space of β due to rest in a point of α is called the
+'α-direction in β.' Consider a motion in the space of α consisting of a
+certain velocity in the β-direction of α and a certain velocity at
+right-angles to it. This motion represents rest in the space of another
+time-system--call it π. Rest in π will also be represented in the space
+of β by a certain velocity in the α-direction in β and a certain
+velocity at right-angles to this α-direction. Thus a certain motion in
+the space of α is correlated to a certain motion in the space of β, as
+both representing the same fact which can also be represented by rest in
+π. Now another time-system, which I will name σ, can be found which is
+such that rest in its space is represented by the same magnitudes of
+velocities along and perpendicular to the α-direction in β as those
+velocities in α, along and perpendicular to the β-direction, which
+represent rest in π. The required axiom of kinetic symmetry is that rest
+in σ will be represented in α by the same velocities along and
+perpendicular to the β-direction in α as those velocities in β along and
+perpendicular to the α-direction which represent rest in π.
+
+A particular case of this axiom is that relative velocities are equal
+and opposite. Namely rest in α is represented in β by a velocity along
+the α-direction which is equal to the velocity along the β-direction in
+α which represents rest in β.
+
+Finally the sixth axiom of congruence is that the relation of congruence
+is transitive. So far as this axiom applies to space, it is superfluous.
+For the property follows from our previous axioms. It is however
+necessary for time as a supplement to the axiom of kinetic symmetry. The
+meaning of the axiom is that if the time-unit of system α is congruent
+to the time-unit of system β, and the time-unit of system β is congruent
+to the time-unit of system γ, then the time-units of α and γ are also
+congruent.
+
+By means of these axioms formulae for the transformation of
+measurements made in one time-system to measurements of the same facts
+of nature made in another time-system can be deduced. These formulae
+will be found to involve one arbitrary constant which I will call k.
+
+It is of the dimensions of the square of a velocity. Accordingly four
+cases arise. In the first case k is zero. This case produces
+nonsensical results in opposition to the elementary deliverances of
+experience. We put this case aside.
+
+In the second case k is infinite. This case yields the ordinary
+formulae for transformation in relative motion, namely those formulae
+which are to be found in every elementary book on dynamics.
+
+In the third case, k is negative. Let us call it -c², where c
+will be of the dimensions of a velocity. This case yields the formulae
+of transformation which Larmor discovered for the transformation of
+Maxwell's equations of the electromagnetic field. These formulae were
+extended by H. A. Lorentz, and used by Einstein and Minkowski as the
+basis of their novel theory of relativity. I am not now speaking of
+Einstein's more recent theory of general relativity by which he deduces
+his modification of the law of gravitation. If this be the case which
+applies to nature, then c must be a close approximation to the
+velocity of light _in vacuo_. Perhaps it is this actual velocity. In
+this connexion '_in vacuo_' must not mean an absence of events, namely
+the absence of the all-pervading ether of events. It must mean the
+absence of certain types of objects.
+
+In the fourth case, k is positive. Let us call it h², where h
+will be of the dimensions of a velocity. This gives a perfectly possible
+type of transformation formulae, but not one which explains any facts
+of experience. It has also another disadvantage. With the assumption of
+this fourth case the distinction between space and time becomes unduly
+blurred. The whole object of these lectures has been to enforce the
+doctrine that space and time spring from a common root, and that the
+ultimate fact of experience is a space-time fact. But after all mankind
+does distinguish very sharply between space and time, and it is owing to
+this sharpness of distinction that the doctrine of these lectures is
+somewhat of a paradox. Now in the third assumption this sharpness of
+distinction is adequately preserved. There is a fundamental distinction
+between the metrical properties of point-tracks and rects. But in the
+fourth assumption this fundamental distinction vanishes.
+
+Neither the third nor the fourth assumption can agree with experience
+unless we assume that the velocity c of the third assumption, and the
+velocity h of the fourth assumption, are extremely large compared to
+the velocities of ordinary experience. If this be the case the formulae
+of both assumptions will obviously reduce to a close approximation to
+the formulae of the second assumption which are the ordinary formulae of
+dynamical textbooks. For the sake of a name, I will call these textbook
+formulae the 'orthodox' formulae.
+
+There can be no question as to the general approximate correctness of
+the orthodox formulae. It would be merely silly to raise doubts on this
+point. But the determination of the status of these formulae is by no
+means settled by this admission. The independence of time and space is
+an unquestioned presupposition of the orthodox thought which has
+produced the orthodox formulae. With this presupposition and given the
+absolute points of one absolute space, the orthodox formulae are
+immediate deductions. Accordingly, these formulae are presented to our
+imaginations as facts which cannot be otherwise, time and space being
+what they are. The orthodox formulae have therefore attained to the
+status of necessities which cannot be questioned in science. Any attempt
+to replace these formulae by others was to abandon the _rôle_ of
+physical explanation and to have recourse to mere mathematical formulae.
+
+But even in physical science difficulties have accumulated round the
+orthodox formulae. In the first place Maxwell's equations of the
+electromagnetic field are not invariant for the transformations of the
+orthodox formulae; whereas they are invariant for the transformations of
+the formulae arising from the third of the four cases mentioned above,
+provided that the velocity c is identified with a famous
+electromagnetic constant quantity.
+
+Again the null results of the delicate experiments to detect the earth's
+variations of motion through the ether in its orbital path are explained
+immediately by the formulae of the third case. But if we assume the
+orthodox formulae we have to make a special and arbitrary assumption as
+to the contraction of matter during motion. I mean the Fitzgerald-Lorentz
+assumption.
+
+Lastly Fresnel's coefficient of drag which represents the variation of
+the velocity of light in a moving medium is explained by the formulae of
+the third case, and requires another arbitrary assumption if we use the
+orthodox formulae.
+
+It appears therefore that on the mere basis of physical explanation
+there are advantages in the formulae of the third case as compared with
+the orthodox formulae. But the way is blocked by the ingrained belief
+that these latter formulae possess a character of necessity. It is
+therefore an urgent requisite for physical science and for philosophy to
+examine critically the grounds for this supposed necessity. The only
+satisfactory method of scrutiny is to recur to the first principles of
+our knowledge of nature. This is exactly what I am endeavouring to do in
+these lectures. I ask what it is that we are aware of in our
+sense-perception of nature. I then proceed to examine those factors in
+nature which lead us to conceive nature as occupying space and
+persisting through time. This procedure has led us to an investigation
+of the characters of space and time. It results from these
+investigations that the formulae of the third case and the orthodox
+formulae are on a level as possible formulae resulting from the basic
+character of our knowledge of nature. The orthodox formulae have thus
+lost any advantage as to necessity which they enjoyed over the serial
+group. The way is thus open to adopt whichever of the two groups best
+accords with observation.
+
+I take this opportunity of pausing for a moment from the course of my
+argument, and of reflecting on the general character which my doctrine
+ascribes to some familiar concepts of science. I have no doubt that some
+of you have felt that in certain aspects this character is very
+paradoxical.
+
+This vein of paradox is partly due to the fact that educated language
+has been made to conform to the prevalent orthodox theory. We are thus,
+in expounding an alternative doctrine, driven to the use of either
+strange terms or of familiar words with unusual meanings. This victory
+of the orthodox theory over language is very natural. Events are named
+after the prominent objects situated in them, and thus both in language
+and in thought the event sinks behind the object, and becomes the mere
+play of its relations. The theory of space is then converted into a
+theory of the relations of objects instead of a theory of the relations
+of events. But objects have not the passage of events. Accordingly space
+as a relation between objects is devoid of any connexion with time. It
+is space at an instant without any determinate relations between the
+spaces at successive instants. It cannot be one timeless space because
+the relations between objects change.
+
+A few minutes ago in speaking of the deduction of the orthodox formulae
+for relative motion I said that they followed as an immediate deduction
+from the assumption of absolute points in absolute space. This reference
+to absolute space was not an oversight. I know that the doctrine of the
+relativity of space at present holds the field both in science and
+philosophy. But I do not think that its inevitable consequences are
+understood. When we really face them the paradox of the presentation of
+the character of space which I have elaborated is greatly mitigated. If
+there is no absolute position, a point must cease to be a simple entity.
+What is a point to one man in a balloon with his eyes fixed on an
+instrument is a track of points to an observer on the earth who is
+watching the balloon through a telescope, and is another track of points
+to an observer in the sun who is watching the balloon through some
+instrument suited to such a being. Accordingly if I am reproached with
+the paradox of my theory of points as classes of event-particles, and of
+my theory of event-particles as groups of abstractive sets, I ask my
+critic to explain exactly what he means by a point. While you explain
+your meaning about anything, however simple, it is always apt to look
+subtle and fine spun. I have at least explained exactly what I do mean
+by a point, what relations it involves and what entities are the relata.
+If you admit the relativity of space, you also must admit that points
+are complex entities, logical constructs involving other entities and
+their relations. Produce your theory, not in a few vague phrases of
+indefinite meaning, but explain it step by step in definite terms
+referring to assigned relations and assigned relata. Also show that your
+theory of points issues in a theory of space. Furthermore note that the
+example of the man in the balloon, the observer on earth, and the
+observer in the sun, shows that every assumption of relative rest
+requires a timeless space with radically different points from those
+which issue from every other such assumption. The theory of the
+relativity of space is inconsistent with any doctrine of one unique set
+of points of one timeless space.
+
+The fact is that there is no paradox in my doctrine of the nature of
+space which is not in essence inherent in the theory of the relativity
+of space. But this doctrine has never really been accepted in science,
+whatever people say. What appears in our dynamical treatises is Newton's
+doctrine of relative motion based on the doctrine of differential motion
+in absolute space. When you once admit that the points are radically
+different entities for differing assumptions of rest, then the orthodox
+formulae lose all their obviousness. They were only obvious because you
+were really thinking of something else. When discussing this topic you
+can only avoid paradox by taking refuge from the flood of criticism in
+the comfortable ark of no meaning.
+
+The new theory provides a definition of the congruence of periods of
+time. The prevalent view provides no such definition. Its position is
+that if we take such time-measurements so that certain familiar
+velocities which seem to us to be uniform are uniform, then the laws of
+motion are true. Now in the first place no change could appear either as
+uniform or non-uniform without involving a definite determination of the
+congruence for time-periods. So in appealing to familiar phenomena it
+allows that there is some factor in nature which we can intellectually
+construct as a congruence theory. It does not however say anything about
+it except that the laws of motion are then true. Suppose that with some
+expositors we cut out the reference to familiar velocities such as the
+rate of rotation of the earth. We are then driven to admit that there is
+no meaning in temporal congruence except that certain assumptions make
+the laws of motion true. Such a statement is historically false. King
+Alfred the Great was ignorant of the laws of motion, but knew very well
+what he meant by the measurement of time, and achieved his purpose by
+means of burning candles. Also no one in past ages justified the use of
+sand in hour-glasses by saying that some centuries later interesting
+laws of motion would be discovered which would give a meaning to the
+statement that the sand was emptied from the bulbs in equal times.
+Uniformity in change is directly perceived, and it follows that mankind
+perceives in nature factors from which a theory of temporal congruence
+can be formed. The prevalent theory entirely fails to produce such
+factors.
+
+The mention of the laws of motion raises another point where the
+prevalent theory has nothing to say and the new theory gives a complete
+explanation. It is well known that the laws of motion are not valid for
+any axes of reference which you may choose to take fixed in any rigid
+body. You must choose a body which is not rotating and has no
+acceleration. For example they do not really apply to axes fixed in the
+earth because of the diurnal rotation of that body. The law which fails
+when you assume the wrong axes as at rest is the third law, that action
+and reaction are equal and opposite. With the wrong axes uncompensated
+centrifugal forces and uncompensated composite centrifugal forces
+appear, due to rotation. The influence of these forces can be
+demonstrated by many facts on the earth's surface, Foucault's pendulum,
+the shape of the earth, the fixed directions of the rotations of
+cyclones and anticyclones. It is difficult to take seriously the
+suggestion that these domestic phenomena on the earth are due to the
+influence of the fixed stars. I cannot persuade myself to believe that a
+little star in its twinkling turned round Foucault's pendulum in the
+Paris Exhibition of 1861. Of course anything is believable when a
+definite physical connexion has been demonstrated, for example the
+influence of sunspots. Here all demonstration is lacking in the form of
+any coherent theory. According to the theory of these lectures the axes
+to which motion is to be referred are axes at rest in the space of some
+time-system. For example, consider the space of a time-system α. There
+are sets of axes at rest in the space of α. These are suitable dynamical
+axes. Also a set of axes in this space which is moving with uniform
+velocity without rotation is another suitable set. All the moving
+points fixed in these moving axes are really tracing out parallel lines
+with one uniform velocity. In other words they are the reflections in
+the space of α of a set of fixed axes in the space of some other
+time-system β. Accordingly the group of dynamical axes required for
+Newton's Laws of Motion is the outcome of the necessity of referring
+motion to a body at rest in the space of some one time-system in order
+to obtain a coherent account of physical properties. If we do not do so
+the meaning of the motion of one portion of our physical configuration
+is different from the meaning of the motion of another portion of the
+same configuration. Thus the meaning of motion being what it is, in
+order to describe the motion of any system of objects without changing
+the meaning of your terms as you proceed with your description, you are
+bound to take one of these sets of axes as axes of reference; though you
+may choose their reflections into the space of any time-system which you
+wish to adopt. A definite physical reason is thereby assigned for the
+peculiar property of the dynamical group of axes.
+
+On the orthodox theory the position of the equations of motion is most
+ambiguous. The space to which they refer is completely undetermined and
+so is the measurement of the lapse of time. Science is simply setting
+out on a fishing expedition to see whether it cannot find some procedure
+which it can call the measurement of space and some procedure which it
+can call the measurement of time, and something which it can call a
+system of forces, and something which it can call masses, so that these
+formulae may be satisfied. The only reason--on this theory--why anyone
+should want to satisfy these formulae is a sentimental regard for
+Galileo, Newton, Euler and Lagrange. The theory, so far from founding
+science on a sound observational basis, forces everything to conform to
+a mere mathematical preference for certain simple formulae.
+
+I do not for a moment believe that this is a true account of the real
+status of the Laws of Motion. These equations want some slight
+adjustment for the new formulae of relativity. But with these
+adjustments, imperceptible in ordinary use, the laws deal with
+fundamental physical quantities which we know very well and wish to
+correlate.
+
+The measurement of time was known to all civilised nations long before
+the laws were thought of. It is this time as thus measured that the laws
+are concerned with. Also they deal with the space of our daily life.
+When we approach to an accuracy of measurement beyond that of
+observation, adjustment is allowable. But within the limits of
+observation we know what we mean when we speak of measurements of space
+and measurements of time and uniformity of change. It is for science to
+give an intellectual account of what is so evident in sense-awareness.
+It is to me thoroughly incredible that the ultimate fact beyond which
+there is no deeper explanation is that mankind has really been swayed by
+an unconscious desire to satisfy the mathematical formulae which we call
+the Laws of Motion, formulae completely unknown till the seventeenth
+century of our epoch.
+
+The correlation of the facts of sense-experience effected by the
+alternative account of nature extends beyond the physical properties of
+motion and the properties of congruence. It gives an account of the
+meaning of the geometrical entities such as points, straight lines, and
+volumes, and connects the kindred ideas of extension in time and
+extension in space. The theory satisfies the true purpose of an
+intellectual explanation in the sphere of natural philosophy. This
+purpose is to exhibit the interconnexions of nature, and to show that
+one set of ingredients in nature requires for the exhibition of its
+character the presence of the other sets of ingredients.
+
+The false idea which we have to get rid of is that of nature as a mere
+aggregate of independent entities, each capable of isolation. According
+to this conception these entities, whose characters are capable of
+isolated definition, come together and by their accidental relations
+form the system of nature. This system is thus thoroughly accidental;
+and, even if it be subject to a mechanical fate, it is only accidentally
+so subject.
+
+With this theory space might be without time, and time might be without
+space. The theory admittedly breaks down when we come to the relations
+of matter and space. The relational theory of space is an admission that
+we cannot know space without matter or matter without space. But the
+seclusion of both from time is still jealously guarded. The relations
+between portions of matter in space are accidental facts owing to the
+absence of any coherent account of how space springs from matter or how
+matter springs from space. Also what we really observe in nature, its
+colours and its sounds and its touches are secondary qualities; in other
+words, they are not in nature at all but are accidental products of the
+relations between nature and mind.
+
+The explanation of nature which I urge as an alternative ideal to this
+accidental view of nature, is that nothing in nature could be what it is
+except as an ingredient in nature as it is. The whole which is present
+for discrimination is posited in sense-awareness as necessary for the
+discriminated parts. An isolated event is not an event, because every
+event is a factor in a larger whole and is significant of that whole.
+There can be no time apart from space; and no space apart from time; and
+no space and no time apart from the passage of the events of nature. The
+isolation of an entity in thought, when we think of it as a bare 'it,'
+has no counterpart in any corresponding isolation in nature. Such
+isolation is merely part of the procedure of intellectual knowledge.
+
+The laws of nature are the outcome of the characters of the entities
+which we find in nature. The entities being what they are, the laws must
+be what they are; and conversely the entities follow from the laws. We
+are a long way from the attainment of such an ideal; but it remains as
+the abiding goal of theoretical science.
+
+
+
+
+CHAPTER VII
+
+OBJECTS
+
+
+The ensuing lecture is concerned with the theory of objects. Objects are
+elements in nature which do not pass. The awareness of an object as some
+factor not sharing in the passage of nature is what I call
+'recognition.' It is impossible to recognise an event, because an event
+is essentially distinct from every other event. Recognition is an
+awareness of sameness. But to call recognition an awareness of sameness
+implies an intellectual act of comparison accompanied with judgment. I
+use recognition for the non-intellectual relation of sense-awareness
+which connects the mind with a factor of nature without passage. On the
+intellectual side of the mind's experience there are comparisons of
+things recognised and consequent judgments of sameness or diversity.
+Probably 'sense-recognition' would be a better term for what I mean by
+'recognition.' I have chosen the simpler term because I think that I
+shall be able to avoid the use of 'recognition' in any other meaning
+than that of 'sense-recognition.' I am quite willing to believe that
+recognition, in my sense of the term, is merely an ideal limit, and that
+there is in fact no recognition without intellectual accompaniments of
+comparison and judgment. But recognition is that relation of the mind to
+nature which provides the material for the intellectual activity.
+
+An object is an ingredient in the character of some event. In fact the
+character of an event is nothing but the objects which are ingredient in
+it and the ways in which those objects make their ingression into the
+event. Thus the theory of objects is the theory of the comparison of
+events. Events are only comparable because they body forth permanences.
+We are comparing objects in events whenever we can say, 'There it is
+again.' Objects are the elements in nature which can 'be again.'
+
+Sometimes permanences can be proved to exist which evade recognition in
+the sense in which I am using that term. The permanences which evade
+recognition appear to us as abstract properties either of events or of
+objects. All the same they are there for recognition although
+undiscriminated in our sense-awareness. The demarcation of events, the
+splitting of nature up into parts is effected by the objects which we
+recognise as their ingredients. The discrimination of nature is the
+recognition of objects amid passing events. It is a compound of the
+awareness of the passage of nature, of the consequent partition of
+nature, and of the definition of certain parts of nature by the modes of
+the ingression of objects into them.
+
+You may have noticed that I am using the term 'ingression' to denote the
+general relation of objects to events. The ingression of an object into
+an event is the way the character of the event shapes itself in virtue
+of the being of the object. Namely the event is what it is, because the
+object is what it is; and when I am thinking of this modification of the
+event by the object, I call the relation between the two 'the ingression
+of the object into the event.' It is equally true to say that objects
+are what they are because events are what they are. Nature is such that
+there can be no events and no objects without the ingression of objects
+into events. Although there are events such that the ingredient objects
+evade our recognition. These are the events in empty space. Such events
+are only analysed for us by the intellectual probing of science.
+
+Ingression is a relation which has various modes. There are obviously
+very various kinds of objects; and no one kind of object can have the
+same sort of relations to events as objects of another kind can have. We
+shall have to analyse out some of the different modes of ingression
+which different kinds of objects have into events.
+
+But even if we stick to one and the same kind of objects, an object of
+that kind has different modes of ingression into different events.
+Science and philosophy have been apt to entangle themselves in a
+simple-minded theory that an object is at one place at any definite
+time, and is in no sense anywhere else. This is in fact the attitude of
+common sense thought, though it is not the attitude of language which is
+naïvely expressing the facts of experience. Every other sentence in a
+work of literature which is endeavouring truly to interpret the facts of
+experience expresses differences in surrounding events due to the
+presence of some object. An object is ingredient throughout its
+neighbourhood, and its neighbourhood is indefinite. Also the
+modification of events by ingression is susceptible of quantitative
+differences. Finally therefore we are driven to admit that each object
+is in some sense ingredient throughout nature; though its ingression may
+be quantitatively irrelevant in the expression of our individual
+experiences.
+
+This admission is not new either in philosophy or science. It is
+obviously a necessary axiom for those philosophers who insist that
+reality is a system. In these lectures we are keeping off the profound
+and vexed question as to what we mean by 'reality.' I am maintaining the
+humbler thesis that nature is a system. But I suppose that in this case
+the less follows from the greater, and that I may claim the support of
+these philosophers. The same doctrine is essentially interwoven in all
+modern physical speculation. As long ago as 1847 Faraday in a paper in
+the _Philosophical Magazine_ remarked that his theory of tubes of force
+implies that in a sense an electric charge is everywhere. The
+modification of the electromagnetic field at every point of space at
+each instant owing to the past history of each electron is another way
+of stating the same fact. We can however illustrate the doctrine by the
+more familiar facts of life without recourse to the abstruse
+speculations of theoretical physics.
+
+The waves as they roll on to the Cornish coast tell of a gale in
+mid-Atlantic; and our dinner witnesses to the ingression of the cook
+into the dining room. It is evident that the ingression of objects into
+events includes the theory of causation. I prefer to neglect this aspect
+of ingression, because causation raises the memory of discussions based
+upon theories of nature which are alien to my own. Also I think that
+some new light may be thrown on the subject by viewing it in this fresh
+aspect.
+
+The examples which I have given of the ingression of objects into events
+remind us that ingression takes a peculiar form in the case of some
+events; in a sense, it is a more concentrated form. For example, the
+electron has a certain position in space and a certain shape. Perhaps it
+is an extremely small sphere in a certain test-tube. The storm is a
+gale situated in mid-Atlantic with a certain latitude and longitude, and
+the cook is in the kitchen. I will call this special form of ingression
+the 'relation of situation'; also, by a double use of the word
+'situation,' I will call the event in which an object is situated 'the
+situation of the object.' Thus a situation is an event which is a
+relatum in the relation of situation. Now our first impression is that
+at last we have come to the simple plain fact of where the object really
+is; and that the vaguer relation which I call ingression should not be
+muddled up with the relation of situation, as if including it as a
+particular case. It seems so obvious that any object is in such and such
+a position, and that it is influencing other events in a totally
+different sense. Namely, in a sense an object is the character of the
+event which is its situation, but it only influences the character of
+other events. Accordingly the relations of situation and influencing are
+not generally the same sort of relation, and should not be subsumed
+under the same term 'ingression.' I believe that this notion is a
+mistake, and that it is impossible to draw a clear distinction between
+the two relations.
+
+For example, Where was your toothache? You went to a dentist and pointed
+out the tooth to him. He pronounced it perfectly sound, and cured you by
+stopping another tooth. Which tooth was the situation of the toothache?
+Again, a man has an arm amputated, and experiences sensations in the
+hand which he has lost. The situation of the imaginary hand is in fact
+merely thin air. You look into a mirror and see a fire. The flames that
+you see are situated behind the mirror. Again at night you watch the
+sky; if some of the stars had vanished from existence hours ago, you
+would not be any the wiser. Even the situations of the planets differ
+from those which science would assign to them.
+
+Anyhow you are tempted to exclaim, the cook is in the kitchen. If you
+mean her mind, I will not agree with you on the point; for I am only
+talking of nature. Let us think only of her bodily presence. What do you
+mean by this notion? We confine ourselves to typical manifestations of
+it. You can see her, touch her, and hear her. But the examples which I
+have given you show that the notions of the situations of what you see,
+what you touch, and what you hear are not so sharply separated out as to
+defy further questioning. You cannot cling to the idea that we have two
+sets of experiences of nature, one of primary qualities which belong to
+the objects perceived, and one of secondary qualities which are the
+products of our mental excitements. All we know of nature is in the same
+boat, to sink or swim together. The constructions of science are merely
+expositions of the characters of things perceived. Accordingly to affirm
+that the cook is a certain dance of molecules and electrons is merely to
+affirm that the things about her which are perceivable have certain
+characters. The situations of the perceived manifestations of her bodily
+presence have only a very general relation to the situations of the
+molecules, to be determined by discussion of the circumstances of
+perception.
+
+In discussing the relations of situation in particular and of ingression
+in general, the first requisite is to note that objects are of radically
+different types. For each type 'situation' and 'ingression' have their
+own special meanings which are different from their meanings for other
+types, though connexions can be pointed out. It is necessary therefore
+in discussing them to determine what type of objects are under
+consideration. There are, I think, an indefinite number of types of
+objects. Happily we need not think of them all. The idea of situation
+has its peculiar importance in reference to three types of objects which
+I call sense-objects, perceptual objects and scientific objects. The
+suitability of these names for the three types is of minor importance,
+so long as I can succeed in explaining what I mean by them.
+
+These three types form an ascending hierarchy, of which each member
+presupposes the type below. The base of the hierarchy is formed by the
+sense-objects. These objects do not presuppose any other type of
+objects. A sense-object is a factor of nature posited by sense-awareness
+which (i), in that it is an object, does not share in the passage of
+nature and (ii) is not a relation between other factors of nature. It
+will of course be a relatum in relations which also implicate other
+factors of nature. But it is always a relatum and never the relation
+itself. Examples of sense-objects are a particular sort of colour, say
+Cambridge blue, or a particular sort of sound, or a particular sort of
+smell, or a particular sort of feeling. I am not talking of a particular
+patch of blue as seen during a particular second of time at a definite
+date. Such a patch is an event where Cambridge blue is situated.
+Similarly I am not talking of any particular concert-room as filled with
+the note. I mean the note itself and not the patch of volume filled by
+the sound for a tenth of a second. It is natural for us to think of the
+note in itself, but in the case of colour we are apt to think of it
+merely as a property of the patch. No one thinks of the note as a
+property of the concert-room. We see the blue and we hear the note. Both
+the blue and the note are immediately posited by the discrimination of
+sense-awareness which relates the mind to nature. The blue is posited as
+in nature related to other factors in nature. In particular it is
+posited as in the relation of being situated in the event which is its
+situation.
+
+The difficulties which cluster around the relation of situation arise
+from the obstinate refusal of philosophers to take seriously the
+ultimate fact of multiple relations. By a multiple relation I mean a
+relation which in any concrete instance of its occurrence necessarily
+involves more than two relata. For example, when John likes Thomas there
+are only two relata, John and Thomas. But when John gives that book to
+Thomas there are three relata, John, that book, and Thomas.
+
+Some schools of philosophy, under the influence of the Aristotelian
+logic and the Aristotelian philosophy, endeavour to get on without
+admitting any relations at all except that of substance and attribute.
+Namely all apparent relations are to be resolvable into the concurrent
+existence of substances with contrasted attributes. It is fairly obvious
+that the Leibnizian monadology is the necessary outcome of any such
+philosophy. If you dislike pluralism, there will be only one monad.
+
+Other schools of philosophy admit relations but obstinately refuse to
+contemplate relations with more than two relata. I do not think that
+this limitation is based on any set purpose or theory. It merely arises
+from the fact that more complicated relations are a bother to people
+without adequate mathematical training, when they are admitted into the
+reasoning.
+
+I must repeat that we have nothing to do in these lectures with the
+ultimate character of reality. It is quite possible that in the true
+philosophy of reality there are only individual substances with
+attributes, or that there are only relations with pairs of relata. I do
+not believe that such is the case; but I am not concerned to argue about
+it now. Our theme is Nature. So long as we confine ourselves to the
+factors posited in the sense-awareness of nature, it seems to me that
+there certainly are instances of multiple relations between these
+factors, and that the relation of situation for sense-objects is one
+example of such multiple relations.
+
+Consider a blue coat, a flannel coat of Cambridge blue belonging to some
+athlete. The coat itself is a perceptual object and its situation is not
+what I am talking about. We are talking of someone's definite
+sense-awareness of Cambridge blue as situated in some event of nature.
+He may be looking at the coat directly. He then sees Cambridge blue as
+situated practically in the same event as the coat at that instant. It
+is true that the blue which he sees is due to light which left the coat
+some inconceivably small fraction of a second before. This difference
+would be important if he were looking at a star whose colour was
+Cambridge blue. The star might have ceased to exist days ago, or even
+years ago. The situation of the blue will not then be very intimately
+connected with the situation (in another sense of 'situation') of any
+perceptual object. This disconnexion of the situation of the blue and
+the situation of some associated perceptual object does not require a
+star for its exemplification. Any looking glass will suffice. Look at
+the coat through a looking glass. Then blue is seen as situated behind
+the mirror. The event which is its situation depends upon the position
+of the observer.
+
+The sense-awareness of the blue as situated in a certain event which I
+call the situation, is thus exhibited as the sense-awareness of a
+relation between the blue, the percipient event of the observer, the
+situation, and intervening events. All nature is in fact required,
+though only certain intervening events require their characters to be of
+certain definite sorts. The ingression of blue into the events of nature
+is thus exhibited as systematically correlated. The awareness of the
+observer depends on the position of the percipient event in this
+systematic correlation. I will use the term 'ingression into nature' for
+this systematic correlation of the blue with nature. Thus the ingression
+of blue into any definite event is a part statement of the fact of the
+ingression of blue into nature.
+
+In respect to the ingression of blue into nature events may be roughly
+put into four classes which overlap and are not very clearly separated.
+These classes are (i) the percipient events, (ii) the situations, (iii)
+the active conditioning events, (iv) the passive conditioning events. To
+understand this classification of events in the general fact of the
+ingression of blue into nature, let us confine attention to one
+situation for one percipient event and to the consequent _rôles_ of the
+conditioning events for the ingression as thus limited. The percipient
+event is the relevant bodily state of the observer. The situation is
+where he sees the blue, say, behind the mirror. The active conditioning
+events are the events whose characters are particularly relevant for the
+event (which is the situation) to be the situation for that percipient
+event, namely the coat, the mirror, and the state of the room as to
+light and atmosphere. The passive conditioning events are the events of
+the rest of nature.
+
+In general the situation is an active conditioning event; namely the
+coat itself, when there is no mirror or other such contrivance to
+produce abnormal effects. But the example of the mirror shows us that
+the situation may be one of the passive conditioning events. We are then
+apt to say that our senses have been cheated, because we demand as a
+right that the situation should be an active condition in the
+ingression.
+
+This demand is not so baseless as it may seem when presented as I have
+put it. All we know of the characters of the events of nature is based
+on the analysis of the relations of situations to percipient events. If
+situations were not in general active conditions, this analysis would
+tell us nothing. Nature would be an unfathomable enigma to us and there
+could be no science. Accordingly the incipient discontent when a
+situation is found to be a passive condition is in a sense justifiable;
+because if that sort of thing went on too often, the _rôle_ of the
+intellect would be ended.
+
+Furthermore the mirror is itself the situation of other sense-objects
+either for the same observer with the same percipient event, or for
+other observers with other percipient events. Thus the fact that an
+event is a situation in the ingression of one set of sense-objects into
+nature is presumptive evidence that that event is an active condition in
+the ingression of other sense-objects into nature which may have other
+situations.
+
+This is a fundamental principle of science which it has derived from
+common sense.
+
+I now turn to perceptual objects. When we look at the coat, we do not in
+general say, There is a patch of Cambridge blue; what naturally occurs
+to us is, There is a coat. Also the judgment that what we have seen is
+a garment of man's attire is a detail. What we perceive is an object
+other than a mere sense-object. It is not a mere patch of colour, but
+something more; and it is that something more which we judge to be a
+coat. I will use the word 'coat' as the name for that crude object which
+is more than a patch of colour, and without any allusion to the
+judgments as to its usefulness as an article of attire either in the
+past or the future. The coat which is perceived--in this sense of the
+word 'coat'--is what I call a perceptual object. We have to investigate
+the general character of these perceptual objects.
+
+It is a law of nature that in general the situation of a sense-object is
+not only the situation of that sense-object for one definite percipient
+event, but is the situation of a variety of sense-objects for a variety
+of percipient events. For example, for any one percipient event, the
+situation of a sense-object of sight is apt also to be the situations of
+sense-objects of sight, of touch, of smell, and of sound. Furthermore
+this concurrence in the situations of sense-objects has led to the
+body--_i.e._ the percipient event--so adapting itself that the
+perception of one sense-object in a certain situation leads to a
+subconscious sense-awareness of other sense-objects in the same
+situation. This interplay is especially the case between touch and
+sight. There is a certain correlation between the ingressions of
+sense-objects of touch and sense-objects of sight into nature, and in a
+slighter degree between the ingressions of other pairs of sense-objects.
+I call this sort of correlation the 'conveyance' of one sense-object by
+another. When you see the blue flannel coat you subconsciously feel
+yourself wearing it or otherwise touching it. If you are a smoker, you
+may also subconsciously be aware of the faint aroma of tobacco. The
+peculiar fact, posited by this sense-awareness of the concurrence of
+subconscious sense-objects along with one or more dominating
+sense-objects in the same situation, is the sense-awareness of the
+perceptual object. The perceptual object is not primarily the issue of a
+judgment. It is a factor of nature directly posited in sense-awareness.
+The element of judgment comes in when we proceed to classify the
+particular perceptual object. For example, we say, That is flannel, and
+we think of the properties of flannel and the uses of athletes' coats.
+But that all takes place after we have got hold of the perceptual
+object. Anticipatory judgments affect the perceptual object perceived by
+focussing and diverting attention.
+
+The perceptual object is the outcome of the habit of experience.
+Anything which conflicts with this habit hinders the sense-awareness of
+such an object. A sense-object is not the product of the association of
+intellectual ideas; it is the product of the association of
+sense-objects in the same situation. This outcome is not intellectual;
+it is an object of peculiar type with its own particular ingression into
+nature.
+
+There are two kinds of perceptual objects, namely, 'delusive perceptual
+objects' and 'physical objects.' The situation of a delusive perceptual
+object is a passive condition in the ingression of that object into
+nature. Also the event which is the situation will have the relation of
+situation to the object only for one particular percipient event. For
+example, an observer sees the image of the blue coat in a mirror. It is
+a blue coat that he sees and not a mere patch of colour. This shows that
+the active conditions for the conveyance of a group of subconscious
+sense-objects by a dominating sense-object are to be found in the
+percipient event. Namely we are to look for them in the investigations
+of medical psychologists. The ingression into nature of the delusive
+sense-object is conditioned by the adaptation of bodily events to the
+more normal occurrence, which is the ingression of the physical object.
+
+A perceptual object is a physical object when (i) its situation is an
+active conditioning event for the ingression of any of its component
+sense-objects, and (ii) the same event can be the situation of the
+perceptual object for an indefinite number of possible percipient
+events. Physical objects are the ordinary objects which we perceive when
+our senses are not cheated, such as chairs, tables and trees. In a way
+physical objects have more insistent perceptive power than
+sense-objects. Attention to the fact of their occurrence in nature is
+the first condition for the survival of complex living organisms. The
+result of this high perceptive power of physical objects is the
+scholastic philosophy of nature which looks on the sense-objects as mere
+attributes of the physical objects. This scholastic point of view is
+directly contradicted by the wealth of sense-objects which enter into
+our experience as situated in events without any connexion with physical
+objects. For example, stray smells, sounds, colours and more subtle
+nameless sense-objects. There is no perception of physical objects
+without perception of sense-objects. But the converse does not hold:
+namely, there is abundant perception of sense-objects unaccompanied by
+any perception of physical objects. This lack of reciprocity in the
+relations between sense-objects and physical objects is fatal to the
+scholastic natural philosophy.
+
+There is a great difference in the _rôles_ of the situations of
+sense-objects and physical objects. The situations of a physical object
+are conditioned by uniqueness and continuity. The uniqueness is an ideal
+limit to which we approximate as we proceed in thought along an
+abstractive set of durations, considering smaller and smaller durations
+in the approach to the ideal limit of the moment of time. In other
+words, when the duration is small enough, the situation of the physical
+object within that duration is practically unique.
+
+The identification of the same physical object as being situated in
+distinct events in distinct durations is effected by the condition of
+continuity. This condition of continuity is the condition that a
+continuity of passage of events, each event being a situation of the
+object in its corresponding duration, can be found from the earlier to
+the later of the two given events. So far as the two events are
+practically adjacent in one specious present, this continuity of passage
+may be directly perceived. Otherwise it is a matter of judgment and
+inference.
+
+The situations of a sense-object are not conditioned by any such
+conditions either of uniqueness or of continuity. In any durations
+however small a sense-object may have any number of situations separated
+from each other. Thus two situations of a sense-object, either in the
+same duration or in different durations, are not necessarily connected
+by any continuous passage of events which are also situations of that
+sense-object.
+
+The characters of the conditioning events involved in the ingression of
+a sense-object into nature can be largely expressed in terms of the
+physical objects which are situated in those events. In one respect this
+is also a tautology. For the physical object is nothing else than the
+habitual concurrence of a certain set of sense-objects in one situation.
+Accordingly when we know all about the physical object, we thereby know
+its component sense-objects. But a physical object is a condition for
+the occurrence of sense-objects other than those which are its
+components. For example, the atmosphere causes the events which are its
+situations to be active conditioning events in the transmission of
+sound. A mirror which is itself a physical object is an active condition
+for the situation of a patch of colour behind it, due to the reflection
+of light in it.
+
+Thus the origin of scientific knowledge is the endeavour to express in
+terms of physical objects the various _rôles_ of events as active
+conditions in the ingression of sense-objects into nature. It is in the
+progress of this investigation that scientific objects emerge. They
+embody those aspects of the character of the situations of the physical
+objects which are most permanent and are expressible without reference
+to a multiple relation including a percipient event. Their relations to
+each other are also characterised by a certain simplicity and
+uniformity. Finally the characters of the observed physical objects and
+sense-objects can be expressed in terms of these scientific objects. In
+fact the whole point of the search for scientific objects is the
+endeavour to obtain this simple expression of the characters of events.
+These scientific objects are not themselves merely formulae for
+calculation; because formulae must refer to things in nature, and the
+scientific objects are the things in nature to which the formulae refer.
+
+A scientific object such as a definite electron is a systematic
+correlation of the characters of all events throughout all nature. It is
+an aspect of the systematic character of nature. The electron is not
+merely where its charge is. The charge is the quantitative character of
+certain events due to the ingression of the electron into nature. The
+electron is its whole field of force. Namely the electron is the
+systematic way in which all events are modified as the expression of its
+ingression. The situation of an electron in any small duration may be
+defined as that event which has the quantitative character which is the
+charge of the electron. We may if we please term the mere charge the
+electron. But then another name is required for the scientific object
+which is the full entity which concerns science, and which I have called
+the electron.
+
+According to this conception of scientific objects, the rival theories
+of action at a distance and action by transmission through a medium are
+both incomplete expressions of the true process of nature. The stream of
+events which form the continuous series of situations of the electron is
+entirely self-determined, both as regards having the intrinsic character
+of being the series of situations of that electron and as regards the
+time-systems with which its various members are cogredient, and the flux
+of their positions in their corresponding durations. This is the
+foundation of the denial of action at a distance; namely the progress of
+the stream of the situations of a scientific object can be determined by
+an analysis of the stream itself.
+
+On the other hand the ingression of every electron into nature modifies
+to some extent the character of every event. Thus the character of the
+stream of events which we are considering bears marks of the existence
+of every other electron throughout the universe. If we like to think of
+the electrons as being merely what I call their charges, then the
+charges act at a distance. But this action consists in the modification
+of the situation of the other electron under consideration. This
+conception of a charge acting at a distance is a wholly artificial one.
+The conception which most fully expresses the character of nature is
+that of each event as modified by the ingression of each electron into
+nature. The ether is the expression of this systematic modification of
+events throughout space and throughout time. The best expression of the
+character of this modification is for physicists to find out. My theory
+has nothing to do with that and is ready to accept any outcome of
+physical research.
+
+The connexion of objects with space requires elucidation. Objects are
+situated in events. The relation of situation is a different relation
+for each type of object, and in the case of sense-objects it cannot be
+expressed as a two-termed relation. It would perhaps be better to use a
+different word for these different types of the relation of situation.
+It has not however been necessary to do so for our purposes in these
+lectures. It must be understood however that, when situation is spoken
+of, some one definite type is under discussion, and it may happen that
+the argument may not apply to situation of another type. In all cases
+however I use situation to express a relation between objects and events
+and not between objects and abstractive elements. There is a derivative
+relation between objects and spatial elements which I call the relation
+of location; and when this relation holds, I say that the object is
+located in the abstractive element. In this sense, an object may be
+located in a moment of time, in a volume of space, an area, a line, or a
+point. There will be a peculiar type of location corresponding to each
+type of situation; and location is in each case derivative from the
+corresponding relation of situation in a way which I will proceed to
+explain.
+
+Also location in the timeless space of some time-system is a relation
+derivative from location in instantaneous spaces of the same
+time-system. Accordingly location in an instantaneous space is the
+primary idea which we have to explain. Great confusion has been
+occasioned in natural philosophy by the neglect to distinguish between
+the different types of objects, the different types of situation, the
+different types of location, and the difference between location and
+situation. It is impossible to reason accurately in the vague concerning
+objects and their positions without keeping these distinctions in view.
+An object is located in an abstractive element, when an abstractive set
+belonging to that element can be found such that each event belonging to
+that set is a situation of the object. It will be remembered that an
+abstractive element is a certain group of abstractive sets, and that
+each abstractive set is a set of events. This definition defines the
+location of an element in any type of abstractive element. In this sense
+we can talk of the existence of an object at an instant, meaning thereby
+its location in some definite moment. It may also be located in some
+spatial element of the instantaneous space of that moment.
+
+A quantity can be said to be located in an abstractive element when an
+abstractive set belonging to the element can be found such that the
+quantitative expressions of the corresponding characters of its events
+converge to the measure of the given quantity as a limit when we pass
+along the abstractive set towards its converging end.
+
+By these definitions location in elements of instantaneous spaces is
+defined. These elements occupy corresponding elements of timeless
+spaces. An object located in an element of an instantaneous space will
+also be said to be located at that moment in the timeless element of the
+timeless space which is occupied by that instantaneous element.
+
+It is not every object which can be located in a moment. An object which
+can be located in every moment of some duration will be called a
+'uniform' object throughout that duration. Ordinary physical objects
+appear to us to be uniform objects, and we habitually assume that
+scientific objects such as electrons are uniform. But some sense-objects
+certainly are not uniform. A tune is an example of a non-uniform object.
+We have perceived it as a whole in a certain duration; but the tune as a
+tune is not at any moment of that duration though one of the individual
+notes may be located there.
+
+It is possible therefore that for the existence of certain sorts of
+objects, _e.g._ electrons, minimum quanta of time are requisite. Some
+such postulate is apparently indicated by the modern quantum theory and
+it is perfectly consistent with the doctrine of objects maintained in
+these lectures.
+
+Also the instance of the distinction between the electron as the mere
+quantitative electric charge of its situation and the electron as
+standing for the ingression of an object throughout nature illustrates
+the indefinite number of types of objects which exist in nature. We can
+intellectually distinguish even subtler and subtler types of objects.
+Here I reckon subtlety as meaning seclusion from the immediate
+apprehension of sense-awareness. Evolution in the complexity of life
+means an increase in the types of objects directly sensed. Delicacy of
+sense-apprehension means perceptions of objects as distinct entities
+which are mere subtle ideas to cruder sensibilities. The phrasing of
+music is a mere abstract subtlety to the unmusical; it is a direct
+sense-apprehension to the initiated. For example, if we could imagine
+some lowly type of organic being thinking and aware of our thoughts, it
+would wonder at the abstract subtleties in which we indulge as we think
+of stones and bricks and drops of water and plants. It only knows of
+vague undifferentiated feelings in nature. It would consider us as given
+over to the play of excessively abstract intellects. But then if it
+could think, it would anticipate; and if it anticipated, it would soon
+perceive for itself.
+
+In these lectures we have been scrutinising the foundations of natural
+philosophy. We are stopping at the very point where a boundless ocean of
+enquiries opens out for our questioning.
+
+I agree that the view of Nature which I have maintained in these
+lectures is not a simple one. Nature appears as a complex system whose
+factors are dimly discerned by us. But, as I ask you, Is not this the
+very truth? Should we not distrust the jaunty assurance with which every
+age prides itself that it at last has hit upon the ultimate concepts in
+which all that happens can be formulated? The aim of science is to seek
+the simplest explanations of complex facts. We are apt to fall into the
+error of thinking that the facts are simple because simplicity is the
+goal of our quest. The guiding motto in the life of every natural
+philosopher should be, Seek simplicity and distrust it.
+
+
+
+
+CHAPTER VIII
+
+SUMMARY
+
+
+There is a general agreement that Einstein's investigations have one
+fundamental merit irrespective of any criticisms which we may feel
+inclined to pass on them. They have made us think. But when we have
+admitted so far, we are most of us faced with a distressing perplexity.
+What is it that we ought to think about? The purport of my lecture this
+afternoon will be to meet this difficulty and, so far as I am able, to
+set in a clear light the changes in the background of our scientific
+thought which are necessitated by any acceptance, however qualified, of
+Einstein's main positions. I remember that I am lecturing to the members
+of a chemical society who are not for the most part versed in advanced
+mathematics. The first point that I would urge upon you is that what
+immediately concerns you is not so much the detailed deductions of the
+new theory as this general change in the background of scientific
+conceptions which will follow from its acceptance. Of course, the
+detailed deductions are important, because unless our colleagues the
+astronomers and the physicists find these predictions to be verified we
+can neglect the theory altogether. But we may now take it as granted
+that in many striking particulars these deductions have been found to be
+in agreement with observation. Accordingly the theory has to be taken
+seriously and we are anxious to know what will be the consequences of
+its final acceptance. Furthermore during the last few weeks the
+scientific journals and the lay press have been filled with articles as
+to the nature of the crucial experiments which have been made and as to
+some of the more striking expressions of the outcome of the new theory.
+'Space caught bending' appeared on the news-sheet of a well-known
+evening paper. This rendering is a terse but not inapt translation of
+Einstein's own way of interpreting his results. I should say at once
+that I am a heretic as to this explanation and that I shall expound to
+you another explanation based upon some work of my own, an explanation
+which seems to me to be more in accordance with our scientific ideas and
+with the whole body of facts which have to be explained. We have to
+remember that a new theory must take account of the old well-attested
+facts of science just as much as of the very latest experimental results
+which have led to its production.
+
+To put ourselves in the position to assimilate and to criticise any
+change in ultimate scientific conceptions we must begin at the
+beginning. So you must bear with me if I commence by making some simple
+and obvious reflections. Let us consider three statements, (i)
+'Yesterday a man was run over on the Chelsea Embankment,' (ii)
+'Cleopatra's Needle is on the Charing Cross Embankment,' and (iii)
+'There are dark lines in the Solar Spectrum.' The first statement about
+the accident to the man is about what we may term an 'occurrence,' a
+'happening,' or an 'event.' I will use the term 'event' because it is
+the shortest. In order to specify an observed event, the place, the
+time, and character of the event are necessary. In specifying the place
+and the time you are really stating the relation of the assigned event
+to the general structure of other observed events. For example, the man
+was run over between your tea and your dinner and adjacently to a
+passing barge in the river and the traffic in the Strand. The point
+which I want to make is this: Nature is known to us in our experience as
+a complex of passing events. In this complex we discern definite mutual
+relations between component events, which we may call their relative
+positions, and these positions we express partly in terms of space and
+partly in terms of time. Also in addition to its mere relative position
+to other events, each particular event has its own peculiar character.
+In other words, nature is a structure of events and each event has its
+position in this structure and its own peculiar character or quality.
+
+Let us now examine the other two statements in the light of this general
+principle as to the meaning of nature. Take the second statement,
+'Cleopatra's Needle is on the Charing Cross Embankment.' At first sight
+we should hardly call this an event. It seems to lack the element of
+time or transitoriness. But does it? If an angel had made the remark
+some hundreds of millions of years ago, the earth was not in existence,
+twenty millions of years ago there was no Thames, eighty years ago there
+was no Thames Embankment, and when I was a small boy Cleopatra's Needle
+was not there. And now that it is there, we none of us expect it to be
+eternal. The static timeless element in the relation of Cleopatra's
+Needle to the Embankment is a pure illusion generated by the fact that
+for purposes of daily intercourse its emphasis is needless. What it
+comes to is this: Amidst the structure of events which form the medium
+within which the daily life of Londoners is passed we know how to
+identify a certain stream of events which maintain permanence of
+character, namely the character of being the situations of Cleopatra's
+Needle. Day by day and hour by hour we can find a certain chunk in the
+transitory life of nature and of that chunk we say, 'There is
+Cleopatra's Needle.' If we define the Needle in a sufficiently abstract
+manner we can say that it never changes. But a physicist who looks on
+that part of the life of nature as a dance of electrons, will tell you
+that daily it has lost some molecules and gained others, and even the
+plain man can see that it gets dirtier and is occasionally washed. Thus
+the question of change in the Needle is a mere matter of definition. The
+more abstract your definition, the more permanent the Needle. But
+whether your Needle change or be permanent, all you mean by stating that
+it is situated on the Charing Cross Embankment, is that amid the
+structure of events you know of a certain continuous limited stream of
+events, such that any chunk of that stream, during any hour, or any day,
+or any second, has the character of being the situation of Cleopatra's
+Needle.
+
+Finally, we come to the third statement, 'There are dark lines in the
+Solar Spectrum.' This is a law of nature. But what does that mean? It
+means merely this. If any event has the character of being an exhibition
+of the solar spectrum under certain assigned circumstances, it will also
+have the character of exhibiting dark lines in that spectrum.
+
+This long discussion brings us to the final conclusion that the concrete
+facts of nature are events exhibiting a certain structure in their
+mutual relations and certain characters of their own. The aim of science
+is to express the relations between their characters in terms of the
+mutual structural relations between the events thus characterised. The
+mutual structural relations between events are both spatial and
+temporal. If you think of them as merely spatial you are omitting the
+temporal element, and if you think of them as merely temporal you are
+omitting the spatial element. Thus when you think of space alone, or of
+time alone, you are dealing in abstractions, namely, you are leaving out
+an essential element in the life of nature as known to you in the
+experience of your senses. Furthermore there are different ways of
+making these abstractions which we think of as space and as time; and
+under some circumstances we adopt one way and under other circumstances
+we adopt another way. Thus there is no paradox in holding that what we
+mean by space under one set of circumstances is not what we mean by
+space under another set of circumstances. And equally what we mean by
+time under one set of circumstances is not what we mean by time under
+another set of circumstances. By saying that space and time are
+abstractions, I do not mean that they do not express for us real facts
+about nature. What I mean is that there are no spatial facts or temporal
+facts apart from physical nature, namely that space and time are merely
+ways of expressing certain truths about the relations between events.
+Also that under different circumstances there are different sets of
+truths about the universe which are naturally presented to us as
+statements about space. In such a case what a being under the one set of
+circumstances means by space will be different from that meant by a
+being under the other set of circumstances. Accordingly when we are
+comparing two observations made under different circumstances we have to
+ask 'Do the two observers mean the same thing by space and the same
+thing by time?' The modern theory of relativity has arisen because
+certain perplexities as to the concordance of certain delicate
+observations such as the motion of the earth through the ether, the
+perihelion of mercury, and the positions of the stars in the
+neighbourhood of the sun, have been solved by reference to this purely
+relative significance of space and time.
+
+I want now to recall your attention to Cleopatra's Needle, which I have
+not yet done with. As you are walking along the Embankment you suddenly
+look up and say, 'Hullo, there's the Needle.' In other words, you
+recognise it. You cannot recognise an event; because when it is gone, it
+is gone. You may observe another event of analogous character, but the
+actual chunk of the life of nature is inseparable from its unique
+occurrence. But a character of an event can be recognised. We all know
+that if we go to the Embankment near Charing Cross we shall observe an
+event having the character which we recognise as Cleopatra's Needle.
+Things which we thus recognise I call objects. An object is situated in
+those events or in that stream of events of which it expresses the
+character. There are many sorts of objects. For example, the colour
+green is an object according to the above definition. It is the purpose
+of science to trace the laws which govern the appearance of objects in
+the various events in which they are found to be situated. For this
+purpose we can mainly concentrate on two types of objects, which I will
+call material physical objects and scientific objects. A material
+physical object is an ordinary bit of matter, Cleopatra's Needle for
+example. This is a much more complicated type of object than a mere
+colour, such as the colour of the Needle. I call these simple objects,
+such as colours or sounds, sense-objects. An artist will train himself
+to attend more particularly to sense-objects where the ordinary person
+attends normally to material objects. Thus if you were walking with an
+artist, when you said 'There's Cleopatra's Needle,' perhaps he
+simultaneously exclaimed 'There's a nice bit of colour.' Yet you were
+both expressing your recognition of different component characters of
+the same event. But in science we have found out that when we know all
+about the adventures amid events of material physical objects and of
+scientific objects we have most of the relevant information which will
+enable us to predict the conditions under which we shall perceive
+sense-objects in specific situations. For example, when we know that
+there is a blazing fire (_i.e._ material and scientific objects
+undergoing various exciting adventures amid events) and opposite to it a
+mirror (which is another material object) and the positions of a man's
+face and eyes gazing into the mirror, we know that he can perceive the
+redness of the flame situated in an event behind the mirror--thus, to a
+large extent, the appearance of sense-objects is conditioned by the
+adventures of material objects. The analysis of these adventures makes
+us aware of another character of events, namely their characters as
+fields of activity which determine the subsequent events to which they
+will pass on the objects situated in them. We express these fields of
+activity in terms of gravitational, electromagnetic, or chemical forces
+and attractions. But the exact expression of the nature of these fields
+of activity forces us intellectually to acknowledge a less obvious type
+of objects as situated in events. I mean molecules and electrons. These
+objects are not recognised in isolation. We cannot well miss Cleopatra's
+Needle, if we are in its neighbourhood; but no one has seen a single
+molecule or a single electron, yet the characters of events are only
+explicable to us by expressing them in terms of these scientific
+objects. Undoubtedly molecules and electrons are abstractions. But then
+so is Cleopatra's Needle. The concrete facts are the events
+themselves--I have already explained to you that to be an abstraction
+does not mean that an entity is nothing. It merely means that its
+existence is only one factor of a more concrete element of nature. So an
+electron is abstract because you cannot wipe out the whole structure of
+events and yet retain the electron in existence. In the same way the
+grin on the cat is abstract; and the molecule is really in the event in
+the same sense as the grin is really on the cat's face. Now the more
+ultimate sciences such as Chemistry or Physics cannot express their
+ultimate laws in terms of such vague objects as the sun, the earth,
+Cleopatra's Needle, or a human body. Such objects more properly belong
+to Astronomy, to Geology, to Engineering, to Archaeology, or to Biology.
+Chemistry and Physics only deal with them as exhibiting statistical
+complexes of the effects of their more intimate laws. In a certain
+sense, they only enter into Physics and Chemistry as technological
+applications. The reason is that they are too vague. Where does
+Cleopatra's Needle begin and where does it end? Is the soot part of it?
+Is it a different object when it sheds a molecule or when its surface
+enters into chemical combination with the acid of a London fog? The
+definiteness and permanence of the Needle is nothing to the possible
+permanent definiteness of a molecule as conceived by science, and the
+permanent definiteness of a molecule in its turn yields to that of an
+electron. Thus science in its most ultimate formulation of law seeks
+objects with the most permanent definite simplicity of character and
+expresses its final laws in terms of them.
+
+Again when we seek definitely to express the relations of events which
+arise from their spatio-temporal structure, we approximate to simplicity
+by progressively diminishing the extent (both temporal and spatial) of
+the events considered. For example, the event which is the life of the
+chunk of nature which is the Needle during one minute has to the life of
+nature within a passing barge during the same minute a very complex
+spatio-temporal relation. But suppose we progressively diminish the time
+considered to a second, to a hundredth of a second, to a thousandth of a
+second, and so on. As we pass along such a series we approximate to an
+ideal simplicity of structural relations of the pairs of events
+successively considered, which ideal we call the spatial relations of
+the Needle to the barge at some instant. Even these relations are too
+complicated for us, and we consider smaller and smaller bits of the
+Needle and of the barge. Thus we finally reach the ideal of an event so
+restricted in its extension as to be without extension in space or
+extension in time. Such an event is a mere spatial point-flash of
+instantaneous duration. I call such an ideal event an 'event-particle.'
+You must not think of the world as ultimately built up of
+event-particles. That is to put the cart before the horse. The world we
+know is a continuous stream of occurrence which we can discriminate into
+finite events forming by their overlappings and containings of each
+other and separations a spatio-temporal structure. We can express the
+properties of this structure in terms of the ideal limits to routes of
+approximation, which I have termed event-particles. Accordingly
+event-particles are abstractions in their relations to the more concrete
+events. But then by this time you will have comprehended that you cannot
+analyse concrete nature without abstracting. Also I repeat, the
+abstractions of science are entities which are truly in nature, though
+they have no meaning in isolation from nature.
+
+The character of the spatio-temporal structure of events can be fully
+expressed in terms of relations between these more abstract
+event-particles. The advantage of dealing with event-particles is that
+though they are abstract and complex in respect to the finite events
+which we directly observe, they are simpler than finite events in
+respect to their mutual relations. Accordingly they express for us the
+demands of an ideal accuracy, and of an ideal simplicity in the
+exposition of relations. These event-particles are the ultimate elements
+of the four-dimensional space-time manifold which the theory of
+relativity presupposes. You will have observed that each event-particle
+is as much an instant of time as it is a point of space. I have called
+it an instantaneous point-flash. Thus in the structure of this
+space-time manifold space is not finally discriminated from time, and
+the possibility remains open for diverse modes of discrimination
+according to the diverse circumstances of observers. It is this
+possibility which makes the fundamental distinction between the new way
+of conceiving the universe and the old way. The secret of understanding
+relativity is to understand this. It is of no use rushing in with
+picturesque paradoxes, such as 'Space caught bending,' if you have not
+mastered this fundamental conception which underlies the whole theory.
+When I say that it underlies the whole theory, I mean that in my opinion
+it ought to underlie it, though I may confess some doubts as to how far
+all expositions of the theory have really understood its implications
+and its premises.
+
+Our measurements when they are expressed in terms of an ideal accuracy
+are measurements which express properties of the space-time manifold.
+Now there are measurements of different sorts. You can measure lengths,
+or angles, or areas, or volumes, or times. There are also other sorts of
+measures such as measurements of intensity of illumination, but I will
+disregard these for the moment and will confine attention to those
+measurements which particularly interest us as being measurements of
+space or of time. It is easy to see that four such measurements of the
+proper characters are necessary to determine the position of an
+event-particle in the space-time manifold in its relation to the rest of
+the manifold. For example, in a rectangular field you start from one
+corner at a given time, you measure a definite distance along one side,
+you then strike out into the field at right angles, and then measure a
+definite distance parallel to the other pair of sides, you then rise
+vertically a definite height and take the time. At the point and at the
+time which you thus reach there is occurring a definite instantaneous
+point-flash of nature. In other words, your four measurements have
+determined a definite event-particle belonging to the four-dimension
+space-time manifold. These measurements have appeared to be very simple
+to the land-surveyor and raise in his mind no philosophic difficulties.
+But suppose there are beings on Mars sufficiently advanced in
+scientific invention to be able to watch in detail the operations of
+this survey on earth. Suppose that they construe the operations of the
+English land-surveyors in reference to the space natural to a being on
+Mars, namely a Martio-centric space in which that planet is fixed. The
+earth is moving relatively to Mars and is rotating. To the beings on
+Mars the operations, construed in this fashion, effect measurements of
+the greatest complication. Furthermore, according to the relativistic
+doctrine, the operation of time-measurement on earth will not correspond
+quite exactly to any time-measurement on Mars.
+
+I have discussed this example in order to make you realise that in
+thinking of the possibilities of measurement in the space-time manifold,
+we must not confine ourselves merely to those minor variations which
+might seem natural to human beings on the earth. Let us make therefore
+the general statement that four measurements, respectively of
+independent types (such as measurements of lengths in three directions
+and a time), can be found such that a definite event-particle is
+determined by them in its relations to other parts of the manifold.
+
+If (p₁, p₂, p₃, p₄) be a set of measurements of this system, then the
+event-particle which is thus determined will be said to have p₁, p₂, p₃,
+p₄ as its co-ordinates in this system of measurement. Suppose that we
+name it the p-system of measurement. Then in the same p-system by
+properly varying (p₁, p₂, p₃, p₄) every event-particle that has been, or
+will be, or instantaneously is now, can be indicated. Furthermore,
+according to any system of measurement that is natural to us, three of
+the co-ordinates will be measurements of space and one will be a
+measurement of time. Let us always take the last co-ordinate to
+represent the time-measurement. Then we should naturally say that (p₁,
+p₂, p₃) determined a point in space and that the event-particle happened
+at that point at the time p₄. But we must not make the mistake of
+thinking that there is a space in addition to the space-time manifold.
+That manifold is all that there is for the determination of the meaning
+of space and time. We have got to determine the meaning of a space-point
+in terms of the event-particles of the four-dimensional manifold. There
+is only one way to do this. Note that if we vary the time and take times
+with the same three space co-ordinates, then the event-particles, thus
+indicated, are all at the same point. But seeing that there is nothing
+else except the event-particles, this can only mean that the point (p₁,
+p₂, p₃) of the space in the p-system is merely the collection of
+event-particles (p₁, p₂, p₃, [p₄]), where p₄ is varied and (p₁, p₂, p₃)
+is kept fixed. It is rather disconcerting to find that a point in space
+is not a simple entity; but it is a conclusion which follows immediately
+from the relative theory of space.
+
+Furthermore the inhabitant of Mars determines event-particles by another
+system of measurements. Call his system the q-system. According to him
+(q₁, q₂, q₃, q₄) determines an event-particle, and (q₁, q₂, q₃)
+determines a point and q₄ a time. But the collection of event-particles
+which he thinks of as a point is entirely different from any such
+collection which the man on earth thinks of as a point. Thus the q-space
+for the man on Mars is quite different from the p-space for the
+land-surveyor on earth.
+
+So far in speaking of space we have been talking of the timeless space
+of physical science, namely, of our concept of eternal space in which
+the world adventures. But the space which we see as we look about is
+instantaneous space. Thus if our natural perceptions are adjustable to
+the p-system of measurements we see instantaneously all the
+event-particles at some definite time p₄, and observe a succession
+of such spaces as time moves on. The timeless space is achieved by
+stringing together all these instantaneous spaces. The points of an
+instantaneous space are event-particles, and the points of an eternal
+space are strings of event-particles occurring in succession. But the
+man on Mars will never perceive the same instantaneous spaces as the man
+on the earth. This system of instantaneous spaces will cut across the
+earth-man's system. For the earth-man there is one instantaneous space
+which is the instantaneous present, there are the past spaces and the
+future spaces. But the present space of the man on Mars cuts across the
+present space of the man on the earth. So that of the event-particles
+which the earth-man thinks of as happening now in the present, the man
+on Mars thinks that some are already past and are ancient history, that
+others are in the future, and others are in the immediate present. This
+break-down in the neat conception of a past, a present, and a future is
+a serious paradox. I call two event-particles which on some or other
+system of measurement are in the same instantaneous space 'co-present'
+event-particles. Then it is possible that A and B may be co-present,
+and that A and C may be co-present, but that B and C may not be
+co-present. For example, at some inconceivable distance from us there
+are events co-present with us now and also co-present with the birth of
+Queen Victoria. If A and B are co-present there will be some systems
+in which A precedes B and some in which B precedes A. Also there
+can be no velocity quick enough to carry a material particle from A to
+B or from B to A. These different measure-systems with their
+divergences of time-reckoning are puzzling, and to some extent affront
+our common sense. It is not the usual way in which we think of the
+Universe. We think of one necessary time-system and one necessary space.
+According to the new theory, there are an indefinite number of
+discordant time-series and an indefinite number of distinct spaces. Any
+correlated pair, a time-system and a space-system, will do in which to
+fit our description of the Universe. We find that under given conditions
+our measurements are necessarily made in some one pair which together
+form our natural measure-system. The difficulty as to discordant
+time-systems is partly solved by distinguishing between what I call the
+creative advance of nature, which is not properly serial at all, and any
+one time series. We habitually muddle together this creative advance,
+which we experience and know as the perpetual transition of nature into
+novelty, with the single-time series which we naturally employ for
+measurement. The various time-series each measure some aspect of the
+creative advance, and the whole bundle of them express all the
+properties of this advance which are measurable. The reason why we have
+not previously noted this difference of time-series is the very small
+difference of properties between any two such series. Any observable
+phenomena due to this cause depend on the square of the ratio of any
+velocity entering into the observation to the velocity of light. Now
+light takes about fifty minutes to get round the earth's orbit; and the
+earth takes rather more than 17,531 half-hours to do the same. Hence all
+the effects due to this motion are of the order of the ratio of one to
+the square of 10,000. Accordingly an earth-man and a sun-man have only
+neglected effects whose quantitative magnitudes all contain the factor
+1/10⁸. Evidently such effects can only be noted by means of the most
+refined observations. They have been observed however. Suppose we
+compare two observations on the velocity of light made with the same
+apparatus as we turn it through a right angle. The velocity of the earth
+relatively to the sun is in one direction, the velocity of light
+relatively to the ether should be the same in all directions. Hence if
+space when we take the ether as at rest means the same thing as space
+when we take the earth as at rest, we ought to find that the velocity of
+light relatively to the earth varies according to the direction from
+which it comes.
+
+These observations on earth constitute the basic principle of the famous
+experiments designed to detect the motion of the earth through the
+ether. You all know that, quite unexpectedly, they gave a null result.
+This is completely explained by the fact that, the space-system and the
+time-system which we are using are in certain minute ways different from
+the space and the time relatively to the sun or relatively to any other
+body with respect to which it is moving.
+
+All this discussion as to the nature of time and space has lifted above
+our horizon a great difficulty which affects the formulation of all the
+ultimate laws of physics--for example, the laws of the electromagnetic
+field, and the law of gravitation. Let us take the law of gravitation
+as an example. Its formulation is as follows: Two material bodies
+attract each other with a force proportional to the product of their
+masses and inversely proportional to the square of their distances.
+In this statement the bodies are supposed to be small enough to be
+treated as material particles in relation to their distances; and we
+need not bother further about that minor point. The difficulty to which
+I want to draw your attention is this: In the formulation of the law one
+definite time and one definite space are presupposed. The two masses are
+assumed to be in simultaneous positions.
+
+But what is simultaneous in one time-system may not be simultaneous in
+another time-system. So according to our new views the law is in this
+respect not formulated so as to have any exact meaning. Furthermore an
+analogous difficulty arises over the question of distance. The distance
+between two instantaneous positions, _i.e._ between two event-particles,
+is different in different space-systems. What space is to be chosen?
+Thus again the law lacks precise formulation, if relativity is accepted.
+Our problem is to seek a fresh interpretation of the law of gravity in
+which these difficulties are evaded. In the first place we must avoid
+the abstractions of space and time in the formulation of our fundamental
+ideas and must recur to the ultimate facts of nature, namely to events.
+Also in order to find the ideal simplicity of expressions of the
+relations between events, we restrict ourselves to event-particles. Thus
+the life of a material particle is its adventure amid a track of
+event-particles strung out as a continuous series or path in the
+four-dimensional space-time manifold. These event-particles are the
+various situations of the material particle. We usually express this
+fact by adopting our natural space-time system and by talking of the
+path in space of the material particle as it exists at successive
+instants of time.
+
+We have to ask ourselves what are the laws of nature which lead the
+material particle to adopt just this path among event-particles and no
+other. Think of the path as a whole. What characteristic has that path
+got which would not be shared by any other slightly varied path? We are
+asking for more than a law of gravity. We want laws of motion and a
+general idea of the way to formulate the effects of physical forces.
+
+In order to answer our question we put the idea of the attracting masses
+in the background and concentrate attention on the field of activity of
+the events in the neighbourhood of the path. In so doing we are acting
+in conformity with the whole trend of scientific thought during the last
+hundred years, which has more and more concentrated attention on the
+field of force as the immediate agent in directing motion, to the
+exclusion of the consideration of the immediate mutual influence between
+two distant bodies. We have got to find the way of expressing the field
+of activity of events in the neighbourhood of some definite
+event-particle E of the four-dimensional manifold. I bring in a
+fundamental physical idea which I call the 'impetus' to express this
+physical field. The event-particle E is related to any neighbouring
+event-particle P by an element of impetus. The assemblage of all the
+elements of impetus relating E to the assemblage of event-particles in
+the neighbourhood of E expresses the character of the field of
+activity in the neighbourhood of E. Where I differ from Einstein is
+that he conceives this quantity which I call the impetus as merely
+expressing the characters of the space and time to be adopted and thus
+ends by talking of the gravitational field expressing a curvature in the
+space-time manifold. I cannot attach any clear conception to his
+interpretation of space and time. My formulae differ slightly from his,
+though they agree in those instances where his results have been
+verified. I need hardly say that in this particular of the formulation
+of the law of gravitation I have drawn on the general method of
+procedure which constitutes his great discovery.
+
+Einstein showed how to express the characters of the assemblage of
+elements of impetus of the field surrounding an event-particle E in
+terms of ten quantities which I will call J_{11}, J_{12}
+(=J_{21}), J_{22}, J_{23}(=J_{32}), etc. It will be noted that
+there are four spatio-temporal measurements relating E to its
+neighbour P, and that there are ten pairs of such measurements if we
+are allowed to take any one measurement twice over to make one such
+pair. The ten J's depend merely on the position of E in the
+four-dimensional manifold, and the element of impetus between E and
+P can be expressed in terms of the ten J's and the ten pairs of the
+four spatio-temporal measurements relating E and P. The numerical
+values of the J's will depend on the system of measurement adopted,
+but are so adjusted to each particular system that the same value is
+obtained for the element of impetus between E and P, whatever be the
+system of measurement adopted. This fact is expressed by saying that the
+ten J's form a 'tensor.' It is not going too far to say that the
+announcement that physicists would have in future to study the theory of
+tensors created a veritable panic among them when the verification of
+Einstein's predictions was first announced.
+
+The ten J's at any event-particle E can be expressed in terms of two
+functions which I call the potential and the 'associate-potential' at
+E. The potential is practically what is meant by the ordinary
+gravitation potential, when we express ourselves in terms of the
+Euclidean space in reference to which the attracting mass is at rest.
+The associate-potential is defined by the modification of substituting
+the direct distance for the inverse distance in the definition of the
+potential, and its calculation can easily be made to depend on that of
+the old-fashioned potential. Thus the calculation of the J's--the
+coefficients of impetus, as I will call them--does not involve anything
+very revolutionary in the mathematical knowledge of physicists. We now
+return to the path of the attracted particle. We add up all the elements
+of impetus in the whole path, and obtain thereby what I call the
+'integral impetus.' The characteristic of the actual path as compared
+with neighbouring alternative paths is that in the actual paths the
+integral impetus would neither gain nor lose, if the particle wobbled
+out of it into a small extremely near alternative path. Mathematicians
+would express this by saying, that the integral impetus is stationary
+for an infinitesimal displacement. In this statement of the law of
+motion I have neglected the existence of other forces. But that would
+lead me too far afield.
+
+The electromagnetic theory has to be modified to allow for the presence
+of a gravitational field. Thus Einstein's investigations lead to the
+first discovery of any relation between gravity and other physical
+phenomena. In the form in which I have put this modification, we deduce
+Einstein's fundamental principle, as to the motion of light along its
+rays, as a first approximation which is absolutely true for infinitely
+short waves. Einstein's principle, thus partially verified, stated in my
+language is that a ray of light always follows a path such that the
+integral impetus along it is zero. This involves that every element of
+impetus along it is zero.
+
+In conclusion, I must apologise. In the first place I have considerably
+toned down the various exciting peculiarities of the original theory and
+have reduced it to a greater conformity with the older physics. I do not
+allow that physical phenomena are due to oddities of space. Also I have
+added to the dullness of the lecture by my respect for the audience. You
+would have enjoyed a more popular lecture with illustrations of
+delightful paradoxes. But I know also that you are serious students who
+are here because you really want to know how the new theories may affect
+your scientific researches.
+
+
+
+
+CHAPTER IX
+
+THE ULTIMATE PHYSICAL CONCEPTS
+
+
+The second chapter of this book lays down the first principle to be
+guarded in framing our physical concept. We must avoid vicious
+bifurcation. Nature is nothing else than the deliverance of
+sense-awareness. We have no principles whatever to tell us what could
+stimulate mind towards sense-awareness. Our sole task is to exhibit in
+one system the characters and inter-relations of all that is observed.
+Our attitude towards nature is purely 'behaviouristic,' so far as
+concerns the formulation of physical concepts.
+
+Our knowledge of nature is an experience of activity (or passage). The
+things previously observed are active entities, the 'events.' They are
+chunks in the life of nature. These events have to each other relations
+which in our knowledge differentiate themselves into space-relations and
+time-relations. But this differentiation between space and time, though
+inherent in nature, is comparatively superficial; and space and time are
+each partial expressions of one fundamental relation between events
+which is neither spatial nor temporal. This relation I call 'extension.'
+The relation of 'extending over' is the relation of 'including,' either
+in a spatial or in a temporal sense, or in both. But the mere
+'inclusion' is more fundamental than either alternative and does not
+require any spatio-temporal differentiation. In respect to extension two
+events are mutually related so that either (i) one includes the other,
+or (ii) one overlaps the other without complete inclusion, or (iii)
+they are entirely separate. But great care is required in the
+definition of spatial and temporal elements from this basis in order to
+avoid tacit limitations really depending on undefined relations and
+properties.
+
+Such fallacies can be avoided by taking account of two elements in our
+experience, namely, (i) our observational 'present,' and (ii) our
+'percipient event.'
+
+Our observational 'present' is what I call a 'duration.' It is the whole
+of nature apprehended in our immediate observation. It has therefore the
+nature of an event, but possesses a peculiar completeness which marks
+out such durations as a special type of events inherent in nature. A
+duration is not instantaneous. It is all that there is of nature with
+certain temporal limitations. In contradistinction to other events a
+duration will be called infinite and the other events are finite[10]. In
+our knowledge of a duration we distinguish (i) certain included events
+which are particularly discriminated as to their peculiar
+individualities, and (ii) the remaining included events which are only
+known as necessarily in being by reason of their relations to the
+discriminated events and to the whole duration. The duration as a whole
+is signified[11] by that quality of relatedness (in respect to
+extension) possessed by the part which is immediately under observation;
+namely, by the fact that there is essentially a beyond to whatever is
+observed. I mean by this that every event is known as being related to
+other events which it does not include. This fact, that every event is
+known as possessing the quality of exclusion, shows that exclusion is as
+positive a relation as inclusion. There are of course no merely
+negative relations in nature, and exclusion is not the mere negative of
+inclusion, though the two relations are contraries. Both relations are
+concerned solely with events, and exclusion is capable of logical
+definition in terms of inclusion.
+
+[10] Cf. note on 'significance,' pp. 197, 198.
+
+[11] Cf. Ch. III, pp. 51 et seq.
+
+Perhaps the most obvious exhibition of significance is to be found in
+our knowledge of the geometrical character of events inside an opaque
+material object. For example we know that an opaque sphere has a centre.
+This knowledge has nothing to do with the material; the sphere may be a
+solid uniform billiard ball or a hollow lawn-tennis ball. Such knowledge
+is essentially the product of significance, since the general character
+of the external discriminated events has informed us that there are
+events within the sphere and has also informed us of their geometrical
+structure.
+
+Some criticisms on 'The Principles of Natural Knowledge' show that
+difficulty has been found in apprehending durations as real
+stratifications of nature. I think that this hesitation arises from the
+unconscious influence of the vicious principle of bifurcation, so deeply
+embedded in modern philosophical thought. We observe nature as extended
+in an immediate present which is simultaneous but not instantaneous, and
+therefore the whole which is immediately discerned or signified as an
+inter-related system forms a stratification of nature which is a
+physical fact. This conclusion immediately follows unless we admit
+bifurcation in the form of the principle of psychic additions, here
+rejected.
+
+Our 'percipient event' is that event included in our observational
+present which we distinguish as being in some peculiar way our
+standpoint for perception. It is roughly speaking that event which is
+our bodily life within the present duration. The theory of perception
+as evolved by medical psychology is based on significance. The distant
+situation of a perceived object is merely known to us as signified by
+our bodily state, _i.e._ by our percipient event. In fact perception
+requires sense-awareness of the significations of our percipient event
+together with sense-awareness of a peculiar relation (situation) between
+certain objects and the events thus signified. Our percipient event is
+saved by being the whole of nature by this fact of its significations.
+This is the meaning of calling the percipient event our standpoint for
+perception. The course of a ray of light is only derivatively connected
+with perception. What we do perceive are objects as related to events
+signified by the bodily states excited by the ray. These signified
+events (as is the case of images seen behind a mirror) may have very
+little to do with the actual course of the ray. In the course of
+evolution those animals have survived whose sense-awareness is
+concentrated on those significations of their bodily states which are on
+the average important for their welfare. The whole world of events is
+signified, but there are some which exact the death penalty for
+inattention.
+
+The percipient event is always here and now in the associated present
+duration. It has, what may be called, an absolute position in that
+duration. Thus one definite duration is associated with a definite
+percipient event, and we are thus aware of a peculiar relation which
+finite events can bear to durations. I call this relation 'cogredience.'
+The notion of rest is derivative from that of cogredience, and the
+notion of motion is derivative from that of inclusion within a duration
+without cogredience with it. In fact motion is a relation (of varying
+character) between an observed event and an observed duration, and
+cogredience is the most simple character or subspecies of motion. To sum
+up, a duration and a percipient event are essentially involved in the
+general character of each observation of nature, and the percipient
+event is cogredient with the duration.
+
+Our knowledge of the peculiar characters of different events depends
+upon our power of comparison. I call the exercise of this factor in our
+knowledge 'recognition,' and the requisite sense-awareness of the
+comparable characters I call 'sense-recognition.' Recognition and
+abstraction essentially involve each other. Each of them exhibits an
+entity for knowledge which is less than the concrete fact, but is a real
+factor in that fact. The most concrete fact capable of separate
+discrimination is the event. We cannot abstract without recognition, and
+we cannot recognise without abstraction. Perception involves
+apprehension of the event and recognition of the factors of its
+character.
+
+The things recognised are what I call 'objects.' In this general sense
+of the term the relation of extension is itself an object. In practice
+however I restrict the term to those objects which can in some sense or
+other be said to have a situation in an event; namely, in the phrase
+'There it is again' I restrict the 'there' to be the indication of a
+special event which is the situation of the object. Even so, there are
+different types of objects, and statements which are true of objects of
+one type are not in general true of objects of other types. The objects
+with which we are here concerned in the formulation of physical laws are
+material objects, such as bits of matter, molecules and electrons. An
+object of one of these types has relations to events other than those
+belonging to the stream of its situations. The fact of its situations
+within this stream has impressed on all other events certain
+modifications of their characters. In truth the object in its
+completeness may be conceived as a specific set of correlated
+modifications of the characters of all events, with the property that
+these modifications attain to a certain focal property for those events
+which belong to the stream of its situations. The total assemblage of
+the modifications of the characters of events due to the existence of an
+object in a stream of situations is what I call the 'physical field' due
+to the object. But the object cannot really be separated from its field.
+The object is in fact nothing else than the systematically adjusted set
+of modifications of the field. The conventional limitation of the object
+to the focal stream of events in which it is said to be 'situated' is
+convenient for some purposes, but it obscures the ultimate fact of
+nature. From this point of view the antithesis between action at a
+distance and action by transmission is meaningless. The doctrine of this
+paragraph is nothing else than another way of expressing the
+unresolvable multiple relation of an object to events.
+
+A complete time-system is formed by any one family of parallel
+durations. Two durations are parallel if either (i) one includes the
+other, or (ii) they overlap so as to include a third duration common to
+both, or (iii) are entirely separate. The excluded case is that of two
+durations overlapping so as to include in common an aggregate of finite
+events but including in common no other complete duration. The
+recognition of the fact of an indefinite number of families of parallel
+durations is what differentiates the concept of nature here put forward
+from the older orthodox concept of the essentially unique time-systems.
+Its divergence from Einstein's concept of nature will be briefly
+indicated later.
+
+The instantaneous spaces of a given time-system are the ideal
+(non-existent) durations of zero temporal thickness indicated by routes
+of approximation along series formed by durations of the associated
+family. Each such instantaneous space represents the ideal of nature at
+an instant and is also a moment of time. Each time-system thus possesses
+an aggregate of moments belonging to it alone. Each event-particle lies
+in one and only one moment of a given time-system. An event-particle has
+three characters[12]: (i) its extrinsic character which is its character
+as a definite route of convergence among events, (ii) its intrinsic
+character which is the peculiar quality of nature in its neighbourhood,
+namely, the character of the physical field in the neighbourhood, and
+(iii) its position.
+
+[12] Cf. pp. 82 et seq.
+
+The position of an event-particle arises from the aggregate of moments
+(no two of the same family) in which it lies. We fix our attention on
+one of these moments which is approximated to by the short duration of
+our immediate experience, and we express position as the position in
+this moment. But the event-particle receives its position in moment M
+in virtue of the whole aggregate of other moments M{'}, M{''}, etc.,
+in which it also lies. The differentiation of M into a geometry of
+event-particles (instantaneous points) expresses the differentiation of
+M by its intersections with moments of alien time-systems. In this way
+planes and straight lines and event-particles themselves find their
+being. Also the parallelism of planes and straight lines arises from the
+parallelism of the moments of one and the same time-system intersecting
+M. Similarly the order of parallel planes and of event-particles on
+straight lines arises from the time-order of these intersecting moments.
+The explanation is not given here[13]. It is sufficient now merely to
+mention the sources from which the whole of geometry receives its
+physical explanation.
+
+[13] Cf. _Principles of Natural Knowledge_, and previous chapters of the
+present work.
+
+The correlation of the various momentary spaces of one time-system is
+achieved by the relation of cogredience. Evidently motion in an
+instantaneous space is unmeaning. Motion expresses a comparison between
+position in one instantaneous space with positions in other
+instantaneous spaces of the same time-system. Cogredience yields the
+simplest outcome of such comparison, namely, rest.
+
+Motion and rest are immediately observed facts. They are relative in the
+sense that they depend on the time-system which is fundamental for the
+observation. A string of event-particles whose successive occupation
+means rest in the given time-system forms a timeless point in the
+timeless space of that time-system. In this way each time-system
+possesses its own permanent timeless space peculiar to it alone, and
+each such space is composed of timeless points which belong to that
+time-system and to no other. The paradoxes of relativity arise from
+neglecting the fact that different assumptions as to rest involve the
+expression of the facts of physical science in terms of radically
+different spaces and times, in which points and moments have different
+meanings.
+
+The source of order has already been indicated and that of congruence is
+now found. It depends on motion. From cogredience, perpendicularity
+arises; and from perpendicularity in conjunction with the reciprocal
+symmetry between the relations of any two time-systems congruence both
+in time and space is completely defined (cf. _loc. cit._).
+
+The resulting formulae are those for the electromagnetic theory of
+relativity, or, as it is now termed, the restricted theory. But there is
+this vital difference: the critical velocity c which occurs in these
+formulae has now no connexion whatever with light or with any other fact
+of the physical field (in distinction from the extensional structure of
+events). It simply marks the fact that our congruence determination
+embraces both times and spaces in one universal system, and therefore if
+two arbitrary units are chosen, one for all spaces and one for all
+times, their ratio will be a velocity which is a fundamental property of
+nature expressing the fact that times and spaces are really comparable.
+
+The physical properties of nature are expressed in terms of material
+objects (electrons, etc.). The physical character of an event arises
+from the fact that it belongs to the field of the whole complex of such
+objects. From another point of view we can say that these objects are
+nothing else than our way of expressing the mutual correlation of the
+physical characters of events.
+
+The spatio-temporal measurableness of nature arises from (i) the
+relation of extension between events, and (ii) the stratified character
+of nature arising from each of the alternative time-systems, and (iii)
+rest and motion, as exhibited in the relations of finite events to
+time-systems. None of these sources of measurement depend on the
+physical characters of finite events as exhibited by the situated
+objects. They are completely signified for events whose physical
+characters are unknown. Thus the spatio-temporal measurements are
+independent of the objectival physical characters. Furthermore the
+character of our knowledge of a whole duration, which is essentially
+derived from the significance of the part within the immediate field of
+discrimination, constructs it for us as a uniform whole independent, so
+far as its extension is concerned, of the unobserved characters of
+remote events. Namely, there is a definite whole of nature,
+simultaneously now present, whatever may be the character of its remote
+events. This consideration reinforces the previous conclusion. This
+conclusion leads to the assertion of the essential uniformity of the
+momentary spaces of the various time-systems, and thence to the
+uniformity of the timeless spaces of which there is one to each
+time-system.
+
+The analysis of the general character of observed nature set forth above
+affords explanations of various fundamental observational facts: (α) It
+explains the differentiation of the one quality of extension into time
+and space. (β) It gives a meaning to the observed facts of geometrical
+and temporal position, of geometrical and temporal order, and of
+geometrical straightness and planeness. (γ) It selects one definite
+system of congruence embracing both space and time, and thus explains
+the concordance as to measurement which is in practice attained. (δ) It
+explains (consistently with the theory of relativity) the observed
+phenomena of rotation, _e.g._ Foucault's pendulum, the equatorial bulge
+of the earth, the fixed senses of rotation of cyclones and anticyclones,
+and the gyro-compass. It does this by its admission of definite
+stratifications of nature which are disclosed by the very character of
+our knowledge of it. (ε) Its explanations of motion are more
+fundamental than those expressed in (δ); for it explains what is meant
+by motion itself. The observed motion of an extended object is the
+relation of its various situations to the stratification of nature
+expressed by the time-system fundamental to the observation. This motion
+expresses a real relation of the object to the rest of nature. The
+quantitative expression of this relation will vary according to the
+time-system selected for its expression.
+
+This theory accords no peculiar character to light beyond that accorded
+to other physical phenomena such as sound. There is no ground for such a
+differentiation. Some objects we know by sight only, and other objects
+we know by sound only, and other objects we observe neither by light nor
+by sound but by touch or smell or otherwise. The velocity of light
+varies according to its medium and so does that of sound. Light moves in
+curved paths under certain conditions and so does sound. Both light and
+sound are waves of disturbance in the physical characters of events; and
+(as has been stated above, p. 188) the actual course of the light is of
+no more importance for perception than is the actual course of the
+sound. To base the whole philosophy of nature upon light is a baseless
+assumption. The Michelson-Morley and analogous experiments show that
+within the limits of our inexactitude of observation the velocity of
+light is an approximation to the critical velocity 'c' which expresses
+the relation between our space and time units. It is provable that the
+assumption as to light by which these experiments and the influence of
+the gravitational field on the light-rays are explained is deducible _as
+an approximation_ from the equations of the electromagnetic field. This
+completely disposes of any necessity for differentiating light from
+other physical phenomena as possessing any peculiar fundamental
+character.
+
+It is to be observed that the measurement of extended nature by means of
+extended objects is meaningless apart from some observed fact of
+simultaneity inherent in nature and not merely a play of thought.
+Otherwise there is no meaning to the concept of one presentation of your
+extended measuring rod AB. Why not AB′ where B′ is the end B
+five minutes later? Measurement presupposes for its possibility nature
+as a simultaneity, and an observed object present then and present now.
+In other words, measurement of extended nature requires some inherent
+character in nature affording a rule of presentation of events.
+Furthermore congruence cannot be defined by the permanence of the
+measuring rod. The permanence is itself meaningless apart from some
+immediate judgment of self-congruence. Otherwise how is an elastic
+string differentiated from a rigid measuring rod? Each remains the same
+self-identical object. Why is one a possible measuring rod and the other
+not so? The meaning of congruence lies beyond the self-identity of the
+object. In other words measurement presupposes the measurable, and the
+theory of the measurable is the theory of congruence.
+
+Furthermore the admission of stratifications of nature bears on the
+formulation of the laws of nature. It has been laid down that these laws
+are to be expressed in differential equations which, as expressed in any
+general system of measurement, should bear no reference to any other
+particular measure-system. This requirement is purely arbitrary. For a
+measure-system measures something inherent in nature; otherwise it has
+no connexion with nature at all. And that something which is measured
+by a particular measure-system may have a special relation to the
+phenomenon whose law is being formulated. For example the gravitational
+field due to a material object at rest in a certain time-system may be
+expected to exhibit in its formulation particular reference to spatial
+and temporal quantities of that time-system. The field can of course be
+expressed in any measure-systems, but the particular reference will
+remain as the simple physical explanation.
+
+
+NOTE: ON THE GREEK CONCEPT OF A POINT
+
+The preceding pages had been passed for press before I had the pleasure
+of seeing Sir T. L. Heath's _Euclid in Greek_[14]. In the original
+Euclid's first definition is
+
+    σημειον εστιν, ου μερος ουθεν.
+
+I have quoted it on p. 86 in the expanded form taught to me in
+childhood, 'without parts and without magnitude.' I should have
+consulted Heath's English edition--a classic from the moment of its
+issue--before committing myself to a statement about Euclid. This is
+however a trivial correction not affecting sense and not worth a note. I
+wish here to draw attention to Heath's own note to this definition in
+his _Euclid in Greek_. He summarises Greek thought on the nature of a
+point, from the Pythagoreans, through Plato and Aristotle, to Euclid. My
+analysis of the requisite character of a point on pp. 89 and 90 is in
+complete agreement with the outcome of the Greek discussion.
+
+[14] Camb. Univ. Press, 1920.
+
+
+NOTE: ON SIGNIFICANCE AND INFINITE EVENTS
+
+The theory of significance has been expanded and made more definite in
+the present volume. It had already been introduced in the _Principles of
+Natural Knowledge_ (cf. subarticles 3.3 to 3.8 and 16.1, 16.2, 19.4, and
+articles 20, 21). In reading over the proofs of the present volume, I
+come to the conclusion that in the light of this development my
+limitation of infinite events to durations is untenable. This limitation
+is stated in article 33 of the _Principles_ and at the beginning of
+Chapter IV (p. 74) of this book. There is not only a significance of the
+discerned events embracing the whole present duration, but there is a
+significance of a cogredient event involving its extension through a
+whole time-system backwards and forwards. In other words the essential
+'beyond' in nature is a definite beyond in time as well as in space [cf.
+pp. 53, 194]. This follows from my whole thesis as to the assimilation
+of time and space and their origin in extension. It also has the same
+basis in the analysis of the character of our knowledge of nature. It
+follows from this admission that it is possible to define point-tracks
+[_i.e._ the points of timeless spaces] as abstractive elements. This is
+a great improvement as restoring the balance between moments and points.
+I still hold however to the statement in subarticle 35.4 of the
+_Principles_ that the intersection of a pair of non-parallel durations
+does not present itself to us as one event. This correction does not
+affect any of the subsequent reasoning in the two books.
+
+I may take this opportunity of pointing out that the 'stationary events'
+of article 57 of the _Principles_ are merely cogredient events got at
+from an abstract mathematical point of view.
+
+
+
+
+INDEX
+
+_In the case of terms of frequent occurrence, only those occurrences are
+indexed which are of peculiar importance for the elucidation of
+meaning._
+
+  A [_or_ an], 11
+
+  Abraham, 105
+
+  Absolute position, 105, 106, 114, 188
+
+  Abstraction, 33, 37, 168, 171, 173;
+    extensive, 65, 79, 85
+
+  Abstractive element, 84;
+    set, 61, 79
+
+  Action at a distance, 159, 190
+
+  Action by transmission, 159, 190
+
+  Active conditions, 158
+
+  Activity, field of, 170, 181
+
+  Adjunction, 101
+
+  Aggregate, 23
+
+  Alexander, Prof., viii
+
+  Alexandria, 71
+
+  Alfred the Great, 137
+
+  Anticipation, 69
+
+  Anti-prime, 88
+
+  Apparent nature, 31, 39
+
+  Area, 99;
+    momental, 103;
+    vagrant, 103
+
+  Aristotelian logic, 150
+
+  Aristotle, 16, 17, 18, 24, 197
+
+  Associate-potential, 183
+
+  Atom, 17
+
+  Attribute, 21, 26, 150
+
+  Awareness, 3
+
+  Axiom, 36, 121
+
+  Axioms of congruence, 128 et seqq.
+
+
+  Bacon, Francis, 78
+
+  Behaviouristic, 185
+
+  Bergson, 54
+
+  Berkeley, 28
+
+  Between, 64
+
+  Beyond, 186, 198
+
+  Bifurcation, vi, 30, 185, 187
+
+  Boundary, 100;
+    moment, 63;
+    particle, 100
+
+  Broad, C. D., viii
+
+
+  Calculation, formula of, 45, 158
+
+  Cambridge, 97
+
+  Causal nature, 31, 39
+
+  Causation, 31, 146
+
+  Centrifugal force, 138
+
+  Change, uniformity of, 140
+
+  Character, extrinsic, 82, 89, 90, 113, 191;
+    intrinsic, 80, 82, 90, 113, 191
+
+  Charge, 160
+
+  Closure of nature, 4
+
+  Coefficient of drag, 133
+
+  Coefficients of impetus, 183
+
+  Cogredience, 110, 188
+
+  Coherence, 29
+
+  Comparison, 124, 125, 143, 189
+
+  Complex, 13
+
+  Conceptual nature, 45;
+    space, 96
+
+  Concrete facts, 167, 171, 189
+
+  Conditioning events, 152
+
+  Conditions, active, 158
+
+  Congruence, 65, 96, 118, 120, 127, 196
+
+  Continuity, 157;
+    Dedekindian, 102;
+    of events, 76;
+    of nature, 59, 76
+
+  Convention, 121
+
+  Convergence, 62, 79;
+    law of, 82
+
+  Conveyance, 154, 155
+
+  Co-present, 177
+
+  Covering, 83
+
+  Creative advance, 178
+
+  Critical velocity, 193, 195
+
+  Curvature of space-time, 182
+
+  Cyclone, 194
+
+
+  Dedekindian continuity, 102
+
+  Definite, 53, 194, 198
+
+  Delusions, 31, 38
+
+  Delusive perceptual object, 153
+
+  Demarcation of events, 144
+
+  Demonstrative phrase, 6
+
+  Descriptive phrase, 6, 10
+
+  Differential equations, 196
+
+  Discrimination, 14, 50, 144
+
+  Diversification of nature, 15
+
+  Duddington, Mrs, 47
+
+  Duration, 37, 53, 55, 186
+
+  Durations, families of, 59, 73, 190
+
+  Dynamical axes, 138
+
+
+  Einstein, vii, 102, 131, 164, 165, 181, 182, 183, 184, 191
+
+  Electromagnetic field, 179
+
+  Electron, 30, 146, 158, 171
+
+  Element, 17;
+    abstractive, 84
+
+  Elliptical phraseology, 7
+
+  Empty space, 145
+
+  Entity, 5, 13
+
+  Equal in abstractive force, 83
+
+  Error, 68
+
+  Ether, 18, 78, 160;
+    material, 78;
+    of events, 78
+
+  Euclid, 85, 94, 197
+
+  Euler, 140
+
+  Event, 15, 52, 75, 165;
+    percipient, 107, 152, 186
+
+  Event-particle, 86, 93, 94, 172, 191
+
+  Events, conditioning, 152;
+    continuity of, 76;
+    demarcation of, 144;
+    ether of, 78;
+    infinite, 197, 198;
+    limited, 74;
+    passage of, 34;
+    signified, 52;
+    stationary, 198;
+    stream of, 167;
+    structure of, 52, 166
+
+  Exclusion, 186
+
+  Explanation, 97, 141
+
+  Extended nature, 196
+
+  Extension, 22, 58, 75, 185
+
+  Extensive abstraction, 65, 79, 85
+
+  Extrinsic character, 82, 89, 90, 113, 191;
+    properties, 62
+
+
+  Fact, 12, 13
+
+  Factors, 12, 13, 15
+
+  Facts, concrete, 167, 171
+
+  Family of durations, 59, 63, 73;
+    of moments, 63
+
+  Faraday, 146
+
+  Field, gravitational, 197;
+    of activity, 170, 181;
+    physical, 190
+
+  Finite truths, 12
+
+  Fitzgerald, 133
+
+  Formula of calculation, 45, 158
+
+  Foucault, 138, 194
+
+  Four-dimensional manifold, 86
+
+  Fresnel, 133
+
+  Future, the, 72, 177
+
+
+  Galileo, 139
+
+  Geometrical order, 194
+
+  Geometry, 36;
+    metrical, 129
+
+  Gravitation, 179 et seqq.
+
+  Gravitational field, 197
+
+  Greek philosophy, 16;
+    thought, 197
+
+  Gyro-compass, 194
+
+
+  Heath, Sir T. L., 197
+
+  Here, 107
+
+
+  Idealists, 70
+
+  Immediacy, 52;
+    of perception, 72
+
+  Impetus, 181, 182;
+    coefficients of, 183;
+    integral, 183
+
+  Inclusion, 186
+
+  Individuality, 13
+
+  Infinite events, 197, 198
+
+  Inge, Dr, 48
+
+  Ingredient, 14
+
+  Ingression, 144, 145, 148, 152
+
+  Inherence, 83
+
+  Inside, 106
+
+  Instant, 33, 35, 57
+
+  Instantaneous plane, 91;
+    present, 72;
+    spaces, 86, 90, 177
+
+  Instantaneousness, 56, 57
+
+  Intersection, locus of, 90
+
+  Intrinsic character, 80, 82, 90, 113, 191;
+    properties, 62
+
+  Ionian thinkers, 19
+
+  Irrelevance, infinitude of, 12
+
+  Irrevocableness, 35, 37
+
+  It, 8
+
+
+  Julius Caesar, 36
+
+  Junction, 76, 101
+
+
+  Kinetic energy, 105;
+    symmetry, 129
+
+  Knowledge, 28, 32
+
+
+  Lagrange, 140
+
+  Larmor, 131
+
+  Law of convergence, 82
+
+  Laws of motion, 137, 139;
+    of nature, 196
+
+  Leibnizian monadology, 150
+
+  Level, 91, 92
+
+  Light, 195;
+    ray of, 188;
+    velocity of, 131
+
+  Limit, 57
+
+  Limited events, 74
+
+  Location, 160, 161
+
+  Locke, 27
+
+  Locus, 102;
+    of intersection, 90
+
+  London, 97
+
+  Lorentz, H. A., 131, 133
+
+  Lossky, 47
+
+
+  Manifold, four-dimensional, 86;
+    space-time, 173
+
+  Material ether, 78;
+    object, 169
+
+  Materialism, 43, 70
+
+  Matrix, 116
+
+  Matter, 16, 17, 19, 20, 26
+
+  Maxwell, 131, 133
+
+  Measurableness, 196;
+    of nature, 193
+
+  Measurement, 96, 120, 174, 196;
+    of time, 65, 140
+
+  Measure-system, 196
+
+  Memory, 68
+
+  Metaphysics, 28, 32
+
+  Metrical geometry, 129
+
+  Michelson-Morley, 195
+
+  Milton, 35
+
+  Mind, 27, 28
+
+  Minkowski, viii, 131
+
+  Molecule, 32, 171
+
+  Moment, 57, 60, 88
+
+  Momental area, 103;
+    route, 103
+
+  Momentum, 105
+
+  Motion, 105, 114, 117, 127, 188, 192
+
+  Multiplicity, 22
+
+
+  Natural philosophy, 29, 30
+
+  Natural science, philosophy of, 46
+
+  Nature, 3;
+    apparent, 31, 39;
+    causal, 31, 39;
+    conceptual, 45;
+    continuity of, 59, 76;
+    discrimination of, 144;
+    extended, 196;
+    laws of, 196;
+    passage of, 54;
+    stratification of, 194, 196;
+    system of, 146
+
+  Newton, 27, 136, 139, 140
+
+
+  Object, 77, 125, 143, 169, 189;
+    delusive perceptual, 155;
+    material, 169;
+    perceptual, 153;
+    physical, 155, 157;
+    scientific, 158, 169;
+    uniform, 162
+
+  Occupation, 22, 34, 36, 100, 101
+
+  Order, source of, 192;
+    spatial, 95, 194;
+    temporal, 64, 95, 194
+
+  Organisation of thought, 79
+
+  Outside, 63, 100
+
+
+  Paradox, 192
+
+  Parallel, 63, 127;
+    durations, 190
+
+  Parallelism, 95, 191
+
+  Parallelogram, 127
+
+  Paris, 87, 138
+
+  Parliament, 120
+
+  Part, 14, 15, 58
+
+  Passage of events, 34;
+    of nature, 54
+
+  Past, the, 72, 177
+
+  Perception, 3
+
+  Perceptual objects, 149, 153
+
+  Percipience, 28
+
+  Percipient event, 107, 152, 186, 187
+
+  Period of time, 51
+
+  Permanence, 144
+
+  Perpendicularity, 117, 127, 193
+
+  Philosophy, 1;
+    natural, 29, 30;
+    of natural science, 46;
+    of the sciences, 2
+
+  Physical field, 190;
+    object, 155, 156, 157
+
+  Physics, speculative, 30
+
+  Place, 51
+
+  Plane, 191;
+    instantaneous, 91
+
+  Plato, 16, 17, 18, 24, 197
+
+  Poincaré, 121, 122, 123
+
+  Point, 35, 89, 91, 114, 173, 176
+
+  Point-flash, 172, 173
+
+  Point of space, 85
+
+  Point, timeless, 192
+
+  Point-track, 113, 198
+
+  Pompey, 36
+
+  Position, 89, 90, 92, 93, 99, 113, 191;
+    absolute, 105, 106, 114, 188
+
+  Potential, 183;
+    associate-, 183
+
+  Predicate, 18
+
+  Predication, 18
+
+  Present, the, 69, 72, 177;
+    instantaneous, 72;
+    observational, 186
+
+  Primary qualities, 27
+
+  Prime, 88
+
+  Process, 53, 54;
+    of nature, 54
+
+  Psychic additions, 29, 187
+
+  Punct, 92, 93, 94
+
+  Pythagoreans, 197
+
+
+  Quality, 27
+
+  Quantum of time, 162
+
+  Quantum theory, 162
+
+
+  Ray of light, 188
+
+  Reality, 30;
+    of durations, 55, 187
+
+  Recognition, 124, 143, 189
+
+  Rect, 91, 92
+
+  Recurrence, 35
+
+  Relative motion, 117;
+    velocity, 130
+
+  Relativity, 169;
+    restricted theory of, 193
+
+  Rest, 105, 114, 188, 192
+
+  Rotation, 138, 194
+
+  Route, 99;
+    momental, 103;
+    straight, 103
+
+  Russell, Bertrand, 11, 122, 123
+
+
+  Schelling, 47
+
+  Science, 2;
+    metaphysical, 32
+
+  Scientific objects, 149, 158, 169
+
+  Secondary qualities, 27
+
+  Self-congruence, 196
+
+  Self-containedness of nature, 4
+
+  Sense-awareness, 3, 67
+
+  Sense-object, 149, 170
+
+  Sense-perception, 3, 14
+
+  Sense-recognition, 143, 189
+
+  Series, temporal, 66, 70, 85, 178
+
+  Set, abstractive, 61, 79
+
+  Significance, 51, 186, 187, 188, 194, 197, 198
+
+  Signified events, 52
+
+  Simplicity, 163, 173
+
+  Simultaneity, 53, 56, 196
+
+  Situation, 15, 78, 147, 148, 152, 160, 189
+
+  Solid, 99, 101, 102;
+    vagrant, 101
+
+  Sound, 195
+
+  Space, 16, 17, 31, 33, 79;
+    empty, 145;
+    timeless, 86, 106, 114;
+    uniformity of, 194
+
+  Spaces, instantaneous, 86, 90
+
+  Space-system, 179
+
+  Space-time manifold, 173
+
+  Spatial-order, 95
+
+  Spatio-temporal structure, 173
+
+  Speculative demonstration, 6
+
+  Speculative physics, 30
+
+  Standpoint for perception, 107, 188
+
+  Station, 103, 104, 113
+
+  Stationary events, 198
+
+  Straight line, 91, 114, 191;
+    route, 103
+
+  Stratification of nature, 187, 194, 196
+
+  Stream of events, 167
+
+  Structure of events, 52, 166
+
+  Structure, spatio-temporal, 173
+
+  Subject, 18
+
+  Substance, 16, 18, 19, 150
+
+  Substratum, 16, 18, 21
+
+  Symmetry, 118, 126;
+    kinetic, 129
+
+  System of nature, 146
+
+  System, time-, 192
+
+
+  Tarner, Edward, v, 1
+
+  Temporal order, 64, 95, 194
+
+  Temporal series, 66, 70, 85
+
+  Tensor, 182
+
+  Terminus, 4
+
+  The, 11
+
+  Theory, quantum, 162
+
+  There, 110, 189
+
+  This, 11
+
+  Thought, 3, 14
+
+  Timaeus, the, 17, 20, 24
+
+  Time, 16, 17, 31, 33, 49, 79;
+    measurement of, 140;
+    quantum of, 162;
+    transcendence of, 39
+
+  Time-series, 178, also cf. Temporal series
+
+  Time-system, see Time-series, also 91, 97, 104, 179, 192
+
+  Timeless point, 192;
+    space, 86, 106, 114, 177
+
+  Totality, 89
+
+  Transcendence of time, 39
+
+  Transmission, 26, 28;
+    action by, 159, 190
+
+  Tubes of force, 146
+
+
+  Unexhaustiveness, 50
+
+  Uniform object, 162
+
+  Uniformity of change, 140;
+    of space, 194
+
+
+  Vagrant area, 103;
+    solid, 101
+
+  Veblen and Young, 36
+
+  Velocity, critical, 193, 195;
+    of light, 131, 195;
+    relative, 130
+
+  Volume, 92, 101
+
+
+  When, 107
+
+  Where, 107
+
+  Whole, 58
+
+  Within, 63
+
+
+  Young, Veblen and, 36
+
+
+
+
+
+End of Project Gutenberg's The Concept of Nature, by Alfred North Whitehead
+
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+Project Gutenberg's The Concept of Nature, by Alfred North Whitehead
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: The Concept of Nature
+       The Tarner Lectures Delivered in Trinity College, November 1919
+
+Author: Alfred North Whitehead
+
+Release Date: July 16, 2006 [EBook #18835]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE CONCEPT OF NATURE ***
+
+
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+Produced by Janet Kegg, Laura Wisewell and the Online
+Distributed Proofreading Team at http://www.pgdp.net
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+  +------------------------------------------------------------------+
+  |                                                                  |
+  | Transcriber's Note: In the parts containing mathematical         |
+  | notation, superscripts are denoted using a carat and subscripts  |
+  | using underscores, for example x^2, e_1, e_{n+1}. Greek          |
+  | letters used as symbols are written out, for example {sigma},    |
+  | but the one Greek phrase has been transliterated. All of these   |
+  | special characters are preserved in the UTF-8 and HTML versions  |
+  | of this ebook.                                                   |
+  |                                                                  |
+  | Italicised words are marked using underscores _like this_, but   |
+  | the letters used in the mathematics (which were all in italic    |
+  | font) have not been marked, to aid legibility and to avoid       |
+  | confusion with the subscripts.                                   |
+  |                                                                  |
+  | Two printer errors have been corrected. These are:               |
+  |                                                                  |
+  | "...relating the entity discriminated by sight with that         |
+  | discriminated by [sight]..." sight has been changed to touch as  |
+  | suggested by the sense.                                          |
+  |                                                                  |
+  | "...[universely] proportional to..." universely has been changed |
+  | to inversely.                                                    |
+  |                                                                  |
+  +------------------------------------------------------------------+
+
+
+
+
+                            The Concept of
+
+
+                                NATURE
+
+
+                         THE TARNER LECTURES
+                     DELIVERED IN TRINITY COLLEGE
+                            NOVEMBER 1919
+
+
+                        Alfred North Whitehead
+
+
+
+
+PREFACE
+
+
+The contents of this book were originally delivered at Trinity College
+in the autumn of 1919 as the inaugural course of Tarner lectures. The
+Tarner lectureship is an occasional office founded by the liberality of
+Mr Edward Tarner. The duty of each of the successive holders of the post
+will be to deliver a course on 'the Philosophy of the Sciences and the
+Relations or Want of Relations between the different Departments of
+Knowledge.' The present book embodies the endeavour of the first
+lecturer of the series to fulfil his task.
+
+The chapters retain their original lecture form and remain as delivered
+with the exception of minor changes designed to remove obscurities of
+expression. The lecture form has the advantage of suggesting an audience
+with a definite mental background which it is the purpose of the lecture
+to modify in a specific way. In the presentation of a novel outlook with
+wide ramifications a single line of communications from premises to
+conclusions is not sufficient for intelligibility. Your audience will
+construe whatever you say into conformity with their pre-existing
+outlook. For this reason the first two chapters and the last two
+chapters are essential for intelligibility though they hardly add to the
+formal completeness of the exposition. Their function is to prevent the
+reader from bolting up side tracks in pursuit of misunderstandings. The
+same reason dictates my avoidance of the existing technical terminology
+of philosophy. The modern natural philosophy is shot through and
+through with the fallacy of bifurcation which is discussed in the second
+chapter of this work. Accordingly all its technical terms in some subtle
+way presuppose a misunderstanding of my thesis. It is perhaps as well to
+state explicitly that if the reader indulges in the facile vice of
+bifurcation not a word of what I have here written will be intelligible.
+
+The last two chapters do not properly belong to the special course.
+Chapter�VIII is a lecture delivered in the spring of 1920 before the
+Chemical Society of the students of the Imperial College of Science and
+Technology. It has been appended here as conveniently summing up and
+applying the doctrine of the book for an audience with one definite type
+of outlook.
+
+This volume on 'the Concept of Nature' forms a companion book to my
+previous work _An Enquiry concerning the Principles of Natural
+Knowledge_. Either book can be read independently, but they supplement
+each other. In part the present book supplies points of view which were
+omitted from its predecessor; in part it traverses the same ground with
+an alternative exposition. For one thing, mathematical notation has been
+carefully avoided, and the results of mathematical deductions are
+assumed. Some of the explanations have been improved and others have
+been set in a new light. On the other hand important points of the
+previous work have been omitted where I have had nothing fresh to say
+about them. On the whole, whereas the former work based itself chiefly
+on ideas directly drawn from mathematical physics, the present book
+keeps closer to certain fields of philosophy and physics to the
+exclusion of mathematics. The two works meet in their discussions of
+some details of space and time.
+
+I am not conscious that I have in any way altered my views. Some
+developments have been made. Those that are capable of a
+non-mathematical exposition have been incorporated in the text. The
+mathematical developments are alluded to in the last two chapters. They
+concern the adaptation of the principles of mathematical physics to the
+form of the relativity principle which is here maintained. Einstein's
+method of using the theory of tensors is adopted, but the application is
+worked out on different lines and from different assumptions. Those of
+his results which have been verified by experience are obtained also by
+my methods. The divergence chiefly arises from the fact that I do not
+accept his theory of non-uniform space or his assumption as to the
+peculiar fundamental character of light-signals. I would not however be
+misunderstood to be lacking in appreciation of the value of his recent
+work on general relativity which has the high merit of first disclosing
+the way in which mathematical physics should proceed in the light of the
+principle of relativity. But in my judgment he has cramped the
+development of his brilliant mathematical method in the narrow bounds of
+a very doubtful philosophy.
+
+The object of the present volume and of its predecessor is to lay the
+basis of a natural philosophy which is the necessary presupposition of a
+reorganised speculative physics. The general assimilation of space and
+time which dominates the constructive thought can claim the independent
+support of Minkowski from the side of science and also of succeeding
+relativists, while on the side of philosophers it was, I believe, one
+theme of Prof. Alexander's Gifford lectures delivered some few years ago
+but not yet published. He also summarised his conclusions on this
+question in a lecture to the Aristotelian Society in the July of 1918.
+Since the publication of _An Enquiry concerning the Principles of
+Natural Knowledge_ I have had the advantage of reading Mr C.�D. Broad's
+_Perception, Physics, and Reality_ [Camb. Univ. Press, 1914]. This
+valuable book has assisted me in my discussion in Chapter�II, though I
+am unaware as to how far Mr Broad would assent to any of my arguments as
+there stated.
+
+It remains for me to thank the staff of the University Press, its
+compositors, its proof-readers, its clerks, and its managing officials,
+not only for the technical excellence of their work, but for the way
+they have co-operated so as to secure my convenience.
+
+A.�N.�W.
+
+    IMPERIAL COLLEGE OF SCIENCE
+        AND TECHNOLOGY.
+            _April_, 1920.
+
+
+
+
+CONTENTS
+
+
+   CHAP.                                                  PAGE
+
+       I NATURE AND THOUGHT                                  1
+
+      II THEORIES OF THE BIFURCATION OF NATURE              26
+
+     III TIME                                               49
+
+      IV THE METHOD OF EXTENSIVE ABSTRACTION                74
+
+       V SPACE AND MOTION                                   99
+
+      VI CONGRUENCE                                        120
+
+     VII OBJECTS                                           143
+
+    VIII SUMMARY                                           164
+
+      IX THE ULTIMATE PHYSICAL CONCEPTS                    185
+
+         NOTE: ON THE GREEK CONCEPT OF A POINT             197
+
+         NOTE: ON SIGNIFICANCE AND INFINITE EVENTS         197
+
+         INDEX                                             199
+
+
+
+
+THE CONCEPT OF NATURE
+
+
+
+
+CHAPTER I
+
+NATURE AND THOUGHT
+
+
+The subject-matter of the Tarner lectures is defined by the founder to
+be 'the Philosophy of the Sciences and the Relations or Want of
+Relations between the different Departments of Knowledge.' It is fitting
+at the first lecture of this new foundation to dwell for a few moments
+on the intentions of the donor as expressed in this definition; and I do
+so the more willingly as I shall thereby be enabled to introduce the
+topics to which the present course is to be devoted.
+
+We are justified, I think, in taking the second clause of the definition
+as in part explanatory of the earlier clause. What is the philosophy of
+the sciences? It is not a bad answer to say that it is the study of the
+relations between the different departments of knowledge. Then with
+admirable solicitude for the freedom of learning there is inserted in
+the definition after the word 'relations' the phrase 'or want of
+relations.' A disproof of relations between sciences would in itself
+constitute a philosophy of the sciences. But we could not dispense
+either with the earlier or the later clause. It is not every relation
+between sciences which enters into their philosophy. For example biology
+and physics are connected by the use of the microscope. Still, I may
+safely assert that a technical description of the uses of the microscope
+in biology is not part of the philosophy of the sciences. Again, you
+cannot abandon the later clause of the definition; namely that
+referring to the relations between the sciences, without abandoning the
+explicit reference to an ideal in the absence of which philosophy must
+languish from lack of intrinsic interest. That ideal is the attainment
+of some unifying concept which will set in assigned relationships within
+itself all that there is for knowledge, for feeling, and for emotion.
+That far off ideal is the motive power of philosophic research; and
+claims allegiance even as you expel it. The philosophic pluralist is a
+strict logician; the Hegelian thrives on contradictions by the help of
+his absolute; the Mohammedan divine bows before the creative will of
+Allah; and the pragmatist will swallow anything so long as it 'works.'
+
+The mention of these vast systems and of the age-long controversies from
+which they spring, warns us to concentrate. Our task is the simpler one
+of the philosophy of the sciences. Now a science has already a certain
+unity which is the very reason why that body of knowledge has been
+instinctively recognised as forming a science. The philosophy of a
+science is the endeavour to express explicitly those unifying
+characteristics which pervade that complex of thoughts and make it to be
+a science. The philosophy of the sciences--conceived as one subject--is
+the endeavour to exhibit all sciences as one science, or--in case of
+defeat--the disproof of such a possibility.
+
+Again I will make a further simplification, and confine attention to the
+natural sciences, that is, to the sciences whose subject-matter is
+nature. By postulating a common subject-matter for this group of
+sciences a unifying philosophy of natural science has been thereby
+presupposed.
+
+What do we mean by nature? We have to discuss the philosophy of natural
+science. Natural science is the science of nature. But--What is nature?
+
+Nature is that which we observe in perception through the senses. In
+this sense-perception we are aware of something which is not thought and
+which is self-contained for thought. This property of being
+self-contained for thought lies at the base of natural science. It means
+that nature can be thought of as a closed system whose mutual relations
+do not require the expression of the fact that they are thought about.
+
+Thus in a sense nature is independent of thought. By this statement no
+metaphysical pronouncement is intended. What I mean is that we can think
+about nature without thinking about thought. I shall say that then we
+are thinking 'homogeneously' about nature.
+
+Of course it is possible to think of nature in conjunction with thought
+about the fact that nature is thought about. In such a case I shall say
+that we are thinking 'heterogeneously' about nature. In fact during the
+last few minutes we have been thinking heterogeneously about nature.
+Natural science is exclusively concerned with homogeneous thoughts about
+nature.
+
+But sense-perception has in it an element which is not thought. It is a
+difficult psychological question whether sense-perception involves
+thought; and if it does involve thought, what is the kind of thought
+which it necessarily involves. Note that it has been stated above that
+sense-perception is an awareness of something which is not thought.
+Namely, nature is not thought. But this is a different question, namely
+that the fact of sense-perception has a factor which is not thought. I
+call this factor 'sense-awareness.' Accordingly the doctrine that
+natural science is exclusively concerned with homogeneous thoughts about
+nature does not immediately carry with it the conclusion that natural
+science is not concerned with sense-awareness.
+
+However, I do assert this further statement; namely, that though natural
+science is concerned with nature which is the terminus of
+sense-perception, it is not concerned with the sense-awareness itself.
+
+I repeat the main line of this argument, and expand it in certain
+directions.
+
+Thought about nature is different from the sense-perception of nature.
+Hence the fact of sense-perception has an ingredient or factor which is
+not thought. I call this ingredient sense-awareness. It is indifferent
+to my argument whether sense-perception has or has not thought as
+another ingredient. If sense-perception does not involve thought, then
+sense-awareness and sense-perception are identical. But the something
+perceived is perceived as an entity which is the terminus of the
+sense-awareness, something which for thought is beyond the fact of that
+sense-awareness. Also the something perceived certainly does not contain
+other sense-awarenesses which are different from the sense-awareness
+which is an ingredient in that perception. Accordingly nature as
+disclosed in sense-perception is self-contained as against
+sense-awareness, in addition to being self-contained as against thought.
+I will also express this self-containedness of nature by saying that
+nature is closed to mind.
+
+This closure of nature does not carry with it any metaphysical doctrine
+of the disjunction of nature and mind. It means that in sense-perception
+nature is disclosed as a complex of entities whose mutual relations are
+expressible in thought without reference to mind, that is, without
+reference either to sense-awareness or to thought. Furthermore, I do not
+wish to be understood as implying that sense-awareness and thought are
+the only activities which are to be ascribed to mind. Also I am not
+denying that there are relations of natural entities to mind or minds
+other than being the termini of the sense-awarenesses of minds.
+Accordingly I will extend the meaning of the terms 'homogeneous
+thoughts' and 'heterogeneous thoughts' which have already been
+introduced. We are thinking 'homogeneously' about nature when we are
+thinking about it without thinking about thought or about
+sense-awareness, and we are thinking 'heterogeneously' about nature when
+we are thinking about it in conjunction with thinking either about
+thought or about sense-awareness or about both.
+
+I also take the homogeneity of thought about nature as excluding any
+reference to moral or aesthetic values whose apprehension is vivid in
+proportion to self-conscious activity. The values of nature are perhaps
+the key to the metaphysical synthesis of existence. But such a synthesis
+is exactly what I am not attempting. I am concerned exclusively with the
+generalisations of widest scope which can be effected respecting that
+which is known to us as the direct deliverance of sense-awareness.
+
+I have said that nature is disclosed in sense-perception as a complex of
+entities. It is worth considering what we mean by an entity in this
+connexion. 'Entity' is simply the Latin equivalent for 'thing' unless
+some arbitrary distinction is drawn between the words for technical
+purposes. All thought has to be about things. We can gain some idea of
+this necessity of things for thought by examination of the structure of
+a proposition.
+
+Let us suppose that a proposition is being communicated by an expositor
+to a recipient. Such a proposition is composed of phrases; some of these
+phrases may be demonstrative and others may be descriptive.
+
+By a demonstrative phrase I mean a phrase which makes the recipient
+aware of an entity in a way which is independent of the particular
+demonstrative phrase. You will understand that I am here using
+'demonstration' in the non-logical sense, namely in the sense in which a
+lecturer demonstrates by the aid of a frog and a microscope the
+circulation of the blood for an elementary class of medical students. I
+will call such demonstration 'speculative' demonstration, remembering
+Hamlet's use of the word 'speculation' when he says,
+
+    There is no speculation in those eyes.
+
+Thus a demonstrative phrase demonstrates an entity speculatively. It may
+happen that the expositor has meant some other entity--namely, the
+phrase demonstrates to him an entity which is diverse from the entity
+which it demonstrates to the recipient. In that case there is confusion;
+for there are two diverse propositions, namely the proposition for the
+expositor and the proposition for the recipient. I put this possibility
+aside as irrelevant for our discussion, though in practice it may be
+difficult for two persons to concur in the consideration of exactly the
+same proposition, or even for one person to have determined exactly the
+proposition which he is considering.
+
+Again the demonstrative phrase may fail to demonstrate any entity. In
+that case there is no proposition for the recipient. I think that we
+may assume (perhaps rashly) that the expositor knows what he means.
+
+A demonstrative phrase is a gesture. It is not itself a constituent of
+the proposition, but the entity which it demonstrates is such a
+constituent. You may quarrel with a demonstrative phrase as in some way
+obnoxious to you; but if it demonstrates the right entity, the
+proposition is unaffected though your taste may be offended. This
+suggestiveness of the phraseology is part of the literary quality of the
+sentence which conveys the proposition. This is because a sentence
+directly conveys one proposition, while in its phraseology it suggests a
+penumbra of other propositions charged with emotional value. We are now
+talking of the one proposition directly conveyed in any phraseology.
+
+This doctrine is obscured by the fact that in most cases what is in form
+a mere part of the demonstrative gesture is in fact a part of the
+proposition which it is desired directly to convey. In such a case we
+will call the phraseology of the proposition elliptical. In ordinary
+intercourse the phraseology of nearly all propositions is elliptical.
+
+Let us take some examples. Suppose that the expositor is in London, say
+in Regent's Park and in Bedford College, the great women's college which
+is situated in that park. He is speaking in the college hall and he
+says,
+
+    'This college building is commodious.'
+
+The phrase 'this college building' is a demonstrative phrase. Now
+suppose the recipient answers,
+
+    'This is not a college building, it is the lion-house in the Zoo.'
+
+Then, provided that the expositor's original proposition has not been
+couched in elliptical phraseology, the expositor sticks to his original
+proposition when he replies,
+
+    'Anyhow, _it_ is commodious.'
+
+Note that the recipient's answer accepts the speculative demonstration
+of the phrase 'This college building.' He does not say, 'What do you
+mean?' He accepts the phrase as demonstrating an entity, but declares
+that same entity to be the lion-house in the Zoo. In his reply, the
+expositor in his turn recognises the success of his original gesture as
+a speculative demonstration, and waives the question of the suitability
+of its mode of suggestiveness with an 'anyhow.' But he is now in a
+position to repeat the original proposition with the aid of a
+demonstrative gesture robbed of any suggestiveness, suitable or
+unsuitable, by saying,
+
+    '_It_ is commodious.'
+
+The '_it_' of this final statement presupposes that thought has seized
+on the entity as a bare objective for consideration.
+
+We confine ourselves to entities disclosed in sense-awareness. The
+entity is so disclosed as a relatum in the complex which is nature. It
+dawns on an observer because of its relations; but it is an objective
+for thought in its own bare individuality. Thought cannot proceed
+otherwise; namely, it cannot proceed without the ideal bare 'it' which
+is speculatively demonstrated. This setting up of the entity as a bare
+objective does not ascribe to it an existence apart from the complex in
+which it has been found by sense-perception. The 'it' for thought is
+essentially a relatum for sense-awareness.
+
+The chances are that the dialogue as to the college building takes
+another form. Whatever the expositor originally meant, he almost
+certainly now takes his former statement as couched in elliptical
+phraseology, and assumes that he was meaning,
+
+    'This is a college building and is commodious.'
+
+Here the demonstrative phrase or the gesture, which demonstrates the
+'it' which is commodious, has now been reduced to 'this'; and the
+attenuated phrase, under the circumstances in which it is uttered, is
+sufficient for the purpose of correct demonstration. This brings out the
+point that the verbal form is never the whole phraseology of the
+proposition; this phraseology also includes the general circumstances of
+its production. Thus the aim of a demonstrative phrase is to exhibit a
+definite 'it' as a bare objective for thought; but the _modus operandi_
+of a demonstrative phrase is to produce an awareness of the entity as a
+particular relatum in an auxiliary complex, chosen merely for the sake
+of the speculative demonstration and irrelevant to the proposition. For
+example, in the above dialogue, colleges and buildings, as related to
+the 'it' speculatively demonstrated by the phrase 'this college
+building,' set that 'it' in an auxiliary complex which is irrelevant to
+the proposition
+
+    'It is commodious.'
+
+Of course in language every phrase is invariably highly elliptical.
+Accordingly the sentence
+
+    'This college building is commodious'
+
+means probably
+
+    'This college building is commodious as a college building.'
+
+But it will be found that in the above discussion we can replace
+'commodious' by 'commodious as a college building' without altering our
+conclusion; though we can guess that the recipient, who thought he was
+in the lion-house of the Zoo, would be less likely to assent to.
+
+    'Anyhow, it is commodious as a college building.'
+
+A more obvious instance of elliptical phraseology arises if the
+expositor should address the recipient with the remark,
+
+    'That criminal is your friend.'
+
+The recipient might answer,
+
+    'He is my friend and you are insulting.'
+
+Here the recipient assumes that the phrase 'That criminal' is elliptical
+and not merely demonstrative. In fact, pure demonstration is impossible
+though it is the ideal of thought. This practical impossibility of pure
+demonstration is a difficulty which arises in the communication of
+thought and in the retention of thought. Namely, a proposition about a
+particular factor in nature can neither be expressed to others nor
+retained for repeated consideration without the aid of auxiliary
+complexes which are irrelevant to it.
+
+I now pass to descriptive phrases. The expositor says,
+
+    'A college in Regent's Park is commodious.'
+
+The recipient knows Regent's Park well. The phrase 'A college in
+Regent's Park' is descriptive for him. If its phraseology is not
+elliptical, which in ordinary life it certainly will be in some way or
+other, this proposition simply means,
+
+    'There is an entity which is a college building in Regent's Park
+    and is commodious.'
+
+If the recipient rejoins,
+
+    'The lion-house in the Zoo is the only commodious building in
+    Regent's Park,'
+
+he now contradicts the expositor, on the assumption that a lion-house in
+a Zoo is not a college building.
+
+Thus whereas in the first dialogue the recipient merely quarrelled with
+the expositor without contradicting him, in this dialogue he contradicts
+him. Thus a descriptive phrase is part of the proposition which it helps
+to express, whereas a demonstrative phrase is not part of the
+proposition which it helps to express.
+
+Again the expositor might be standing in Green Park--where there are no
+college buildings--and say,
+
+    'This college building is commodious.'
+
+Probably no proposition will be received by the recipient because the
+demonstrative phrase,
+
+    'This college building'
+
+has failed to demonstrate owing to the absence of the background of
+sense-awareness which it presupposes.
+
+But if the expositor had said,
+
+    'A college building in Green Park is commodious,'
+
+the recipient would have received a proposition, but a false one.
+
+Language is usually ambiguous and it is rash to make general assertions
+as to its meanings. But phrases which commence with 'this' or 'that' are
+usually demonstrative, whereas phrases which commence with 'the' or 'a'
+are often descriptive. In studying the theory of propositional
+expression it is important to remember the wide difference between the
+analogous modest words 'this' and 'that' on the one hand and 'a' and
+'the' on the other hand. The sentence
+
+    'The college building in Regent's Park is commodious'
+
+means, according to the analysis first made by Bertrand Russell, the
+proposition,
+
+   'There is an entity which (i) is a college building in Regent's
+   Park and (ii) is commodious and (iii) is such that any college
+   building in Regent's Park is identical with it.'
+
+The descriptive character of the phrase 'The college building in
+Regent's Park' is thus evident. Also the proposition is denied by the
+denial of any one of its three component clauses or by the denial of any
+combination of the component clauses. If we had substituted 'Green Park'
+for 'Regent's Park' a false proposition would have resulted. Also the
+erection of a second college in Regent's Park would make the proposition
+false, though in ordinary life common sense would politely treat it as
+merely ambiguous.
+
+'The Iliad' for a classical scholar is usually a demonstrative phrase;
+for it demonstrates to him a well-known poem. But for the majority of
+mankind the phrase is descriptive, namely, it is synonymous with 'The
+poem named "the Iliad".'
+
+Names may be either demonstrative or descriptive phrases. For example
+'Homer' is for us a descriptive phrase, namely, the word with some
+slight difference in suggestiveness means 'The man who wrote the Iliad.'
+
+This discussion illustrates that thought places before itself bare
+objectives, entities as we call them, which the thinking clothes by
+expressing their mutual relations. Sense-awareness discloses fact with
+factors which are the entities for thought. The separate distinction of
+an entity in thought is not a metaphysical assertion, but a method of
+procedure necessary for the finite expression of individual
+propositions. Apart from entities there could be no finite truths; they
+are the means by which the infinitude of irrelevance is kept out of
+thought.
+
+To sum up: the termini for thought are entities, primarily with bare
+individuality, secondarily with properties and relations ascribed to
+them in the procedure of thought; the termini for sense-awareness are
+factors in the fact of nature, primarily relata and only secondarily
+discriminated as distinct individualities.
+
+No characteristic of nature which is immediately posited for knowledge
+by sense-awareness can be explained. It is impenetrable by thought, in
+the sense that its peculiar essential character which enters into
+experience by sense-awareness is for thought merely the guardian of its
+individuality as a bare entity. Thus for thought 'red' is merely a
+definite entity, though for awareness 'red' has the content of its
+individuality. The transition from the 'red' of awareness to the 'red'
+of thought is accompanied by a definite loss of content, namely by the
+transition from the factor 'red' to the entity 'red.' This loss in the
+transition to thought is compensated by the fact that thought is
+communicable whereas sense-awareness is incommunicable.
+
+Thus there are three components in our knowledge of nature, namely,
+fact, factors, and entities. Fact is the undifferentiated terminus of
+sense-awareness; factors are termini of sense-awareness, differentiated
+as elements of fact; entities are factors in their function as the
+termini of thought. The entities thus spoken of are natural entities.
+Thought is wider than nature, so that there are entities for thought
+which are not natural entities.
+
+When we speak of nature as a complex of related entities, the 'complex'
+is fact as an entity for thought, to whose bare individuality is
+ascribed the property of embracing in its complexity the natural
+entities. It is our business to analyse this conception and in the
+course of the analysis space and time should appear. Evidently the
+relations holding between natural entities are themselves natural
+entities, namely they are also factors of fact, there for
+sense-awareness. Accordingly the structure of the natural complex can
+never be completed in thought, just as the factors of fact can never be
+exhausted in sense-awareness. Unexhaustiveness is an essential character
+of our knowledge of nature. Also nature does not exhaust the matter for
+thought, namely there are thoughts which would not occur in any
+homogeneous thinking about nature.
+
+The question as to whether sense-perception involves thought is largely
+verbal. If sense-perception involves a cognition of individuality
+abstracted from the actual position of the entity as a factor in fact,
+then it undoubtedly does involve thought. But if it is conceived as
+sense-awareness of a factor in fact competent to evoke emotion and
+purposeful action without further cognition, then it does not involve
+thought. In such a case the terminus of the sense-awareness is something
+for mind, but nothing for thought. The sense-perception of some lower
+forms of life may be conjectured to approximate to this character
+habitually. Also occasionally our own sense-perception in moments when
+thought-activity has been lulled to quiescence is not far off the
+attainment of this ideal limit.
+
+The process of discrimination in sense-awareness has two distinct sides.
+There is the discrimination of fact into parts, and the discrimination
+of any part of fact as exhibiting relations to entities which are not
+parts of fact though they are ingredients in it. Namely the immediate
+fact for awareness is the whole occurrence of nature. It is nature as an
+event present for sense-awareness, and essentially passing. There is no
+holding nature still and looking at it. We cannot redouble our efforts
+to improve our knowledge of the terminus of our present sense-awareness;
+it is our subsequent opportunity in subsequent sense-awareness which
+gains the benefit of our good resolution. Thus the ultimate fact for
+sense-awareness is an event. This whole event is discriminated by us
+into partial events. We are aware of an event which is our bodily life,
+of an event which is the course of nature within this room, and of a
+vaguely perceived aggregate of other partial events. This is the
+discrimination in sense-awareness of fact into parts.
+
+I shall use the term 'part' in the arbitrarily limited sense of an event
+which is part of the whole fact disclosed in awareness.
+
+Sense-awareness also yields to us other factors in nature which are not
+events. For example, sky-blue is seen as situated in a certain event.
+This relation of situation requires further discussion which is
+postponed to a later lecture. My present point is that sky-blue is found
+in nature with a definite implication in events, but is not an event
+itself. Accordingly in addition to events, there are other factors in
+nature directly disclosed to us in sense-awareness. The conception in
+thought of all the factors in nature as distinct entities with definite
+natural relations is what I have in another place[1] called the
+'diversification of nature.'
+
+[1] Cf. _Enquiry_.
+
+There is one general conclusion to be drawn from the foregoing
+discussion. It is that the first task of a philosophy of science should
+be some general classification of the entities disclosed to us in
+sense-perception.
+
+Among the examples of entities in addition to 'events' which we have
+used for the purpose of illustration are the buildings of Bedford
+College, Homer, and sky-blue. Evidently these are very different sorts
+of things; and it is likely that statements which are made about one
+kind of entity will not be true about other kinds. If human thought
+proceeded with the orderly method which abstract logic would suggest to
+it, we might go further and say that a classification of natural
+entities should be the first step in science itself. Perhaps you will be
+inclined to reply that this classification has already been effected,
+and that science is concerned with the adventures of material entities
+in space and time.
+
+The history of the doctrine of matter has yet to be written. It is the
+history of the influence of Greek philosophy on science. That influence
+has issued in one long misconception of the metaphysical status of
+natural entities. The entity has been separated from the factor which is
+the terminus of sense-awareness. It has become the substratum for that
+factor, and the factor has been degraded into an attribute of the
+entity. In this way a distinction has been imported into nature which is
+in truth no distinction at all. A natural entity is merely a factor of
+fact, considered in itself. Its disconnexion from the complex of fact is
+a mere abstraction. It is not the substratum of the factor, but the very
+factor itself as bared in thought. Thus what is a mere procedure of mind
+in the translation of sense-awareness into discursive knowledge has been
+transmuted into a fundamental character of nature. In this way matter
+has emerged as being the metaphysical substratum of its properties, and
+the course of nature is interpreted as the history of matter.
+
+Plato and Aristotle found Greek thought preoccupied with the quest for
+the simple substances in terms of which the course of events could be
+expressed. We may formulate this state of mind in the question, What is
+nature made of? The answers which their genius gave to this question,
+and more particularly the concepts which underlay the terms in which
+they framed their answers, have determined the unquestioned
+presuppositions as to time, space and matter which have reigned in
+science.
+
+In Plato the forms of thought are more fluid than in Aristotle, and
+therefore, as I venture to think, the more valuable. Their importance
+consists in the evidence they yield of cultivated thought about nature
+before it had been forced into a uniform mould by the long tradition of
+scientific philosophy. For example in the _Timaeus_ there is a
+presupposition, somewhat vaguely expressed, of a distinction between the
+general becoming of nature and the measurable time of nature. In a later
+lecture I have to distinguish between what I call the passage of nature
+and particular time-systems which exhibit certain characteristics of
+that passage. I will not go so far as to claim Plato in direct support
+of this doctrine, but I do think that the sections of the _Timaeus_
+which deal with time become clearer if my distinction is admitted.
+
+This is however a digression. I am now concerned with the origin of the
+scientific doctrine of matter in Greek thought. In the _Timaeus_ Plato
+asserts that nature is made of fire and earth with air and water as
+intermediate between them, so that 'as fire is to air so is air to
+water, and as air is to water so is water to earth.' He also suggests a
+molecular hypothesis for these four elements. In this hypothesis
+everything depends on the shape of the atoms; for earth it is cubical
+and for fire it is pyramidal. To-day physicists are again discussing
+the structure of the atom, and its shape is no slight factor in that
+structure. Plato's guesses read much more fantastically than does
+Aristotle's systematic analysis; but in some ways they are more
+valuable. The main outline of his ideas is comparable with that of
+modern science. It embodies concepts which any theory of natural
+philosophy must retain and in some sense must explain. Aristotle asked
+the fundamental question, What do we mean by 'substance'? Here the
+reaction between his philosophy and his logic worked very unfortunately.
+In his logic, the fundamental type of affirmative proposition is the
+attribution of a predicate to a subject. Accordingly, amid the many
+current uses of the term 'substance' which he analyses, he emphasises
+its meaning as 'the ultimate substratum which is no longer predicated of
+anything else.'
+
+The unquestioned acceptance of the Aristotelian logic has led to an
+ingrained tendency to postulate a substratum for whatever is disclosed
+in sense-awareness, namely, to look below what we are aware of for the
+substance in the sense of the 'concrete thing.' This is the origin of
+the modern scientific concept of matter and of ether, namely they are
+the outcome of this insistent habit of postulation.
+
+Accordingly ether has been invented by modern science as the substratum
+of the events which are spread through space and time beyond the reach
+of ordinary ponderable matter. Personally, I think that predication is a
+muddled notion confusing many different relations under a convenient
+common form of speech. For example, I hold that the relation of green to
+a blade of grass is entirely different from the relation of green to
+the event which is the life history of that blade for some short period,
+and is different from the relation of the blade to that event. In a
+sense I call the event the situation of the green, and in another sense
+it is the situation of the blade. Thus in one sense the blade is a
+character or property which can be predicated of the situation, and in
+another sense the green is a character or property of the same event
+which is also its situation. In this way the predication of properties
+veils radically different relations between entities.
+
+Accordingly 'substance,' which is a correlative term to 'predication,'
+shares in the ambiguity. If we are to look for substance anywhere, I
+should find it in events which are in some sense the ultimate substance
+of nature.
+
+Matter, in its modern scientific sense, is a return to the Ionian effort
+to find in space and time some stuff which composes nature. It has a
+more refined signification than the early guesses at earth and water by
+reason of a certain vague association with the Aristotelian idea of
+substance.
+
+Earth, water, air, fire, and matter, and finally ether are related in
+direct succession so far as concerns their postulated characters of
+ultimate substrata of nature. They bear witness to the undying vitality
+of Greek philosophy in its search for the ultimate entities which are
+the factors of the fact disclosed in sense-awareness. This search is the
+origin of science.
+
+The succession of ideas starting from the crude guesses of the early
+Ionian thinkers and ending in the nineteenth century ether reminds us
+that the scientific doctrine of matter is really a hybrid through which
+philosophy passed on its way to the refined Aristotelian concept of
+substance and to which science returned as it reacted against
+philosophic abstractions. Earth, fire, and water in the Ionic philosophy
+and the shaped elements in the _Timaeus_ are comparable to the matter
+and ether of modern scientific doctrine. But substance represents the
+final philosophic concept of the substratum which underlies any
+attribute. Matter (in the scientific sense) is already in space and
+time. Thus matter represents the refusal to think away spatial and
+temporal characteristics and to arrive at the bare concept of an
+individual entity. It is this refusal which has caused the muddle of
+importing the mere procedure of thought into the fact of nature. The
+entity, bared of all characteristics except those of space and time, has
+acquired a physical status as the ultimate texture of nature; so that
+the course of nature is conceived as being merely the fortunes of matter
+in its adventure through space.
+
+Thus the origin of the doctrine of matter is the outcome of uncritical
+acceptance of space and time as external conditions for natural
+existence. By this I do not mean that any doubt should be thrown on
+facts of space and time as ingredients in nature. What I do mean is 'the
+unconscious presupposition of space and time as being that within which
+nature is set.' This is exactly the sort of presupposition which tinges
+thought in any reaction against the subtlety of philosophical criticism.
+My theory of the formation of the scientific doctrine of matter is that
+first philosophy illegitimately transformed the bare entity, which is
+simply an abstraction necessary for the method of thought, into the
+metaphysical substratum of these factors in nature which in various
+senses are assigned to entities as their attributes; and that, as a
+second step, scientists (including philosophers who were scientists) in
+conscious or unconscious ignoration of philosophy presupposed this
+substratum, _qua_ substratum for attributes, as nevertheless in time and
+space.
+
+This is surely a muddle. The whole being of substance is as a substratum
+for attributes. Thus time and space should be attributes of the
+substance. This they palpably are not, if the matter be the substance of
+nature, since it is impossible to express spatio-temporal truths without
+having recourse to relations involving relata other than bits of matter.
+I waive this point however, and come to another. It is not the substance
+which is in space, but the attributes. What we find in space are the red
+of the rose and the smell of the jasmine and the noise of cannon. We
+have all told our dentists where our toothache is. Thus space is not a
+relation between substances, but between attributes.
+
+Thus even if you admit that the adherents of substance can be allowed to
+conceive substance as matter, it is a fraud to slip substance into space
+on the plea that space expresses relations between substances. On the
+face of it space has nothing to do with substances, but only with their
+attributes. What I mean is, that if you choose--as I think wrongly--to
+construe our experience of nature as an awareness of the attributes of
+substances, we are by this theory precluded from finding any analogous
+direct relations between substances as disclosed in our experience. What
+we do find are relations between the attributes of substances. Thus if
+matter is looked on as substance in space, the space in which it finds
+itself has very little to do with the space of our experience.
+
+The above argument has been expressed in terms of the relational theory
+of space. But if space be absolute--namely, if it have a being
+independent of things in it--the course of the argument is hardly
+changed. For things in space must have a certain fundamental relation to
+space which we will call occupation. Thus the objection that it is the
+attributes which are observed as related to space, still holds.
+
+The scientific doctrine of matter is held in conjunction with an
+absolute theory of time. The same arguments apply to the relations
+between matter and time as apply to the relations between space and
+matter. There is however (in the current philosophy) a difference in the
+connexions of space with matter from those of time with matter, which I
+will proceed to explain.
+
+Space is not merely an ordering of material entities so that any one
+entity bears certain relations to other material entities. The
+occupation of space impresses a certain character on each material
+entity in itself. By reason of its occupation of space matter has
+extension. By reason of its extension each bit of matter is divisible
+into parts, and each part is a numerically distinct entity from every
+other such part. Accordingly it would seem that every material entity is
+not really one entity. It is an essential multiplicity of entities.
+There seems to be no stopping this dissociation of matter into
+multiplicities short of finding each ultimate entity occupying one
+individual point. This essential multiplicity of material entities is
+certainly not what is meant by science, nor does it correspond to
+anything disclosed in sense-awareness. It is absolutely necessary that
+at a certain stage in this dissociation of matter a halt should be
+called, and that the material entities thus obtained should be treated
+as units. The stage of arrest may be arbitrary or may be set by the
+characteristics of nature; but all reasoning in science ultimately drops
+its space-analysis and poses to itself the problem, 'Here is one
+material entity, what is happening to it as a unit entity?' Yet this
+material entity is still retaining its extension, and as thus extended
+is a mere multiplicity. Thus there is an essential atomic property in
+nature which is independent of the dissociation of extension. There is
+something which in itself is one, and which is more than the logical
+aggregate of entities occupying points within the volume which the unit
+occupies. Indeed we may well be sceptical as to these ultimate entities
+at points, and doubt whether there are any such entities at all. They
+have the suspicious character that we are driven to accept them by
+abstract logic and not by observed fact.
+
+Time (in the current philosophy) does not exert the same disintegrating
+effect on matter which occupies it. If matter occupies a duration of
+time, the whole matter occupies every part of that duration. Thus the
+connexion between matter and time differs from the connexion between
+matter and space as expressed in current scientific philosophy. There is
+obviously a greater difficulty in conceiving time as the outcome of
+relations between different bits of matter than there is in the
+analogous conception of space. At an instant distinct volumes of space
+are occupied by distinct bits of matter. Accordingly there is so far no
+intrinsic difficulty in conceiving that space is merely the resultant of
+relations between the bits of matter. But in the one-dimensional time
+the same bit of matter occupies different portions of time. Accordingly
+time would have to be expressible in terms of the relations of a bit of
+matter with itself. My own view is a belief in the relational theory
+both of space and of time, and of disbelief in the current form of the
+relational theory of space which exhibits bits of matter as the relata
+for spatial relations. The true relata are events. The distinction which
+I have just pointed out between time and space in their connexion with
+matter makes it evident that any assimilation of time and space cannot
+proceed along the traditional line of taking matter as a fundamental
+element in space-formation.
+
+The philosophy of nature took a wrong turn during its development by
+Greek thought. This erroneous presupposition is vague and fluid in
+Plato's _Timaeus_. The general groundwork of the thought is still
+uncommitted and can be construed as merely lacking due explanation and
+the guarding emphasis. But in Aristotle's exposition the current
+conceptions were hardened and made definite so as to produce a faulty
+analysis of the relation between the matter and the form of nature as
+disclosed in sense-awareness. In this phrase the term 'matter' is not
+used in its scientific sense.
+
+I will conclude by guarding myself against a misapprehension. It is
+evident that the current doctrine of matter enshrines some fundamental
+law of nature. Any simple illustration will exemplify what I mean. For
+example, in a museum some specimen is locked securely in a glass case.
+It stays there for years: it loses its colour, and perhaps falls to
+pieces. But it is the same specimen; and the same chemical elements and
+the same quantities of those elements are present within the case at the
+end as were present at the beginning. Again the engineer and the
+astronomer deal with the motions of real permanences in nature. Any
+theory of nature which for one moment loses sight of these great basic
+facts of experience is simply silly. But it is permissible to point out
+that the scientific expression of these facts has become entangled in a
+maze of doubtful metaphysics; and that, when we remove the metaphysics
+and start afresh on an unprejudiced survey of nature, a new light is
+thrown on many fundamental concepts which dominate science and guide the
+progress of research.
+
+
+
+
+CHAPTER II
+
+THEORIES OF THE BIFURCATION OF NATURE
+
+
+In my previous lecture I criticised the concept of matter as the
+substance whose attributes we perceive. This way of thinking of matter
+is, I think, the historical reason for its introduction into science,
+and is still the vague view of it at the background of our thoughts
+which makes the current scientific doctrine appear so obvious. Namely we
+conceive ourselves as perceiving attributes of things, and bits of
+matter are the things whose attributes we perceive.
+
+In the seventeenth century the sweet simplicity of this aspect of matter
+received a rude shock. The transmission doctrines of science were then
+in process of elaboration and by the end of the century were
+unquestioned, though their particular forms have since been modified.
+The establishment of these transmission theories marks a turning point
+in the relation between science and philosophy. The doctrines to which I
+am especially alluding are the theories of light and sound. I have no
+doubt that the theories had been vaguely floating about before as
+obvious suggestions of common sense; for nothing in thought is ever
+completely new. But at that epoch they were systematised and made exact,
+and their complete consequences were ruthlessly deduced. It is the
+establishment of this procedure of taking the consequences seriously
+which marks the real discovery of a theory. Systematic doctrines of
+light and sound as being something proceeding from the emitting bodies
+were definitely established, and in particular the connexion of light
+with colour was laid bare by Newton.
+
+The result completely destroyed the simplicity of the 'substance and
+attribute' theory of perception. What we see depends on the light
+entering the eye. Furthermore we do not even perceive what enters the
+eye. The things transmitted are waves or--as Newton thought--minute
+particles, and the things seen are colours. Locke met this difficulty by
+a theory of primary and secondary qualities. Namely, there are some
+attributes of the matter which we do perceive. These are the primary
+qualities, and there are other things which we perceive, such as
+colours, which are not attributes of matter, but are perceived by us as
+if they were such attributes. These are the secondary qualities of
+matter.
+
+Why should we perceive secondary qualities? It seems an extremely
+unfortunate arrangement that we should perceive a lot of things that are
+not there. Yet this is what the theory of secondary qualities in fact
+comes to. There is now reigning in philosophy and in science an
+apathetic acquiescence in the conclusion that no coherent account can be
+given of nature as it is disclosed to us in sense-awareness, without
+dragging in its relations to mind. The modern account of nature is not,
+as it should be, merely an account of what the mind knows of nature; but
+it is also confused with an account of what nature does to the mind. The
+result has been disastrous both to science and to philosophy, but
+chiefly to philosophy. It has transformed the grand question of the
+relations between nature and mind into the petty form of the interaction
+between the human body and mind.
+
+Berkeley's polemic against matter was based on this confusion introduced
+by the transmission theory of light. He advocated, rightly as I think,
+the abandonment of the doctrine of matter in its present form. He had
+however nothing to put in its place except a theory of the relation of
+finite minds to the divine mind.
+
+But we are endeavouring in these lectures to limit ourselves to nature
+itself and not to travel beyond entities which are disclosed in
+sense-awareness.
+
+Percipience in itself is taken for granted. We consider indeed
+conditions for percipience, but only so far as those conditions are
+among the disclosures of perception. We leave to metaphysics the
+synthesis of the knower and the known. Some further explanation and
+defence of this position is necessary, if the line of argument of these
+lectures is to be comprehensible.
+
+The immediate thesis for discussion is that any metaphysical
+interpretation is an illegitimate importation into the philosophy of
+natural science. By a metaphysical interpretation I mean any discussion
+of the how (beyond nature) and of the why (beyond nature) of thought and
+sense-awareness. In the philosophy of science we seek the general
+notions which apply to nature, namely, to what we are aware of in
+perception. It is the philosophy of the thing perceived, and it should
+not be confused with the metaphysics of reality of which the scope
+embraces both perceiver and perceived. No perplexity concerning the
+object of knowledge can be solved by saying that there is a mind knowing
+it[2].
+
+[2] Cf. _Enquiry_, preface.
+
+In other words, the ground taken is this: sense-awareness is an
+awareness of something. What then is the general character of that
+something of which we are aware? We do not ask about the percipient or
+about the process, but about the perceived. I emphasise this point
+because discussions on the philosophy of science are usually extremely
+metaphysical--in my opinion, to the great detriment of the subject.
+
+The recourse to metaphysics is like throwing a match into the powder
+magazine. It blows up the whole arena. This is exactly what scientific
+philosophers do when they are driven into a corner and convicted of
+incoherence. They at once drag in the mind and talk of entities in the
+mind or out of the mind as the case may be. For natural philosophy
+everything perceived is in nature. We may not pick and choose. For us
+the red glow of the sunset should be as much part of nature as are the
+molecules and electric waves by which men of science would explain the
+phenomenon. It is for natural philosophy to analyse how these various
+elements of nature are connected.
+
+In making this demand I conceive myself as adopting our immediate
+instinctive attitude towards perceptual knowledge which is only
+abandoned under the influence of theory. We are instinctively willing to
+believe that by due attention, more can be found in nature than that
+which is observed at first sight. But we will not be content with less.
+What we ask from the philosophy of science is some account of the
+coherence of things perceptively known.
+
+This means a refusal to countenance any theory of psychic additions to
+the object known in perception. For example, what is given in perception
+is the green grass. This is an object which we know as an ingredient in
+nature. The theory of psychic additions would treat the greenness as a
+psychic addition furnished by the perceiving mind, and would leave to
+nature merely the molecules and the radiant energy which influence the
+mind towards that perception. My argument is that this dragging in of
+the mind as making additions of its own to the thing posited for
+knowledge by sense-awareness is merely a way of shirking the problem of
+natural philosophy. That problem is to discuss the relations _inter se_
+of things known, abstracted from the bare fact that they are known.
+Natural philosophy should never ask, what is in the mind and what is in
+nature. To do so is a confession that it has failed to express relations
+between things perceptively known, namely to express those natural
+relations whose expression is natural philosophy. It may be that the
+task is too hard for us, that the relations are too complex and too
+various for our apprehension, or are too trivial to be worth the trouble
+of exposition. It is indeed true that we have gone but a very small way
+in the adequate formulation of such relations. But at least do not let
+us endeavour to conceal failure under a theory of the byplay of the
+perceiving mind.
+
+What I am essentially protesting against is the bifurcation of nature
+into two systems of reality, which, in so far as they are real, are real
+in different senses. One reality would be the entities such as electrons
+which are the study of speculative physics. This would be the reality
+which is there for knowledge; although on this theory it is never known.
+For what is known is the other sort of reality, which is the byplay of
+the mind. Thus there would be two natures, one is the conjecture and the
+other is the dream.
+
+Another way of phrasing this theory which I am arguing against is to
+bifurcate nature into two divisions, namely into the nature apprehended
+in awareness and the nature which is the cause of awareness. The nature
+which is the fact apprehended in awareness holds within it the greenness
+of the trees, the song of the birds, the warmth of the sun, the hardness
+of the chairs, and the feel of the velvet. The nature which is the cause
+of awareness is the conjectured system of molecules and electrons which
+so affects the mind as to produce the awareness of apparent nature. The
+meeting point of these two natures is the mind, the causal nature being
+influent and the apparent nature being effluent.
+
+There are four questions which at once suggest themselves for discussion
+in connexion with this bifurcation theory of nature. They concern (i)
+causality, (ii) time, (iii) space, and (iv) delusions. These questions
+are not really separable. They merely constitute four distinct starting
+points from which to enter upon the discussion of the theory.
+
+Causal nature is the influence on the mind which is the cause of the
+effluence of apparent nature from the mind. This conception of causal
+nature is not to be confused with the distinct conception of one part of
+nature as being the cause of another part. For example, the burning of
+the fire and the passage of heat from it through intervening space is
+the cause of the body, its nerves and its brain, functioning in certain
+ways. But this is not an action of nature on the mind. It is an
+interaction within nature. The causation involved in this interaction is
+causation in a different sense from the influence of this system of
+bodily interactions within nature on the alien mind which thereupon
+perceives redness and warmth.
+
+The bifurcation theory is an attempt to exhibit natural science as an
+investigation of the cause of the fact of knowledge. Namely, it is an
+attempt to exhibit apparent nature as an effluent from the mind because
+of causal nature. The whole notion is partly based on the implicit
+assumption that the mind can only know that which it has itself produced
+and retains in some sense within itself, though it requires an exterior
+reason both as originating and as determining the character of its
+activity. But in considering knowledge we should wipe out all these
+spatial metaphors, such as 'within the mind' and 'without the mind.'
+Knowledge is ultimate. There can be no explanation of the 'why' of
+knowledge; we can only describe the 'what' of knowledge. Namely we can
+analyse the content and its internal relations, but we cannot explain
+why there is knowledge. Thus causal nature is a metaphysical chimera;
+though there is need of a metaphysics whose scope transcends the
+limitation to nature. The object of such a metaphysical science is not
+to explain knowledge, but exhibit in its utmost completeness our concept
+of reality.
+
+However, we must admit that the causality theory of nature has its
+strong suit. The reason why the bifurcation of nature is always creeping
+back into scientific philosophy is the extreme difficulty of exhibiting
+the perceived redness and warmth of the fire in one system of relations
+with the agitated molecules of carbon and oxygen, with the radiant
+energy from them, and with the various functionings of the material
+body. Unless we produce the all-embracing relations, we are faced with a
+bifurcated nature; namely, warmth and redness on one side, and
+molecules, electrons and ether on the other side. Then the two factors
+are explained as being respectively the cause and the mind's reaction to
+the cause.
+
+Time and space would appear to provide these all-embracing relations
+which the advocates of the philosophy of the unity of nature require.
+The perceived redness of the fire and the warmth are definitely related
+in time and in space to the molecules of the fire and the molecules of
+the body.
+
+It is hardly more than a pardonable exaggeration to say that the
+determination of the meaning of nature reduces itself principally to the
+discussion of the character of time and the character of space. In
+succeeding lectures I shall explain my own view of time and space. I
+shall endeavour to show that they are abstractions from more concrete
+elements of nature, namely, from events. The discussion of the details
+of the process of abstraction will exhibit time and space as
+interconnected, and will finally lead us to the sort of connexions
+between their measurements which occur in the modern theory of
+electromagnetic relativity. But this is anticipating our subsequent line
+of development. At present I wish to consider how the ordinary views of
+time and space help, or fail to help, in unifying our conception of
+nature.
+
+First, consider the absolute theories of time and space. We are to
+consider each, namely both time and space, to be a separate and
+independent system of entities, each system known to us in itself and
+for itself concurrently with our knowledge of the events of nature. Time
+is the ordered succession of durationless instants; and these instants
+are known to us merely as the relata in the serial relation which is the
+time-ordering relation, and the time-ordering relation is merely known
+to us as relating the instants. Namely, the relation and the instants
+are jointly known to us in our apprehension of time, each implying the
+other.
+
+This is the absolute theory of time. Frankly, I confess that it seems to
+me to be very unplausible. I cannot in my own knowledge find anything
+corresponding to the bare time of the absolute theory. Time is known to
+me as an abstraction from the passage of events. The fundamental fact
+which renders this abstraction possible is the passing of nature, its
+development, its creative advance, and combined with this fact is
+another characteristic of nature, namely the extensive relation between
+events. These two facts, namely the passage of events and the extension
+of events over each other, are in my opinion the qualities from which
+time and space originate as abstractions. But this is anticipating my
+own later speculations.
+
+Meanwhile, returning to the absolute theory, we are to suppose that time
+is known to us independently of any events in time. What happens in time
+occupies time. This relation of events to the time occupied, namely this
+relation of occupation, is a fundamental relation of nature to time.
+Thus the theory requires that we are aware of two fundamental relations,
+the time-ordering relation between instants, and the time-occupation
+relation between instants of time and states of nature which happen at
+those instants.
+
+There are two considerations which lend powerful support to the reigning
+theory of absolute time. In the first place time extends beyond nature.
+Our thoughts are in time. Accordingly it seems impossible to derive time
+merely from relations between elements of nature. For in that case
+temporal relations could not relate thoughts. Thus, to use a metaphor,
+time would apparently have deeper roots in reality than has nature. For
+we can imagine thoughts related in time without any perception of
+nature. For example we can imagine one of Milton's angels with thoughts
+succeeding each other in time, who does not happen to have noticed that
+the Almighty has created space and set therein a material universe. As a
+matter of fact I think that Milton set space on the same absolute level
+as time. But that need not disturb the illustration. In the second place
+it is difficult to derive the true serial character of time from the
+relative theory. Each instant is irrevocable. It can never recur by the
+very character of time. But if on the relative theory an instant of time
+is simply the state of nature at that time, and the time-ordering
+relation is simply the relation between such states, then the
+irrevocableness of time would seem to mean that an actual state of all
+nature can never return. I admit it seems unlikely that there should
+ever be such a recurrence down to the smallest particular. But extreme
+unlikeliness is not the point. Our ignorance is so abysmal that our
+judgments of likeliness and unlikeliness of future events hardly count.
+The real point is that the exact recurrence of a state of nature seems
+merely unlikely, while the recurrence of an instant of time violates our
+whole concept of time-order. The instants of time which have passed, are
+passed, and can never be again.
+
+Any alternative theory of time must reckon with these two considerations
+which are buttresses of the absolute theory. But I will not now continue
+their discussion.
+
+The absolute theory of space is analogous to the corresponding theory of
+time, but the reasons for its maintenance are weaker. Space, on this
+theory, is a system of extensionless points which are the relata in
+space-ordering relations which can technically be combined into one
+relation. This relation does not arrange the points in one linear series
+analogously to the simple method of the time-ordering relation for
+instants. The essential logical characteristics of this relation from
+which all the properties of space spring are expressed by mathematicians
+in the axioms of geometry. From these axioms[3] as framed by modern
+mathematicians the whole science of geometry can be deduced by the
+strictest logical reasoning. The details of these axioms do not now
+concern us. The points and the relations are jointly known to us in our
+apprehension of space, each implying the other. What happens in space,
+occupies space. This relation of occupation is not usually stated for
+events but for objects. For example, Pompey's statue would be said to
+occupy space, but not the event which was the assassination of Julius
+Caesar. In this I think that ordinary usage is unfortunate, and I hold
+that the relations of events to space and to time are in all respects
+analogous. But here I am intruding my own opinions which are to be
+discussed in subsequent lectures. Thus the theory of absolute space
+requires that we are aware of two fundamental relations, the
+space-ordering relation, which holds between points, and the
+space-occupation relation between points of space and material objects.
+
+[3] Cf. (for example) _Projective Geometry_ by Veblen and Young, vol.�i.
+1910, vol.�ii. 1917, Ginn and Company, Boston, U.S.A.
+
+This theory lacks the two main supports of the corresponding theory of
+absolute time. In the first place space does not extend beyond nature in
+the sense that time seems to do. Our thoughts do not seem to occupy
+space in quite the same intimate way in which they occupy time. For
+example, I have been thinking in a room, and to that extent my thoughts
+are in space. But it seems nonsense to ask how much volume of the room
+they occupied, whether it was a cubic foot or a cubic inch; whereas the
+same thoughts occupy a determinate duration of time, say, from eleven to
+twelve on a certain date.
+
+Thus whereas the relations of a relative theory of time are required to
+relate thoughts, it does not seem so obvious that the relations of a
+relative theory of space are required to relate them. The connexion of
+thought with space seems to have a certain character of indirectness
+which appears to be lacking in the connexion of thought with time.
+
+Again the irrevocableness of time does not seem to have any parallel for
+space. Space, on the relative theory, is the outcome of certain
+relations between objects commonly said to be in space; and whenever
+there are the objects, so related, there is the space. No difficulty
+seems to arise like that of the inconvenient instants of time which
+might conceivably turn up again when we thought that we had done with
+them.
+
+The absolute theory of space is not now generally popular. The knowledge
+of bare space, as a system of entities known to us in itself and for
+itself independently of our knowledge of the events in nature, does not
+seem to correspond to anything in our experience. Space, like time,
+would appear to be an abstraction from events. According to my own
+theory it only differentiates itself from time at a somewhat developed
+stage of the abstractive process. The more usual way of expressing the
+relational theory of space would be to consider space as an abstraction
+from the relations between material objects.
+
+Suppose now we assume absolute time and absolute space. What bearing
+has this assumption on the concept of nature as bifurcated into causal
+nature and apparent nature? Undoubtedly the separation between the two
+natures is now greatly mitigated. We can provide them with two systems
+of relations in common; for both natures can be presumed to occupy the
+same space and the same time. The theory now is this: Causal events
+occupy certain periods of the absolute time and occupy certain positions
+of the absolute space. These events influence a mind which thereupon
+perceives certain apparent events which occupy certain periods in the
+absolute time and occupy certain positions of the absolute space; and
+the periods and positions occupied by the apparent events bear a
+determinate relation to the periods and positions occupied by the causal
+events.
+
+Furthermore definite causal events produce for the mind definite
+apparent events. Delusions are apparent events which appear in temporal
+periods and spatial positions without the intervention of these causal
+events which are proper for influencing of the mind to their perception.
+
+The whole theory is perfectly logical. In these discussions we cannot
+hope to drive an unsound theory to a logical contradiction. A reasoner,
+apart from mere slips, only involves himself in a contradiction when he
+is shying at a _reductio ad absurdum_. The substantial reason for
+rejecting a philosophical theory is the 'absurdum' to which it reduces
+us. In the case of the philosophy of natural science the 'absurdum' can
+only be that our perceptual knowledge has not the character assigned to
+it by the theory. If our opponent affirms that his knowledge has that
+character, we can only--after making doubly sure that we understand
+each other--agree to differ. Accordingly the first duty of an expositor
+in stating a theory in which he disbelieves is to exhibit it as logical.
+It is not there where his trouble lies.
+
+Let me summarise the previously stated objections to this theory of
+nature. In the first place it seeks for the cause of the knowledge of
+the thing known instead of seeking for the character of the thing known:
+secondly it assumes a knowledge of time in itself apart from events
+related in time: thirdly it assumes a knowledge of space in itself apart
+from events related in space. There are in addition to these objections
+other flaws in the theory.
+
+Some light is thrown on the artificial status of causal nature in this
+theory by asking, why causal nature is presumed to occupy time and
+space. This really raises the fundamental question as to what
+characteristics causal nature should have in common with apparent
+nature. Why--on this theory--should the cause which influences the mind
+to perception have any characteristics in common with the effluent
+apparent nature? In particular, why should it be in space? Why should it
+be in time? And more generally, What do we know about mind which would
+allow us to infer any particular characteristics of a cause which should
+influence mind to particular effects?
+
+The transcendence of time beyond nature gives some slight reason for
+presuming that causal nature should occupy time. For if the mind
+occupies periods of time, there would seem to be some vague reason for
+assuming that influencing causes occupy the same periods of time, or at
+least, occupy periods which are strictly related to the mental periods.
+But if the mind does not occupy volumes of space, there seems to be no
+reason why causal nature should occupy any volumes of space. Thus space
+would seem to be merely apparent in the same sense as apparent nature is
+merely apparent. Accordingly if science is really investigating causes
+which operate on the mind, it would seem to be entirely on the wrong
+tack in presuming that the causes which it is seeking for have spatial
+relations. Furthermore there is nothing else in our knowledge analogous
+to these causes which influence the mind to perception. Accordingly,
+beyond the rashly presumed fact that they occupy time, there is really
+no ground by which we can determine any point of their character. They
+must remain for ever unknown.
+
+Now I assume as an axiom that science is not a fairy tale. It is not
+engaged in decking out unknowable entities with arbitrary and fantastic
+properties. What then is it that science is doing, granting that it is
+effecting something of importance? My answer is that it is determining
+the character of things known, namely the character of apparent nature.
+But we may drop the term 'apparent'; for there is but one nature, namely
+the nature which is before us in perceptual knowledge. The characters
+which science discerns in nature are subtle characters, not obvious at
+first sight. They are relations of relations and characters of
+characters. But for all their subtlety they are stamped with a certain
+simplicity which makes their consideration essential in unravelling the
+complex relations between characters of more perceptive insistence.
+
+The fact that the bifurcation of nature into causal and apparent
+components does not express what we mean by our knowledge is brought
+before us when we realise our thoughts in any discussion of the causes
+of our perceptions. For example, the fire is burning and we see a red
+coal. This is explained in science by radiant energy from the coal
+entering our eyes. But in seeking for such an explanation we are not
+asking what are the sort of occurrences which are fitted to cause a mind
+to see red. The chain of causation is entirely different. The mind is
+cut out altogether. The real question is, When red is found in nature,
+what else is found there also? Namely we are asking for an analysis of
+the accompaniments in nature of the discovery of red in nature. In a
+subsequent lecture I shall expand this line of thought. I simply draw
+attention to it here in order to point out that the wave-theory of light
+has not been adopted because waves are just the sort of things which
+ought to make a mind perceive colours. This is no part of the evidence
+which has ever been adduced for the wave-theory, yet on the causal
+theory of perception, it is really the only relevant part. In other
+words, science is not discussing the causes of knowledge, but the
+coherence of knowledge. The understanding which is sought by science is
+an understanding of relations within nature.
+
+So far I have discussed the bifurcation of nature in connexion with the
+theories of absolute time and of absolute space. My reason has been that
+the introduction of the relational theories only weakens the case for
+bifurcation, and I wished to discuss this case on its strongest grounds.
+
+For instance, suppose we adopt the relational theory of space. Then the
+space in which apparent nature is set is the expression of certain
+relations between the apparent objects. It is a set of apparent
+relations between apparent relata. Apparent nature is the dream, and
+the apparent relations of space are dream relations, and the space is
+the dream space. Similarly the space in which causal nature is set is
+the expression of certain relations between the causal objects. It is
+the expression of certain facts about the causal activity which is going
+on behind the scenes. Accordingly causal space belongs to a different
+order of reality to apparent space. Hence there is no pointwise
+connexion between the two and it is meaningless to say that the
+molecules of the grass are in any place which has a determinate spatial
+relation to the place occupied by the grass which we see. This
+conclusion is very paradoxical and makes nonsense of all scientific
+phraseology. The case is even worse if we admit the relativity of time.
+For the same arguments apply, and break up time into the dream time and
+causal time which belong to different orders of reality.
+
+I have however been discussing an extreme form of the bifurcation
+theory. It is, as I think, the most defensible form. But its very
+definiteness makes it the more evidently obnoxious to criticism. The
+intermediate form allows that the nature we are discussing is always the
+nature directly known, and so far it rejects the bifurcation theory. But
+it holds that there are psychic additions to nature as thus known, and
+that these additions are in no proper sense part of nature. For example,
+we perceive the red billiard ball at its proper time, in its proper
+place, with its proper motion, with its proper hardness, and with its
+proper inertia. But its redness and its warmth, and the sound of the
+click as a cannon is made off it are psychic additions, namely,
+secondary qualities which are only the mind's way of perceiving nature.
+This is not only the vaguely prevalent theory, but is, I believe, the
+historical form of the bifurcation theory in so far as it is derived
+from philosophy. I shall call it the theory of psychic additions.
+
+This theory of psychic additions is a sound common-sense theory which
+lays immense stress on the obvious reality of time, space, solidity and
+inertia, but distrusts the minor artistic additions of colour, warmth
+and sound.
+
+The theory is the outcome of common-sense in retreat. It arose in an
+epoch when the transmission theories of science were being elaborated.
+For example, colour is the result of a transmission from the material
+object to the perceiver's eye; and what is thus transmitted is not
+colour. Thus colour is not part of the reality of the material object.
+Similarly for the same reason sounds evaporate from nature. Also warmth
+is due to the transfer of something which is not temperature. Thus we
+are left with spatio-temporal positions, and what I may term the
+'pushiness' of the body. This lands us to eighteenth and nineteenth
+century materialism, namely, the belief that what is real in nature is
+matter, in time and in space and with inertia.
+
+Evidently a distinction in quality has been presupposed separating off
+some perceptions due to touch from other perceptions. These
+touch-perceptions are perceptions of the real inertia, whereas the other
+perceptions are psychic additions which must be explained on the causal
+theory. This distinction is the product of an epoch in which physical
+science has got ahead of medical pathology and of physiology.
+Perceptions of push are just as much the outcome of transmission as are
+perceptions of colour. When colour is perceived the nerves of the body
+are excited in one way and transmit their message towards the brain, and
+when push is perceived other nerves of the body are excited in another
+way and transmit their message towards the brain. The message of the one
+set is not the conveyance of colour, and the message of the other set is
+not the conveyance of push. But in one case colour is perceived and in
+the other case the push due to the object. If you snip certain nerves,
+there is an end to the perception of colour; and if you snip certain
+other nerves, there is an end to the perception of push. It would appear
+therefore that any reasons which should remove colour from the reality
+of nature should also operate to remove inertia.
+
+Thus the attempted bifurcation of apparent nature into two parts of
+which one part is both causal for its own appearance and for the
+appearance of the other part, which is purely apparent, fails owing to
+the failure to establish any fundamental distinction between our ways of
+knowing about the two parts of nature as thus partitioned. I am not
+denying that the feeling of muscular effort historically led to the
+formulation of the concept of force. But this historical fact does not
+warrant us in assigning a superior reality in nature to material inertia
+over colour or sound. So far as reality is concerned all our
+sense-perceptions are in the same boat, and must be treated on the same
+principle. The evenness of treatment is exactly what this compromise
+theory fails to achieve.
+
+The bifurcation theory however dies hard. The reason is that there
+really is a difficulty to be faced in relating within the same system of
+entities the redness of the fire with the agitation of the molecules. In
+another lecture I will give my own explanation of the origin of the
+difficulty and of its solution.
+
+Another favourite solution, the most attenuated form which the
+bifurcation theory assumes, is to maintain that the molecules and ether
+of science are purely conceptual. Thus there is but one nature, namely
+apparent nature, and atoms and ether are merely names for logical terms
+in conceptual formulae of calculation.
+
+But what is a formula of calculation? It is presumably a statement that
+something or other is true for natural occurrences. Take the simplest of
+all formulae, Two and two make four. This--so far as it applies to
+nature--asserts that if you take two natural entities, and then again
+two other natural entities, the combined class contains four natural
+entities. Such formulae which are true for any entities cannot result in
+the production of the concepts of atoms. Then again there are formulae
+which assert that there are entities in nature with such and such
+special properties, say, for example, with the properties of the atoms
+of hydrogen. Now if there are no such entities, I fail to see how any
+statements about them can apply to nature. For example, the assertion
+that there is green cheese in the moon cannot be a premiss in any
+deduction of scientific importance, unless indeed the presence of green
+cheese in the moon has been verified by experiment. The current answer
+to these objections is that, though atoms are merely conceptual, yet
+they are an interesting and picturesque way of saying something else
+which is true of nature. But surely if it is something else that you
+mean, for heaven's sake say it. Do away with this elaborate machinery of
+a conceptual nature which consists of assertions about things which
+don't exist in order to convey truths about things which do exist. I am
+maintaining the obvious position that scientific laws, if they are true,
+are statements about entities which we obtain knowledge of as being in
+nature; and that, if the entities to which the statements refer are not
+to be found in nature, the statements about them have no relevance to
+any purely natural occurrence. Thus the molecules and electrons of
+scientific theory are, so far as science has correctly formulated its
+laws, each of them factors to be found in nature. The electrons are only
+hypothetical in so far as we are not quite certain that the electron
+theory is true. But their hypothetical character does not arise from the
+essential nature of the theory in itself after its truth has been
+granted.
+
+Thus at the end of this somewhat complex discussion, we return to the
+position which was affirmed at its beginning. The primary task of a
+philosophy of natural science is to elucidate the concept of nature,
+considered as one complex fact for knowledge, to exhibit the fundamental
+entities and the fundamental relations between entities in terms of
+which all laws of nature have to be stated, and to secure that the
+entities and relations thus exhibited are adequate for the expression of
+all the relations between entities which occur in nature.
+
+The third requisite, namely that of adequacy, is the one over which all
+the difficulty occurs. The ultimate data of science are commonly assumed
+to be time, space, material, qualities of material, and relations
+between material objects. But data as they occur in the scientific laws
+do not relate all the entities which present themselves in our
+perception of nature. For example, the wave-theory of light is an
+excellent well-established theory; but unfortunately it leaves out
+colour as perceived. Thus the perceived redness--or, other colour--has
+to be cut out of nature and made into the reaction of the mind under the
+impulse of the actual events of nature. In other words this concept of
+the fundamental relations within nature is inadequate. Thus we have to
+bend our energies to the enunciation of adequate concepts.
+
+But in so doing, are we not in fact endeavouring to solve a metaphysical
+problem? I do not think so. We are merely endeavouring to exhibit the
+type of relations which hold between the entities which we in fact
+perceive as in nature. We are not called on to make any pronouncement as
+to the psychological relation of subjects to objects or as to the status
+of either in the realm of reality. It is true that the issue of our
+endeavour may provide material which is relevant evidence for a
+discussion on that question. It can hardly fail to do so. But it is only
+evidence, and is not itself the metaphysical discussion. In order to
+make clear the character of this further discussion which is out of our
+ken, I will set before you two quotations. One is from Schelling and I
+extract the quotation from the work of the Russian philosopher Lossky
+which has recently been so excellently translated into English[4]--'In
+the "Philosophy of Nature" I considered the subject-object called nature
+in its activity of self-constructing. In order to understand it, we must
+rise to an intellectual intuition of nature. The empiricist does not
+rise thereto, and for this reason in all his explanations it is always
+_he himself_ that proves to be constructing nature. It is no wonder,
+then, that his construction and that which was to be constructed so
+seldom coincide. A _Natur-philosoph_ raises nature to independence, and
+makes it construct itself, and he never feels, therefore, the necessity
+of opposing nature as constructed (_i.e._ as experience) to real
+nature, or of correcting the one by means of the other.'
+
+[4] _The Intuitive Basis of Knowledge_, by N.�O. Lossky, transl. by Mrs
+Duddington, Macmillan and Co., 1919.
+
+The other quotation is from a paper read by the Dean of St Paul's before
+the Aristotelian Society in May of 1919. Dr Inge's paper is entitled
+'Platonism and Human Immortality,' and in it there occurs the following
+statement: 'To sum up. The Platonic doctrine of immortality rests on the
+_independence_ of the spiritual world. The spiritual world is not a
+world of unrealised ideals, over against a real world of unspiritual
+fact. It is, on the contrary, the real world, of which we have a true
+though very incomplete knowledge, over against a world of common
+experience which, as a complete whole, is not real, since it is
+compacted out of miscellaneous data, not all on the same level, by the
+help of the imagination. There is no world corresponding to the world of
+our common experience. Nature makes abstractions for us, deciding what
+range of vibrations we are to see and hear, what things we are to notice
+and remember.'
+
+I have cited these statements because both of them deal with topics
+which, though they lie outside the range of our discussion, are always
+being confused with it. The reason is that they lie proximate to our
+field of thought, and are topics which are of burning interest to the
+metaphysically minded. It is difficult for a philosopher to realise that
+anyone really is confining his discussion within the limits that I have
+set before you. The boundary is set up just where he is beginning to get
+excited. But I submit to you that among the necessary prolegomena for
+philosophy and for natural science is a thorough understanding of the
+types of entities, and types of relations among those entities, which
+are disclosed to us in our perceptions of nature.
+
+
+
+
+CHAPTER III
+
+TIME
+
+
+The two previous lectures of this course have been mainly critical. In
+the present lecture I propose to enter upon a survey of the kinds of
+entities which are posited for knowledge in sense-awareness. My purpose
+is to investigate the sorts of relations which these entities of various
+kinds can bear to each other. A classification of natural entities is
+the beginning of natural philosophy. To-day we commence with the
+consideration of Time.
+
+In the first place there is posited for us a general fact: namely,
+something is going on; there is an occurrence for definition.
+
+This general fact at once yields for our apprehension two factors, which
+I will name, the 'discerned' and the 'discernible.' The discerned is
+comprised of those elements of the general fact which are discriminated
+with their own individual peculiarities. It is the field directly
+perceived. But the entities of this field have relations to other
+entities which are not particularly discriminated in this individual
+way. These other entities are known merely as the relata in relation to
+the entities of the discerned field. Such an entity is merely a
+'something' which has such-and-such definite relations to some definite
+entity or entities in the discerned field. As being thus related, they
+are--owing to the particular character of these relations--known as
+elements of the general fact which is going on. But we are not aware of
+them except as entities fulfilling the functions of relata in these
+relations.
+
+Thus the complete general fact, posited as occurring, comprises both
+sets of entities, namely the entities perceived in their own
+individuality and other entities merely apprehended as relata without
+further definition. This complete general fact is the discernible and it
+comprises the discerned. The discernible is all nature as disclosed in
+that sense-awareness, and extends beyond and comprises all of nature as
+actually discriminated or discerned in that sense-awareness. The
+discerning or discrimination of nature is a peculiar awareness of
+special factors in nature in respect to their peculiar characters. But
+the factors in nature of which we have this peculiar sense-awareness are
+known as not comprising all the factors which together form the whole
+complex of related entities within the general fact there for
+discernment. This peculiarity of knowledge is what I call its
+unexhaustive character. This character may be metaphorically described
+by the statement that nature as perceived always has a ragged edge. For
+example, there is a world beyond the room to which our sight is confined
+known to us as completing the space-relations of the entities discerned
+within the room. The junction of the interior world of the room with the
+exterior world beyond is never sharp. Sounds and subtler factors
+disclosed in sense-awareness float in from the outside. Every type of
+sense has its own set of discriminated entities which are known to be
+relata in relation with entities not discriminated by that sense. For
+example we see something which we do not touch and we touch something
+which we do not see, and we have a general sense of the space-relations
+between the entity disclosed in sight and the entity disclosed in touch.
+Thus in the first place each of these two entities is known as a relatum
+in a general system of space-relations and in the second place the
+particular mutual relation of these two entities as related to each
+other in this general system is determined. But the general system of
+space-relations relating the entity discriminated by sight with that
+discriminated by sight is not dependent on the peculiar character of the
+other entity as reported by the alternative sense. For example, the
+space-relations of the thing seen would have necessitated an entity as a
+relatum in the place of the thing touched even although certain elements
+of its character had not been disclosed by touch. Thus apart from the
+touch an entity with a certain specific relation to the thing seen would
+have been disclosed by sense-awareness but not otherwise discriminated
+in respect to its individual character. An entity merely known as
+spatially related to some discerned entity is what we mean by the bare
+idea of 'place.' The concept of place marks the disclosure in
+sense-awareness of entities in nature known merely by their spatial
+relations to discerned entities. It is the disclosure of the discernible
+by means of its relations to the discerned.
+
+This disclosure of an entity as a relatum without further specific
+discrimination of quality is the basis of our concept of significance.
+In the above example the thing seen was significant, in that it
+disclosed its spatial relations to other entities not necessarily
+otherwise entering into consciousness. Thus significance is relatedness,
+but it is relatedness with the emphasis on one end only of the relation.
+
+For the sake of simplicity I have confined the argument to spatial
+relations; but the same considerations apply to temporal relations. The
+concept of 'period of time' marks the disclosure in sense-awareness of
+entities in nature known merely by their temporal relations to
+discerned entities. Still further, this separation of the ideas of space
+and time has merely been adopted for the sake of gaining simplicity of
+exposition by conformity to current language. What we discern is the
+specific character of a place through a period of time. This is what I
+mean by an 'event.' We discern some specific character of an event. But
+in discerning an event we are also aware of its significance as a
+relatum in the structure of events. This structure of events is the
+complex of events as related by the two relations of extension and
+cogredience. The most simple expression of the properties of this
+structure are to be found in our spatial and temporal relations. A
+discerned event is known as related in this structure to other events
+whose specific characters are otherwise not disclosed in that immediate
+awareness except so far as that they are relata within the structure.
+
+The disclosure in sense-awareness of the structure of events classifies
+events into those which are discerned in respect to some further
+individual character and those which are not otherwise disclosed except
+as elements of the structure. These signified events must include events
+in the remote past as well as events in the future. We are aware of
+these as the far off periods of unbounded time. But there is another
+classification of events which is also inherent in sense-awareness.
+These are the events which share the immediacy of the immediately
+present discerned events. These are the events whose characters together
+with those of the discerned events comprise all nature present for
+discernment. They form the complete general fact which is all nature now
+present as disclosed in that sense-awareness. It is in this second
+classification of events that the differentiation of space from time
+takes its origin. The germ of space is to be found in the mutual
+relations of events within the immediate general fact which is all
+nature now discernible, namely within the one event which is the
+totality of present nature. The relations of other events to this
+totality of nature form the texture of time.
+
+The unity of this general present fact is expressed by the concept of
+simultaneity. The general fact is the whole simultaneous occurrence of
+nature which is now for sense-awareness. This general fact is what I
+have called the discernible. But in future I will call it a 'duration,'
+meaning thereby a certain whole of nature which is limited only by the
+property of being a simultaneity. Further in obedience to the principle
+of comprising within nature the whole terminus of sense-awareness,
+simultaneity must not be conceived as an irrelevant mental concept
+imposed upon nature. Our sense-awareness posits for immediate
+discernment a certain whole, here called a 'duration'; thus a duration
+is a definite natural entity. A duration is discriminated as a complex
+of partial events, and the natural entities which are components of this
+complex are thereby said to be 'simultaneous with this duration.' Also
+in a derivative sense they are simultaneous with each other in respect
+to this duration. Thus simultaneity is a definite natural relation. The
+word 'duration' is perhaps unfortunate in so far as it suggests a mere
+abstract stretch of time. This is not what I mean. A duration is a
+concrete slab of nature limited by simultaneity which is an essential
+factor disclosed in sense-awareness.
+
+Nature is a process. As in the case of everything directly exhibited in
+sense-awareness, there can be no explanation of this characteristic of
+nature. All that can be done is to use language which may speculatively
+demonstrate it, and also to express the relation of this factor in
+nature to other factors.
+
+It is an exhibition of the process of nature that each duration happens
+and passes. The process of nature can also be termed the passage of
+nature. I definitely refrain at this stage from using the word 'time,'
+since the measurable time of science and of civilised life generally
+merely exhibits some aspects of the more fundamental fact of the passage
+of nature. I believe that in this doctrine I am in full accord with
+Bergson, though he uses 'time' for the fundamental fact which I call the
+'passage of nature.' Also the passage of nature is exhibited equally in
+spatial transition as well as in temporal transition. It is in virtue of
+its passage that nature is always moving on. It is involved in the
+meaning of this property of 'moving on' that not only is any act of
+sense-awareness just that act and no other, but the terminus of each act
+is also unique and is the terminus of no other act. Sense-awareness
+seizes its only chance and presents for knowledge something which is for
+it alone.
+
+There are two senses in which the terminus of sense-awareness is unique.
+It is unique for the sense-awareness of an individual mind and it is
+unique for the sense-awareness of all minds which are operating under
+natural conditions. There is an important distinction between the two
+cases. (i) For one mind not only is the discerned component of the
+general fact exhibited in any act of sense-awareness distinct from the
+discerned component of the general fact exhibited in any other act of
+sense-awareness of that mind, but the two corresponding durations which
+are respectively related by simultaneity to the two discerned components
+are necessarily distinct. This is an exhibition of the temporal passage
+of nature; namely, one duration has passed into the other. Thus not only
+is the passage of nature an essential character of nature in its _r�le_
+of the terminus of sense-awareness, but it is also essential for
+sense-awareness in itself. It is this truth which makes time appear to
+extend beyond nature. But what extends beyond nature to mind is not the
+serial and measurable time, which exhibits merely the character of
+passage in nature, but the quality of passage itself which is in no way
+measurable except so far as it obtains in nature. That is to say,
+'passage' is not measurable except as it occurs in nature in connexion
+with extension. In passage we reach a connexion of nature with the
+ultimate metaphysical reality. The quality of passage in durations is a
+particular exhibition in nature of a quality which extends beyond
+nature. For example passage is a quality not only of nature, which is
+the thing known, but also of sense-awareness which is the procedure of
+knowing. Durations have all the reality that nature has, though what
+that may be we need not now determine. The measurableness of time is
+derivative from the properties of durations. So also is the serial
+character of time. We shall find that there are in nature competing
+serial time-systems derived from different families of durations. These
+are a peculiarity of the character of passage as it is found in nature.
+This character has the reality of nature, but we must not necessarily
+transfer natural time to extra-natural entities. (ii) For two minds, the
+discerned components of the general facts exhibited in their respective
+acts of sense-awareness must be different. For each mind, in its
+awareness of nature is aware of a certain complex of related natural
+entities in their relations to the living body as a focus. But the
+associated durations may be identical. Here we are touching on that
+character of the passage nature which issues in the spatial relations of
+simultaneous bodies. This possible identity of the durations in the case
+of the sense-awareness of distinct minds is what binds into one nature
+the private experiences of sentient beings. We are here considering the
+spatial side of the passage of nature. Passage in this aspect of it also
+seems to extend beyond nature to mind.
+
+It is important to distinguish simultaneity from instantaneousness. I
+lay no stress on the mere current usage of the two terms. There are two
+concepts which I want to distinguish, and one I call simultaneity and
+the other instantaneousness. I hope that the words are judiciously
+chosen; but it really does not matter so long as I succeed in explaining
+my meaning. Simultaneity is the property of a group of natural elements
+which in some sense are components of a duration. A duration can be all
+nature present as the immediate fact posited by sense-awareness. A
+duration retains within itself the passage of nature. There are within
+it antecedents and consequents which are also durations which may be the
+complete specious presents of quicker consciousnesses. In other words a
+duration retains temporal thickness. Any concept of all nature as
+immediately known is always a concept of some duration though it may be
+enlarged in its temporal thickness beyond the possible specious present
+of any being known to us as existing within nature. Thus simultaneity is
+an ultimate factor in nature, immediate for sense-awareness.
+
+Instantaneousness is a complex logical concept of a procedure in thought
+by which constructed logical entities are produced for the sake of the
+simple expression in thought of properties of nature. Instantaneousness
+is the concept of all nature at an instant, where an instant is
+conceived as deprived of all temporal extension. For example we conceive
+of the distribution of matter in space at an instant. This is a very
+useful concept in science especially in applied mathematics; but it is a
+very complex idea so far as concerns its connexions with the immediate
+facts of sense-awareness. There is no such thing as nature at an instant
+posited by sense-awareness. What sense-awareness delivers over for
+knowledge is nature through a period. Accordingly nature at an instant,
+since it is not itself a natural entity, must be defined in terms of
+genuine natural entities. Unless we do so, our science, which employs
+the concept of instantaneous nature, must abandon all claim to be
+founded upon observation.
+
+I will use the term 'moment' to mean 'all nature at an instant.' A
+moment, in the sense in which the term is here used, has no temporal
+extension, and is in this respect to be contrasted with a duration which
+has such extension. What is directly yielded to our knowledge by
+sense-awareness is a duration. Accordingly we have now to explain how
+moments are derived from durations, and also to explain the purpose
+served by their introduction.
+
+A moment is a limit to which we approach as we confine attention to
+durations of minimum extension. Natural relations among the ingredients
+of a duration gain in complexity as we consider durations of increasing
+temporal extension. Accordingly there is an approach to ideal simplicity
+as we approach an ideal diminution of extension.
+
+The word 'limit' has a precise signification in the logic of number and
+even in the logic of non-numerical one-dimensional series. As used here
+it is so far a mere metaphor, and it is necessary to explain directly
+the concept which it is meant to indicate.
+
+Durations can have the two-termed relational property of extending one
+over the other. Thus the duration which is all nature during a certain
+minute extends over the duration which is all nature during the
+30th�second of that minute. This relation of 'extending
+over'--'extension' as I shall call it--is a fundamental natural relation
+whose field comprises more than durations. It is a relation which two
+limited events can have to each other. Furthermore as holding between
+durations the relation appears to refer to the purely temporal
+extension. I shall however maintain that the same relation of extension
+lies at the base both of temporal and spatial extension. This discussion
+can be postponed; and for the present we are simply concerned with the
+relation of extension as it occurs in its temporal aspect for the
+limited field of durations.
+
+The concept of extension exhibits in thought one side of the ultimate
+passage of nature. This relation holds because of the special character
+which passage assumes in nature; it is the relation which in the case of
+durations expresses the properties of 'passing over.' Thus the duration
+which was one definite minute passed over the duration which was its
+30th�second. The duration of the 30th�second was part of the duration of
+the minute. I shall use the terms 'whole' and 'part' exclusively in this
+sense, that the 'part' is an event which is extended over by the other
+event which is the 'whole.' Thus in my nomenclature 'whole' and 'part'
+refer exclusively to this fundamental relation of extension; and
+accordingly in this technical usage only events can be either wholes or
+parts.
+
+The continuity of nature arises from extension. Every event extends over
+other events, and every event is extended over by other events. Thus in
+the special case of durations which are now the only events directly
+under consideration, every duration is part of other durations; and
+every duration has other durations which are parts of it. Accordingly
+there are no maximum durations and no minimum durations. Thus there is
+no atomic structure of durations, and the perfect definition of a
+duration, so as to mark out its individuality and distinguish it from
+highly analogous durations over which it is passing, or which are
+passing over it, is an arbitrary postulate of thought. Sense-awareness
+posits durations as factors in nature but does not clearly enable
+thought to use it as distinguishing the separate individualities of the
+entities of an allied group of slightly differing durations. This is one
+instance of the indeterminateness of sense-awareness. Exactness is an
+ideal of thought, and is only realised in experience by the selection of
+a route of approximation.
+
+The absence of maximum and minimum durations does not exhaust the
+properties of nature which make up its continuity. The passage of nature
+involves the existence of a family of durations. When two durations
+belong to the same family either one contains the other, or they overlap
+each other in a subordinate duration without either containing the
+other; or they are completely separate. The excluded case is that of
+durations overlapping in finite events but not containing a third
+duration as a common part.
+
+It is evident that the relation of extension is transitive; namely as
+applied to durations, if duration A is part of duration B, and
+duration B is part of duration C, then A is part of C. Thus the
+first two cases may be combined into one and we can say that two
+durations which belong to the same family _either_ are such that there
+are durations which are parts of both _or_ are completely separate.
+
+Furthermore the converse of this proposition holds; namely, if two
+durations have other durations which are parts of both _or_ if the two
+durations are completely separate, then they belong to the same family.
+
+The further characteristics of the continuity of nature--so far as
+durations are concerned--which has not yet been formulated arises in
+connexion with a family of durations. It can be stated in this way:
+There are durations which contain as parts any two durations of the same
+family. For example a week contains as parts any two of its days. It is
+evident that a containing duration satisfies the conditions for
+belonging to the same family as the two contained durations.
+
+We are now prepared to proceed to the definition of a moment of time.
+Consider a set of durations all taken from the same family. Let it have
+the following properties: (i) of any two members of the set one contains
+the other as a part, and (ii) there is no duration which is a common
+part of every member of the set.
+
+Now the relation of whole and part is asymmetrical; and by this I mean
+that if A is part of B, then B is not part of A. Also we have
+already noted that the relation is transitive. Accordingly we can easily
+see that the durations of any set with the properties just enumerated
+must be arranged in a one-dimensional serial order in which as we
+descend the series we progressively reach durations of smaller and
+smaller temporal extension. The series may start with any arbitrarily
+assumed duration of any temporal extension, but in descending the
+series the temporal extension progressively contracts and the successive
+durations are packed one within the other like the nest of boxes of a
+Chinese toy. But the set differs from the toy in this particular: the
+toy has a smallest box which forms the end box of its series; but the
+set of durations can have no smallest duration nor can it converge
+towards a duration as its limit. For the parts either of the end
+duration or of the limit would be parts of all the durations of the set
+and thus the second condition for the set would be violated.
+
+I will call such a set of durations an 'abstractive set' of durations.
+It is evident that an abstractive set as we pass along it converges to
+the ideal of all nature with no temporal extension, namely, to the ideal
+of all nature at an instant. But this ideal is in fact the ideal of a
+nonentity. What the abstractive set is in fact doing is to guide thought
+to the consideration of the progressive simplicity of natural relations
+as we progressively diminish the temporal extension of the duration
+considered. Now the whole point of the procedure is that the
+quantitative expressions of these natural properties do converge to
+limits though the abstractive set does not converge to any limiting
+duration. The laws relating these quantitative limits are the laws of
+nature 'at an instant,' although in truth there is no nature at an
+instant and there is only the abstractive set. Thus an abstractive set
+is effectively the entity meant when we consider an instant of time
+without temporal extension. It subserves all the necessary purposes of
+giving a definite meaning to the concept of the properties of nature at
+an instant. I fully agree that this concept is fundamental in the
+expression of physical science. The difficulty is to express our
+meaning in terms of the immediate deliverances of sense-awareness, and I
+offer the above explanation as a complete solution of the problem.
+
+In this explanation a moment is the set of natural properties reached by
+a route of approximation. An abstractive series is a route of
+approximation. There are different routes of approximation to the same
+limiting set of the properties of nature. In other words there are
+different abstractive sets which are to be regarded as routes of
+approximation to the same moment. Accordingly there is a certain amount
+of technical detail necessary in explaining the relations of such
+abstractive sets with the same convergence and in guarding against
+possible exceptional cases. Such details are not suitable for exposition
+in these lectures, and I have dealt with them fully elsewhere[5].
+
+[5] Cf. _An Enquiry concerning the Principles of Natural Knowledge_,
+Cambridge University Press, 1919.
+
+It is more convenient for technical purposes to look on a moment as
+being the class of all abstractive sets of durations with the same
+convergence. With this definition (provided that we can successfully
+explain what we mean by the 'same convergence' apart from a detailed
+knowledge of the set of natural properties arrived at by approximation)
+a moment is merely a class of sets of durations whose relations of
+extension in respect to each other have certain definite peculiarities.
+We may term these connexions of the component durations the 'extrinsic'
+properties of a moment; the 'intrinsic' properties of the moment are the
+properties of nature arrived at as a limit as we proceed along any one
+of its abstractive sets. These are the properties of nature 'at that
+moment,' or 'at that instant.'
+
+The durations which enter into the composition of a moment all belong to
+one family. Thus there is one family of moments corresponding to one
+family of durations. Also if we take two moments of the same family,
+among the durations which enter into the composition of one moment the
+smaller durations are completely separated from the smaller durations
+which enter into the composition of the other moment. Thus the two
+moments in their intrinsic properties must exhibit the limits of
+completely different states of nature. In this sense the two moments are
+completely separated. I will call two moments of the same family
+'parallel.'
+
+Corresponding to each duration there are two moments of the associated
+family of moments which are the boundary moments of that duration. A
+'boundary moment' of a duration can be defined in this way. There are
+durations of the same family as the given duration which overlap it but
+are not contained in it. Consider an abstractive set of such durations.
+Such a set defines a moment which is just as much without the duration
+as within it. Such a moment is a boundary moment of the duration. Also
+we call upon our sense-awareness of the passage of nature to inform us
+that there are two such boundary moments, namely the earlier one and the
+later one. We will call them the initial and the final boundaries.
+
+There are also moments of the same family such that the shorter
+durations in their composition are entirely separated from the given
+duration. Such moments will be said to lie 'outside' the given duration.
+Again other moments of the family are such that the shorter durations in
+their composition are parts of the given duration. Such moments are said
+to lie 'within' the given duration or to 'inhere' in it. The whole
+family of parallel moments is accounted for in this way by reference to
+any given duration of the associated family of durations. Namely, there
+are moments of the family which lie without the given duration, there
+are the two moments which are the boundary moments of the given
+duration, and the moments which lie within the given duration.
+Furthermore any two moments of the same family are the boundary moments
+of some one duration of the associated family of durations.
+
+It is now possible to define the serial relation of temporal order among
+the moments of a family. For let A and C be any two moments of the
+family, these moments are the boundary moments of one duration d of
+the associated family, and any moment B which lies within the duration
+d will be said to lie between the moments A and C. Thus the
+three-termed relation of 'lying-between' as relating three moments A,
+B, and C is completely defined. Also our knowledge of the passage of
+nature assures us that this relation distributes the moments of the
+family into a serial order. I abstain from enumerating the definite
+properties which secure this result, I have enumerated them in my
+recently published book[6] to which I have already referred. Furthermore
+the passage of nature enables us to know that one direction along the
+series corresponds to passage into the future and the other direction
+corresponds to retrogression towards the past.
+
+[6] Cf. _Enquiry_.
+
+Such an ordered series of moments is what we mean by time defined as a
+series. Each element of the series exhibits an instantaneous state of
+nature. Evidently this serial time is the result of an intellectual
+process of abstraction. What I have done is to give precise definitions
+of the procedure by which the abstraction is effected. This procedure is
+merely a particular case of the general method which in my book I name
+the 'method of extensive abstraction.' This serial time is evidently not
+the very passage of nature itself. It exhibits some of the natural
+properties which flow from it. The state of nature 'at a moment' has
+evidently lost this ultimate quality of passage. Also the temporal
+series of moments only retains it as an extrinsic relation of entities
+and not as the outcome of the essential being of the terms of the
+series.
+
+Nothing has yet been said as to the measurement of time. Such
+measurement does not follow from the mere serial property of time; it
+requires a theory of congruence which will be considered in a later
+lecture.
+
+In estimating the adequacy of this definition of the temporal series as
+a formulation of experience it is necessary to discriminate between the
+crude deliverance of sense-awareness and our intellectual theories. The
+lapse of time is a measurable serial quantity. The whole of scientific
+theory depends on this assumption and any theory of time which fails to
+provide such a measurable series stands self-condemned as unable to
+account for the most salient fact in experience. Our difficulties only
+begin when we ask what it is that is measured. It is evidently something
+so fundamental in experience that we can hardly stand back from it and
+hold it apart so as to view it in its own proportions.
+
+We have first to make up our minds whether time is to be found in nature
+or nature is to be found in time. The difficulty of the latter
+alternative--namely of making time prior to nature--is that time then
+becomes a metaphysical enigma. What sort of entities are its instants
+or its periods? The dissociation of time from events discloses to our
+immediate inspection that the attempt to set up time as an independent
+terminus for knowledge is like the effort to find substance in a shadow.
+There is time because there are happenings, and apart from happenings
+there is nothing.
+
+It is necessary however to make a distinction. In some sense time
+extends beyond nature. It is not true that a timeless sense-awareness
+and a timeless thought combine to contemplate a timeful nature.
+Sense-awareness and thought are themselves processes as well as their
+termini in nature. In other words there is a passage of sense-awareness
+and a passage of thought. Thus the reign of the quality of passage
+extends beyond nature. But now the distinction arises between passage
+which is fundamental and the temporal series which is a logical
+abstraction representing some of the properties of nature. A temporal
+series, as we have defined it, represents merely certain properties of a
+family of durations--properties indeed which durations only possess
+because of their partaking of the character of passage, but on the other
+hand properties which only durations do possess. Accordingly time in the
+sense of a measurable temporal series is a character of nature only, and
+does not extend to the processes of thought and of sense-awareness
+except by a correlation of these processes with the temporal series
+implicated in their procedures.
+
+So far the passage of nature has been considered in connexion with the
+passage of durations; and in this connexion it is peculiarly associated
+with temporal series. We must remember however that the character of
+passage is peculiarly associated with the extension of events, and that
+from this extension spatial transition arises just as much as temporal
+transition. The discussion of this point is reserved for a later lecture
+but it is necessary to remember it now that we are proceeding to discuss
+the application of the concept of passage beyond nature, otherwise we
+shall have too narrow an idea of the essence of passage.
+
+It is necessary to dwell on the subject of sense-awareness in this
+connexion as an example of the way in which time concerns mind, although
+measurable time is a mere abstract from nature and nature is closed to
+mind.
+
+Consider sense-awareness--not its terminus which is nature, but
+sense-awareness in itself as a procedure of mind. Sense-awareness is a
+relation of mind to nature. Accordingly we are now considering mind as a
+relatum in sense-awareness. For mind there is the immediate
+sense-awareness and there is memory. The distinction between memory and
+the present immediacy has a double bearing. On the one hand it discloses
+that mind is not impartially aware of all those natural durations to
+which it is related by awareness. Its awareness shares in the passage of
+nature. We can imagine a being whose awareness, conceived as his private
+possession, suffers no transition, although the terminus of his
+awareness is our own transient nature. There is no essential reason why
+memory should not be raised to the vividness of the present fact; and
+then from the side of mind, What is the difference between the present
+and the past? Yet with this hypothesis we can also suppose that the
+vivid remembrance and the present fact are posited in awareness as in
+their temporal serial order. Accordingly we must admit that though we
+can imagine that mind in the operation of sense-awareness might be free
+from any character of passage, yet in point of fact our experience of
+sense-awareness exhibits our minds as partaking in this character.
+
+On the other hand the mere fact of memory is an escape from transience.
+In memory the past is present. It is not present as overleaping the
+temporal succession of nature, but it is present as an immediate fact
+for the mind. Accordingly memory is a disengagement of the mind from the
+mere passage of nature; for what has passed for nature has not passed
+for mind.
+
+Furthermore the distinction between memory and the immediate present is
+not so clear as it is conventional to suppose. There is an intellectual
+theory of time as a moving knife-edge, exhibiting a present fact without
+temporal extension. This theory arises from the concept of an ideal
+exactitude of observation. Astronomical observations are successively
+refined to be exact to tenths, to hundredths, and to thousandths of
+seconds. But the final refinements are arrived at by a system of
+averaging, and even then present us with a stretch of time as a margin
+of error. Here error is merely a conventional term to express the fact
+that the character of experience does not accord with the ideal of
+thought. I have already explained how the concept of a moment
+conciliates the observed fact with this ideal; namely, there is a
+limiting simplicity in the quantitative expression of the properties of
+durations, which is arrived at by considering any one of the abstractive
+sets included in the moment. In other words the extrinsic character of
+the moment as an aggregate of durations has associated with it the
+intrinsic character of the moment which is the limiting expression of
+natural properties.
+
+Thus the character of a moment and the ideal of exactness which it
+enshrines do not in any way weaken the position that the ultimate
+terminus of awareness is a duration with temporal thickness. This
+immediate duration is not clearly marked out for our apprehension. Its
+earlier boundary is blurred by a fading into memory, and its later
+boundary is blurred by an emergence from anticipation. There is no sharp
+distinction either between memory and the present immediacy or between
+the present immediacy and anticipation. The present is a wavering
+breadth of boundary between the two extremes. Thus our own
+sense-awareness with its extended present has some of the character of
+the sense-awareness of the imaginary being whose mind was free from
+passage and who contemplated all nature as an immediate fact. Our own
+present has its antecedents and its consequents, and for the imaginary
+being all nature has its antecedent and its consequent durations. Thus
+the only difference in this respect between us and the imaginary being
+is that for him all nature shares in the immediacy of our present
+duration.
+
+The conclusion of this discussion is that so far as sense-awareness is
+concerned there is a passage of mind which is distinguishable from the
+passage of nature though closely allied with it. We may speculate, if we
+like, that this alliance of the passage of mind with the passage of
+nature arises from their both sharing in some ultimate character of
+passage which dominates all being. But this is a speculation in which we
+have no concern. The immediate deduction which is sufficient for us is
+that--so far as sense-awareness is concerned--mind is not in time or in
+space in the same sense in which the events of nature are in time, but
+that it is derivatively in time and in space by reason of the peculiar
+alliance of its passage with the passage of nature. Thus mind is in time
+and in space in a sense peculiar to itself. This has been a long
+discussion to arrive at a very simple and obvious conclusion. We all
+feel that in some sense our minds are here in this room and at this
+time. But it is not quite in the same sense as that in which the events
+of nature which are the existences of our brains have their spatial and
+temporal positions. The fundamental distinction to remember is that
+immediacy for sense-awareness is not the same as instantaneousness for
+nature. This last conclusion bears on the next discussion with which I
+will terminate this lecture. This question can be formulated thus, Can
+alternative temporal series be found in nature?
+
+A few years ago such a suggestion would have been put aside as being
+fantastically impossible. It would have had no bearing on the science
+then current, and was akin to no ideas which had ever entered into the
+dreams of philosophy. The eighteenth and nineteenth centuries accepted
+as their natural philosophy a certain circle of concepts which were as
+rigid and definite as those of the philosophy of the middle ages, and
+were accepted with as little critical research. I will call this natural
+philosophy 'materialism.' Not only were men of science materialists, but
+also adherents of all schools of philosophy. The idealists only differed
+from the philosophic materialists on question of the alignment of nature
+in reference to mind. But no one had any doubt that the philosophy of
+nature considered in itself was of the type which I have called
+materialism. It is the philosophy which I have already examined in my
+two lectures of this course preceding the present one. It can be
+summarised as the belief that nature is an aggregate of material and
+that this material exists in some sense _at_ each successive member of a
+one-dimensional series of extensionless instants of time. Furthermore
+the mutual relations of the material entities at each instant formed
+these entities into a spatial configuration in an unbounded space. It
+would seem that space--on this theory--would be as instantaneous as the
+instants, and that some explanation is required of the relations between
+the successive instantaneous spaces. The materialistic theory is however
+silent on this point; and the succession of instantaneous spaces is
+tacitly combined into one persistent space. This theory is a purely
+intellectual rendering of experience which has had the luck to get
+itself formulated at the dawn of scientific thought. It has dominated
+the language and the imagination of science since science flourished in
+Alexandria, with the result that it is now hardly possible to speak
+without appearing to assume its immediate obviousness.
+
+But when it is distinctly formulated in the abstract terms in which I
+have just stated it, the theory is very far from obvious. The passing
+complex of factors which compose the fact which is the terminus of
+sense-awareness places before us nothing corresponding to the trinity of
+this natural materialism. This trinity is composed (i) of the temporal
+series of extensionless instants, (ii) of the aggregate of material
+entities, and (iii) of space which is the outcome of relations of
+matter.
+
+There is a wide gap between these presuppositions of the intellectual
+theory of materialism and the immediate deliverances of sense-awareness.
+I do not question that this materialistic trinity embodies important
+characters of nature. But it is necessary to express these characters in
+terms of the facts of experience. This is exactly what in this lecture I
+have been endeavouring to do so far as time is concerned; and we have
+now come up against the question, Is there only one temporal series? The
+uniqueness of the temporal series is presupposed in the materialist
+philosophy of nature. But that philosophy is merely a theory, like the
+Aristotelian scientific theories so firmly believed in the middle ages.
+If in this lecture I have in any way succeeded in getting behind the
+theory to the immediate facts, the answer is not nearly so certain. The
+question can be transformed into this alternative form, Is there only
+one family of durations? In this question the meaning of a 'family of
+durations' has been defined earlier in this lecture. The answer is now
+not at all obvious. On the materialistic theory the instantaneous
+present is the only field for the creative activity of nature. The past
+is gone and the future is not yet. Thus (on this theory) the immediacy
+of perception is of an instantaneous present, and this unique present is
+the outcome of the past and the promise of the future. But we deny this
+immediately given instantaneous present. There is no such thing to be
+found in nature. As an ultimate fact it is a nonentity. What is
+immediate for sense-awareness is a duration. Now a duration has within
+itself a past and a future; and the temporal breadths of the immediate
+durations of sense-awareness are very indeterminate and dependent on the
+individual percipient. Accordingly there is no unique factor in nature
+which for every percipient is pre-eminently and necessarily the present.
+The passage of nature leaves nothing between the past and the future.
+What we perceive as present is the vivid fringe of memory tinged with
+anticipation. This vividness lights up the discriminated field within a
+duration. But no assurance can thereby be given that the happenings of
+nature cannot be assorted into other durations of alternative families.
+We cannot even know that the series of immediate durations posited by
+the sense-awareness of one individual mind all necessarily belong to the
+same family of durations. There is not the slightest reason to believe
+that this is so. Indeed if my theory of nature be correct, it will not
+be the case.
+
+The materialistic theory has all the completeness of the thought of the
+middle ages, which had a complete answer to everything, be it in heaven
+or in hell or in nature. There is a trimness about it, with its
+instantaneous present, its vanished past, its non-existent future, and
+its inert matter. This trimness is very medieval and ill accords with
+brute fact.
+
+The theory which I am urging admits a greater ultimate mystery and a
+deeper ignorance. The past and the future meet and mingle in the
+ill-defined present. The passage of nature which is only another name
+for the creative force of existence has no narrow ledge of definite
+instantaneous present within which to operate. Its operative presence
+which is now urging nature forward must be sought for throughout the
+whole, in the remotest past as well as in the narrowest breadth of any
+present duration. Perhaps also in the unrealised future. Perhaps also in
+the future which might be as well as the actual future which will be. It
+is impossible to meditate on time and the mystery of the creative
+passage of nature without an overwhelming emotion at the limitations of
+human intelligence.
+
+
+
+
+CHAPTER IV
+
+THE METHOD OF EXTENSIVE ABSTRACTION
+
+
+To-day's lecture must commence with the consideration of limited events.
+We shall then be in a position to enter upon an investigation of the
+factors in nature which are represented by our conception of space.
+
+The duration which is the immediate disclosure of our sense-awareness is
+discriminated into parts. There is the part which is the life of all
+nature within a room, and there is the part which is the life of all
+nature within a table in the room. These parts are limited events. They
+have the endurance of the present duration, and they are parts of it.
+But whereas a duration is an unlimited whole and in a certain limited
+sense is all that there is, a limited event possesses a completely
+defined limitation of extent which is expressed for us in
+spatio-temporal terms.
+
+We are accustomed to associate an event with a certain melodramatic
+quality. If a man is run over, that is an event comprised within certain
+spatio-temporal limits. We are not accustomed to consider the endurance
+of the Great Pyramid throughout any definite day as an event. But the
+natural fact which is the Great Pyramid throughout a day, meaning
+thereby all nature within it, is an event of the same character as the
+man's accident, meaning thereby all nature with spatio-temporal
+limitations so as to include the man and the motor during the period
+when they were in contact.
+
+We are accustomed to analyse these events into three factors, time,
+space, and material. In fact, we at once apply to them the concepts of
+the materialistic theory of nature. I do not deny the utility of this
+analysis for the purpose of expressing important laws of nature. What I
+am denying is that anyone of these factors is posited for us in
+sense-awareness in concrete independence. We perceive one unit factor in
+nature; and this factor is that something is going on then--there. For
+example, we perceive the going-on of the Great Pyramid in its relations
+to the goings-on of the surrounding Egyptian events. We are so trained,
+both by language and by formal teaching and by the resulting
+convenience, to express our thoughts in terms of this materialistic
+analysis that intellectually we tend to ignore the true unity of the
+factor really exhibited in sense-awareness. It is this unit factor,
+retaining in itself the passage of nature, which is the primary concrete
+element discriminated in nature. These primary factors are what I mean
+by events.
+
+Events are the field of a two-termed relation, namely the relation of
+extension which was considered in the last lecture. Events are the
+things related by the relation of extension. If an event A extends
+over an event B, then B is 'part of' A, and A is a 'whole' of
+which B is a part. Whole and part are invariably used in these
+lectures in this definite sense. It follows that in reference to this
+relation any two events A and B may have any one of four relations
+to each other, namely (i) A may extend over B, or (ii) B may
+extend over A, or (iii) A and B may both extend over some third
+event C, but neither over the other, or (iv) A and B may be
+entirely separate. These alternatives can obviously be illustrated by
+Euler's diagrams as they appear in logical textbooks.
+
+The continuity of nature is the continuity of events. This continuity is
+merely the name for the aggregate of a variety of properties of events
+in connexion with the relation of extension.
+
+In the first place, this relation is transitive; secondly, every event
+contains other events as parts of itself; thirdly every event is a part
+of other events; fourthly given any two finite events there are events
+each of which contains both of them as parts; and fifthly there is a
+special relation between events which I term 'junction.'
+
+Two events have junction when there is a third event of which both
+events are parts, and which is such that no part of it is separated from
+both of the two given events. Thus two events with junction make up
+exactly one event which is in a sense their sum.
+
+Only certain pairs of events have this property. In general any event
+containing two events also contains parts which are separated from both
+events.
+
+There is an alternative definition of the junction of two events which I
+have adopted in my recent book[7]. Two events have junction when there
+is a third event such that (i) it overlaps both events and (ii) it has
+no part which is separated from both the given events. If either of
+these alternative definitions is adopted as the definition of junction,
+the other definition appears as an axiom respecting the character of
+junction as we know it in nature. But we are not thinking of logical
+definition so much as the formulation of the results of direct
+observation. There is a certain continuity inherent in the observed
+unity of an event, and these two definitions of junction are really
+axioms based on observation respecting the character of this continuity.
+
+[7] Cf. _Enquiry_.
+
+The relations of whole and part and of overlapping are particular cases
+of the junction of events. But it is possible for events to have
+junction when they are separate from each other; for example, the upper
+and the lower part of the Great Pyramid are divided by some imaginary
+horizontal plane.
+
+The continuity which nature derives from events has been obscured by the
+illustrations which I have been obliged to give. For example I have
+taken the existence of the Great Pyramid as a fairly well-known fact to
+which I could safely appeal as an illustration. This is a type of event
+which exhibits itself to us as the situation of a recognisable object;
+and in the example chosen the object is so widely recognised that it has
+received a name. An object is an entity of a different type from an
+event. For example, the event which is the life of nature within the
+Great Pyramid yesterday and to-day is divisible into two parts, namely
+the Great Pyramid yesterday and the Great Pyramid to-day. But the
+recognisable object which is also called the Great Pyramid is the same
+object to-day as it was yesterday. I shall have to consider the theory
+of objects in another lecture.
+
+The whole subject is invested with an unmerited air of subtlety by the
+fact that when the event is the situation of a well-marked object, we
+have no language to distinguish the event from the object. In the case
+of the Great Pyramid, the object is the perceived unit entity which as
+perceived remains self-identical throughout the ages; while the whole
+dance of molecules and the shifting play of the electromagnetic field
+are ingredients of the event. An object is in a sense out of time. It is
+only derivatively in time by reason of its having the relation to events
+which I term 'situation.' This relation of situation will require
+discussion in a subsequent lecture.
+
+The point which I want to make now is that being the situation of a
+well-marked object is not an inherent necessity for an event. Wherever
+and whenever something is going on, there is an event. Furthermore
+'wherever and whenever' in themselves presuppose an event, for space and
+time in themselves are abstractions from events. It is therefore a
+consequence of this doctrine that something is always going on
+everywhere, even in so-called empty space. This conclusion is in accord
+with modern physical science which presupposes the play of an
+electromagnetic field throughout space and time. This doctrine of
+science has been thrown into the materialistic form of an all-pervading
+ether. But the ether is evidently a mere idle concept--in the
+phraseology which Bacon applied to the doctrine of final causes, it is a
+barren virgin. Nothing is deduced from it; and the ether merely
+subserves the purpose of satisfying the demands of the materialistic
+theory. The important concept is that of the shifting facts of the
+fields of force. This is the concept of an ether of events which should
+be substituted for that of a material ether.
+
+It requires no illustration to assure you that an event is a complex
+fact, and the relations between two events form an almost impenetrable
+maze. The clue discovered by the common sense of mankind and
+systematically utilised in science is what I have elsewhere[8] called
+the law of convergence to simplicity by diminution of extent.
+
+[8] Cf. _Organisation of Thought_, pp.�146 et�seq. Williams and Norgate,
+1917.
+
+If A and B are two events, and A' is part of A and B' is part
+of B, then in many respects the relations between the parts A' and
+B' will be simpler than the relations between A and B. This is the
+principle which presides over all attempts at exact observation.
+
+The first outcome of the systematic use of this law has been the
+formulation of the abstract concepts of Time and Space. In the previous
+lecture I sketched how the principle was applied to obtain the
+time-series. I now proceed to consider how the spatial entities are
+obtained by the same method. The systematic procedure is identical in
+principle in both cases, and I have called the general type of procedure
+the 'method of extensive abstraction.'
+
+You will remember that in my last lecture I defined the concept of an
+abstractive set of durations. This definition can be extended so as to
+apply to any events, limited events as well as durations. The only
+change that is required is the substitution of the word 'event' for the
+word 'duration.' Accordingly an abstractive set of events is any set of
+events which possesses the two properties, (i) of any two members of the
+set one contains the other as a part, and (ii) there is no event which
+is a common part of every member of the set. Such a set, as you will
+remember, has the properties of the Chinese toy which is a nest of
+boxes, one within the other, with the difference that the toy has a
+smallest box, while the abstractive class has neither a smallest event
+nor does it converge to a limiting event which is not a member of the
+set.
+
+Thus, so far as the abstractive sets of events are concerned, an
+abstractive set converges to nothing. There is the set with its members
+growing indefinitely smaller and smaller as we proceed in thought
+towards the smaller end of the series; but there is no absolute minimum
+of any sort which is finally reached. In fact the set is just itself and
+indicates nothing else in the way of events, except itself. But each
+event has an intrinsic character in the way of being a situation of
+objects and of having parts which are situations of objects and--to
+state the matter more generally--in the way of being a field of the life
+of nature. This character can be defined by quantitative expressions
+expressing relations between various quantities intrinsic to the event
+or between such quantities and other quantities intrinsic to other
+events. In the case of events of considerable spatio-temporal extension
+this set of quantitative expressions is of bewildering complexity. If
+e be an event, let us denote by q(e) the set of quantitative expressions
+defining its character including its connexions with the rest of nature.
+Let e_1, e_2, e_3, etc. be an abstractive set, the members being so
+arranged that each member such as e_{n} extends over all the succeeding
+members such as e_{n+1}, e_{n+2} and so on. Then corresponding to the
+series
+
+    e_1, e_2, e_3, ..., e_{n}, e_{n+1}, ...,
+
+there is the series
+
+    q(e_1), q(e_2), q(e_3), ..., q(e_{n}), q(e_{n+1}), ....
+
+Call the series of events s and the series of quantitative expressions
+q(s). The series s has no last term and no events which are contained
+in every member of the series. Accordingly the series of events
+converges to nothing. It is just itself. Also the series q(s) has no
+last term. But the sets of homologous quantities running through the
+various terms of the series do converge to definite limits. For example
+if Q_1 be a quantitative measurement found in q(e_1), and Q_2 the homologue
+to Q_1 to be found in q(e_2), and Q_3 the homologue to Q_1 and Q_2 to be
+found in q(e_3), and so on, then the series
+
+    Q_1, Q_2, Q_3, ..., Q_{n}, Q_{n+1}, ...,
+
+though it has no last term, does in general converge to a definite
+limit. Accordingly there is a class of limits l(s) which is the
+class of the limits of those members of q(e_{n}) which have
+homologues throughout the series q(s) as n indefinitely increases.
+We can represent this statement diagrammatically by using an arrow (-->)
+to mean 'converges to.' Then
+
+    e_1, e_2, e_3, ..., e_{n}, e_{n+1}, ... --> nothing,
+
+and
+
+    q(e_1), q(e_2), q(e_3), ..., q(e_{n}), q(e_{n+1}), ... --> l(s).
+
+The mutual relations between the limits in the set l(s), and also
+between these limits and the limits in other sets l(s'), l(s"), ...,
+which arise from other abstractive sets s', s", etc., have a peculiar
+simplicity.
+
+Thus the set s does indicate an ideal simplicity of natural relations,
+though this simplicity is not the character of any actual event in s.
+We can make an approximation to such a simplicity which, as estimated
+numerically, is as close as we like by considering an event which is far
+enough down the series towards the small end. It will be noted that it
+is the infinite series, as it stretches away in unending succession
+towards the small end, which is of importance. The arbitrarily large
+event with which the series starts has no importance at all. We can
+arbitrarily exclude any set of events at the big end of an abstractive
+set without the loss of any important property to the set as thus
+modified.
+
+I call the limiting character of natural relations which is indicated by
+an abstractive set, the 'intrinsic character' of the set; also the
+properties, connected with the relation of whole and part as concerning
+its members, by which an abstractive set is defined together form what I
+call its 'extrinsic character.' The fact that the extrinsic character of
+an abstractive set determines a definite intrinsic character is the
+reason of the importance of the precise concepts of space and time. This
+emergence of a definite intrinsic character from an abstractive set is
+the precise meaning of the law of convergence.
+
+For example, we see a train approaching during a minute. The event which
+is the life of nature within that train during the minute is of great
+complexity and the expression of its relations and of the ingredients of
+its character baffles us. If we take one second of that minute, the more
+limited event which is thus obtained is simpler in respect to its
+ingredients, and shorter and shorter times such as a tenth of that
+second, or a hundredth, or a thousandth--so long as we have a definite
+rule giving a definite succession of diminishing events--give events
+whose ingredient characters converge to the ideal simplicity of the
+character of the train at a definite instant. Furthermore there are
+different types of such convergence to simplicity. For example, we can
+converge as above to the limiting character expressing nature at an
+instant within the whole volume of the train at that instant, or to
+nature at an instant within some portion of that volume--for example
+within the boiler of the engine--or to nature at an instant on some area
+of surface, or to nature at an instant on some line within the train, or
+to nature at an instant at some point of the train. In the last case the
+simple limiting characters arrived at will be expressed as densities,
+specific gravities, and types of material. Furthermore we need not
+necessarily converge to an abstraction which involves nature at an
+instant. We may converge to the physical ingredients of a certain point
+track throughout the whole minute. Accordingly there are different types
+of extrinsic character of convergence which lead to the approximation to
+different types of intrinsic characters as limits.
+
+We now pass to the investigation of possible connexions between
+abstractive sets. One set may 'cover' another. I define 'covering' as
+follows: An abstractive set p covers an abstractive set q when every
+member of p contains as its parts some members of q. It is evident
+that if any event e contains as a part any member of the set q, then
+owing to the transitive property of extension every succeeding member of
+the small end of q is part of e. In such a case I will say that the
+abstractive set q 'inheres in' the event e. Thus when an abstractive
+set p covers an abstractive set q, the abstractive set q inheres
+in every member of p.
+
+Two abstractive sets may each cover the other. When this is the case I
+shall call the two sets 'equal in abstractive force.' When there is no
+danger of misunderstanding I shall shorten this phrase by simply saying
+that the two abstractive sets are 'equal.' The possibility of this
+equality of abstractive sets arises from the fact that both sets, p
+and q, are infinite series towards their small ends. Thus the equality
+means, that given any event x belonging to p, we can always by
+proceeding far enough towards the small end of q find an event y
+which is part of x, and that then by proceeding far enough towards the
+small end of p we can find an event z which is part of y, and so
+on indefinitely.
+
+The importance of the equality of abstractive sets arises from the
+assumption that the intrinsic characters of the two sets are identical.
+If this were not the case exact observation would be at an end.
+
+It is evident that any two abstractive sets which are equal to a third
+abstractive set are equal to each other. An 'abstractive element' is the
+whole group of abstractive sets which are equal to any one of
+themselves. Thus all abstractive sets belonging to the same element are
+equal and converge to the same intrinsic character. Thus an abstractive
+element is the group of routes of approximation to a definite intrinsic
+character of ideal simplicity to be found as a limit among natural
+facts.
+
+If an abstractive set p covers an abstractive set q, then any
+abstractive set belonging to the abstractive element of which p is a
+member will cover any abstractive set belonging to the element of which
+q is a member. Accordingly it is useful to stretch the meaning of the
+term 'covering,' and to speak of one abstractive element 'covering'
+another abstractive element. If we attempt in like manner to stretch the
+term 'equal' in the sense of 'equal in abstractive force,' it is obvious
+that an abstractive element can only be equal to itself. Thus an
+abstractive element has a unique abstractive force and is the construct
+from events which represents one definite intrinsic character which is
+arrived at as a limit by the use of the principle of convergence to
+simplicity by diminution of extent.
+
+When an abstractive element A covers an abstractive element B, the
+intrinsic character of A in a sense includes the intrinsic character
+of B. It results that statements about the intrinsic character of B
+are in a sense statements about the intrinsic character of A; but the
+intrinsic character of A is more complex than that of B.
+
+The abstractive elements form the fundamental elements of space and
+time, and we now turn to the consideration of the properties involved in
+the formation of special classes of such elements. In my last lecture I
+have already investigated one class of abstractive elements, namely
+moments. Each moment is a group of abstractive sets, and the events
+which are members of these sets are all members of one family of
+durations. The moments of one family form a temporal series; and,
+allowing the existence of different families of moments, there will be
+alternative temporal series in nature. Thus the method of extensive
+abstraction explains the origin of temporal series in terms of the
+immediate facts of experience and at the same time allows for the
+existence of the alternative temporal series which are demanded by the
+modern theory of electromagnetic relativity.
+
+We now turn to space. The first thing to do is to get hold of the class
+of abstractive elements which are in some sense the points of space.
+Such an abstractive element must in some sense exhibit a convergence to
+an absolute minimum of intrinsic character. Euclid has expressed for all
+time the general idea of a point, as being without parts and without
+magnitude. It is this character of being an absolute minimum which we
+want to get at and to express in terms of the extrinsic characters of
+the abstractive sets which make up a point. Furthermore, points which
+are thus arrived at represent the ideal of events without any extension,
+though there are in fact no such entities as these ideal events. These
+points will not be the points of an external timeless space but of
+instantaneous spaces. We ultimately want to arrive at the timeless space
+of physical science, and also of common thought which is now tinged with
+the concepts of science. It will be convenient to reserve the term
+'point' for these spaces when we get to them. I will therefore use the
+name 'event-particles' for the ideal minimum limits to events. Thus an
+event-particle is an abstractive element and as such is a group of
+abstractive sets; and a point--namely a point of timeless space--will be
+a class of event-particles.
+
+Furthermore there is a separate timeless space corresponding to each
+separate temporal series, that is to each separate family of durations.
+We will come back to points in timeless spaces later. I merely mention
+them now that we may understand the stages of our investigation. The
+totality of event-particles will form a four-dimensional manifold, the
+extra dimension arising from time--in other words--arising from the
+points of a timeless space being each a class of event-particles.
+
+The required character of the abstractive sets which form
+event-particles would be secured if we could define them as having the
+property of being covered by any abstractive set which they cover. For
+then any other abstractive set which an abstractive set of an
+event-particle covered, would be equal to it, and would therefore be a
+member of the same event-particle. Accordingly an event-particle could
+cover no other abstractive element. This is the definition which I
+originally proposed at a congress in Paris in 1914[9]. There is however
+a difficulty involved in this definition if adopted without some further
+addition, and I am now not satisfied with the way in which I attempted
+to get over that difficulty in the paper referred to.
+
+[9] Cf. 'La Th�orie Relationniste de l'Espace,' _Rev. de M�taphysique et
+de Morale_, vol.�XXIII, 1916.
+
+The difficulty is this: When event-particles have once been defined it
+is easy to define the aggregate of event-particles forming the boundary
+of an event; and thence to define the point-contact at their boundaries
+possible for a pair of events of which one is part of the other. We can
+then conceive all the intricacies of tangency. In particular we can
+conceive an abstractive set of which all the members have point-contact
+at the same event-particle. It is then easy to prove that there will be
+no abstractive set with the property of being covered by every
+abstractive set which it covers. I state this difficulty at some length
+because its existence guides the development of our line of argument. We
+have got to annex some condition to the root property of being covered
+by any abstractive set which it covers. When we look into this question
+of suitable conditions we find that in addition to event-particles all
+the other relevant spatial and spatio-temporal abstractive elements can
+be defined in the same way by suitably varying the conditions.
+Accordingly we proceed in a general way suitable for employment beyond
+event-particles.
+
+Let {sigma} be the name of any condition which some abstractive sets
+fulfil. I say that an abstractive set is '{sigma}-prime' when it has the
+two properties, (i) that it satisfies the condition {sigma} and (ii)
+that it is covered by every abstractive set which both is covered by it
+and satisfies the condition {sigma}.
+
+In other words you cannot get any abstractive set satisfying the
+condition {sigma} which exhibits intrinsic character more simple than
+that of a {sigma}-prime.
+
+There are also the correlative abstractive sets which I call the sets of
+{sigma}-antiprimes. An abstractive set is a {sigma}-antiprime when it
+has the two properties, (i) that it satisfies the condition {sigma} and
+(ii) that it covers every abstractive set which both covers it and
+satisfies the condition {sigma}. In other words you cannot get any
+abstractive set satisfying the condition {sigma} which exhibits an
+intrinsic character more complex than that of a {sigma}-antiprime.
+
+The intrinsic character of a {sigma}-prime has a certain minimum of
+fullness among those abstractive sets which are subject to the condition
+of satisfying {sigma}; whereas the intrinsic character of a
+{sigma}-antiprime has a corresponding maximum of fullness, and includes
+all it can in the circumstances.
+
+Let us first consider what help the notion of antiprimes could give us
+in the definition of moments which we gave in the last lecture. Let the
+condition {sigma} be the property of being a class whose members are all
+durations. An abstractive set which satisfies this condition is thus an
+abstractive set composed wholly of durations. It is convenient then to
+define a moment as the group of abstractive sets which are equal to some
+{sigma}-antiprime, where the condition {sigma} has this special meaning.
+It will be found on consideration (i) that each abstractive set forming
+a moment is a {sigma}-antiprime, where {sigma} has this special meaning,
+and (ii) that we have excluded from membership of moments abstractive
+sets of durations which all have one common boundary, either the initial
+boundary or the final boundary. We thus exclude special cases which are
+apt to confuse general reasoning. The new definition of a moment, which
+supersedes our previous definition, is (by the aid of the notion of
+antiprimes) the more precisely drawn of the two, and the more useful.
+
+The particular condition which '{sigma}' stood for in the definition of
+moments included something additional to anything which can be derived
+from the bare notion of extension. A duration exhibits for thought a
+totality. The notion of totality is something beyond that of extension,
+though the two are interwoven in the notion of a duration.
+
+In the same way the particular condition '{sigma}' required for the
+definition of an event-particle must be looked for beyond the mere
+notion of extension. The same remark is also true of the particular
+conditions requisite for the other spatial elements. This additional
+notion is obtained by distinguishing between the notion of 'position'
+and the notion of convergence to an ideal zero of extension as exhibited
+by an abstractive set of events.
+
+In order to understand this distinction consider a point of the
+instantaneous space which we conceive as apparent to us in an almost
+instantaneous glance. This point is an event-particle. It has two
+aspects. In one aspect it is there, where it is. This is its position in
+the space. In another aspect it is got at by ignoring the circumambient
+space, and by concentrating attention on the smaller and smaller set of
+events which approximate to it. This is its extrinsic character. Thus a
+point has three characters, namely, its position in the whole
+instantaneous space, its extrinsic character, and its intrinsic
+character. The same is true of any other spatial element. For example an
+instantaneous volume in instantaneous space has three characters,
+namely, its position, its extrinsic character as a group of abstractive
+sets, and its intrinsic character which is the limit of natural
+properties which is indicated by any one of these abstractive sets.
+
+Before we can talk about position in instantaneous space, we must
+evidently be quite clear as to what we mean by instantaneous space in
+itself. Instantaneous space must be looked for as a character of a
+moment. For a moment is all nature at an instant. It cannot be the
+intrinsic character of the moment. For the intrinsic character tells us
+the limiting character of nature in space at that instant. Instantaneous
+space must be an assemblage of abstractive elements considered in their
+mutual relations. Thus an instantaneous space is the assemblage of
+abstractive elements covered by some one moment, and it is the
+instantaneous space of that moment.
+
+We have now to ask what character we have found in nature which is
+capable of according to the elements of an instantaneous space different
+qualities of position. This question at once brings us to the
+intersection of moments, which is a topic not as yet considered in these
+lectures.
+
+The locus of intersection of two moments is the assemblage of
+abstractive elements covered by both of them. Now two moments of the
+same temporal series cannot intersect. Two moments respectively of
+different families necessarily intersect. Accordingly in the
+instantaneous space of a moment we should expect the fundamental
+properties to be marked by the intersections with moments of other
+families. If M be a given moment, the intersection of M with another
+moment A is an instantaneous plane in the instantaneous space of M; and
+if B be a third moment intersecting both M and A, the intersection of M
+and B is another plane in the space M. Also the common intersection of
+A, B, and M is the intersection of the two planes in the space M, namely
+it is a straight line in the space M. An exceptional case arises if B
+and M intersect in the same plane as A and M. Furthermore if C be a
+fourth moment, then apart from special cases which we need not consider,
+it intersects M in a plane which the straight line (A, B, M) meets. Thus
+there is in general a common intersection of four moments of different
+families. This common intersection is an assemblage of abstractive
+elements which are each covered (or 'lie in') all four moments. The
+three-dimensional property of instantaneous space comes to this, that
+(apart from special relations between the four moments) any fifth moment
+either contains the whole of their common intersection or none of it. No
+further subdivision of the common intersection is possible by means of
+moments. The 'all or none' principle holds. This is not an _�priori_
+truth but an empirical fact of nature.
+
+It will be convenient to reserve the ordinary spatial terms 'plane,'
+'straight line,' 'point' for the elements of the timeless space of a
+time-system. Accordingly an instantaneous plane in the instantaneous
+space of a moment will be called a 'level,' an instantaneous straight
+line will be called a 'rect,' and an instantaneous point will be called
+a 'punct.' Thus a punct is the assemblage of abstractive elements which
+lie in each of four moments whose families have no special relations to
+each other. Also if P be any moment, either every abstractive element
+belonging to a given punct lies in P, or no abstractive element of
+that punct lies in P.
+
+Position is the quality which an abstractive element possesses in virtue
+of the moments in which it lies. The abstractive elements which lie in
+the instantaneous space of a given moment M are differentiated from
+each other by the various other moments which intersect M so as to
+contain various selections of these abstractive elements. It is this
+differentiation of the elements which constitutes their differentiation
+of position. An abstractive element which belongs to a punct has the
+simplest type of position in M, an abstractive element which belongs
+to a rect but not to a punct has a more complex quality of position, an
+abstractive element which belongs to a level and not to a rect has a
+still more complex quality of position, and finally the most complex
+quality of position belongs to an abstractive element which belongs to a
+volume and not to a level. A volume however has not yet been defined.
+This definition will be given in the next lecture.
+
+Evidently levels, rects, and puncts in their capacity as infinite
+aggregates cannot be the termini of sense-awareness, nor can they be
+limits which are approximated to in sense-awareness. Any one member of a
+level has a certain quality arising from its character as also belonging
+to a certain set of moments, but the level as a whole is a mere logical
+notion without any route of approximation along entities posited in
+sense-awareness.
+
+On the other hand an event-particle is defined so as to exhibit this
+character of being a route of approximation marked out by entities
+posited in sense-awareness. A definite event-particle is defined in
+reference to a definite punct in the following manner: Let the condition
+{sigma} mean the property of covering all the abstractive elements which
+are members of that punct; so that an abstractive set which satisfies
+the condition {sigma} is an abstractive set which covers every
+abstractive element belonging to the punct. Then the definition of the
+event-particle associated with the punct is that it is the group of all
+the {sigma}-primes, where {sigma} has this particular meaning.
+
+It is evident that--with this meaning of {sigma}--every abstractive set
+equal to a {sigma}-prime is itself a {sigma}-prime. Accordingly an
+event-particle as thus defined is an abstractive element, namely it is
+the group of those abstractive sets which are each equal to some given
+abstractive set. If we write out the definition of the event-particle
+associated with some given punct, which we will call {pi}, it is as
+follows: The event-particle associated with {pi} is the group of
+abstractive classes each of which has the two properties (i) that it
+covers every abstractive set in {pi} and (ii) that all the abstractive
+sets which also satisfy the former condition as to {pi} and which it
+covers, also cover it.
+
+An event-particle has position by reason of its association with a
+punct, and conversely the punct gains its derived character as a route
+of approximation from its association with the event-particle. These two
+characters of a point are always recurring in any treatment of the
+derivation of a point from the observed facts of nature, but in general
+there is no clear recognition of their distinction.
+
+The peculiar simplicity of an instantaneous point has a twofold origin,
+one connected with position, that is to say with its character as a
+punct, and the other connected with its character as an event-particle.
+The simplicity of the punct arises from its indivisibility by a moment.
+
+The simplicity of an event-particle arises from the indivisibility of
+its intrinsic character. The intrinsic character of an event-particle is
+indivisible in the sense that every abstractive set covered by it
+exhibits the same intrinsic character. It follows that, though there are
+diverse abstractive elements covered by event-particles, there is no
+advantage to be gained by considering them since we gain no additional
+simplicity in the expression of natural properties.
+
+These two characters of simplicity enjoyed respectively by
+event-particles and puncts define a meaning for Euclid's phrase,
+'without parts and without magnitude.'
+
+It is obviously convenient to sweep away out of our thoughts all these
+stray abstractive sets which are covered by event-particles without
+themselves being members of them. They give us nothing new in the way of
+intrinsic character. Accordingly we can think of rects and levels as
+merely loci of event-particles. In so doing we are also cutting out
+those abstractive elements which cover sets of event-particles, without
+these elements being event-particles themselves. There are classes of
+these abstractive elements which are of great importance. I will
+consider them later on in this and in other lectures. Meanwhile we will
+ignore them. Also I will always speak of 'event-particles' in preference
+to 'puncts,' the latter being an artificial word for which I have no
+great affection.
+
+Parallelism among rects and levels is now explicable.
+
+Consider the instantaneous space belonging to a moment A, and let A
+belong to the temporal series of moments which I will call {alpha}.
+Consider any other temporal series of moments which I will call {beta}.
+The moments of {beta} do not intersect each other and they intersect the
+moment A in a family of levels. None of these levels can intersect, and
+they form a family of parallel instantaneous planes in the instantaneous
+space of moment A. Thus the parallelism of moments in a temporal series
+begets the parallelism of levels in an instantaneous space, and
+thence--as it is easy to see--the parallelism of rects. Accordingly the
+Euclidean property of space arises from the parabolic property of time.
+It may be that there is reason to adopt a hyperbolic theory of time and
+a corresponding hyperbolic theory of space. Such a theory has not been
+worked out, so it is not possible to judge as to the character of the
+evidence which could be brought forward in its favour.
+
+The theory of order in an instantaneous space is immediately derived
+from time-order. For consider the space of a moment M. Let {alpha} be
+the name of a time-system to which M does not belong. Let A_1, A_2, A_3
+etc. be moments of {alpha} in the order of their occurrences. Then A_1,
+A_2, A_3, etc. intersect M in parallel levels l_1, l_2, l_3, etc. Then
+the relative order of the parallel levels in the space of M is the same
+as the relative order of the corresponding moments in the time-system
+{alpha}. Any rect in M which intersects all these levels in its set of
+puncts, thereby receives for its puncts an order of position on it. So
+spatial order is derivative from temporal order. Furthermore there are
+alternative time-systems, but there is only one definite spatial order
+in each instantaneous space. Accordingly the various modes of deriving
+spatial order from diverse time-systems must harmonise with one spatial
+order in each instantaneous space. In this way also diverse time-orders
+are comparable.
+
+We have two great questions still on hand to be settled before our
+theory of space is fully adjusted. One of these is the question of the
+determination of the methods of measurement within the space, in other
+words, the congruence-theory of the space. The measurement of space will
+be found to be closely connected with the measurement of time, with
+respect to which no principles have as yet been determined. Thus our
+congruence-theory will be a theory both for space and for time. Secondly
+there is the determination of the timeless space which corresponds to
+any particular time-system with its infinite set of instantaneous spaces
+in its successive moments. This is the space--or rather, these are the
+spaces--of physical science. It is very usual to dismiss this space by
+saying that this is conceptual. I do not understand the virtue of these
+phrases. I suppose that it is meant that the space is the conception of
+something in nature. Accordingly if the space of physical science is to
+be called conceptual, I ask, What in nature is it the conception of? For
+example, when we speak of a point in the timeless space of physical
+science, I suppose that we are speaking of something in nature. If we
+are not so speaking, our scientists are exercising their wits in the
+realms of pure fantasy, and this is palpably not the case. This demand
+for a definite Habeas Corpus Act for the production of the relevant
+entities in nature applies whether space be relative or absolute. On the
+theory of relative space, it may perhaps be argued that there is no
+timeless space for physical science, and that there is only the
+momentary series of instantaneous spaces.
+
+An explanation must then be asked for the meaning of the very common
+statement that such and such a man walked four miles in some definite
+hour. How can you measure distance from one space into another space? I
+understand walking out of the sheet of an ordnance map. But the meaning
+of saying that Cambridge at 10�o'clock this morning in the appropriate
+instantaneous space for that instant is 52�miles from London at
+11�o'clock this morning in the appropriate instantaneous space for that
+instant beats me entirely. I think that, by the time a meaning has been
+produced for this statement, you will find that you have constructed
+what is in fact a timeless space. What I cannot understand is how to
+produce an explanation of meaning without in effect making some such
+construction. Also I may add that I do not know how the instantaneous
+spaces are thus correlated into one space by any method which is
+available on the current theories of space.
+
+You will have noticed that by the aid of the assumption of alternative
+time-systems, we are arriving at an explanation of the character of
+space. In natural science 'to explain' means merely to discover
+'interconnexions.' For example, in one sense there is no explanation of
+the red which you see. It is red, and there is nothing else to be said
+about it. Either it is posited before you in sense-awareness or you are
+ignorant of the entity red. But science has explained red. Namely it has
+discovered interconnexions between red as a factor in nature and other
+factors in nature, for example waves of light which are waves of
+electromagnetic disturbances. There are also various pathological
+states of the body which lead to the seeing of red without the
+occurrence of light waves. Thus connexions have been discovered between
+red as posited in sense-awareness and various other factors in nature.
+The discovery of these connexions constitutes the scientific explanation
+of our vision of colour. In like manner the dependence of the character
+of space on the character of time constitutes an explanation in the
+sense in which science seeks to explain. The systematising intellect
+abhors bare facts. The character of space has hitherto been presented as
+a collection of bare facts, ultimate and disconnected. The theory which
+I am expounding sweeps away this disconnexion of the facts of space.
+
+
+
+
+CHAPTER V
+
+SPACE AND MOTION
+
+
+The topic for this lecture is the continuation of the task of explaining
+the construction of spaces as abstracts from the facts of nature. It was
+noted at the close of the previous lecture that the question of
+congruence had not been considered, nor had the construction of a
+timeless space which should correlate the successive momentary spaces of
+a given time-system. Furthermore it was also noted that there were many
+spatial abstractive elements which we had not yet defined. We will first
+consider the definition of some of these abstractive elements, namely
+the definitions of solids, of areas, and of routes. By a 'route' I mean
+a linear segment, whether straight or curved. The exposition of these
+definitions and the preliminary explanations necessary will, I hope,
+serve as a general explanation of the function of event-particles in the
+analysis of nature.
+
+We note that event-particles have 'position' in respect to each other.
+In the last lecture I explained that 'position' was quality gained by a
+spatial element in virtue of the intersecting moments which covered it.
+Thus each event-particle has position in this sense. The simplest mode
+of expressing the position in nature of an event-particle is by first
+fixing on any definite time-system. Call it {alpha}. There will be one
+moment of the temporal series of {alpha} which covers the given
+event-particle. Thus the position of the event-particle in the temporal
+series {alpha} is defined by this moment, which we will call M. The
+position of the particle in the space of M is then fixed in the ordinary
+way by three levels which intersect in it and in it only. This procedure
+of fixing the position of an event-particle shows that the aggregate of
+event-particles forms a four-dimensional manifold. A finite event
+occupies a limited chunk of this manifold in a sense which I now proceed
+to explain.
+
+Let e be any given event. The manifold of event-particles falls into
+three sets in reference to e. Each event-particle is a group of equal
+abstractive sets and each abstractive set towards its small-end is
+composed of smaller and smaller finite events. When we select from these
+finite events which enter into the make-up of a given event-particle
+those which are small enough, one of three cases must occur. Either (i)
+all of these small events are entirely separate from the given event
+e, or (ii) all of these small events are parts of the event e, or
+(iii) all of these small events overlap the event e but are not parts
+of it. In the first case the event-particle will be said to 'lie
+outside' the event e, in the second case the event-particle will be
+said to 'lie inside' the event e, and in the third case the
+event-particle will be said to be a 'boundary-particle' of the event
+e. Thus there are three sets of particles, namely the set of those
+which lie outside the event e, the set of those which lie inside the
+event e, and the boundary of the event e which is the set of
+boundary-particles of e. Since an event is four-dimensional, the
+boundary of an event is a three-dimensional manifold. For a finite event
+there is a continuity of boundary; for a duration the boundary consists
+of those event-particles which are covered by either of the two bounding
+moments. Thus the boundary of a duration consists of two momentary
+three-dimensional spaces. An event will be said to 'occupy' the
+aggregate of event-particles which lie within it.
+
+Two events which have 'junction' in the sense in which junction was
+described in my last lecture, and yet are separated so that neither
+event either overlaps or is part of the other event, are said to be
+'adjoined.'
+
+This relation of adjunction issues in a peculiar relation between the
+boundaries of the two events. The two boundaries must have a common
+portion which is in fact a continuous three-dimensional locus of
+event-particles in the four-dimensional manifold.
+
+A three-dimensional locus of event-particles which is the common portion
+of the boundary of two adjoined events will be called a 'solid.' A solid
+may or may not lie completely in one moment. A solid which does not lie
+in one moment will be called 'vagrant.' A solid which does lie in one
+moment will be called a volume. A volume may be defined as the locus of
+the event-particles in which a moment intersects an event, provided that
+the two do intersect. The intersection of a moment and an event will
+evidently consist of those event-particles which are covered by the
+moment and lie in the event. The identity of the two definitions of a
+volume is evident when we remember that an intersecting moment divides
+the event into two adjoined events.
+
+A solid as thus defined, whether it be vagrant or be a volume, is a mere
+aggregate of event-particles illustrating a certain quality of position.
+We can also define a solid as an abstractive element. In order to do so
+we recur to the theory of primes explained in the preceding lecture. Let
+the condition named {sigma} stand for the fact that each of the events
+of any abstractive set satisfying it has all the event-particles of some
+particular solid lying in it. Then the group of all the {sigma}-primes
+is the abstractive element which is associated with the given solid. I
+will call this abstractive element the solid as an abstractive element,
+and I will call the aggregate of event-particles the solid as a locus.
+The instantaneous volumes in instantaneous space which are the ideals of
+our sense-perception are volumes as abstractive elements. What we really
+perceive with all our efforts after exactness are small events far
+enough down some abstractive set belonging to the volume as an
+abstractive element.
+
+It is difficult to know how far we approximate to any perception of
+vagrant solids. We certainly do not think that we make any such
+approximation. But then our thoughts--in the case of people who do think
+about such topics--are so much under the control of the materialistic
+theory of nature that they hardly count for evidence. If Einstein's
+theory of gravitation has any truth in it, vagrant solids are of great
+importance in science. The whole boundary of a finite event may be
+looked on as a particular example of a vagrant solid as a locus. Its
+particular property of being closed prevents it from being definable as
+an abstractive element.
+
+When a moment intersects an event, it also intersects the boundary of
+that event. This locus, which is the portion of the boundary contained
+in the moment, is the bounding surface of the corresponding volume of
+that event contained in the moment. It is a two-dimensional locus.
+
+The fact that every volume has a bounding surface is the origin of the
+Dedekindian continuity of space.
+
+Another event may be cut by the same moment in another volume and this
+volume will also have its boundary. These two volumes in the
+instantaneous space of one moment may mutually overlap in the familiar
+way which I need not describe in detail and thus cut off portions from
+each other's surfaces. These portions of surfaces are 'momental areas.'
+
+It is unnecessary at this stage to enter into the complexity of a
+definition of vagrant areas. Their definition is simple enough when the
+four-dimensional manifold of event-particles has been more fully
+explored as to its properties.
+
+Momental areas can evidently be defined as abstractive elements by
+exactly the same method as applied to solids. We have merely to
+substitute 'area' for a 'solid' in the words of the definition already
+given. Also, exactly as in the analogous case of a solid, what we
+perceive as an approximation to our ideal of an area is a small event
+far enough down towards the small end of one of the equal abstractive
+sets which belongs to the area as an abstractive element.
+
+Two momental areas lying in the same moment can cut each other in a
+momental segment which is not necessarily rectilinear. Such a segment
+can also be defined as an abstractive element. It is then called a
+'momental route.' We will not delay over any general consideration of
+these momental routes, nor is it important for us to proceed to the
+still wider investigation of vagrant routes in general. There are
+however two simple sets of routes which are of vital importance. One is
+a set of momental routes and the other of vagrant routes. Both sets can
+be classed together as straight routes. We proceed to define them
+without any reference to the definitions of volumes and surfaces.
+
+The two types of straight routes will be called rectilinear routes and
+stations. Rectilinear routes are momental routes and stations are
+vagrant routes. Rectilinear routes are routes which in a sense lie in
+rects. Any two event-particles on a rect define the set of
+event-particles which lie between them on that rect. Let the
+satisfaction of the condition {sigma} by an abstractive set mean that
+the two given event-particles and the event-particles lying between them
+on the rect all lie in every event belonging to the abstractive set. The
+group of {sigma}-primes, where {sigma} has this meaning, form an
+abstractive element. Such abstractive elements are rectilinear routes.
+They are the segments of instantaneous straight lines which are the
+ideals of exact perception. Our actual perception, however exact, will
+be the perception of a small event sufficiently far down one of the
+abstractive sets of the abstractive element.
+
+A station is a vagrant route and no moment can intersect any station in
+more than one event-particle. Thus a station carries with it a
+comparison of the positions in their respective moments of the
+event-particles covered by it. Rects arise from the intersection of
+moments. But as yet no properties of events have been mentioned by which
+any analogous vagrant loci can be found out.
+
+The general problem for our investigation is to determine a method of
+comparison of position in one instantaneous space with positions in
+other instantaneous spaces. We may limit ourselves to the spaces of the
+parallel moments of one time-system. How are positions in these various
+spaces to be compared? In other words, What do we mean by motion? It is
+the fundamental question to be asked of any theory of relative space,
+and like many other fundamental questions it is apt to be left
+unanswered. It is not an answer to reply, that we all know what we mean
+by motion. Of course we do, so far as sense-awareness is concerned. I am
+asking that your theory of space should provide nature with something to
+be observed. You have not settled the question by bringing forward a
+theory according to which there is nothing to be observed, and by then
+reiterating that nevertheless we do observe this non-existent fact.
+Unless motion is something as a fact in nature, kinetic energy and
+momentum and all that depends on these physical concepts evaporate from
+our list of physical realities. Even in this revolutionary age my
+conservatism resolutely opposes the identification of momentum and
+moonshine.
+
+Accordingly I assume it as an axiom, that motion is a physical fact. It
+is something that we perceive as in nature. Motion presupposes rest.
+Until theory arose to vitiate immediate intuition, that is to say to
+vitiate the uncriticised judgments which immediately arise from
+sense-awareness, no one doubted that in motion you leave behind that
+which is at rest. Abraham in his wanderings left his birthplace where it
+had ever been. A theory of motion and a theory of rest are the same
+thing viewed from different aspects with altered emphasis.
+
+Now you cannot have a theory of rest without in some sense admitting a
+theory of absolute position. It is usually assumed that relative space
+implies that there is no absolute position. This is, according to my
+creed, a mistake. The assumption arises from the failure to make another
+distinction; namely, that there may be alternative definitions of
+absolute position. This possibility enters with the admission of
+alternative time-systems. Thus the series of spaces in the parallel
+moments of one temporal series may have their own definition of absolute
+position correlating sets of event-particles in these successive spaces,
+so that each set consists of event-particles, one from each space, all
+with the property of possessing the same absolute position in that
+series of spaces. Such a set of event-particles will form a point in the
+timeless space of that time-system. Thus a point is really an absolute
+position in the timeless space of a given time-system.
+
+But there are alternative time-systems, and each time-system has its own
+peculiar group of points--that is to say, its own peculiar definition of
+absolute position. This is exactly the theory which I will elaborate.
+
+In looking to nature for evidence of absolute position it is of no use
+to recur to the four-dimensional manifold of event-particles. This
+manifold has been obtained by the extension of thought beyond the
+immediacy of observation. We shall find nothing in it except what we
+have put there to represent the ideas in thought which arise from our
+direct sense-awareness of nature. To find evidence of the properties
+which are to be found in the manifold of event-particles we must always
+recur to the observation of relations between events. Our problem is to
+determine those relations between events which issue in the property of
+absolute position in a timeless space. This is in fact the problem of
+the determination of the very meaning of the timeless spaces of physical
+science.
+
+In reviewing the factors of nature as immediately disclosed in
+sense-awareness, we should note the fundamental character of the percept
+of 'being here.' We discern an event merely as a factor in a determinate
+complex in which each factor has its own peculiar share.
+
+There are two factors which are always ingredient in this complex, one
+is the duration which is represented in thought by the concept of all
+nature that is present now, and the other is the peculiar _locus standi_
+for mind involved in the sense-awareness. This _locus standi_ in nature
+is what is represented in thought by the concept of 'here,' namely of an
+'event here.'
+
+This is the concept of a definite factor in nature. This factor is an
+event in nature which is the focus in nature for that act of awareness,
+and the other events are perceived as referred to it. This event is part
+of the associated duration. I call it the 'percipient event.' This event
+is not the mind, that is to say, not the percipient. It is that in
+nature from which the mind perceives. The complete foothold of the mind
+in nature is represented by the pair of events, namely, the present
+duration which marks the 'when' of awareness and the percipient event
+which marks the 'where' of awareness and the 'how' of awareness. This
+percipient event is roughly speaking the bodily life of the incarnate
+mind. But this identification is only a rough one. For the functions of
+the body shade off into those of other events in nature; so that for
+some purposes the percipient event is to be reckoned as merely part of
+the bodily life and for other purposes it may even be reckoned as more
+than the bodily life. In many respects the demarcation is purely
+arbitrary, depending upon where in a sliding scale you choose to draw
+the line.
+
+I have already in my previous lecture on Time discussed the association
+of mind with nature. The difficulty of the discussion lies in the
+liability of constant factors to be overlooked. We never note them by
+contrast with their absences. The purpose of a discussion of such
+factors may be described as being to make obvious things look odd. We
+cannot envisage them unless we manage to invest them with some of the
+freshness which is due to strangeness.
+
+It is because of this habit of letting constant factors slip from
+consciousness that we constantly fall into the error of thinking of the
+sense-awareness of a particular factor in nature as being a two-termed
+relation between the mind and the factor. For example, I perceive a
+green leaf. Language in this statement suppresses all reference to any
+factors other than the percipient mind and the green leaf and the
+relation of sense-awareness. It discards the obvious inevitable factors
+which are essential elements in the perception. I am here, the leaf is
+there; and the event here and the event which is the life of the leaf
+there are both embedded in a totality of nature which is now, and within
+this totality there are other discriminated factors which it is
+irrelevant to mention. Thus language habitually sets before the mind a
+misleading abstract of the indefinite complexity of the fact of
+sense-awareness.
+
+What I now want to discuss is the special relation of the percipient
+event which is 'here' to the duration which is 'now.' This relation is a
+fact in nature, namely the mind is aware of nature as being with these
+two factors in this relation.
+
+Within the short present duration the 'here' of the percipient event has
+a definite meaning of some sort. This meaning of 'here' is the content
+of the special relation of the percipient event to its associated
+duration. I will call this relation 'cogredience.' Accordingly I ask for
+a description of the character of the relation of cogredience. The
+present snaps into a past and a present when the 'here' of cogredience
+loses its single determinate meaning. There has been a passage of nature
+from the 'here' of perception within the past duration to the different
+'here' of perception within the present duration. But the two 'heres' of
+sense-awareness within neighbouring durations may be indistinguishable.
+In this case there has been a passage from the past to the present, but
+a more retentive perceptive force might have retained the passing nature
+as one complete present instead of letting the earlier duration slip
+into the past. Namely, the sense of rest helps the integration of
+durations into a prolonged present, and the sense of motion
+differentiates nature into a succession of shortened durations. As we
+look out of a railway carriage in an express train, the present is past
+before reflexion can seize it. We live in snippits too quick for
+thought. On the other hand the immediate present is prolonged according
+as nature presents itself to us in an aspect of unbroken rest. Any
+change in nature provides ground for a differentiation among durations
+so as to shorten the present. But there is a great distinction between
+self-change in nature and change in external nature. Self-change in
+nature is change in the quality of the standpoint of the percipient
+event. It is the break up of the 'here' which necessitates the break up
+of the present duration. Change in external nature is compatible with a
+prolongation of the present of contemplation rooted in a given
+standpoint. What I want to bring out is that the preservation of a
+peculiar relation to a duration is a necessary condition for the
+function of that duration as a present duration for sense-awareness.
+This peculiar relation is the relation of cogredience between the
+percipient event and the duration. Cogredience is the preservation of
+unbroken quality of standpoint within the duration. It is the
+continuance of identity of station within the whole of nature which is
+the terminus of sense-awareness. The duration may comprise change within
+itself, but cannot--so far as it is one present duration--comprise
+change in the quality of its peculiar relation to the contained
+percipient event.
+
+In other words, perception is always 'here,' and a duration can only be
+posited as present for sense-awareness on condition that it affords one
+unbroken meaning of 'here' in its relation to the percipient event. It
+is only in the past that you can have been 'there' with a standpoint
+distinct from your present 'here.'
+
+Events there and events here are facts of nature, and the qualities of
+being 'there' and 'here' are not merely qualities of awareness as a
+relation between nature and mind. The quality of determinate station in
+the duration which belongs to an event which is 'here' in one
+determinate sense of 'here' is the same kind of quality of station which
+belongs to an event which is 'there' in one determinate sense of
+'there.' Thus cogredience has nothing to do with any biological
+character of the event which is related by it to the associated
+duration. This biological character is apparently a further condition
+for the peculiar connexion of a percipient event with the percipience of
+mind; but it has nothing to do with the relation of the percipient event
+to the duration which is the present whole of nature posited as the
+disclosure of the percipience.
+
+Given the requisite biological character, the event in its character of
+a percipient event selects that duration with which the operative past
+of the event is practically cogredient within the limits of the
+exactitude of observation. Namely, amid the alternative time-systems
+which nature offers there will be one with a duration giving the best
+average of cogredience for all the subordinate parts of the percipient
+event. This duration will be the whole of nature which is the terminus
+posited by sense-awareness. Thus the character of the percipient event
+determines the time-system immediately evident in nature. As the
+character of the percipient event changes with the passage of
+nature--or, in other words, as the percipient mind in its passage
+correlates itself with the passage of the percipient event into another
+percipient event--the time-system correlated with the percipience of
+that mind may change. When the bulk of the events perceived are
+cogredient in a duration other than that of the percipient event, the
+percipience may include a double consciousness of cogredience, namely
+the consciousness of the whole within which the observer in the train is
+'here,' and the consciousness of the whole within which the trees and
+bridges and telegraph posts are definitely 'there.' Thus in perceptions
+under certain circumstances the events discriminated assert their own
+relations of cogredience. This assertion of cogredience is peculiarly
+evident when the duration to which the perceived event is cogredient is
+the same as the duration which is the present whole of nature--in other
+words, when the event and the percipient event are both cogredient to
+the same duration.
+
+We are now prepared to consider the meaning of stations in a duration,
+where stations are a peculiar kind of routes, which define absolute
+position in the associated timeless space.
+
+There are however some preliminary explanations. A finite event will be
+said to extend throughout a duration when it is part of the duration
+and is intersected by any moment which lies in the duration. Such an
+event begins with the duration and ends with it. Furthermore every event
+which begins with the duration and ends with it, extends throughout the
+duration. This is an axiom based on the continuity of events. By
+beginning with a duration and ending with it, I mean (i) that the event
+is part of the duration, and (ii) that both the initial and final
+boundary moments of the duration cover some event-particles on the
+boundary of the event.
+
+Every event which is cogredient with a duration extends throughout that
+duration.
+
+It is not true that all the parts of an event cogredient with a duration
+are also cogredient with the duration. The relation of cogredience may
+fail in either of two ways. One reason for failure may be that the part
+does not extend throughout the duration. In this case the part may be
+cogredient with another duration which is part of the given duration,
+though it is not cogredient with the given duration itself. Such a part
+would be cogredient if its existence were sufficiently prolonged in that
+time-system. The other reason for failure arises from the
+four-dimensional extension of events so that there is no determinate
+route of transition of events in linear series. For example, the tunnel
+of a tube railway is an event at rest in a certain time-system, that is
+to say, it is cogredient with a certain duration. A train travelling in
+it is part of that tunnel, but is not itself at rest.
+
+If an event e be cogredient with a duration d, and d' be any
+duration which is part of d. Then d' belongs to the same time-system
+as d. Also d' intersects e in an event e' which is part of e
+and is cogredient with d'.
+
+Let P be any event-particle lying in a given duration d. Consider
+the aggregate of events in which P lies and which are also cogredient
+with d. Each of these events occupies its own aggregate of
+event-particles. These aggregates will have a common portion, namely the
+class of event-particle lying in all of them. This class of
+event-particles is what I call the 'station' of the event-particle P
+in the duration d. This is the station in the character of a locus. A
+station can also be defined in the character of an abstractive element.
+Let the property {sigma} be the name of the property which an
+abstractive set possesses when (i) each of its events is cogredient with
+the duration d and (ii) the event-particle P lies in each of its events.
+Then the group of {sigma}-primes, where {sigma} has this meaning, is an
+abstractive element and is the station of P in d as an abstractive
+element. The locus of event-particles covered by the station of P in d
+as an abstractive element is the station of P in d as a locus. A station
+has accordingly the usual three characters, namely, its character of
+position, its extrinsic character as an abstractive element, and its
+intrinsic character.
+
+It follows from the peculiar properties of rest that two stations
+belonging to the same duration cannot intersect. Accordingly every
+event-particle on a station of a duration has that station as its
+station in the duration. Also every duration which is part of a given
+duration intersects the stations of the given duration in loci which are
+its own stations. By means of these properties we can utilise the
+overlappings of the durations of one family--that is, of one
+time-system--to prolong stations indefinitely backwards and forwards.
+Such a prolonged station will be called a point-track. A point-track is
+a locus of event-particles. It is defined by reference to one particular
+time-system, {alpha} say. Corresponding to any other time-system these
+will be a different group of point-tracks. Every event-particle will lie
+on one and only one point-track of the group belonging to any one
+time-system. The group of point-tracks of the time-system {alpha} is the
+group of points of the timeless space of {alpha}. Each such point
+indicates a certain quality of absolute position in reference to the
+durations of the family associated with {alpha}, and thence in reference
+to the successive instantaneous spaces lying in the successive moments
+of {alpha}. Each moment of {alpha} will intersect a point-track in one
+and only one event-particle.
+
+This property of the unique intersection of a moment and a point-track
+is not confined to the case when the moment and the point-track belong
+to the same time-system. Any two event-particles on a point-track are
+sequential, so that they cannot lie in the same moment. Accordingly no
+moment can intersect a point-track more than once, and every moment
+intersects a point-track in one event-particle.
+
+Anyone who at the successive moments of {alpha} should be at the
+event-particles where those moments intersect a given point of {alpha}
+will be at rest in the timeless space of time-system {alpha}. But in any
+other timeless space belonging to another time-system he will be at a
+different point at each succeeding moment of that time-system. In other
+words he will be moving. He will be moving in a straight line with
+uniform velocity. We might take this as the definition of a straight
+line. Namely, a straight line in the space of time-system {beta} is the
+locus of those points of {beta} which all intersect some one point-track
+which is a point in the space of some other time-system. Thus each point
+in the space of a time-system {alpha} is associated with one and only
+one straight line of the space of any other time-system {beta}.
+Furthermore the set of straight lines in space {beta} which are thus
+associated with points in space {alpha} form a complete family of
+parallel straight lines in space {beta}. Thus there is a one-to-one
+correlation of points in space {alpha} with the straight lines of a
+certain definite family of parallel straight lines in space {beta}.
+Conversely there is an analogous one-to-one correlation of the points in
+space {beta} with the straight lines of a certain family of parallel
+straight lines in space {alpha}. These families will be called
+respectively the family of parallels in {beta} associated with {alpha},
+and the family of parallels in {alpha} associated with {beta}. The
+direction in the space of {beta} indicated by the family of parallels in
+{beta} will be called the direction of {alpha} in space {beta}, and the
+family of parallels in {alpha} is the direction of {beta} in space
+{alpha}. Thus a being at rest at a point of space {alpha} will be moving
+uniformly along a line in space {beta} which is in the direction of
+{alpha} in space {beta}, and a being at rest at a point of space {beta}
+will be moving uniformly along a line in space {alpha} which is in the
+direction of {beta} in space {alpha}.
+
+I have been speaking of the timeless spaces which are associated with
+time-systems. These are the spaces of physical science and of any
+concept of space as eternal and unchanging. But what we actually
+perceive is an approximation to the instantaneous space indicated by
+event-particles which lie within some moment of the time-system
+associated with our awareness. The points of such an instantaneous space
+are event-particles and the straight lines are rects. Let the
+time-system be named {alpha}, and let the moment of time-system {alpha}
+to which our quick perception of nature approximates be called M. Any
+straight line r in space {alpha} is a locus of points and each point is
+a point-track which is a locus of event-particles. Thus in the
+four-dimensional geometry of all event-particles there is a
+two-dimensional locus which is the locus of all event-particles on
+points lying on the straight line r. I will call this locus of
+event-particles the matrix of the straight line r. A matrix intersects
+any moment in a rect. Thus the matrix of r intersects the moment M in a
+rect {rho}. Thus {rho} is the instantaneous rect in M which occupies at
+the moment M the straight line r in the space of {alpha}. Accordingly
+when one sees instantaneously a moving being and its path ahead of it,
+what one really sees is the being at some event-particle A lying in the
+rect {rho} which is the apparent path on the assumption of uniform
+motion. But the actual rect {rho} which is a locus of event-particles is
+never traversed by the being. These event-particles are the
+instantaneous facts which pass with the instantaneous moment. What is
+really traversed are other event-particles which at succeeding instants
+occupy the same points of space {alpha} as those occupied by the
+event-particles of the rect {rho}. For example, we see a stretch of road
+and a lorry moving along it. The instantaneously seen road is a portion
+of the rect {rho}--of course only an approximation to it. The lorry is
+the moving object. But the road as seen is never traversed. It is
+thought of as being traversed because the intrinsic characters of the
+later events are in general so similar to those of the instantaneous
+road that we do not trouble to discriminate. But suppose a land mine
+under the road has been exploded before the lorry gets there. Then it is
+fairly obvious that the lorry does not traverse what we saw at first.
+Suppose the lorry is at rest in space {beta}. Then the straight line r
+of space {alpha} is in the direction of {beta} in space {alpha}, and the
+rect {rho} is the representative in the moment M of the line r of space
+{alpha}. The direction of {rho} in the instantaneous space of the moment
+M is the direction of {beta} in M, where M is a moment of time-system
+{alpha}. Again the matrix of the line r of space {alpha} will also be
+the matrix of some line s of space {beta} which will be in the direction
+of {alpha} in space {beta}. Thus if the lorry halts at some point P of
+space {alpha} which lies on the line r, it is now moving along the line
+s of space {beta}. This is the theory of relative motion; the common
+matrix is the bond which connects the motion of {beta} in space {alpha}
+with the motions of {alpha} in space {beta}.
+
+Motion is essentially a relation between some object of nature and the
+one timeless space of a time-system. An instantaneous space is static,
+being related to the static nature at an instant. In perception when we
+see things moving in an approximation to an instantaneous space, the
+future lines of motion as immediately perceived are rects which are
+never traversed. These approximate rects are composed of small events,
+namely approximate routes and event-particles, which are passed away
+before the moving objects reach them. Assuming that our forecasts of
+rectilinear motion are correct, these rects occupy the straight lines in
+timeless space which are traversed. Thus the rects are symbols in
+immediate sense-awareness of a future which can only be expressed in
+terms of timeless space.
+
+We are now in a position to explore the fundamental character of
+perpendicularity. Consider the two time-systems {alpha} and {beta}, each
+with its own timeless space and its own family of instantaneous moments
+with their instantaneous spaces. Let M and N be respectively a moment of
+{alpha} and a moment of {beta}. In M there is the direction of {beta}
+and in N there is the direction of {alpha}. But M and N, being moments
+of different time-systems, intersect in a level. Call this level
+{lambda}. Then {lambda} is an instantaneous plane in the instantaneous
+space of M and also in the instantaneous space of N. It is the locus of
+all the event-particles which lie both in M and in N.
+
+In the instantaneous space of M the level {lambda} is perpendicular to
+the direction of {beta} in M, and in the instantaneous space of N the
+level {lambda} is perpendicular to the direction of {alpha} in N. This
+is the fundamental property which forms the definition of
+perpendicularity. The symmetry of perpendicularity is a particular
+instance of the symmetry of the mutual relations between two
+time-systems. We shall find in the next lecture that it is from this
+symmetry that the theory of congruence is deduced.
+
+The theory of perpendicularity in the timeless space of any time-system
+{alpha} follows immediately from this theory of perpendicularity in each
+of its instantaneous spaces. Let {rho} be any rect in the moment M of
+{alpha} and let {lambda} be a level in M which is perpendicular to
+{rho}. The locus of those points of the space of {alpha} which intersect
+M in event-particles on {rho} is the straight line r of space {alpha},
+and the locus of those points of the space of {alpha} which intersect M
+in event-particles on {lambda} is the plane l of space {alpha}. Then the
+plane l is perpendicular to the line r.
+
+In this way we have pointed out unique and definite properties in nature
+which correspond to perpendicularity. We shall find that this discovery
+of definite unique properties defining perpendicularity is of critical
+importance in the theory of congruence which is the topic for the next
+lecture.
+
+I regret that it has been necessary for me in this lecture to administer
+such a large dose of four-dimensional geometry. I do not apologise,
+because I am really not responsible for the fact that nature in its most
+fundamental aspect is four-dimensional. Things are what they are; and it
+is useless to disguise the fact that 'what things are' is often very
+difficult for our intellects to follow. It is a mere evasion of the
+ultimate problems to shirk such obstacles.
+
+
+
+
+CHAPTER VI
+
+CONGRUENCE
+
+
+The aim of this lecture is to establish a theory of congruence. You must
+understand at once that congruence is a controversial question. It is
+the theory of measurement in space and in time. The question seems
+simple. In fact it is simple enough for a standard procedure to have
+been settled by act of parliament; and devotion to metaphysical
+subtleties is almost the only crime which has never been imputed to any
+English parliament. But the procedure is one thing and its meaning is
+another.
+
+First let us fix attention on the purely mathematical question. When the
+segment between two points A and B is congruent to that between the
+two points C and D, the quantitative measurements of the two
+segments are equal. The equality of the numerical measures and the
+congruence of the two segments are not always clearly discriminated, and
+are lumped together under the term equality. But the procedure of
+measurement presupposes congruence. For example, a yard measure is
+applied successively to measure two distances between two pairs of
+points on the floor of a room. It is of the essence of the procedure of
+measurement that the yard measure remains unaltered as it is transferred
+from one position to another. Some objects can palpably alter as they
+move--for example, an elastic thread; but a yard measure does not alter
+if made of the proper material. What is this but a judgment of
+congruence applied to the train of successive positions of the yard
+measure? We know that it does not alter because we judge it to be
+congruent to itself in various positions. In the case of the thread we
+can observe the loss of self-congruence. Thus immediate judgments of
+congruence are presupposed in measurement, and the process of
+measurement is merely a procedure to extend the recognition of
+congruence to cases where these immediate judgments are not available.
+Thus we cannot define congruence by measurement.
+
+In modern expositions of the axioms of geometry certain conditions are
+laid down which the relation of congruence between segments is to
+satisfy. It is supposed that we have a complete theory of points,
+straight lines, planes, and the order of points on planes--in fact, a
+complete theory of non-metrical geometry. We then enquire about
+congruence and lay down the set of conditions--or axioms as they are
+called--which this relation satisfies. It has then been proved that
+there are alternative relations which satisfy these conditions equally
+well and that there is nothing intrinsic in the theory of space to lead
+us to adopt any one of these relations in preference to any other as the
+relation of congruence which we adopt. In other words there are
+alternative metrical geometries which all exist by an equal right so far
+as the intrinsic theory of space is concerned.
+
+Poincar�, the great French mathematician, held that our actual choice
+among these geometries is guided purely by convention, and that the
+effect of a change of choice would be simply to alter our expression of
+the physical laws of nature. By 'convention' I understand Poincar� to
+mean that there is nothing inherent in nature itself giving any peculiar
+_r�le_ to one of these congruence relations, and that the choice of one
+particular relation is guided by the volitions of the mind at the other
+end of the sense-awareness. The principle of guidance is intellectual
+convenience and not natural fact.
+
+This position has been misunderstood by many of Poincar�'s expositors.
+They have muddled it up with another question, namely that owing to the
+inexactitude of observation it is impossible to make an exact statement
+in the comparison of measures. It follows that a certain subset of
+closely allied congruence relations can be assigned of which each member
+equally well agrees with that statement of observed congruence when the
+statement is properly qualified with its limits of error.
+
+This is an entirely different question and it presupposes a rejection of
+Poincar�'s position. The absolute indetermination of nature in respect
+of all the relations of congruence is replaced by the indetermination of
+observation with respect to a small subgroup of these relations.
+
+Poincar�'s position is a strong one. He in effect challenges anyone to
+point out any factor in nature which gives a preeminent status to the
+congruence relation which mankind has actually adopted. But undeniably
+the position is very paradoxical. Bertrand Russell had a controversy
+with him on this question, and pointed out that on Poincar�'s principles
+there was nothing in nature to determine whether the earth is larger or
+smaller than some assigned billiard ball. Poincar� replied that the
+attempt to find reasons in nature for the selection of a definite
+congruence relation in space is like trying to determine the position of
+a ship in the ocean by counting the crew and observing the colour of
+the captain's eyes.
+
+In my opinion both disputants were right, assuming the grounds on which
+the discussion was based. Russell in effect pointed out that apart from
+minor inexactitudes a determinate congruence relation is among the
+factors in nature which our sense-awareness posits for us. Poincar� asks
+for information as to the factor in nature which might lead any
+particular congruence relation to play a preeminent _r�le_ among the
+factors posited in sense-awareness. I cannot see the answer to either of
+these contentions provided that you admit the materialistic theory of
+nature. With this theory nature at an instant in space is an independent
+fact. Thus we have to look for our preeminent congruence relation amid
+nature in instantaneous space; and Poincar� is undoubtedly right in
+saying that nature on this hypothesis gives us no help in finding it.
+
+On the other hand Russell is in an equally strong position when he
+asserts that, as a fact of observation, we do find it, and what is more
+agree in finding the same congruence relation. On this basis it is one
+of the most extraordinary facts of human experience that all mankind
+without any assignable reason should agree in fixing attention on just
+one congruence relation amid the indefinite number of indistinguishable
+competitors for notice. One would have expected disagreement on this
+fundamental choice to have divided nations and to have rent families.
+But the difficulty was not even discovered till the close of the
+nineteenth century by a few mathematical philosophers and philosophic
+mathematicians. The case is not like that of our agreement on some
+fundamental fact of nature such as the three dimensions of space. If
+space has only three dimensions we should expect all mankind to be aware
+of the fact, as they are aware of it. But in the case of congruence,
+mankind agree in an arbitrary interpretation of sense-awareness when
+there is nothing in nature to guide it.
+
+I look on it as no slight recommendation of the theory of nature which I
+am expounding to you that it gives a solution of this difficulty by
+pointing out the factor in nature which issues in the preeminence of one
+congruence relation over the indefinite herd of other such relations.
+
+The reason for this result is that nature is no longer confined within
+space at an instant. Space and time are now interconnected; and this
+peculiar factor of time which is so immediately distinguished among the
+deliverances of our sense-awareness, relates itself to one particular
+congruence relation in space.
+
+Congruence is a particular example of the fundamental fact of
+recognition. In perception we recognise. This recognition does not
+merely concern the comparison of a factor of nature posited by memory
+with a factor posited by immediate sense-awareness. Recognition takes
+place within the present without any intervention of pure memory. For
+the present fact is a duration with its antecedent and consequent
+durations which are parts of itself. The discrimination in
+sense-awareness of a finite event with its quality of passage is also
+accompanied by the discrimination of other factors of nature which do
+not share in the passage of events. Whatever passes is an event. But we
+find entities in nature which do not pass; namely we recognise
+samenesses in nature. Recognition is not primarily an intellectual act
+of comparison; it is in its essence merely sense-awareness in its
+capacity of positing before us factors in nature which do not pass. For
+example, green is perceived as situated in a certain finite event within
+the present duration. This green preserves its self-identity throughout,
+whereas the event passes and thereby obtains the property of breaking
+into parts. The green patch has parts. But in talking of the green patch
+we are speaking of the event in its sole capacity of being for us the
+situation of green. The green itself is numerically one self-identical
+entity, without parts because it is without passage.
+
+Factors in nature which are without passage will be called objects.
+There are radically different kinds of objects which will be considered
+in the succeeding lecture.
+
+Recognition is reflected into the intellect as comparison. The
+recognised objects of one event are compared with the recognised objects
+of another event. The comparison may be between two events in the
+present, or it may be between two events of which one is posited by
+memory-awareness and the other by immediate sense-awareness. But it is
+not the events which are compared. For each event is essentially unique
+and incomparable. What are compared are the objects and relations of
+objects situated in events. The event considered as a relation between
+objects has lost its passage and in this aspect is itself an object.
+This object is not the event but only an intellectual abstraction. The
+same object can be situated in many events; and in this sense even the
+whole event, viewed as an object, can recur, though not the very event
+itself with its passage and its relations to other events.
+
+Objects which are not posited by sense-awareness may be known to the
+intellect. For example, relations between objects and relations between
+relations may be factors in nature not disclosed in sense-awareness but
+known by logical inference as necessarily in being. Thus objects for our
+knowledge may be merely logical abstractions. For example, a complete
+event is never disclosed in sense-awareness, and thus the object which
+is the sum total of objects situated in an event as thus inter-related
+is a mere abstract concept. Again a right-angle is a perceived object
+which can be situated in many events; but, though rectangularity is
+posited by sense-awareness, the majority of geometrical relations are
+not so posited. Also rectangularity is in fact often not perceived when
+it can be proved to have been there for perception. Thus an object is
+often known merely as an abstract relation not directly posited in
+sense-awareness although it is there in nature.
+
+The identity of quality between congruent segments is generally of this
+character. In certain special cases this identity of quality can be
+directly perceived. But in general it is inferred by a process of
+measurement depending on our direct sense-awareness of selected cases
+and a logical inference from the transitive character of congruence.
+
+Congruence depends on motion, and thereby is generated the connexion
+between spatial congruence and temporal congruence. Motion along a
+straight line has a symmetry round that line. This symmetry is expressed
+by the symmetrical geometrical relations of the line to the family of
+planes normal to it.
+
+Also another symmetry in the theory of motion arises from the fact that
+rest in the points of {beta} corresponds to uniform motion along a
+definite family of parallel straight lines in the space of {alpha}. We
+must note the three characteristics, (i) of the uniformity of the motion
+corresponding to any point of {beta} along its correlated straight line
+in {alpha}, and (ii) of the equality in magnitude of the velocities
+along the various lines of {alpha} correlated to rest in the various
+points of {beta}, and (iii) of the parallelism of the lines of this
+family.
+
+We are now in possession of a theory of parallels and a theory of
+perpendiculars and a theory of motion, and from these theories the
+theory of congruence can be constructed. It will be remembered that a
+family of parallel levels in any moment is the family of levels in which
+that moment is intersected by the family of moments of some other
+time-system. Also a family of parallel moments is the family of moments
+of some one time-system. Thus we can enlarge our concept of a family of
+parallel levels so as to include levels in different moments of one
+time-system. With this enlarged concept we say that a complete family of
+parallel levels in a time-system {alpha} is the complete family of
+levels in which the moments of {alpha} intersect the moments of {beta}.
+This complete family of parallel levels is also evidently a family lying
+in the moments of the time-system {beta}. By introducing a third
+time-system {gamma}, parallel rects are obtained. Also all the points of
+any one time-system form a family of parallel point-tracks. Thus there
+are three types of parallelograms in the four-dimensional manifold of
+event-particles.
+
+In parallelograms of the first type the two pairs of parallel sides are
+both of them pairs of rects. In parallelograms of the second type one
+pair of parallel sides is a pair of rects and the other pair is a pair
+of point-tracks. In parallelograms of the third type the two pairs of
+parallel sides are both of them pairs of point-tracks.
+
+The first axiom of congruence is that the opposite sides of any
+parallelogram are congruent. This axiom enables us to compare the
+lengths of any two segments either respectively on parallel rects or on
+the same rect. Also it enables us to compare the lengths of any two
+segments either respectively on parallel point-tracks or on the same
+point-track. It follows from this axiom that two objects at rest in any
+two points of a time-system {beta} are moving with equal velocities in any
+other time-system {alpha} along parallel lines. Thus we can speak of the
+velocity in {alpha} due to the time-system {beta} without specifying any
+particular point in {beta}. The axiom also enables us to measure time in
+any time-system; but does not enable us to compare times in different
+time-systems.
+
+The second axiom of congruence concerns parallelograms on congruent
+bases and between the same parallels, which have also their other pairs
+of sides parallel. The axiom asserts that the rect joining the two
+event-particles of intersection of the diagonals is parallel to the rect
+on which the bases lie. By the aid of this axiom it easily follows that
+the diagonals of a parallelogram bisect each other.
+
+Congruence is extended in any space beyond parallel rects to all rects
+by two axioms depending on perpendicularity. The first of these axioms,
+which is the third axiom of congruence, is that if ABC is a triangle
+of rects in any moment and D is the middle event-particle of the base
+BC, then the level through D perpendicular to BC contains A when
+and only when AB is congruent to AC. This axiom evidently expresses
+the symmetry of perpendicularity, and is the essence of the famous pons
+asinorum expressed as an axiom.
+
+The second axiom depending on perpendicularity, and the fourth axiom of
+congruence, is that if r and A be a rect and an event-particle in the
+same moment and AB and AC be a pair of rectangular rects intersecting r
+in B and C, and AD and AE be another pair of rectangular rects
+intersecting r in D and E, then either D or E lies in the segment BC and
+the other one of the two does not lie in this segment. Also as a
+particular case of this axiom, if AB be perpendicular to r and in
+consequence AC be parallel to r, then D and E lie on opposite sides of B
+respectively. By the aid of these two axioms the theory of congruence
+can be extended so as to compare lengths of segments on any two rects.
+Accordingly Euclidean metrical geometry in space is completely
+established and lengths in the spaces of different time-systems are
+comparable as the result of definite properties of nature which indicate
+just that particular method of comparison.
+
+The comparison of time-measurements in diverse time-systems requires two
+other axioms. The first of these axioms, forming the fifth axiom of
+congruence, will be called the axiom of 'kinetic symmetry.' It expresses
+the symmetry of the quantitative relations between two time-systems when
+the times and lengths in the two systems are measured in congruent
+units.
+
+The axiom can be explained as follows: Let {alpha} and {beta} be the names
+of two time-systems. The directions of motion in the space of {alpha} due
+to rest in a point of {beta} is called the '{beta}-direction in {alpha}'
+and the direction of motion in the space of {beta} due to rest in a
+point of {alpha} is called the '{alpha}-direction in {beta}.' Consider a
+motion in the space of {alpha} consisting of a certain velocity in the
+{beta}-direction of {alpha} and a certain velocity at right-angles to
+it. This motion represents rest in the space of another time-system--call
+it {pi}. Rest in {pi} will also be represented in the space of {beta} by
+a certain velocity in the {alpha}-direction in {beta} and a certain
+velocity at right-angles to this {alpha}-direction. Thus a certain
+motion in the space of {alpha} is correlated to a certain motion in the
+space of {beta}, as both representing the same fact which can also be
+represented by rest in {pi}. Now another time-system, which I will name
+{sigma}, can be found which is such that rest in its space is
+represented by the same magnitudes of velocities along and perpendicular
+to the {alpha}-direction in {beta} as those velocities in {alpha}, along
+and perpendicular to the {beta}-direction, which represent rest in {pi}.
+The required axiom of kinetic symmetry is that rest in {sigma} will be
+represented in {alpha} by the same velocities along and perpendicular to
+the {beta}-direction in {alpha} as those velocities in {beta} along and
+perpendicular to the {alpha}-direction which represent rest in {pi}.
+
+A particular case of this axiom is that relative velocities are equal
+and opposite. Namely rest in {alpha} is represented in {beta} by a
+velocity along the {alpha}-direction which is equal to the velocity
+along the {beta}-direction in {alpha} which represents rest in {beta}.
+
+Finally the sixth axiom of congruence is that the relation of congruence
+is transitive. So far as this axiom applies to space, it is superfluous.
+For the property follows from our previous axioms. It is however
+necessary for time as a supplement to the axiom of kinetic symmetry. The
+meaning of the axiom is that if the time-unit of system {alpha} is
+congruent to the time-unit of system {beta}, and the time-unit of system
+{beta} is congruent to the time-unit of system {gamma}, then the
+time-units of {alpha} and {gamma} are also congruent.
+
+By means of these axioms formulae for the transformation of
+measurements made in one time-system to measurements of the same facts
+of nature made in another time-system can be deduced. These formulae
+will be found to involve one arbitrary constant which I will call k.
+
+It is of the dimensions of the square of a velocity. Accordingly four
+cases arise. In the first case k is zero. This case produces
+nonsensical results in opposition to the elementary deliverances of
+experience. We put this case aside.
+
+In the second case k is infinite. This case yields the ordinary
+formulae for transformation in relative motion, namely those formulae
+which are to be found in every elementary book on dynamics.
+
+In the third case, k is negative. Let us call it -c�, where c
+will be of the dimensions of a velocity. This case yields the formulae
+of transformation which Larmor discovered for the transformation of
+Maxwell's equations of the electromagnetic field. These formulae were
+extended by H.�A. Lorentz, and used by Einstein and Minkowski as the
+basis of their novel theory of relativity. I am not now speaking of
+Einstein's more recent theory of general relativity by which he deduces
+his modification of the law of gravitation. If this be the case which
+applies to nature, then c must be a close approximation to the
+velocity of light _in vacuo_. Perhaps it is this actual velocity. In
+this connexion '_in vacuo_' must not mean an absence of events, namely
+the absence of the all-pervading ether of events. It must mean the
+absence of certain types of objects.
+
+In the fourth case, k is positive. Let us call it h�, where h
+will be of the dimensions of a velocity. This gives a perfectly possible
+type of transformation formulae, but not one which explains any facts
+of experience. It has also another disadvantage. With the assumption of
+this fourth case the distinction between space and time becomes unduly
+blurred. The whole object of these lectures has been to enforce the
+doctrine that space and time spring from a common root, and that the
+ultimate fact of experience is a space-time fact. But after all mankind
+does distinguish very sharply between space and time, and it is owing to
+this sharpness of distinction that the doctrine of these lectures is
+somewhat of a paradox. Now in the third assumption this sharpness of
+distinction is adequately preserved. There is a fundamental distinction
+between the metrical properties of point-tracks and rects. But in the
+fourth assumption this fundamental distinction vanishes.
+
+Neither the third nor the fourth assumption can agree with experience
+unless we assume that the velocity c of the third assumption, and the
+velocity h of the fourth assumption, are extremely large compared to
+the velocities of ordinary experience. If this be the case the formulae
+of both assumptions will obviously reduce to a close approximation to
+the formulae of the second assumption which are the ordinary formulae of
+dynamical textbooks. For the sake of a name, I will call these textbook
+formulae the 'orthodox' formulae.
+
+There can be no question as to the general approximate correctness of
+the orthodox formulae. It would be merely silly to raise doubts on this
+point. But the determination of the status of these formulae is by no
+means settled by this admission. The independence of time and space is
+an unquestioned presupposition of the orthodox thought which has
+produced the orthodox formulae. With this presupposition and given the
+absolute points of one absolute space, the orthodox formulae are
+immediate deductions. Accordingly, these formulae are presented to our
+imaginations as facts which cannot be otherwise, time and space being
+what they are. The orthodox formulae have therefore attained to the
+status of necessities which cannot be questioned in science. Any attempt
+to replace these formulae by others was to abandon the _r�le_ of
+physical explanation and to have recourse to mere mathematical formulae.
+
+But even in physical science difficulties have accumulated round the
+orthodox formulae. In the first place Maxwell's equations of the
+electromagnetic field are not invariant for the transformations of the
+orthodox formulae; whereas they are invariant for the transformations of
+the formulae arising from the third of the four cases mentioned above,
+provided that the velocity c is identified with a famous
+electromagnetic constant quantity.
+
+Again the null results of the delicate experiments to detect the earth's
+variations of motion through the ether in its orbital path are explained
+immediately by the formulae of the third case. But if we assume the
+orthodox formulae we have to make a special and arbitrary assumption as
+to the contraction of matter during motion. I mean the Fitzgerald-Lorentz
+assumption.
+
+Lastly Fresnel's coefficient of drag which represents the variation of
+the velocity of light in a moving medium is explained by the formulae of
+the third case, and requires another arbitrary assumption if we use the
+orthodox formulae.
+
+It appears therefore that on the mere basis of physical explanation
+there are advantages in the formulae of the third case as compared with
+the orthodox formulae. But the way is blocked by the ingrained belief
+that these latter formulae possess a character of necessity. It is
+therefore an urgent requisite for physical science and for philosophy to
+examine critically the grounds for this supposed necessity. The only
+satisfactory method of scrutiny is to recur to the first principles of
+our knowledge of nature. This is exactly what I am endeavouring to do in
+these lectures. I ask what it is that we are aware of in our
+sense-perception of nature. I then proceed to examine those factors in
+nature which lead us to conceive nature as occupying space and
+persisting through time. This procedure has led us to an investigation
+of the characters of space and time. It results from these
+investigations that the formulae of the third case and the orthodox
+formulae are on a level as possible formulae resulting from the basic
+character of our knowledge of nature. The orthodox formulae have thus
+lost any advantage as to necessity which they enjoyed over the serial
+group. The way is thus open to adopt whichever of the two groups best
+accords with observation.
+
+I take this opportunity of pausing for a moment from the course of my
+argument, and of reflecting on the general character which my doctrine
+ascribes to some familiar concepts of science. I have no doubt that some
+of you have felt that in certain aspects this character is very
+paradoxical.
+
+This vein of paradox is partly due to the fact that educated language
+has been made to conform to the prevalent orthodox theory. We are thus,
+in expounding an alternative doctrine, driven to the use of either
+strange terms or of familiar words with unusual meanings. This victory
+of the orthodox theory over language is very natural. Events are named
+after the prominent objects situated in them, and thus both in language
+and in thought the event sinks behind the object, and becomes the mere
+play of its relations. The theory of space is then converted into a
+theory of the relations of objects instead of a theory of the relations
+of events. But objects have not the passage of events. Accordingly space
+as a relation between objects is devoid of any connexion with time. It
+is space at an instant without any determinate relations between the
+spaces at successive instants. It cannot be one timeless space because
+the relations between objects change.
+
+A few minutes ago in speaking of the deduction of the orthodox formulae
+for relative motion I said that they followed as an immediate deduction
+from the assumption of absolute points in absolute space. This reference
+to absolute space was not an oversight. I know that the doctrine of the
+relativity of space at present holds the field both in science and
+philosophy. But I do not think that its inevitable consequences are
+understood. When we really face them the paradox of the presentation of
+the character of space which I have elaborated is greatly mitigated. If
+there is no absolute position, a point must cease to be a simple entity.
+What is a point to one man in a balloon with his eyes fixed on an
+instrument is a track of points to an observer on the earth who is
+watching the balloon through a telescope, and is another track of points
+to an observer in the sun who is watching the balloon through some
+instrument suited to such a being. Accordingly if I am reproached with
+the paradox of my theory of points as classes of event-particles, and of
+my theory of event-particles as groups of abstractive sets, I ask my
+critic to explain exactly what he means by a point. While you explain
+your meaning about anything, however simple, it is always apt to look
+subtle and fine spun. I have at least explained exactly what I do mean
+by a point, what relations it involves and what entities are the relata.
+If you admit the relativity of space, you also must admit that points
+are complex entities, logical constructs involving other entities and
+their relations. Produce your theory, not in a few vague phrases of
+indefinite meaning, but explain it step by step in definite terms
+referring to assigned relations and assigned relata. Also show that your
+theory of points issues in a theory of space. Furthermore note that the
+example of the man in the balloon, the observer on earth, and the
+observer in the sun, shows that every assumption of relative rest
+requires a timeless space with radically different points from those
+which issue from every other such assumption. The theory of the
+relativity of space is inconsistent with any doctrine of one unique set
+of points of one timeless space.
+
+The fact is that there is no paradox in my doctrine of the nature of
+space which is not in essence inherent in the theory of the relativity
+of space. But this doctrine has never really been accepted in science,
+whatever people say. What appears in our dynamical treatises is Newton's
+doctrine of relative motion based on the doctrine of differential motion
+in absolute space. When you once admit that the points are radically
+different entities for differing assumptions of rest, then the orthodox
+formulae lose all their obviousness. They were only obvious because you
+were really thinking of something else. When discussing this topic you
+can only avoid paradox by taking refuge from the flood of criticism in
+the comfortable ark of no meaning.
+
+The new theory provides a definition of the congruence of periods of
+time. The prevalent view provides no such definition. Its position is
+that if we take such time-measurements so that certain familiar
+velocities which seem to us to be uniform are uniform, then the laws of
+motion are true. Now in the first place no change could appear either as
+uniform or non-uniform without involving a definite determination of the
+congruence for time-periods. So in appealing to familiar phenomena it
+allows that there is some factor in nature which we can intellectually
+construct as a congruence theory. It does not however say anything about
+it except that the laws of motion are then true. Suppose that with some
+expositors we cut out the reference to familiar velocities such as the
+rate of rotation of the earth. We are then driven to admit that there is
+no meaning in temporal congruence except that certain assumptions make
+the laws of motion true. Such a statement is historically false. King
+Alfred the Great was ignorant of the laws of motion, but knew very well
+what he meant by the measurement of time, and achieved his purpose by
+means of burning candles. Also no one in past ages justified the use of
+sand in hour-glasses by saying that some centuries later interesting
+laws of motion would be discovered which would give a meaning to the
+statement that the sand was emptied from the bulbs in equal times.
+Uniformity in change is directly perceived, and it follows that mankind
+perceives in nature factors from which a theory of temporal congruence
+can be formed. The prevalent theory entirely fails to produce such
+factors.
+
+The mention of the laws of motion raises another point where the
+prevalent theory has nothing to say and the new theory gives a complete
+explanation. It is well known that the laws of motion are not valid for
+any axes of reference which you may choose to take fixed in any rigid
+body. You must choose a body which is not rotating and has no
+acceleration. For example they do not really apply to axes fixed in the
+earth because of the diurnal rotation of that body. The law which fails
+when you assume the wrong axes as at rest is the third law, that action
+and reaction are equal and opposite. With the wrong axes uncompensated
+centrifugal forces and uncompensated composite centrifugal forces
+appear, due to rotation. The influence of these forces can be
+demonstrated by many facts on the earth's surface, Foucault's pendulum,
+the shape of the earth, the fixed directions of the rotations of
+cyclones and anticyclones. It is difficult to take seriously the
+suggestion that these domestic phenomena on the earth are due to the
+influence of the fixed stars. I cannot persuade myself to believe that a
+little star in its twinkling turned round Foucault's pendulum in the
+Paris Exhibition of 1861. Of course anything is believable when a
+definite physical connexion has been demonstrated, for example the
+influence of sunspots. Here all demonstration is lacking in the form of
+any coherent theory. According to the theory of these lectures the axes
+to which motion is to be referred are axes at rest in the space of some
+time-system. For example, consider the space of a time-system {alpha}.
+There are sets of axes at rest in the space of {alpha}. These are
+suitable dynamical axes. Also a set of axes in this space which is
+moving with uniform velocity without rotation is another suitable set.
+All the moving points fixed in these moving axes are really tracing out
+parallel lines with one uniform velocity. In other words they are the
+reflections in the space of {alpha} of a set of fixed axes in the space
+of some other time-system {beta}. Accordingly the group of dynamical
+axes required for Newton's Laws of Motion is the outcome of the
+necessity of referring motion to a body at rest in the space of some one
+time-system in order to obtain a coherent account of physical
+properties. If we do not do so the meaning of the motion of one portion
+of our physical configuration is different from the meaning of the
+motion of another portion of the same configuration. Thus the meaning of
+motion being what it is, in order to describe the motion of any system
+of objects without changing the meaning of your terms as you proceed
+with your description, you are bound to take one of these sets of axes
+as axes of reference; though you may choose their reflections into the
+space of any time-system which you wish to adopt. A definite physical
+reason is thereby assigned for the peculiar property of the dynamical
+group of axes.
+
+On the orthodox theory the position of the equations of motion is most
+ambiguous. The space to which they refer is completely undetermined and
+so is the measurement of the lapse of time. Science is simply setting
+out on a fishing expedition to see whether it cannot find some procedure
+which it can call the measurement of space and some procedure which it
+can call the measurement of time, and something which it can call a
+system of forces, and something which it can call masses, so that these
+formulae may be satisfied. The only reason--on this theory--why anyone
+should want to satisfy these formulae is a sentimental regard for
+Galileo, Newton, Euler and Lagrange. The theory, so far from founding
+science on a sound observational basis, forces everything to conform to
+a mere mathematical preference for certain simple formulae.
+
+I do not for a moment believe that this is a true account of the real
+status of the Laws of Motion. These equations want some slight
+adjustment for the new formulae of relativity. But with these
+adjustments, imperceptible in ordinary use, the laws deal with
+fundamental physical quantities which we know very well and wish to
+correlate.
+
+The measurement of time was known to all civilised nations long before
+the laws were thought of. It is this time as thus measured that the laws
+are concerned with. Also they deal with the space of our daily life.
+When we approach to an accuracy of measurement beyond that of
+observation, adjustment is allowable. But within the limits of
+observation we know what we mean when we speak of measurements of space
+and measurements of time and uniformity of change. It is for science to
+give an intellectual account of what is so evident in sense-awareness.
+It is to me thoroughly incredible that the ultimate fact beyond which
+there is no deeper explanation is that mankind has really been swayed by
+an unconscious desire to satisfy the mathematical formulae which we call
+the Laws of Motion, formulae completely unknown till the seventeenth
+century of our epoch.
+
+The correlation of the facts of sense-experience effected by the
+alternative account of nature extends beyond the physical properties of
+motion and the properties of congruence. It gives an account of the
+meaning of the geometrical entities such as points, straight lines, and
+volumes, and connects the kindred ideas of extension in time and
+extension in space. The theory satisfies the true purpose of an
+intellectual explanation in the sphere of natural philosophy. This
+purpose is to exhibit the interconnexions of nature, and to show that
+one set of ingredients in nature requires for the exhibition of its
+character the presence of the other sets of ingredients.
+
+The false idea which we have to get rid of is that of nature as a mere
+aggregate of independent entities, each capable of isolation. According
+to this conception these entities, whose characters are capable of
+isolated definition, come together and by their accidental relations
+form the system of nature. This system is thus thoroughly accidental;
+and, even if it be subject to a mechanical fate, it is only accidentally
+so subject.
+
+With this theory space might be without time, and time might be without
+space. The theory admittedly breaks down when we come to the relations
+of matter and space. The relational theory of space is an admission that
+we cannot know space without matter or matter without space. But the
+seclusion of both from time is still jealously guarded. The relations
+between portions of matter in space are accidental facts owing to the
+absence of any coherent account of how space springs from matter or how
+matter springs from space. Also what we really observe in nature, its
+colours and its sounds and its touches are secondary qualities; in other
+words, they are not in nature at all but are accidental products of the
+relations between nature and mind.
+
+The explanation of nature which I urge as an alternative ideal to this
+accidental view of nature, is that nothing in nature could be what it is
+except as an ingredient in nature as it is. The whole which is present
+for discrimination is posited in sense-awareness as necessary for the
+discriminated parts. An isolated event is not an event, because every
+event is a factor in a larger whole and is significant of that whole.
+There can be no time apart from space; and no space apart from time; and
+no space and no time apart from the passage of the events of nature. The
+isolation of an entity in thought, when we think of it as a bare 'it,'
+has no counterpart in any corresponding isolation in nature. Such
+isolation is merely part of the procedure of intellectual knowledge.
+
+The laws of nature are the outcome of the characters of the entities
+which we find in nature. The entities being what they are, the laws must
+be what they are; and conversely the entities follow from the laws. We
+are a long way from the attainment of such an ideal; but it remains as
+the abiding goal of theoretical science.
+
+
+
+
+CHAPTER VII
+
+OBJECTS
+
+
+The ensuing lecture is concerned with the theory of objects. Objects are
+elements in nature which do not pass. The awareness of an object as some
+factor not sharing in the passage of nature is what I call
+'recognition.' It is impossible to recognise an event, because an event
+is essentially distinct from every other event. Recognition is an
+awareness of sameness. But to call recognition an awareness of sameness
+implies an intellectual act of comparison accompanied with judgment. I
+use recognition for the non-intellectual relation of sense-awareness
+which connects the mind with a factor of nature without passage. On the
+intellectual side of the mind's experience there are comparisons of
+things recognised and consequent judgments of sameness or diversity.
+Probably 'sense-recognition' would be a better term for what I mean by
+'recognition.' I have chosen the simpler term because I think that I
+shall be able to avoid the use of 'recognition' in any other meaning
+than that of 'sense-recognition.' I am quite willing to believe that
+recognition, in my sense of the term, is merely an ideal limit, and that
+there is in fact no recognition without intellectual accompaniments of
+comparison and judgment. But recognition is that relation of the mind to
+nature which provides the material for the intellectual activity.
+
+An object is an ingredient in the character of some event. In fact the
+character of an event is nothing but the objects which are ingredient in
+it and the ways in which those objects make their ingression into the
+event. Thus the theory of objects is the theory of the comparison of
+events. Events are only comparable because they body forth permanences.
+We are comparing objects in events whenever we can say, 'There it is
+again.' Objects are the elements in nature which can 'be again.'
+
+Sometimes permanences can be proved to exist which evade recognition in
+the sense in which I am using that term. The permanences which evade
+recognition appear to us as abstract properties either of events or of
+objects. All the same they are there for recognition although
+undiscriminated in our sense-awareness. The demarcation of events, the
+splitting of nature up into parts is effected by the objects which we
+recognise as their ingredients. The discrimination of nature is the
+recognition of objects amid passing events. It is a compound of the
+awareness of the passage of nature, of the consequent partition of
+nature, and of the definition of certain parts of nature by the modes of
+the ingression of objects into them.
+
+You may have noticed that I am using the term 'ingression' to denote the
+general relation of objects to events. The ingression of an object into
+an event is the way the character of the event shapes itself in virtue
+of the being of the object. Namely the event is what it is, because the
+object is what it is; and when I am thinking of this modification of the
+event by the object, I call the relation between the two 'the ingression
+of the object into the event.' It is equally true to say that objects
+are what they are because events are what they are. Nature is such that
+there can be no events and no objects without the ingression of objects
+into events. Although there are events such that the ingredient objects
+evade our recognition. These are the events in empty space. Such events
+are only analysed for us by the intellectual probing of science.
+
+Ingression is a relation which has various modes. There are obviously
+very various kinds of objects; and no one kind of object can have the
+same sort of relations to events as objects of another kind can have. We
+shall have to analyse out some of the different modes of ingression
+which different kinds of objects have into events.
+
+But even if we stick to one and the same kind of objects, an object of
+that kind has different modes of ingression into different events.
+Science and philosophy have been apt to entangle themselves in a
+simple-minded theory that an object is at one place at any definite
+time, and is in no sense anywhere else. This is in fact the attitude of
+common sense thought, though it is not the attitude of language which is
+na�vely expressing the facts of experience. Every other sentence in a
+work of literature which is endeavouring truly to interpret the facts of
+experience expresses differences in surrounding events due to the
+presence of some object. An object is ingredient throughout its
+neighbourhood, and its neighbourhood is indefinite. Also the
+modification of events by ingression is susceptible of quantitative
+differences. Finally therefore we are driven to admit that each object
+is in some sense ingredient throughout nature; though its ingression may
+be quantitatively irrelevant in the expression of our individual
+experiences.
+
+This admission is not new either in philosophy or science. It is
+obviously a necessary axiom for those philosophers who insist that
+reality is a system. In these lectures we are keeping off the profound
+and vexed question as to what we mean by 'reality.' I am maintaining the
+humbler thesis that nature is a system. But I suppose that in this case
+the less follows from the greater, and that I may claim the support of
+these philosophers. The same doctrine is essentially interwoven in all
+modern physical speculation. As long ago as 1847 Faraday in a paper in
+the _Philosophical Magazine_ remarked that his theory of tubes of force
+implies that in a sense an electric charge is everywhere. The
+modification of the electromagnetic field at every point of space at
+each instant owing to the past history of each electron is another way
+of stating the same fact. We can however illustrate the doctrine by the
+more familiar facts of life without recourse to the abstruse
+speculations of theoretical physics.
+
+The waves as they roll on to the Cornish coast tell of a gale in
+mid-Atlantic; and our dinner witnesses to the ingression of the cook
+into the dining room. It is evident that the ingression of objects into
+events includes the theory of causation. I prefer to neglect this aspect
+of ingression, because causation raises the memory of discussions based
+upon theories of nature which are alien to my own. Also I think that
+some new light may be thrown on the subject by viewing it in this fresh
+aspect.
+
+The examples which I have given of the ingression of objects into events
+remind us that ingression takes a peculiar form in the case of some
+events; in a sense, it is a more concentrated form. For example, the
+electron has a certain position in space and a certain shape. Perhaps it
+is an extremely small sphere in a certain test-tube. The storm is a
+gale situated in mid-Atlantic with a certain latitude and longitude, and
+the cook is in the kitchen. I will call this special form of ingression
+the 'relation of situation'; also, by a double use of the word
+'situation,' I will call the event in which an object is situated 'the
+situation of the object.' Thus a situation is an event which is a
+relatum in the relation of situation. Now our first impression is that
+at last we have come to the simple plain fact of where the object really
+is; and that the vaguer relation which I call ingression should not be
+muddled up with the relation of situation, as if including it as a
+particular case. It seems so obvious that any object is in such and such
+a position, and that it is influencing other events in a totally
+different sense. Namely, in a sense an object is the character of the
+event which is its situation, but it only influences the character of
+other events. Accordingly the relations of situation and influencing are
+not generally the same sort of relation, and should not be subsumed
+under the same term 'ingression.' I believe that this notion is a
+mistake, and that it is impossible to draw a clear distinction between
+the two relations.
+
+For example, Where was your toothache? You went to a dentist and pointed
+out the tooth to him. He pronounced it perfectly sound, and cured you by
+stopping another tooth. Which tooth was the situation of the toothache?
+Again, a man has an arm amputated, and experiences sensations in the
+hand which he has lost. The situation of the imaginary hand is in fact
+merely thin air. You look into a mirror and see a fire. The flames that
+you see are situated behind the mirror. Again at night you watch the
+sky; if some of the stars had vanished from existence hours ago, you
+would not be any the wiser. Even the situations of the planets differ
+from those which science would assign to them.
+
+Anyhow you are tempted to exclaim, the cook is in the kitchen. If you
+mean her mind, I will not agree with you on the point; for I am only
+talking of nature. Let us think only of her bodily presence. What do you
+mean by this notion? We confine ourselves to typical manifestations of
+it. You can see her, touch her, and hear her. But the examples which I
+have given you show that the notions of the situations of what you see,
+what you touch, and what you hear are not so sharply separated out as to
+defy further questioning. You cannot cling to the idea that we have two
+sets of experiences of nature, one of primary qualities which belong to
+the objects perceived, and one of secondary qualities which are the
+products of our mental excitements. All we know of nature is in the same
+boat, to sink or swim together. The constructions of science are merely
+expositions of the characters of things perceived. Accordingly to affirm
+that the cook is a certain dance of molecules and electrons is merely to
+affirm that the things about her which are perceivable have certain
+characters. The situations of the perceived manifestations of her bodily
+presence have only a very general relation to the situations of the
+molecules, to be determined by discussion of the circumstances of
+perception.
+
+In discussing the relations of situation in particular and of ingression
+in general, the first requisite is to note that objects are of radically
+different types. For each type 'situation' and 'ingression' have their
+own special meanings which are different from their meanings for other
+types, though connexions can be pointed out. It is necessary therefore
+in discussing them to determine what type of objects are under
+consideration. There are, I think, an indefinite number of types of
+objects. Happily we need not think of them all. The idea of situation
+has its peculiar importance in reference to three types of objects which
+I call sense-objects, perceptual objects and scientific objects. The
+suitability of these names for the three types is of minor importance,
+so long as I can succeed in explaining what I mean by them.
+
+These three types form an ascending hierarchy, of which each member
+presupposes the type below. The base of the hierarchy is formed by the
+sense-objects. These objects do not presuppose any other type of
+objects. A sense-object is a factor of nature posited by sense-awareness
+which (i), in that it is an object, does not share in the passage of
+nature and (ii) is not a relation between other factors of nature. It
+will of course be a relatum in relations which also implicate other
+factors of nature. But it is always a relatum and never the relation
+itself. Examples of sense-objects are a particular sort of colour, say
+Cambridge blue, or a particular sort of sound, or a particular sort of
+smell, or a particular sort of feeling. I am not talking of a particular
+patch of blue as seen during a particular second of time at a definite
+date. Such a patch is an event where Cambridge blue is situated.
+Similarly I am not talking of any particular concert-room as filled with
+the note. I mean the note itself and not the patch of volume filled by
+the sound for a tenth of a second. It is natural for us to think of the
+note in itself, but in the case of colour we are apt to think of it
+merely as a property of the patch. No one thinks of the note as a
+property of the concert-room. We see the blue and we hear the note. Both
+the blue and the note are immediately posited by the discrimination of
+sense-awareness which relates the mind to nature. The blue is posited as
+in nature related to other factors in nature. In particular it is
+posited as in the relation of being situated in the event which is its
+situation.
+
+The difficulties which cluster around the relation of situation arise
+from the obstinate refusal of philosophers to take seriously the
+ultimate fact of multiple relations. By a multiple relation I mean a
+relation which in any concrete instance of its occurrence necessarily
+involves more than two relata. For example, when John likes Thomas there
+are only two relata, John and Thomas. But when John gives that book to
+Thomas there are three relata, John, that book, and Thomas.
+
+Some schools of philosophy, under the influence of the Aristotelian
+logic and the Aristotelian philosophy, endeavour to get on without
+admitting any relations at all except that of substance and attribute.
+Namely all apparent relations are to be resolvable into the concurrent
+existence of substances with contrasted attributes. It is fairly obvious
+that the Leibnizian monadology is the necessary outcome of any such
+philosophy. If you dislike pluralism, there will be only one monad.
+
+Other schools of philosophy admit relations but obstinately refuse to
+contemplate relations with more than two relata. I do not think that
+this limitation is based on any set purpose or theory. It merely arises
+from the fact that more complicated relations are a bother to people
+without adequate mathematical training, when they are admitted into the
+reasoning.
+
+I must repeat that we have nothing to do in these lectures with the
+ultimate character of reality. It is quite possible that in the true
+philosophy of reality there are only individual substances with
+attributes, or that there are only relations with pairs of relata. I do
+not believe that such is the case; but I am not concerned to argue about
+it now. Our theme is Nature. So long as we confine ourselves to the
+factors posited in the sense-awareness of nature, it seems to me that
+there certainly are instances of multiple relations between these
+factors, and that the relation of situation for sense-objects is one
+example of such multiple relations.
+
+Consider a blue coat, a flannel coat of Cambridge blue belonging to some
+athlete. The coat itself is a perceptual object and its situation is not
+what I am talking about. We are talking of someone's definite
+sense-awareness of Cambridge blue as situated in some event of nature.
+He may be looking at the coat directly. He then sees Cambridge blue as
+situated practically in the same event as the coat at that instant. It
+is true that the blue which he sees is due to light which left the coat
+some inconceivably small fraction of a second before. This difference
+would be important if he were looking at a star whose colour was
+Cambridge blue. The star might have ceased to exist days ago, or even
+years ago. The situation of the blue will not then be very intimately
+connected with the situation (in another sense of 'situation') of any
+perceptual object. This disconnexion of the situation of the blue and
+the situation of some associated perceptual object does not require a
+star for its exemplification. Any looking glass will suffice. Look at
+the coat through a looking glass. Then blue is seen as situated behind
+the mirror. The event which is its situation depends upon the position
+of the observer.
+
+The sense-awareness of the blue as situated in a certain event which I
+call the situation, is thus exhibited as the sense-awareness of a
+relation between the blue, the percipient event of the observer, the
+situation, and intervening events. All nature is in fact required,
+though only certain intervening events require their characters to be of
+certain definite sorts. The ingression of blue into the events of nature
+is thus exhibited as systematically correlated. The awareness of the
+observer depends on the position of the percipient event in this
+systematic correlation. I will use the term 'ingression into nature' for
+this systematic correlation of the blue with nature. Thus the ingression
+of blue into any definite event is a part statement of the fact of the
+ingression of blue into nature.
+
+In respect to the ingression of blue into nature events may be roughly
+put into four classes which overlap and are not very clearly separated.
+These classes are (i) the percipient events, (ii) the situations, (iii)
+the active conditioning events, (iv) the passive conditioning events. To
+understand this classification of events in the general fact of the
+ingression of blue into nature, let us confine attention to one
+situation for one percipient event and to the consequent _r�les_ of the
+conditioning events for the ingression as thus limited. The percipient
+event is the relevant bodily state of the observer. The situation is
+where he sees the blue, say, behind the mirror. The active conditioning
+events are the events whose characters are particularly relevant for the
+event (which is the situation) to be the situation for that percipient
+event, namely the coat, the mirror, and the state of the room as to
+light and atmosphere. The passive conditioning events are the events of
+the rest of nature.
+
+In general the situation is an active conditioning event; namely the
+coat itself, when there is no mirror or other such contrivance to
+produce abnormal effects. But the example of the mirror shows us that
+the situation may be one of the passive conditioning events. We are then
+apt to say that our senses have been cheated, because we demand as a
+right that the situation should be an active condition in the
+ingression.
+
+This demand is not so baseless as it may seem when presented as I have
+put it. All we know of the characters of the events of nature is based
+on the analysis of the relations of situations to percipient events. If
+situations were not in general active conditions, this analysis would
+tell us nothing. Nature would be an unfathomable enigma to us and there
+could be no science. Accordingly the incipient discontent when a
+situation is found to be a passive condition is in a sense justifiable;
+because if that sort of thing went on too often, the _r�le_ of the
+intellect would be ended.
+
+Furthermore the mirror is itself the situation of other sense-objects
+either for the same observer with the same percipient event, or for
+other observers with other percipient events. Thus the fact that an
+event is a situation in the ingression of one set of sense-objects into
+nature is presumptive evidence that that event is an active condition in
+the ingression of other sense-objects into nature which may have other
+situations.
+
+This is a fundamental principle of science which it has derived from
+common sense.
+
+I now turn to perceptual objects. When we look at the coat, we do not in
+general say, There is a patch of Cambridge blue; what naturally occurs
+to us is, There is a coat. Also the judgment that what we have seen is
+a garment of man's attire is a detail. What we perceive is an object
+other than a mere sense-object. It is not a mere patch of colour, but
+something more; and it is that something more which we judge to be a
+coat. I will use the word 'coat' as the name for that crude object which
+is more than a patch of colour, and without any allusion to the
+judgments as to its usefulness as an article of attire either in the
+past or the future. The coat which is perceived--in this sense of the
+word 'coat'--is what I call a perceptual object. We have to investigate
+the general character of these perceptual objects.
+
+It is a law of nature that in general the situation of a sense-object is
+not only the situation of that sense-object for one definite percipient
+event, but is the situation of a variety of sense-objects for a variety
+of percipient events. For example, for any one percipient event, the
+situation of a sense-object of sight is apt also to be the situations of
+sense-objects of sight, of touch, of smell, and of sound. Furthermore
+this concurrence in the situations of sense-objects has led to the
+body--_i.e._ the percipient event--so adapting itself that the
+perception of one sense-object in a certain situation leads to a
+subconscious sense-awareness of other sense-objects in the same
+situation. This interplay is especially the case between touch and
+sight. There is a certain correlation between the ingressions of
+sense-objects of touch and sense-objects of sight into nature, and in a
+slighter degree between the ingressions of other pairs of sense-objects.
+I call this sort of correlation the 'conveyance' of one sense-object by
+another. When you see the blue flannel coat you subconsciously feel
+yourself wearing it or otherwise touching it. If you are a smoker, you
+may also subconsciously be aware of the faint aroma of tobacco. The
+peculiar fact, posited by this sense-awareness of the concurrence of
+subconscious sense-objects along with one or more dominating
+sense-objects in the same situation, is the sense-awareness of the
+perceptual object. The perceptual object is not primarily the issue of a
+judgment. It is a factor of nature directly posited in sense-awareness.
+The element of judgment comes in when we proceed to classify the
+particular perceptual object. For example, we say, That is flannel, and
+we think of the properties of flannel and the uses of athletes' coats.
+But that all takes place after we have got hold of the perceptual
+object. Anticipatory judgments affect the perceptual object perceived by
+focussing and diverting attention.
+
+The perceptual object is the outcome of the habit of experience.
+Anything which conflicts with this habit hinders the sense-awareness of
+such an object. A sense-object is not the product of the association of
+intellectual ideas; it is the product of the association of
+sense-objects in the same situation. This outcome is not intellectual;
+it is an object of peculiar type with its own particular ingression into
+nature.
+
+There are two kinds of perceptual objects, namely, 'delusive perceptual
+objects' and 'physical objects.' The situation of a delusive perceptual
+object is a passive condition in the ingression of that object into
+nature. Also the event which is the situation will have the relation of
+situation to the object only for one particular percipient event. For
+example, an observer sees the image of the blue coat in a mirror. It is
+a blue coat that he sees and not a mere patch of colour. This shows that
+the active conditions for the conveyance of a group of subconscious
+sense-objects by a dominating sense-object are to be found in the
+percipient event. Namely we are to look for them in the investigations
+of medical psychologists. The ingression into nature of the delusive
+sense-object is conditioned by the adaptation of bodily events to the
+more normal occurrence, which is the ingression of the physical object.
+
+A perceptual object is a physical object when (i) its situation is an
+active conditioning event for the ingression of any of its component
+sense-objects, and (ii) the same event can be the situation of the
+perceptual object for an indefinite number of possible percipient
+events. Physical objects are the ordinary objects which we perceive when
+our senses are not cheated, such as chairs, tables and trees. In a way
+physical objects have more insistent perceptive power than
+sense-objects. Attention to the fact of their occurrence in nature is
+the first condition for the survival of complex living organisms. The
+result of this high perceptive power of physical objects is the
+scholastic philosophy of nature which looks on the sense-objects as mere
+attributes of the physical objects. This scholastic point of view is
+directly contradicted by the wealth of sense-objects which enter into
+our experience as situated in events without any connexion with physical
+objects. For example, stray smells, sounds, colours and more subtle
+nameless sense-objects. There is no perception of physical objects
+without perception of sense-objects. But the converse does not hold:
+namely, there is abundant perception of sense-objects unaccompanied by
+any perception of physical objects. This lack of reciprocity in the
+relations between sense-objects and physical objects is fatal to the
+scholastic natural philosophy.
+
+There is a great difference in the _r�les_ of the situations of
+sense-objects and physical objects. The situations of a physical object
+are conditioned by uniqueness and continuity. The uniqueness is an ideal
+limit to which we approximate as we proceed in thought along an
+abstractive set of durations, considering smaller and smaller durations
+in the approach to the ideal limit of the moment of time. In other
+words, when the duration is small enough, the situation of the physical
+object within that duration is practically unique.
+
+The identification of the same physical object as being situated in
+distinct events in distinct durations is effected by the condition of
+continuity. This condition of continuity is the condition that a
+continuity of passage of events, each event being a situation of the
+object in its corresponding duration, can be found from the earlier to
+the later of the two given events. So far as the two events are
+practically adjacent in one specious present, this continuity of passage
+may be directly perceived. Otherwise it is a matter of judgment and
+inference.
+
+The situations of a sense-object are not conditioned by any such
+conditions either of uniqueness or of continuity. In any durations
+however small a sense-object may have any number of situations separated
+from each other. Thus two situations of a sense-object, either in the
+same duration or in different durations, are not necessarily connected
+by any continuous passage of events which are also situations of that
+sense-object.
+
+The characters of the conditioning events involved in the ingression of
+a sense-object into nature can be largely expressed in terms of the
+physical objects which are situated in those events. In one respect this
+is also a tautology. For the physical object is nothing else than the
+habitual concurrence of a certain set of sense-objects in one situation.
+Accordingly when we know all about the physical object, we thereby know
+its component sense-objects. But a physical object is a condition for
+the occurrence of sense-objects other than those which are its
+components. For example, the atmosphere causes the events which are its
+situations to be active conditioning events in the transmission of
+sound. A mirror which is itself a physical object is an active condition
+for the situation of a patch of colour behind it, due to the reflection
+of light in it.
+
+Thus the origin of scientific knowledge is the endeavour to express in
+terms of physical objects the various _r�les_ of events as active
+conditions in the ingression of sense-objects into nature. It is in the
+progress of this investigation that scientific objects emerge. They
+embody those aspects of the character of the situations of the physical
+objects which are most permanent and are expressible without reference
+to a multiple relation including a percipient event. Their relations to
+each other are also characterised by a certain simplicity and
+uniformity. Finally the characters of the observed physical objects and
+sense-objects can be expressed in terms of these scientific objects. In
+fact the whole point of the search for scientific objects is the
+endeavour to obtain this simple expression of the characters of events.
+These scientific objects are not themselves merely formulae for
+calculation; because formulae must refer to things in nature, and the
+scientific objects are the things in nature to which the formulae refer.
+
+A scientific object such as a definite electron is a systematic
+correlation of the characters of all events throughout all nature. It is
+an aspect of the systematic character of nature. The electron is not
+merely where its charge is. The charge is the quantitative character of
+certain events due to the ingression of the electron into nature. The
+electron is its whole field of force. Namely the electron is the
+systematic way in which all events are modified as the expression of its
+ingression. The situation of an electron in any small duration may be
+defined as that event which has the quantitative character which is the
+charge of the electron. We may if we please term the mere charge the
+electron. But then another name is required for the scientific object
+which is the full entity which concerns science, and which I have called
+the electron.
+
+According to this conception of scientific objects, the rival theories
+of action at a distance and action by transmission through a medium are
+both incomplete expressions of the true process of nature. The stream of
+events which form the continuous series of situations of the electron is
+entirely self-determined, both as regards having the intrinsic character
+of being the series of situations of that electron and as regards the
+time-systems with which its various members are cogredient, and the flux
+of their positions in their corresponding durations. This is the
+foundation of the denial of action at a distance; namely the progress of
+the stream of the situations of a scientific object can be determined by
+an analysis of the stream itself.
+
+On the other hand the ingression of every electron into nature modifies
+to some extent the character of every event. Thus the character of the
+stream of events which we are considering bears marks of the existence
+of every other electron throughout the universe. If we like to think of
+the electrons as being merely what I call their charges, then the
+charges act at a distance. But this action consists in the modification
+of the situation of the other electron under consideration. This
+conception of a charge acting at a distance is a wholly artificial one.
+The conception which most fully expresses the character of nature is
+that of each event as modified by the ingression of each electron into
+nature. The ether is the expression of this systematic modification of
+events throughout space and throughout time. The best expression of the
+character of this modification is for physicists to find out. My theory
+has nothing to do with that and is ready to accept any outcome of
+physical research.
+
+The connexion of objects with space requires elucidation. Objects are
+situated in events. The relation of situation is a different relation
+for each type of object, and in the case of sense-objects it cannot be
+expressed as a two-termed relation. It would perhaps be better to use a
+different word for these different types of the relation of situation.
+It has not however been necessary to do so for our purposes in these
+lectures. It must be understood however that, when situation is spoken
+of, some one definite type is under discussion, and it may happen that
+the argument may not apply to situation of another type. In all cases
+however I use situation to express a relation between objects and events
+and not between objects and abstractive elements. There is a derivative
+relation between objects and spatial elements which I call the relation
+of location; and when this relation holds, I say that the object is
+located in the abstractive element. In this sense, an object may be
+located in a moment of time, in a volume of space, an area, a line, or a
+point. There will be a peculiar type of location corresponding to each
+type of situation; and location is in each case derivative from the
+corresponding relation of situation in a way which I will proceed to
+explain.
+
+Also location in the timeless space of some time-system is a relation
+derivative from location in instantaneous spaces of the same
+time-system. Accordingly location in an instantaneous space is the
+primary idea which we have to explain. Great confusion has been
+occasioned in natural philosophy by the neglect to distinguish between
+the different types of objects, the different types of situation, the
+different types of location, and the difference between location and
+situation. It is impossible to reason accurately in the vague concerning
+objects and their positions without keeping these distinctions in view.
+An object is located in an abstractive element, when an abstractive set
+belonging to that element can be found such that each event belonging to
+that set is a situation of the object. It will be remembered that an
+abstractive element is a certain group of abstractive sets, and that
+each abstractive set is a set of events. This definition defines the
+location of an element in any type of abstractive element. In this sense
+we can talk of the existence of an object at an instant, meaning thereby
+its location in some definite moment. It may also be located in some
+spatial element of the instantaneous space of that moment.
+
+A quantity can be said to be located in an abstractive element when an
+abstractive set belonging to the element can be found such that the
+quantitative expressions of the corresponding characters of its events
+converge to the measure of the given quantity as a limit when we pass
+along the abstractive set towards its converging end.
+
+By these definitions location in elements of instantaneous spaces is
+defined. These elements occupy corresponding elements of timeless
+spaces. An object located in an element of an instantaneous space will
+also be said to be located at that moment in the timeless element of the
+timeless space which is occupied by that instantaneous element.
+
+It is not every object which can be located in a moment. An object which
+can be located in every moment of some duration will be called a
+'uniform' object throughout that duration. Ordinary physical objects
+appear to us to be uniform objects, and we habitually assume that
+scientific objects such as electrons are uniform. But some sense-objects
+certainly are not uniform. A tune is an example of a non-uniform object.
+We have perceived it as a whole in a certain duration; but the tune as a
+tune is not at any moment of that duration though one of the individual
+notes may be located there.
+
+It is possible therefore that for the existence of certain sorts of
+objects, _e.g._ electrons, minimum quanta of time are requisite. Some
+such postulate is apparently indicated by the modern quantum theory and
+it is perfectly consistent with the doctrine of objects maintained in
+these lectures.
+
+Also the instance of the distinction between the electron as the mere
+quantitative electric charge of its situation and the electron as
+standing for the ingression of an object throughout nature illustrates
+the indefinite number of types of objects which exist in nature. We can
+intellectually distinguish even subtler and subtler types of objects.
+Here I reckon subtlety as meaning seclusion from the immediate
+apprehension of sense-awareness. Evolution in the complexity of life
+means an increase in the types of objects directly sensed. Delicacy of
+sense-apprehension means perceptions of objects as distinct entities
+which are mere subtle ideas to cruder sensibilities. The phrasing of
+music is a mere abstract subtlety to the unmusical; it is a direct
+sense-apprehension to the initiated. For example, if we could imagine
+some lowly type of organic being thinking and aware of our thoughts, it
+would wonder at the abstract subtleties in which we indulge as we think
+of stones and bricks and drops of water and plants. It only knows of
+vague undifferentiated feelings in nature. It would consider us as given
+over to the play of excessively abstract intellects. But then if it
+could think, it would anticipate; and if it anticipated, it would soon
+perceive for itself.
+
+In these lectures we have been scrutinising the foundations of natural
+philosophy. We are stopping at the very point where a boundless ocean of
+enquiries opens out for our questioning.
+
+I agree that the view of Nature which I have maintained in these
+lectures is not a simple one. Nature appears as a complex system whose
+factors are dimly discerned by us. But, as I ask you, Is not this the
+very truth? Should we not distrust the jaunty assurance with which every
+age prides itself that it at last has hit upon the ultimate concepts in
+which all that happens can be formulated? The aim of science is to seek
+the simplest explanations of complex facts. We are apt to fall into the
+error of thinking that the facts are simple because simplicity is the
+goal of our quest. The guiding motto in the life of every natural
+philosopher should be, Seek simplicity and distrust it.
+
+
+
+
+CHAPTER VIII
+
+SUMMARY
+
+
+There is a general agreement that Einstein's investigations have one
+fundamental merit irrespective of any criticisms which we may feel
+inclined to pass on them. They have made us think. But when we have
+admitted so far, we are most of us faced with a distressing perplexity.
+What is it that we ought to think about? The purport of my lecture this
+afternoon will be to meet this difficulty and, so far as I am able, to
+set in a clear light the changes in the background of our scientific
+thought which are necessitated by any acceptance, however qualified, of
+Einstein's main positions. I remember that I am lecturing to the members
+of a chemical society who are not for the most part versed in advanced
+mathematics. The first point that I would urge upon you is that what
+immediately concerns you is not so much the detailed deductions of the
+new theory as this general change in the background of scientific
+conceptions which will follow from its acceptance. Of course, the
+detailed deductions are important, because unless our colleagues the
+astronomers and the physicists find these predictions to be verified we
+can neglect the theory altogether. But we may now take it as granted
+that in many striking particulars these deductions have been found to be
+in agreement with observation. Accordingly the theory has to be taken
+seriously and we are anxious to know what will be the consequences of
+its final acceptance. Furthermore during the last few weeks the
+scientific journals and the lay press have been filled with articles as
+to the nature of the crucial experiments which have been made and as to
+some of the more striking expressions of the outcome of the new theory.
+'Space caught bending' appeared on the news-sheet of a well-known
+evening paper. This rendering is a terse but not inapt translation of
+Einstein's own way of interpreting his results. I should say at once
+that I am a heretic as to this explanation and that I shall expound to
+you another explanation based upon some work of my own, an explanation
+which seems to me to be more in accordance with our scientific ideas and
+with the whole body of facts which have to be explained. We have to
+remember that a new theory must take account of the old well-attested
+facts of science just as much as of the very latest experimental results
+which have led to its production.
+
+To put ourselves in the position to assimilate and to criticise any
+change in ultimate scientific conceptions we must begin at the
+beginning. So you must bear with me if I commence by making some simple
+and obvious reflections. Let us consider three statements, (i)
+'Yesterday a man was run over on the Chelsea Embankment,' (ii)
+'Cleopatra's Needle is on the Charing Cross Embankment,' and (iii)
+'There are dark lines in the Solar Spectrum.' The first statement about
+the accident to the man is about what we may term an 'occurrence,' a
+'happening,' or an 'event.' I will use the term 'event' because it is
+the shortest. In order to specify an observed event, the place, the
+time, and character of the event are necessary. In specifying the place
+and the time you are really stating the relation of the assigned event
+to the general structure of other observed events. For example, the man
+was run over between your tea and your dinner and adjacently to a
+passing barge in the river and the traffic in the Strand. The point
+which I want to make is this: Nature is known to us in our experience as
+a complex of passing events. In this complex we discern definite mutual
+relations between component events, which we may call their relative
+positions, and these positions we express partly in terms of space and
+partly in terms of time. Also in addition to its mere relative position
+to other events, each particular event has its own peculiar character.
+In other words, nature is a structure of events and each event has its
+position in this structure and its own peculiar character or quality.
+
+Let us now examine the other two statements in the light of this general
+principle as to the meaning of nature. Take the second statement,
+'Cleopatra's Needle is on the Charing Cross Embankment.' At first sight
+we should hardly call this an event. It seems to lack the element of
+time or transitoriness. But does it? If an angel had made the remark
+some hundreds of millions of years ago, the earth was not in existence,
+twenty millions of years ago there was no Thames, eighty years ago there
+was no Thames Embankment, and when I was a small boy Cleopatra's Needle
+was not there. And now that it is there, we none of us expect it to be
+eternal. The static timeless element in the relation of Cleopatra's
+Needle to the Embankment is a pure illusion generated by the fact that
+for purposes of daily intercourse its emphasis is needless. What it
+comes to is this: Amidst the structure of events which form the medium
+within which the daily life of Londoners is passed we know how to
+identify a certain stream of events which maintain permanence of
+character, namely the character of being the situations of Cleopatra's
+Needle. Day by day and hour by hour we can find a certain chunk in the
+transitory life of nature and of that chunk we say, 'There is
+Cleopatra's Needle.' If we define the Needle in a sufficiently abstract
+manner we can say that it never changes. But a physicist who looks on
+that part of the life of nature as a dance of electrons, will tell you
+that daily it has lost some molecules and gained others, and even the
+plain man can see that it gets dirtier and is occasionally washed. Thus
+the question of change in the Needle is a mere matter of definition. The
+more abstract your definition, the more permanent the Needle. But
+whether your Needle change or be permanent, all you mean by stating that
+it is situated on the Charing Cross Embankment, is that amid the
+structure of events you know of a certain continuous limited stream of
+events, such that any chunk of that stream, during any hour, or any day,
+or any second, has the character of being the situation of Cleopatra's
+Needle.
+
+Finally, we come to the third statement, 'There are dark lines in the
+Solar Spectrum.' This is a law of nature. But what does that mean? It
+means merely this. If any event has the character of being an exhibition
+of the solar spectrum under certain assigned circumstances, it will also
+have the character of exhibiting dark lines in that spectrum.
+
+This long discussion brings us to the final conclusion that the concrete
+facts of nature are events exhibiting a certain structure in their
+mutual relations and certain characters of their own. The aim of science
+is to express the relations between their characters in terms of the
+mutual structural relations between the events thus characterised. The
+mutual structural relations between events are both spatial and
+temporal. If you think of them as merely spatial you are omitting the
+temporal element, and if you think of them as merely temporal you are
+omitting the spatial element. Thus when you think of space alone, or of
+time alone, you are dealing in abstractions, namely, you are leaving out
+an essential element in the life of nature as known to you in the
+experience of your senses. Furthermore there are different ways of
+making these abstractions which we think of as space and as time; and
+under some circumstances we adopt one way and under other circumstances
+we adopt another way. Thus there is no paradox in holding that what we
+mean by space under one set of circumstances is not what we mean by
+space under another set of circumstances. And equally what we mean by
+time under one set of circumstances is not what we mean by time under
+another set of circumstances. By saying that space and time are
+abstractions, I do not mean that they do not express for us real facts
+about nature. What I mean is that there are no spatial facts or temporal
+facts apart from physical nature, namely that space and time are merely
+ways of expressing certain truths about the relations between events.
+Also that under different circumstances there are different sets of
+truths about the universe which are naturally presented to us as
+statements about space. In such a case what a being under the one set of
+circumstances means by space will be different from that meant by a
+being under the other set of circumstances. Accordingly when we are
+comparing two observations made under different circumstances we have to
+ask 'Do the two observers mean the same thing by space and the same
+thing by time?' The modern theory of relativity has arisen because
+certain perplexities as to the concordance of certain delicate
+observations such as the motion of the earth through the ether, the
+perihelion of mercury, and the positions of the stars in the
+neighbourhood of the sun, have been solved by reference to this purely
+relative significance of space and time.
+
+I want now to recall your attention to Cleopatra's Needle, which I have
+not yet done with. As you are walking along the Embankment you suddenly
+look up and say, 'Hullo, there's the Needle.' In other words, you
+recognise it. You cannot recognise an event; because when it is gone, it
+is gone. You may observe another event of analogous character, but the
+actual chunk of the life of nature is inseparable from its unique
+occurrence. But a character of an event can be recognised. We all know
+that if we go to the Embankment near Charing Cross we shall observe an
+event having the character which we recognise as Cleopatra's Needle.
+Things which we thus recognise I call objects. An object is situated in
+those events or in that stream of events of which it expresses the
+character. There are many sorts of objects. For example, the colour
+green is an object according to the above definition. It is the purpose
+of science to trace the laws which govern the appearance of objects in
+the various events in which they are found to be situated. For this
+purpose we can mainly concentrate on two types of objects, which I will
+call material physical objects and scientific objects. A material
+physical object is an ordinary bit of matter, Cleopatra's Needle for
+example. This is a much more complicated type of object than a mere
+colour, such as the colour of the Needle. I call these simple objects,
+such as colours or sounds, sense-objects. An artist will train himself
+to attend more particularly to sense-objects where the ordinary person
+attends normally to material objects. Thus if you were walking with an
+artist, when you said 'There's Cleopatra's Needle,' perhaps he
+simultaneously exclaimed 'There's a nice bit of colour.' Yet you were
+both expressing your recognition of different component characters of
+the same event. But in science we have found out that when we know all
+about the adventures amid events of material physical objects and of
+scientific objects we have most of the relevant information which will
+enable us to predict the conditions under which we shall perceive
+sense-objects in specific situations. For example, when we know that
+there is a blazing fire (_i.e._ material and scientific objects
+undergoing various exciting adventures amid events) and opposite to it a
+mirror (which is another material object) and the positions of a man's
+face and eyes gazing into the mirror, we know that he can perceive the
+redness of the flame situated in an event behind the mirror--thus, to a
+large extent, the appearance of sense-objects is conditioned by the
+adventures of material objects. The analysis of these adventures makes
+us aware of another character of events, namely their characters as
+fields of activity which determine the subsequent events to which they
+will pass on the objects situated in them. We express these fields of
+activity in terms of gravitational, electromagnetic, or chemical forces
+and attractions. But the exact expression of the nature of these fields
+of activity forces us intellectually to acknowledge a less obvious type
+of objects as situated in events. I mean molecules and electrons. These
+objects are not recognised in isolation. We cannot well miss Cleopatra's
+Needle, if we are in its neighbourhood; but no one has seen a single
+molecule or a single electron, yet the characters of events are only
+explicable to us by expressing them in terms of these scientific
+objects. Undoubtedly molecules and electrons are abstractions. But then
+so is Cleopatra's Needle. The concrete facts are the events
+themselves--I have already explained to you that to be an abstraction
+does not mean that an entity is nothing. It merely means that its
+existence is only one factor of a more concrete element of nature. So an
+electron is abstract because you cannot wipe out the whole structure of
+events and yet retain the electron in existence. In the same way the
+grin on the cat is abstract; and the molecule is really in the event in
+the same sense as the grin is really on the cat's face. Now the more
+ultimate sciences such as Chemistry or Physics cannot express their
+ultimate laws in terms of such vague objects as the sun, the earth,
+Cleopatra's Needle, or a human body. Such objects more properly belong
+to Astronomy, to Geology, to Engineering, to Archaeology, or to Biology.
+Chemistry and Physics only deal with them as exhibiting statistical
+complexes of the effects of their more intimate laws. In a certain
+sense, they only enter into Physics and Chemistry as technological
+applications. The reason is that they are too vague. Where does
+Cleopatra's Needle begin and where does it end? Is the soot part of it?
+Is it a different object when it sheds a molecule or when its surface
+enters into chemical combination with the acid of a London fog? The
+definiteness and permanence of the Needle is nothing to the possible
+permanent definiteness of a molecule as conceived by science, and the
+permanent definiteness of a molecule in its turn yields to that of an
+electron. Thus science in its most ultimate formulation of law seeks
+objects with the most permanent definite simplicity of character and
+expresses its final laws in terms of them.
+
+Again when we seek definitely to express the relations of events which
+arise from their spatio-temporal structure, we approximate to simplicity
+by progressively diminishing the extent (both temporal and spatial) of
+the events considered. For example, the event which is the life of the
+chunk of nature which is the Needle during one minute has to the life of
+nature within a passing barge during the same minute a very complex
+spatio-temporal relation. But suppose we progressively diminish the time
+considered to a second, to a hundredth of a second, to a thousandth of a
+second, and so on. As we pass along such a series we approximate to an
+ideal simplicity of structural relations of the pairs of events
+successively considered, which ideal we call the spatial relations of
+the Needle to the barge at some instant. Even these relations are too
+complicated for us, and we consider smaller and smaller bits of the
+Needle and of the barge. Thus we finally reach the ideal of an event so
+restricted in its extension as to be without extension in space or
+extension in time. Such an event is a mere spatial point-flash of
+instantaneous duration. I call such an ideal event an 'event-particle.'
+You must not think of the world as ultimately built up of
+event-particles. That is to put the cart before the horse. The world we
+know is a continuous stream of occurrence which we can discriminate into
+finite events forming by their overlappings and containings of each
+other and separations a spatio-temporal structure. We can express the
+properties of this structure in terms of the ideal limits to routes of
+approximation, which I have termed event-particles. Accordingly
+event-particles are abstractions in their relations to the more concrete
+events. But then by this time you will have comprehended that you cannot
+analyse concrete nature without abstracting. Also I repeat, the
+abstractions of science are entities which are truly in nature, though
+they have no meaning in isolation from nature.
+
+The character of the spatio-temporal structure of events can be fully
+expressed in terms of relations between these more abstract
+event-particles. The advantage of dealing with event-particles is that
+though they are abstract and complex in respect to the finite events
+which we directly observe, they are simpler than finite events in
+respect to their mutual relations. Accordingly they express for us the
+demands of an ideal accuracy, and of an ideal simplicity in the
+exposition of relations. These event-particles are the ultimate elements
+of the four-dimensional space-time manifold which the theory of
+relativity presupposes. You will have observed that each event-particle
+is as much an instant of time as it is a point of space. I have called
+it an instantaneous point-flash. Thus in the structure of this
+space-time manifold space is not finally discriminated from time, and
+the possibility remains open for diverse modes of discrimination
+according to the diverse circumstances of observers. It is this
+possibility which makes the fundamental distinction between the new way
+of conceiving the universe and the old way. The secret of understanding
+relativity is to understand this. It is of no use rushing in with
+picturesque paradoxes, such as 'Space caught bending,' if you have not
+mastered this fundamental conception which underlies the whole theory.
+When I say that it underlies the whole theory, I mean that in my opinion
+it ought to underlie it, though I may confess some doubts as to how far
+all expositions of the theory have really understood its implications
+and its premises.
+
+Our measurements when they are expressed in terms of an ideal accuracy
+are measurements which express properties of the space-time manifold.
+Now there are measurements of different sorts. You can measure lengths,
+or angles, or areas, or volumes, or times. There are also other sorts of
+measures such as measurements of intensity of illumination, but I will
+disregard these for the moment and will confine attention to those
+measurements which particularly interest us as being measurements of
+space or of time. It is easy to see that four such measurements of the
+proper characters are necessary to determine the position of an
+event-particle in the space-time manifold in its relation to the rest of
+the manifold. For example, in a rectangular field you start from one
+corner at a given time, you measure a definite distance along one side,
+you then strike out into the field at right angles, and then measure a
+definite distance parallel to the other pair of sides, you then rise
+vertically a definite height and take the time. At the point and at the
+time which you thus reach there is occurring a definite instantaneous
+point-flash of nature. In other words, your four measurements have
+determined a definite event-particle belonging to the four-dimension
+space-time manifold. These measurements have appeared to be very simple
+to the land-surveyor and raise in his mind no philosophic difficulties.
+But suppose there are beings on Mars sufficiently advanced in
+scientific invention to be able to watch in detail the operations of
+this survey on earth. Suppose that they construe the operations of the
+English land-surveyors in reference to the space natural to a being on
+Mars, namely a Martio-centric space in which that planet is fixed. The
+earth is moving relatively to Mars and is rotating. To the beings on
+Mars the operations, construed in this fashion, effect measurements of
+the greatest complication. Furthermore, according to the relativistic
+doctrine, the operation of time-measurement on earth will not correspond
+quite exactly to any time-measurement on Mars.
+
+I have discussed this example in order to make you realise that in
+thinking of the possibilities of measurement in the space-time manifold,
+we must not confine ourselves merely to those minor variations which
+might seem natural to human beings on the earth. Let us make therefore
+the general statement that four measurements, respectively of
+independent types (such as measurements of lengths in three directions
+and a time), can be found such that a definite event-particle is
+determined by them in its relations to other parts of the manifold.
+
+If (p_1, p_2, p_3, p_4) be a set of measurements of this system, then
+the event-particle which is thus determined will be said to have p_1,
+p_2, p_3, p_4 as its co-ordinates in this system of measurement. Suppose
+that we name it the p-system of measurement. Then in the same p-system
+by properly varying (p_1, p_2, p_3, p_4) every event-particle that has
+been, or will be, or instantaneously is now, can be indicated.
+Furthermore, according to any system of measurement that is natural to
+us, three of the co-ordinates will be measurements of space and one will
+be a measurement of time. Let us always take the last co-ordinate to
+represent the time-measurement. Then we should naturally say that (p_1,
+p_2, p_3) determined a point in space and that the event-particle
+happened at that point at the time p_4. But we must not make the mistake
+of thinking that there is a space in addition to the space-time
+manifold. That manifold is all that there is for the determination of
+the meaning of space and time. We have got to determine the meaning of a
+space-point in terms of the event-particles of the four-dimensional
+manifold. There is only one way to do this. Note that if we vary the
+time and take times with the same three space co-ordinates, then the
+event-particles, thus indicated, are all at the same point. But seeing
+that there is nothing else except the event-particles, this can only
+mean that the point (p_1, p_2, p_3) of the space in the p-system is
+merely the collection of event-particles (p_1, p_2, p_3, [p_4]), where
+p_4 is varied and (p_1, p_2, p_3) is kept fixed. It is rather
+disconcerting to find that a point in space is not a simple entity; but
+it is a conclusion which follows immediately from the relative theory of
+space.
+
+Furthermore the inhabitant of Mars determines event-particles by another
+system of measurements. Call his system the q-system. According to him
+(q_1, q_2, q_3, q_4) determines an event-particle, and (q_1, q_2, q_3)
+determines a point and q_4 a time. But the collection of event-particles
+which he thinks of as a point is entirely different from any such
+collection which the man on earth thinks of as a point. Thus the q-space
+for the man on Mars is quite different from the p-space for the
+land-surveyor on earth.
+
+So far in speaking of space we have been talking of the timeless space
+of physical science, namely, of our concept of eternal space in which
+the world adventures. But the space which we see as we look about is
+instantaneous space. Thus if our natural perceptions are adjustable to
+the p-system of measurements we see instantaneously all the
+event-particles at some definite time p_4, and observe a succession
+of such spaces as time moves on. The timeless space is achieved by
+stringing together all these instantaneous spaces. The points of an
+instantaneous space are event-particles, and the points of an eternal
+space are strings of event-particles occurring in succession. But the
+man on Mars will never perceive the same instantaneous spaces as the man
+on the earth. This system of instantaneous spaces will cut across the
+earth-man's system. For the earth-man there is one instantaneous space
+which is the instantaneous present, there are the past spaces and the
+future spaces. But the present space of the man on Mars cuts across the
+present space of the man on the earth. So that of the event-particles
+which the earth-man thinks of as happening now in the present, the man
+on Mars thinks that some are already past and are ancient history, that
+others are in the future, and others are in the immediate present. This
+break-down in the neat conception of a past, a present, and a future is
+a serious paradox. I call two event-particles which on some or other
+system of measurement are in the same instantaneous space 'co-present'
+event-particles. Then it is possible that A and B may be co-present,
+and that A and C may be co-present, but that B and C may not be
+co-present. For example, at some inconceivable distance from us there
+are events co-present with us now and also co-present with the birth of
+Queen Victoria. If A and B are co-present there will be some systems
+in which A precedes B and some in which B precedes A. Also there
+can be no velocity quick enough to carry a material particle from A to
+B or from B to A. These different measure-systems with their
+divergences of time-reckoning are puzzling, and to some extent affront
+our common sense. It is not the usual way in which we think of the
+Universe. We think of one necessary time-system and one necessary space.
+According to the new theory, there are an indefinite number of
+discordant time-series and an indefinite number of distinct spaces. Any
+correlated pair, a time-system and a space-system, will do in which to
+fit our description of the Universe. We find that under given conditions
+our measurements are necessarily made in some one pair which together
+form our natural measure-system. The difficulty as to discordant
+time-systems is partly solved by distinguishing between what I call the
+creative advance of nature, which is not properly serial at all, and any
+one time series. We habitually muddle together this creative advance,
+which we experience and know as the perpetual transition of nature into
+novelty, with the single-time series which we naturally employ for
+measurement. The various time-series each measure some aspect of the
+creative advance, and the whole bundle of them express all the
+properties of this advance which are measurable. The reason why we have
+not previously noted this difference of time-series is the very small
+difference of properties between any two such series. Any observable
+phenomena due to this cause depend on the square of the ratio of any
+velocity entering into the observation to the velocity of light. Now
+light takes about fifty minutes to get round the earth's orbit; and the
+earth takes rather more than 17,531�half-hours to do the same. Hence all
+the effects due to this motion are of the order of the ratio of one to
+the square of 10,000. Accordingly an earth-man and a sun-man have only
+neglected effects whose quantitative magnitudes all contain the factor
+1/10^8. Evidently such effects can only be noted by means of the most
+refined observations. They have been observed however. Suppose we
+compare two observations on the velocity of light made with the same
+apparatus as we turn it through a right angle. The velocity of the earth
+relatively to the sun is in one direction, the velocity of light
+relatively to the ether should be the same in all directions. Hence if
+space when we take the ether as at rest means the same thing as space
+when we take the earth as at rest, we ought to find that the velocity of
+light relatively to the earth varies according to the direction from
+which it comes.
+
+These observations on earth constitute the basic principle of the famous
+experiments designed to detect the motion of the earth through the
+ether. You all know that, quite unexpectedly, they gave a null result.
+This is completely explained by the fact that, the space-system and the
+time-system which we are using are in certain minute ways different from
+the space and the time relatively to the sun or relatively to any other
+body with respect to which it is moving.
+
+All this discussion as to the nature of time and space has lifted above
+our horizon a great difficulty which affects the formulation of all the
+ultimate laws of physics--for example, the laws of the electromagnetic
+field, and the law of gravitation. Let us take the law of gravitation
+as an example. Its formulation is as follows: Two material bodies
+attract each other with a force proportional to the product of their
+masses and inversely proportional to the square of their distances.
+In this statement the bodies are supposed to be small enough to be
+treated as material particles in relation to their distances; and we
+need not bother further about that minor point. The difficulty to which
+I want to draw your attention is this: In the formulation of the law one
+definite time and one definite space are presupposed. The two masses are
+assumed to be in simultaneous positions.
+
+But what is simultaneous in one time-system may not be simultaneous in
+another time-system. So according to our new views the law is in this
+respect not formulated so as to have any exact meaning. Furthermore an
+analogous difficulty arises over the question of distance. The distance
+between two instantaneous positions, _i.e._ between two event-particles,
+is different in different space-systems. What space is to be chosen?
+Thus again the law lacks precise formulation, if relativity is accepted.
+Our problem is to seek a fresh interpretation of the law of gravity in
+which these difficulties are evaded. In the first place we must avoid
+the abstractions of space and time in the formulation of our fundamental
+ideas and must recur to the ultimate facts of nature, namely to events.
+Also in order to find the ideal simplicity of expressions of the
+relations between events, we restrict ourselves to event-particles. Thus
+the life of a material particle is its adventure amid a track of
+event-particles strung out as a continuous series or path in the
+four-dimensional space-time manifold. These event-particles are the
+various situations of the material particle. We usually express this
+fact by adopting our natural space-time system and by talking of the
+path in space of the material particle as it exists at successive
+instants of time.
+
+We have to ask ourselves what are the laws of nature which lead the
+material particle to adopt just this path among event-particles and no
+other. Think of the path as a whole. What characteristic has that path
+got which would not be shared by any other slightly varied path? We are
+asking for more than a law of gravity. We want laws of motion and a
+general idea of the way to formulate the effects of physical forces.
+
+In order to answer our question we put the idea of the attracting masses
+in the background and concentrate attention on the field of activity of
+the events in the neighbourhood of the path. In so doing we are acting
+in conformity with the whole trend of scientific thought during the last
+hundred years, which has more and more concentrated attention on the
+field of force as the immediate agent in directing motion, to the
+exclusion of the consideration of the immediate mutual influence between
+two distant bodies. We have got to find the way of expressing the field
+of activity of events in the neighbourhood of some definite
+event-particle E of the four-dimensional manifold. I bring in a
+fundamental physical idea which I call the 'impetus' to express this
+physical field. The event-particle E is related to any neighbouring
+event-particle P by an element of impetus. The assemblage of all the
+elements of impetus relating E to the assemblage of event-particles in
+the neighbourhood of E expresses the character of the field of
+activity in the neighbourhood of E. Where I differ from Einstein is
+that he conceives this quantity which I call the impetus as merely
+expressing the characters of the space and time to be adopted and thus
+ends by talking of the gravitational field expressing a curvature in the
+space-time manifold. I cannot attach any clear conception to his
+interpretation of space and time. My formulae differ slightly from his,
+though they agree in those instances where his results have been
+verified. I need hardly say that in this particular of the formulation
+of the law of gravitation I have drawn on the general method of
+procedure which constitutes his great discovery.
+
+Einstein showed how to express the characters of the assemblage of
+elements of impetus of the field surrounding an event-particle E in
+terms of ten quantities which I will call J_{11}, J_{12}
+(=J_{21}), J_{22}, J_{23}(=J_{32}), etc. It will be noted that
+there are four spatio-temporal measurements relating E to its
+neighbour P, and that there are ten pairs of such measurements if we
+are allowed to take any one measurement twice over to make one such
+pair. The ten J's depend merely on the position of E in the
+four-dimensional manifold, and the element of impetus between E and
+P can be expressed in terms of the ten J's and the ten pairs of the
+four spatio-temporal measurements relating E and P. The numerical
+values of the J's will depend on the system of measurement adopted,
+but are so adjusted to each particular system that the same value is
+obtained for the element of impetus between E and P, whatever be the
+system of measurement adopted. This fact is expressed by saying that the
+ten J's form a 'tensor.' It is not going too far to say that the
+announcement that physicists would have in future to study the theory of
+tensors created a veritable panic among them when the verification of
+Einstein's predictions was first announced.
+
+The ten J's at any event-particle E can be expressed in terms of two
+functions which I call the potential and the 'associate-potential' at
+E. The potential is practically what is meant by the ordinary
+gravitation potential, when we express ourselves in terms of the
+Euclidean space in reference to which the attracting mass is at rest.
+The associate-potential is defined by the modification of substituting
+the direct distance for the inverse distance in the definition of the
+potential, and its calculation can easily be made to depend on that of
+the old-fashioned potential. Thus the calculation of the J's--the
+coefficients of impetus, as I will call them--does not involve anything
+very revolutionary in the mathematical knowledge of physicists. We now
+return to the path of the attracted particle. We add up all the elements
+of impetus in the whole path, and obtain thereby what I call the
+'integral impetus.' The characteristic of the actual path as compared
+with neighbouring alternative paths is that in the actual paths the
+integral impetus would neither gain nor lose, if the particle wobbled
+out of it into a small extremely near alternative path. Mathematicians
+would express this by saying, that the integral impetus is stationary
+for an infinitesimal displacement. In this statement of the law of
+motion I have neglected the existence of other forces. But that would
+lead me too far afield.
+
+The electromagnetic theory has to be modified to allow for the presence
+of a gravitational field. Thus Einstein's investigations lead to the
+first discovery of any relation between gravity and other physical
+phenomena. In the form in which I have put this modification, we deduce
+Einstein's fundamental principle, as to the motion of light along its
+rays, as a first approximation which is absolutely true for infinitely
+short waves. Einstein's principle, thus partially verified, stated in my
+language is that a ray of light always follows a path such that the
+integral impetus along it is zero. This involves that every element of
+impetus along it is zero.
+
+In conclusion, I must apologise. In the first place I have considerably
+toned down the various exciting peculiarities of the original theory and
+have reduced it to a greater conformity with the older physics. I do not
+allow that physical phenomena are due to oddities of space. Also I have
+added to the dullness of the lecture by my respect for the audience. You
+would have enjoyed a more popular lecture with illustrations of
+delightful paradoxes. But I know also that you are serious students who
+are here because you really want to know how the new theories may affect
+your scientific researches.
+
+
+
+
+CHAPTER IX
+
+THE ULTIMATE PHYSICAL CONCEPTS
+
+
+The second chapter of this book lays down the first principle to be
+guarded in framing our physical concept. We must avoid vicious
+bifurcation. Nature is nothing else than the deliverance of
+sense-awareness. We have no principles whatever to tell us what could
+stimulate mind towards sense-awareness. Our sole task is to exhibit in
+one system the characters and inter-relations of all that is observed.
+Our attitude towards nature is purely 'behaviouristic,' so far as
+concerns the formulation of physical concepts.
+
+Our knowledge of nature is an experience of activity (or passage). The
+things previously observed are active entities, the 'events.' They are
+chunks in the life of nature. These events have to each other relations
+which in our knowledge differentiate themselves into space-relations and
+time-relations. But this differentiation between space and time, though
+inherent in nature, is comparatively superficial; and space and time are
+each partial expressions of one fundamental relation between events
+which is neither spatial nor temporal. This relation I call 'extension.'
+The relation of 'extending over' is the relation of 'including,' either
+in a spatial or in a temporal sense, or in both. But the mere
+'inclusion' is more fundamental than either alternative and does not
+require any spatio-temporal differentiation. In respect to extension two
+events are mutually related so that either (i) one includes the other,
+or (ii) one overlaps the other without complete inclusion, or (iii)
+they are entirely separate. But great care is required in the
+definition of spatial and temporal elements from this basis in order to
+avoid tacit limitations really depending on undefined relations and
+properties.
+
+Such fallacies can be avoided by taking account of two elements in our
+experience, namely, (i) our observational 'present,' and (ii) our
+'percipient event.'
+
+Our observational 'present' is what I call a 'duration.' It is the whole
+of nature apprehended in our immediate observation. It has therefore the
+nature of an event, but possesses a peculiar completeness which marks
+out such durations as a special type of events inherent in nature. A
+duration is not instantaneous. It is all that there is of nature with
+certain temporal limitations. In contradistinction to other events a
+duration will be called infinite and the other events are finite[10]. In
+our knowledge of a duration we distinguish (i) certain included events
+which are particularly discriminated as to their peculiar
+individualities, and (ii) the remaining included events which are only
+known as necessarily in being by reason of their relations to the
+discriminated events and to the whole duration. The duration as a whole
+is signified[11] by that quality of relatedness (in respect to
+extension) possessed by the part which is immediately under observation;
+namely, by the fact that there is essentially a beyond to whatever is
+observed. I mean by this that every event is known as being related to
+other events which it does not include. This fact, that every event is
+known as possessing the quality of exclusion, shows that exclusion is as
+positive a relation as inclusion. There are of course no merely
+negative relations in nature, and exclusion is not the mere negative of
+inclusion, though the two relations are contraries. Both relations are
+concerned solely with events, and exclusion is capable of logical
+definition in terms of inclusion.
+
+[10] Cf. note on 'significance,' pp.�197, 198.
+
+[11] Cf. Ch.�III, pp.�51 et�seq.
+
+Perhaps the most obvious exhibition of significance is to be found in
+our knowledge of the geometrical character of events inside an opaque
+material object. For example we know that an opaque sphere has a centre.
+This knowledge has nothing to do with the material; the sphere may be a
+solid uniform billiard ball or a hollow lawn-tennis ball. Such knowledge
+is essentially the product of significance, since the general character
+of the external discriminated events has informed us that there are
+events within the sphere and has also informed us of their geometrical
+structure.
+
+Some criticisms on 'The Principles of Natural Knowledge' show that
+difficulty has been found in apprehending durations as real
+stratifications of nature. I think that this hesitation arises from the
+unconscious influence of the vicious principle of bifurcation, so deeply
+embedded in modern philosophical thought. We observe nature as extended
+in an immediate present which is simultaneous but not instantaneous, and
+therefore the whole which is immediately discerned or signified as an
+inter-related system forms a stratification of nature which is a
+physical fact. This conclusion immediately follows unless we admit
+bifurcation in the form of the principle of psychic additions, here
+rejected.
+
+Our 'percipient event' is that event included in our observational
+present which we distinguish as being in some peculiar way our
+standpoint for perception. It is roughly speaking that event which is
+our bodily life within the present duration. The theory of perception
+as evolved by medical psychology is based on significance. The distant
+situation of a perceived object is merely known to us as signified by
+our bodily state, _i.e._ by our percipient event. In fact perception
+requires sense-awareness of the significations of our percipient event
+together with sense-awareness of a peculiar relation (situation) between
+certain objects and the events thus signified. Our percipient event is
+saved by being the whole of nature by this fact of its significations.
+This is the meaning of calling the percipient event our standpoint for
+perception. The course of a ray of light is only derivatively connected
+with perception. What we do perceive are objects as related to events
+signified by the bodily states excited by the ray. These signified
+events (as is the case of images seen behind a mirror) may have very
+little to do with the actual course of the ray. In the course of
+evolution those animals have survived whose sense-awareness is
+concentrated on those significations of their bodily states which are on
+the average important for their welfare. The whole world of events is
+signified, but there are some which exact the death penalty for
+inattention.
+
+The percipient event is always here and now in the associated present
+duration. It has, what may be called, an absolute position in that
+duration. Thus one definite duration is associated with a definite
+percipient event, and we are thus aware of a peculiar relation which
+finite events can bear to durations. I call this relation 'cogredience.'
+The notion of rest is derivative from that of cogredience, and the
+notion of motion is derivative from that of inclusion within a duration
+without cogredience with it. In fact motion is a relation (of varying
+character) between an observed event and an observed duration, and
+cogredience is the most simple character or subspecies of motion. To sum
+up, a duration and a percipient event are essentially involved in the
+general character of each observation of nature, and the percipient
+event is cogredient with the duration.
+
+Our knowledge of the peculiar characters of different events depends
+upon our power of comparison. I call the exercise of this factor in our
+knowledge 'recognition,' and the requisite sense-awareness of the
+comparable characters I call 'sense-recognition.' Recognition and
+abstraction essentially involve each other. Each of them exhibits an
+entity for knowledge which is less than the concrete fact, but is a real
+factor in that fact. The most concrete fact capable of separate
+discrimination is the event. We cannot abstract without recognition, and
+we cannot recognise without abstraction. Perception involves
+apprehension of the event and recognition of the factors of its
+character.
+
+The things recognised are what I call 'objects.' In this general sense
+of the term the relation of extension is itself an object. In practice
+however I restrict the term to those objects which can in some sense or
+other be said to have a situation in an event; namely, in the phrase
+'There it is again' I restrict the 'there' to be the indication of a
+special event which is the situation of the object. Even so, there are
+different types of objects, and statements which are true of objects of
+one type are not in general true of objects of other types. The objects
+with which we are here concerned in the formulation of physical laws are
+material objects, such as bits of matter, molecules and electrons. An
+object of one of these types has relations to events other than those
+belonging to the stream of its situations. The fact of its situations
+within this stream has impressed on all other events certain
+modifications of their characters. In truth the object in its
+completeness may be conceived as a specific set of correlated
+modifications of the characters of all events, with the property that
+these modifications attain to a certain focal property for those events
+which belong to the stream of its situations. The total assemblage of
+the modifications of the characters of events due to the existence of an
+object in a stream of situations is what I call the 'physical field' due
+to the object. But the object cannot really be separated from its field.
+The object is in fact nothing else than the systematically adjusted set
+of modifications of the field. The conventional limitation of the object
+to the focal stream of events in which it is said to be 'situated' is
+convenient for some purposes, but it obscures the ultimate fact of
+nature. From this point of view the antithesis between action at a
+distance and action by transmission is meaningless. The doctrine of this
+paragraph is nothing else than another way of expressing the
+unresolvable multiple relation of an object to events.
+
+A complete time-system is formed by any one family of parallel
+durations. Two durations are parallel if either (i) one includes the
+other, or (ii) they overlap so as to include a third duration common to
+both, or (iii) are entirely separate. The excluded case is that of two
+durations overlapping so as to include in common an aggregate of finite
+events but including in common no other complete duration. The
+recognition of the fact of an indefinite number of families of parallel
+durations is what differentiates the concept of nature here put forward
+from the older orthodox concept of the essentially unique time-systems.
+Its divergence from Einstein's concept of nature will be briefly
+indicated later.
+
+The instantaneous spaces of a given time-system are the ideal
+(non-existent) durations of zero temporal thickness indicated by routes
+of approximation along series formed by durations of the associated
+family. Each such instantaneous space represents the ideal of nature at
+an instant and is also a moment of time. Each time-system thus possesses
+an aggregate of moments belonging to it alone. Each event-particle lies
+in one and only one moment of a given time-system. An event-particle has
+three characters[12]: (i) its extrinsic character which is its character
+as a definite route of convergence among events, (ii) its intrinsic
+character which is the peculiar quality of nature in its neighbourhood,
+namely, the character of the physical field in the neighbourhood, and
+(iii) its position.
+
+[12] Cf. pp.�82 et�seq.
+
+The position of an event-particle arises from the aggregate of moments
+(no two of the same family) in which it lies. We fix our attention on
+one of these moments which is approximated to by the short duration of
+our immediate experience, and we express position as the position in
+this moment. But the event-particle receives its position in moment M
+in virtue of the whole aggregate of other moments M{'}, M{''}, etc.,
+in which it also lies. The differentiation of M into a geometry of
+event-particles (instantaneous points) expresses the differentiation of
+M by its intersections with moments of alien time-systems. In this way
+planes and straight lines and event-particles themselves find their
+being. Also the parallelism of planes and straight lines arises from the
+parallelism of the moments of one and the same time-system intersecting
+M. Similarly the order of parallel planes and of event-particles on
+straight lines arises from the time-order of these intersecting moments.
+The explanation is not given here[13]. It is sufficient now merely to
+mention the sources from which the whole of geometry receives its
+physical explanation.
+
+[13] Cf. _Principles of Natural Knowledge_, and previous chapters of the
+present work.
+
+The correlation of the various momentary spaces of one time-system is
+achieved by the relation of cogredience. Evidently motion in an
+instantaneous space is unmeaning. Motion expresses a comparison between
+position in one instantaneous space with positions in other
+instantaneous spaces of the same time-system. Cogredience yields the
+simplest outcome of such comparison, namely, rest.
+
+Motion and rest are immediately observed facts. They are relative in the
+sense that they depend on the time-system which is fundamental for the
+observation. A string of event-particles whose successive occupation
+means rest in the given time-system forms a timeless point in the
+timeless space of that time-system. In this way each time-system
+possesses its own permanent timeless space peculiar to it alone, and
+each such space is composed of timeless points which belong to that
+time-system and to no other. The paradoxes of relativity arise from
+neglecting the fact that different assumptions as to rest involve the
+expression of the facts of physical science in terms of radically
+different spaces and times, in which points and moments have different
+meanings.
+
+The source of order has already been indicated and that of congruence is
+now found. It depends on motion. From cogredience, perpendicularity
+arises; and from perpendicularity in conjunction with the reciprocal
+symmetry between the relations of any two time-systems congruence both
+in time and space is completely defined (cf. _loc. cit._).
+
+The resulting formulae are those for the electromagnetic theory of
+relativity, or, as it is now termed, the restricted theory. But there is
+this vital difference: the critical velocity c which occurs in these
+formulae has now no connexion whatever with light or with any other fact
+of the physical field (in distinction from the extensional structure of
+events). It simply marks the fact that our congruence determination
+embraces both times and spaces in one universal system, and therefore if
+two arbitrary units are chosen, one for all spaces and one for all
+times, their ratio will be a velocity which is a fundamental property of
+nature expressing the fact that times and spaces are really comparable.
+
+The physical properties of nature are expressed in terms of material
+objects (electrons, etc.). The physical character of an event arises
+from the fact that it belongs to the field of the whole complex of such
+objects. From another point of view we can say that these objects are
+nothing else than our way of expressing the mutual correlation of the
+physical characters of events.
+
+The spatio-temporal measurableness of nature arises from (i) the
+relation of extension between events, and (ii) the stratified character
+of nature arising from each of the alternative time-systems, and (iii)
+rest and motion, as exhibited in the relations of finite events to
+time-systems. None of these sources of measurement depend on the
+physical characters of finite events as exhibited by the situated
+objects. They are completely signified for events whose physical
+characters are unknown. Thus the spatio-temporal measurements are
+independent of the objectival physical characters. Furthermore the
+character of our knowledge of a whole duration, which is essentially
+derived from the significance of the part within the immediate field of
+discrimination, constructs it for us as a uniform whole independent, so
+far as its extension is concerned, of the unobserved characters of
+remote events. Namely, there is a definite whole of nature,
+simultaneously now present, whatever may be the character of its remote
+events. This consideration reinforces the previous conclusion. This
+conclusion leads to the assertion of the essential uniformity of the
+momentary spaces of the various time-systems, and thence to the
+uniformity of the timeless spaces of which there is one to each
+time-system.
+
+The analysis of the general character of observed nature set forth above
+affords explanations of various fundamental observational facts:
+({alpha}) It explains the differentiation of the one quality of
+extension into time and space. ({beta}) It gives a meaning to the
+observed facts of geometrical and temporal position, of geometrical and
+temporal order, and of geometrical straightness and planeness. ({gamma})
+It selects one definite system of congruence embracing both space and
+time, and thus explains the concordance as to measurement which is in
+practice attained. ({delta}) It explains (consistently with the theory
+of relativity) the observed phenomena of rotation, _e.g._ Foucault's
+pendulum, the equatorial bulge of the earth, the fixed senses of
+rotation of cyclones and anticyclones, and the gyro-compass. It does
+this by its admission of definite stratifications of nature which are
+disclosed by the very character of our knowledge of it. ({epsilon}) Its
+explanations of motion are more fundamental than those expressed in
+({delta}); for it explains what is meant by motion itself. The observed
+motion of an extended object is the relation of its various situations
+to the stratification of nature expressed by the time-system fundamental
+to the observation. This motion expresses a real relation of the object
+to the rest of nature. The quantitative expression of this relation will
+vary according to the time-system selected for its expression.
+
+This theory accords no peculiar character to light beyond that accorded
+to other physical phenomena such as sound. There is no ground for such a
+differentiation. Some objects we know by sight only, and other objects
+we know by sound only, and other objects we observe neither by light nor
+by sound but by touch or smell or otherwise. The velocity of light
+varies according to its medium and so does that of sound. Light moves in
+curved paths under certain conditions and so does sound. Both light and
+sound are waves of disturbance in the physical characters of events; and
+(as has been stated above, p.�188) the actual course of the light is of
+no more importance for perception than is the actual course of the
+sound. To base the whole philosophy of nature upon light is a baseless
+assumption. The Michelson-Morley and analogous experiments show that
+within the limits of our inexactitude of observation the velocity of
+light is an approximation to the critical velocity 'c' which expresses
+the relation between our space and time units. It is provable that the
+assumption as to light by which these experiments and the influence of
+the gravitational field on the light-rays are explained is deducible _as
+an approximation_ from the equations of the electromagnetic field. This
+completely disposes of any necessity for differentiating light from
+other physical phenomena as possessing any peculiar fundamental
+character.
+
+It is to be observed that the measurement of extended nature by means of
+extended objects is meaningless apart from some observed fact of
+simultaneity inherent in nature and not merely a play of thought.
+Otherwise there is no meaning to the concept of one presentation of your
+extended measuring rod AB. Why not AB' where B' is the end B
+five minutes later? Measurement presupposes for its possibility nature
+as a simultaneity, and an observed object present then and present now.
+In other words, measurement of extended nature requires some inherent
+character in nature affording a rule of presentation of events.
+Furthermore congruence cannot be defined by the permanence of the
+measuring rod. The permanence is itself meaningless apart from some
+immediate judgment of self-congruence. Otherwise how is an elastic
+string differentiated from a rigid measuring rod? Each remains the same
+self-identical object. Why is one a possible measuring rod and the other
+not so? The meaning of congruence lies beyond the self-identity of the
+object. In other words measurement presupposes the measurable, and the
+theory of the measurable is the theory of congruence.
+
+Furthermore the admission of stratifications of nature bears on the
+formulation of the laws of nature. It has been laid down that these laws
+are to be expressed in differential equations which, as expressed in any
+general system of measurement, should bear no reference to any other
+particular measure-system. This requirement is purely arbitrary. For a
+measure-system measures something inherent in nature; otherwise it has
+no connexion with nature at all. And that something which is measured
+by a particular measure-system may have a special relation to the
+phenomenon whose law is being formulated. For example the gravitational
+field due to a material object at rest in a certain time-system may be
+expected to exhibit in its formulation particular reference to spatial
+and temporal quantities of that time-system. The field can of course be
+expressed in any measure-systems, but the particular reference will
+remain as the simple physical explanation.
+
+
+NOTE: ON THE GREEK CONCEPT OF A POINT
+
+The preceding pages had been passed for press before I had the pleasure
+of seeing Sir T.�L. Heath's _Euclid in Greek_[14]. In the original
+Euclid's first definition is
+
+    s�meion estin, ou meros outhen.
+
+I have quoted it on p.�86 in the expanded form taught to me in
+childhood, 'without parts and without magnitude.' I should have
+consulted Heath's English edition--a classic from the moment of its
+issue--before committing myself to a statement about Euclid. This is
+however a trivial correction not affecting sense and not worth a note. I
+wish here to draw attention to Heath's own note to this definition in
+his _Euclid in Greek_. He summarises Greek thought on the nature of a
+point, from the Pythagoreans, through Plato and Aristotle, to Euclid. My
+analysis of the requisite character of a point on pp.�89 and 90 is in
+complete agreement with the outcome of the Greek discussion.
+
+[14] Camb. Univ. Press, 1920.
+
+
+NOTE: ON SIGNIFICANCE AND INFINITE EVENTS
+
+The theory of significance has been expanded and made more definite in
+the present volume. It had already been introduced in the _Principles of
+Natural Knowledge_ (cf. subarticles�3.3 to 3.8 and 16.1, 16.2, 19.4, and
+articles�20, 21). In reading over the proofs of the present volume, I
+come to the conclusion that in the light of this development my
+limitation of infinite events to durations is untenable. This limitation
+is stated in article�33 of the _Principles_ and at the beginning of
+Chapter�IV (p.�74) of this book. There is not only a significance of the
+discerned events embracing the whole present duration, but there is a
+significance of a cogredient event involving its extension through a
+whole time-system backwards and forwards. In other words the essential
+'beyond' in nature is a definite beyond in time as well as in space [cf.
+pp.�53, 194]. This follows from my whole thesis as to the assimilation
+of time and space and their origin in extension. It also has the same
+basis in the analysis of the character of our knowledge of nature. It
+follows from this admission that it is possible to define point-tracks
+[_i.e._ the points of timeless spaces] as abstractive elements. This is
+a great improvement as restoring the balance between moments and points.
+I still hold however to the statement in subarticle�35.4 of the
+_Principles_ that the intersection of a pair of non-parallel durations
+does not present itself to us as one event. This correction does not
+affect any of the subsequent reasoning in the two books.
+
+I may take this opportunity of pointing out that the 'stationary events'
+of article�57 of the _Principles_ are merely cogredient events got at
+from an abstract mathematical point of view.
+
+
+
+
+INDEX
+
+_In the case of terms of frequent occurrence, only those occurrences are
+indexed which are of peculiar importance for the elucidation of
+meaning._
+
+  A [_or_ an], 11
+
+  Abraham, 105
+
+  Absolute position, 105, 106, 114, 188
+
+  Abstraction, 33, 37, 168, 171, 173;
+    extensive, 65, 79, 85
+
+  Abstractive element, 84;
+    set, 61, 79
+
+  Action at a distance, 159, 190
+
+  Action by transmission, 159, 190
+
+  Active conditions, 158
+
+  Activity, field of, 170, 181
+
+  Adjunction, 101
+
+  Aggregate, 23
+
+  Alexander, Prof., viii
+
+  Alexandria, 71
+
+  Alfred the Great, 137
+
+  Anticipation, 69
+
+  Anti-prime, 88
+
+  Apparent nature, 31, 39
+
+  Area, 99;
+    momental, 103;
+    vagrant, 103
+
+  Aristotelian logic, 150
+
+  Aristotle, 16, 17, 18, 24, 197
+
+  Associate-potential, 183
+
+  Atom, 17
+
+  Attribute, 21, 26, 150
+
+  Awareness, 3
+
+  Axiom, 36, 121
+
+  Axioms of congruence, 128 et�seqq.
+
+
+  Bacon, Francis, 78
+
+  Behaviouristic, 185
+
+  Bergson, 54
+
+  Berkeley, 28
+
+  Between, 64
+
+  Beyond, 186, 198
+
+  Bifurcation, vi, 30, 185, 187
+
+  Boundary, 100;
+    moment, 63;
+    particle, 100
+
+  Broad, C.�D., viii
+
+
+  Calculation, formula of, 45, 158
+
+  Cambridge, 97
+
+  Causal nature, 31, 39
+
+  Causation, 31, 146
+
+  Centrifugal force, 138
+
+  Change, uniformity of, 140
+
+  Character, extrinsic, 82, 89, 90, 113, 191;
+    intrinsic, 80, 82, 90, 113, 191
+
+  Charge, 160
+
+  Closure of nature, 4
+
+  Coefficient of drag, 133
+
+  Coefficients of impetus, 183
+
+  Cogredience, 110, 188
+
+  Coherence, 29
+
+  Comparison, 124, 125, 143, 189
+
+  Complex, 13
+
+  Conceptual nature, 45;
+    space, 96
+
+  Concrete facts, 167, 171, 189
+
+  Conditioning events, 152
+
+  Conditions, active, 158
+
+  Congruence, 65, 96, 118, 120, 127, 196
+
+  Continuity, 157;
+    Dedekindian, 102;
+    of events, 76;
+    of nature, 59, 76
+
+  Convention, 121
+
+  Convergence, 62, 79;
+    law of, 82
+
+  Conveyance, 154, 155
+
+  Co-present, 177
+
+  Covering, 83
+
+  Creative advance, 178
+
+  Critical velocity, 193, 195
+
+  Curvature of space-time, 182
+
+  Cyclone, 194
+
+
+  Dedekindian continuity, 102
+
+  Definite, 53, 194, 198
+
+  Delusions, 31, 38
+
+  Delusive perceptual object, 153
+
+  Demarcation of events, 144
+
+  Demonstrative phrase, 6
+
+  Descriptive phrase, 6, 10
+
+  Differential equations, 196
+
+  Discrimination, 14, 50, 144
+
+  Diversification of nature, 15
+
+  Duddington, Mrs, 47
+
+  Duration, 37, 53, 55, 186
+
+  Durations, families of, 59, 73, 190
+
+  Dynamical axes, 138
+
+
+  Einstein, vii, 102, 131, 164, 165, 181, 182, 183, 184, 191
+
+  Electromagnetic field, 179
+
+  Electron, 30, 146, 158, 171
+
+  Element, 17;
+    abstractive, 84
+
+  Elliptical phraseology, 7
+
+  Empty space, 145
+
+  Entity, 5, 13
+
+  Equal in abstractive force, 83
+
+  Error, 68
+
+  Ether, 18, 78, 160;
+    material, 78;
+    of events, 78
+
+  Euclid, 85, 94, 197
+
+  Euler, 140
+
+  Event, 15, 52, 75, 165;
+    percipient, 107, 152, 186
+
+  Event-particle, 86, 93, 94, 172, 191
+
+  Events, conditioning, 152;
+    continuity of, 76;
+    demarcation of, 144;
+    ether of, 78;
+    infinite, 197, 198;
+    limited, 74;
+    passage of, 34;
+    signified, 52;
+    stationary, 198;
+    stream of, 167;
+    structure of, 52, 166
+
+  Exclusion, 186
+
+  Explanation, 97, 141
+
+  Extended nature, 196
+
+  Extension, 22, 58, 75, 185
+
+  Extensive abstraction, 65, 79, 85
+
+  Extrinsic character, 82, 89, 90, 113, 191;
+    properties, 62
+
+
+  Fact, 12, 13
+
+  Factors, 12, 13, 15
+
+  Facts, concrete, 167, 171
+
+  Family of durations, 59, 63, 73;
+    of moments, 63
+
+  Faraday, 146
+
+  Field, gravitational, 197;
+    of activity, 170, 181;
+    physical, 190
+
+  Finite truths, 12
+
+  Fitzgerald, 133
+
+  Formula of calculation, 45, 158
+
+  Foucault, 138, 194
+
+  Four-dimensional manifold, 86
+
+  Fresnel, 133
+
+  Future, the, 72, 177
+
+
+  Galileo, 139
+
+  Geometrical order, 194
+
+  Geometry, 36;
+    metrical, 129
+
+  Gravitation, 179 et�seqq.
+
+  Gravitational field, 197
+
+  Greek philosophy, 16;
+    thought, 197
+
+  Gyro-compass, 194
+
+
+  Heath, Sir T.�L., 197
+
+  Here, 107
+
+
+  Idealists, 70
+
+  Immediacy, 52;
+    of perception, 72
+
+  Impetus, 181, 182;
+    coefficients of, 183;
+    integral, 183
+
+  Inclusion, 186
+
+  Individuality, 13
+
+  Infinite events, 197, 198
+
+  Inge, Dr, 48
+
+  Ingredient, 14
+
+  Ingression, 144, 145, 148, 152
+
+  Inherence, 83
+
+  Inside, 106
+
+  Instant, 33, 35, 57
+
+  Instantaneous plane, 91;
+    present, 72;
+    spaces, 86, 90, 177
+
+  Instantaneousness, 56, 57
+
+  Intersection, locus of, 90
+
+  Intrinsic character, 80, 82, 90, 113, 191;
+    properties, 62
+
+  Ionian thinkers, 19
+
+  Irrelevance, infinitude of, 12
+
+  Irrevocableness, 35, 37
+
+  It, 8
+
+
+  Julius Caesar, 36
+
+  Junction, 76, 101
+
+
+  Kinetic energy, 105;
+    symmetry, 129
+
+  Knowledge, 28, 32
+
+
+  Lagrange, 140
+
+  Larmor, 131
+
+  Law of convergence, 82
+
+  Laws of motion, 137, 139;
+    of nature, 196
+
+  Leibnizian monadology, 150
+
+  Level, 91, 92
+
+  Light, 195;
+    ray of, 188;
+    velocity of, 131
+
+  Limit, 57
+
+  Limited events, 74
+
+  Location, 160, 161
+
+  Locke, 27
+
+  Locus, 102;
+    of intersection, 90
+
+  London, 97
+
+  Lorentz, H.�A., 131, 133
+
+  Lossky, 47
+
+
+  Manifold, four-dimensional, 86;
+    space-time, 173
+
+  Material ether, 78;
+    object, 169
+
+  Materialism, 43, 70
+
+  Matrix, 116
+
+  Matter, 16, 17, 19, 20, 26
+
+  Maxwell, 131, 133
+
+  Measurableness, 196;
+    of nature, 193
+
+  Measurement, 96, 120, 174, 196;
+    of time, 65, 140
+
+  Measure-system, 196
+
+  Memory, 68
+
+  Metaphysics, 28, 32
+
+  Metrical geometry, 129
+
+  Michelson-Morley, 195
+
+  Milton, 35
+
+  Mind, 27, 28
+
+  Minkowski, viii, 131
+
+  Molecule, 32, 171
+
+  Moment, 57, 60, 88
+
+  Momental area, 103;
+    route, 103
+
+  Momentum, 105
+
+  Motion, 105, 114, 117, 127, 188, 192
+
+  Multiplicity, 22
+
+
+  Natural philosophy, 29, 30
+
+  Natural science, philosophy of, 46
+
+  Nature, 3;
+    apparent, 31, 39;
+    causal, 31, 39;
+    conceptual, 45;
+    continuity of, 59, 76;
+    discrimination of, 144;
+    extended, 196;
+    laws of, 196;
+    passage of, 54;
+    stratification of, 194, 196;
+    system of, 146
+
+  Newton, 27, 136, 139, 140
+
+
+  Object, 77, 125, 143, 169, 189;
+    delusive perceptual, 155;
+    material, 169;
+    perceptual, 153;
+    physical, 155, 157;
+    scientific, 158, 169;
+    uniform, 162
+
+  Occupation, 22, 34, 36, 100, 101
+
+  Order, source of, 192;
+    spatial, 95, 194;
+    temporal, 64, 95, 194
+
+  Organisation of thought, 79
+
+  Outside, 63, 100
+
+
+  Paradox, 192
+
+  Parallel, 63, 127;
+    durations, 190
+
+  Parallelism, 95, 191
+
+  Parallelogram, 127
+
+  Paris, 87, 138
+
+  Parliament, 120
+
+  Part, 14, 15, 58
+
+  Passage of events, 34;
+    of nature, 54
+
+  Past, the, 72, 177
+
+  Perception, 3
+
+  Perceptual objects, 149, 153
+
+  Percipience, 28
+
+  Percipient event, 107, 152, 186, 187
+
+  Period of time, 51
+
+  Permanence, 144
+
+  Perpendicularity, 117, 127, 193
+
+  Philosophy, 1;
+    natural, 29, 30;
+    of natural science, 46;
+    of the sciences, 2
+
+  Physical field, 190;
+    object, 155, 156, 157
+
+  Physics, speculative, 30
+
+  Place, 51
+
+  Plane, 191;
+    instantaneous, 91
+
+  Plato, 16, 17, 18, 24, 197
+
+  Poincar�, 121, 122, 123
+
+  Point, 35, 89, 91, 114, 173, 176
+
+  Point-flash, 172, 173
+
+  Point of space, 85
+
+  Point, timeless, 192
+
+  Point-track, 113, 198
+
+  Pompey, 36
+
+  Position, 89, 90, 92, 93, 99, 113, 191;
+    absolute, 105, 106, 114, 188
+
+  Potential, 183;
+    associate-, 183
+
+  Predicate, 18
+
+  Predication, 18
+
+  Present, the, 69, 72, 177;
+    instantaneous, 72;
+    observational, 186
+
+  Primary qualities, 27
+
+  Prime, 88
+
+  Process, 53, 54;
+    of nature, 54
+
+  Psychic additions, 29, 187
+
+  Punct, 92, 93, 94
+
+  Pythagoreans, 197
+
+
+  Quality, 27
+
+  Quantum of time, 162
+
+  Quantum theory, 162
+
+
+  Ray of light, 188
+
+  Reality, 30;
+    of durations, 55, 187
+
+  Recognition, 124, 143, 189
+
+  Rect, 91, 92
+
+  Recurrence, 35
+
+  Relative motion, 117;
+    velocity, 130
+
+  Relativity, 169;
+    restricted theory of, 193
+
+  Rest, 105, 114, 188, 192
+
+  Rotation, 138, 194
+
+  Route, 99;
+    momental, 103;
+    straight, 103
+
+  Russell, Bertrand, 11, 122, 123
+
+
+  Schelling, 47
+
+  Science, 2;
+    metaphysical, 32
+
+  Scientific objects, 149, 158, 169
+
+  Secondary qualities, 27
+
+  Self-congruence, 196
+
+  Self-containedness of nature, 4
+
+  Sense-awareness, 3, 67
+
+  Sense-object, 149, 170
+
+  Sense-perception, 3, 14
+
+  Sense-recognition, 143, 189
+
+  Series, temporal, 66, 70, 85, 178
+
+  Set, abstractive, 61, 79
+
+  Significance, 51, 186, 187, 188, 194, 197, 198
+
+  Signified events, 52
+
+  Simplicity, 163, 173
+
+  Simultaneity, 53, 56, 196
+
+  Situation, 15, 78, 147, 148, 152, 160, 189
+
+  Solid, 99, 101, 102;
+    vagrant, 101
+
+  Sound, 195
+
+  Space, 16, 17, 31, 33, 79;
+    empty, 145;
+    timeless, 86, 106, 114;
+    uniformity of, 194
+
+  Spaces, instantaneous, 86, 90
+
+  Space-system, 179
+
+  Space-time manifold, 173
+
+  Spatial-order, 95
+
+  Spatio-temporal structure, 173
+
+  Speculative demonstration, 6
+
+  Speculative physics, 30
+
+  Standpoint for perception, 107, 188
+
+  Station, 103, 104, 113
+
+  Stationary events, 198
+
+  Straight line, 91, 114, 191;
+    route, 103
+
+  Stratification of nature, 187, 194, 196
+
+  Stream of events, 167
+
+  Structure of events, 52, 166
+
+  Structure, spatio-temporal, 173
+
+  Subject, 18
+
+  Substance, 16, 18, 19, 150
+
+  Substratum, 16, 18, 21
+
+  Symmetry, 118, 126;
+    kinetic, 129
+
+  System of nature, 146
+
+  System, time-, 192
+
+
+  Tarner, Edward, v, 1
+
+  Temporal order, 64, 95, 194
+
+  Temporal series, 66, 70, 85
+
+  Tensor, 182
+
+  Terminus, 4
+
+  The, 11
+
+  Theory, quantum, 162
+
+  There, 110, 189
+
+  This, 11
+
+  Thought, 3, 14
+
+  Timaeus, the, 17, 20, 24
+
+  Time, 16, 17, 31, 33, 49, 79;
+    measurement of, 140;
+    quantum of, 162;
+    transcendence of, 39
+
+  Time-series, 178, also cf. Temporal series
+
+  Time-system, see Time-series, also 91, 97, 104, 179, 192
+
+  Timeless point, 192;
+    space, 86, 106, 114, 177
+
+  Totality, 89
+
+  Transcendence of time, 39
+
+  Transmission, 26, 28;
+    action by, 159, 190
+
+  Tubes of force, 146
+
+
+  Unexhaustiveness, 50
+
+  Uniform object, 162
+
+  Uniformity of change, 140;
+    of space, 194
+
+
+  Vagrant area, 103;
+    solid, 101
+
+  Veblen and Young, 36
+
+  Velocity, critical, 193, 195;
+    of light, 131, 195;
+    relative, 130
+
+  Volume, 92, 101
+
+
+  When, 107
+
+  Where, 107
+
+  Whole, 58
+
+  Within, 63
+
+
+  Young, Veblen and, 36
+
+
+
+
+
+End of Project Gutenberg's The Concept of Nature, by Alfred North Whitehead
+
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+<pre>
+
+Project Gutenberg's The Concept of Nature, by Alfred North Whitehead
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: The Concept of Nature
+       The Tarner Lectures Delivered in Trinity College, November 1919
+
+Author: Alfred North Whitehead
+
+Release Date: July 16, 2006 [EBook #18835]
+
+Language: English
+
+Character set encoding: ISO-8859-1
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+*** START OF THIS PROJECT GUTENBERG EBOOK THE CONCEPT OF NATURE ***
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+</pre>
+
+
+<div class="transnote">
+<h4>Transcriber&#8217;s Note</h4>
+<p class="sf"><b>Special characters</b> This file uses the following special characters:</p>
+<p class="center">&#8594; &#8230; &prime; &Prime; &#945; &#946; &#947; &#948; &#949;
+ &#951; &#952; &#953; &#955; &#956; &#957; &#959; &#960; &#961; &#962;
+  &#963; &#964; &#965; &agrave; &eacute; &ecirc; &iuml; &ocirc; &ldquo;
+  &rdquo; &lsquo; &rsquo; &mdash;</p>
+<p class="sf">If these do not display, you might try another font or browser, or use the
+ISO-8859-1 or ASCII text version of this ebook.</p>
+<p class="sf"><b>Printer errors</b> Two printer errors have been corrected:  On page&nbsp;<a href="#err1">51</a> the word &ldquo;sight&rdquo; has been changed to &ldquo;touch&rdquo; as suggested by the sense; and on page&nbsp;<a href="#err2">180</a> the word &ldquo;universely&rdquo; has been changed to &ldquo;inversely&rdquo;.  These are marked in the text by <ins class="correction" title="Like this.">mouse-hovers</ins>.</p>
+</div>
+<h1>
+The Concept of
+<br />
+<big>NATURE</big>
+<br />
+<br />
+<small class="smcap">The Tarner Lectures<br />
+Delivered in Trinity College<br />
+November 1919</small></h1>
+
+
+<h2>Alfred North Whitehead</h2>
+
+
+
+
+
+<hr />
+<h2><span class="pagenum" title="Page&nbsp;v">&nbsp;</span><a name="Page_v" id="Page_v"></a><a name="PREFACE" id="PREFACE"></a>PREFACE</h2>
+
+
+<p>The contents of this book were originally delivered at Trinity College
+in the autumn of 1919 as the inaugural course of Tarner lectures. The
+Tarner lectureship is an occasional office founded by the liberality of
+Mr Edward Tarner. The duty of each of the successive holders of the post
+will be to deliver a course on &lsquo;the Philosophy of the Sciences and the
+Relations or Want of Relations between the different Departments of
+Knowledge.&rsquo; The present book embodies the endeavour of the first
+lecturer of the series to fulfil his task.</p>
+
+<p>The chapters retain their original lecture form and remain as delivered
+with the exception of minor changes designed to remove obscurities of
+expression. The lecture form has the advantage of suggesting an audience
+with a definite mental background which it is the purpose of the lecture
+to modify in a specific way. In the presentation of a novel outlook with
+wide ramifications a single line of communications from premises to
+conclusions is not sufficient for intelligibility. Your audience will
+construe whatever you say into conformity with their pre-existing
+outlook. For this reason the first two chapters and the last two
+chapters are essential for intelligibility though they hardly add to the
+formal completeness of the exposition. Their function is to prevent the
+reader from bolting up side tracks in pursuit of misunderstandings. The
+same reason dictates my avoidance of the existing technical terminology
+<span class="pagenum" title="Page&nbsp;vi">&nbsp;</span><a name="Page_vi" id="Page_vi"></a>of philosophy. The modern natural philosophy is shot through and
+through with the fallacy of bifurcation which is discussed in the second
+chapter of this work. Accordingly all its technical terms in some subtle
+way presuppose a misunderstanding of my thesis. It is perhaps as well to
+state explicitly that if the reader indulges in the facile vice of
+bifurcation not a word of what I have here written will be intelligible.</p>
+
+<p>The last two chapters do not properly belong to the special course.
+<a href="#CHAPTER_VIII">Chapter&nbsp;VIII</a> is a lecture delivered in the spring of 1920 before the
+Chemical Society of the students of the Imperial College of Science and
+Technology. It has been appended here as conveniently summing up and
+applying the doctrine of the book for an audience with one definite type
+of outlook.</p>
+
+<p>This volume on &lsquo;the Concept of Nature&rsquo; forms a companion book to my
+previous work <i>An Enquiry concerning the Principles of Natural
+Knowledge</i>. Either book can be read independently, but they supplement
+each other. In part the present book supplies points of view which were
+omitted from its predecessor; in part it traverses the same ground with
+an alternative exposition. For one thing, mathematical notation has been
+carefully avoided, and the results of mathematical deductions are
+assumed. Some of the explanations have been improved and others have
+been set in a new light. On the other hand important points of the
+previous work have been omitted where I have had nothing fresh to say
+about them. On the whole, whereas the former work based itself chiefly
+on ideas directly drawn from<span class="pagenum" title="Page&nbsp;vii">&nbsp;</span><a name="Page_vii" id="Page_vii"></a> mathematical physics, the present book
+keeps closer to certain fields of philosophy and physics to the
+exclusion of mathematics. The two works meet in their discussions of
+some details of space and time.</p>
+
+<p>I am not conscious that I have in any way altered my views. Some
+developments have been made. Those that are capable of a
+non-mathematical exposition have been incorporated in the text. The
+mathematical developments are alluded to in the last two chapters. They
+concern the adaptation of the principles of mathematical physics to the
+form of the relativity principle which is here maintained. Einstein&#8217;s
+method of using the theory of tensors is adopted, but the application is
+worked out on different lines and from different assumptions. Those of
+his results which have been verified by experience are obtained also by
+my methods. The divergence chiefly arises from the fact that I do not
+accept his theory of non-uniform space or his assumption as to the
+peculiar fundamental character of light-signals. I would not however be
+misunderstood to be lacking in appreciation of the value of his recent
+work on general relativity which has the high merit of first disclosing
+the way in which mathematical physics should proceed in the light of the
+principle of relativity. But in my judgment he has cramped the
+development of his brilliant mathematical method in the narrow bounds of
+a very doubtful philosophy.</p>
+
+<p>The object of the present volume and of its predecessor is to lay the
+basis of a natural philosophy which is the necessary presupposition of a
+reorganised specu<span class="pagenum" title="Page&nbsp;viii">&nbsp;</span><a name="Page_viii" id="Page_viii"></a>lative physics. The general assimilation of space and
+time which dominates the constructive thought can claim the independent
+support of Minkowski from the side of science and also of succeeding
+relativists, while on the side of philosophers it was, I believe, one
+theme of Prof. Alexander&#8217;s Gifford lectures delivered some few years ago
+but not yet published. He also summarised his conclusions on this
+question in a lecture to the Aristotelian Society in the July of 1918.
+Since the publication of <i>An Enquiry concerning the Principles of
+Natural Knowledge</i> I have had the advantage of reading Mr C.&nbsp;D. Broad&#8217;s
+<i>Perception, Physics, and Reality</i> [Camb. Univ. Press, 1914]. This
+valuable book has assisted me in my discussion in <a href="#CHAPTER_II">Chapter&nbsp;II</a>, though I
+am unaware as to how far Mr Broad would assent to any of my arguments as
+there stated.</p>
+
+<p>It remains for me to thank the staff of the University Press, its
+compositors, its proof-readers, its clerks, and its managing officials,
+not only for the technical excellence of their work, but for the way
+they have co-operated so as to secure my convenience.</p>
+
+<p class="quotsig">A.&nbsp;N.&nbsp;W.</p>
+
+<p style="text-indent:0;">
+<span style="margin-left: 2em;" class="allsc">IMPERIAL COLLEGE OF SCIENCE</span><br />
+<span style="margin-left: 4em;" class="allsc">AND TECHNOLOGY.</span><br />
+<span style="margin-left: 6em;"><i>April</i>, 1920.</span><br />
+</p>
+
+<hr />
+
+<h2><span class="pagenum" title="Page&nbsp;ix">&nbsp;</span><a name="Page_ix" id="Page_ix"></a><a name="CONTENTS" id="CONTENTS"></a>CONTENTS</h2>
+
+<ol class="prelist">
+<li class="off allsc"><span class="lalign">CHAP.</span>&nbsp;<span class="ralign">PAGE</span></li>
+</ol>
+<ol class="toc">
+<li><a href="#CHAPTER_I">NATURE AND THOUGHT</a>  <span class="ralign"><a href="#Page_1">1</a></span></li>
+<li><a href="#CHAPTER_II">THEORIES OF THE BIFURCATION OF NATURE</a>  <span class="ralign"><a href="#Page_26">26</a></span></li>
+<li><a href="#CHAPTER_III">TIME</a>  <span class="ralign"><a href="#Page_49">49</a></span></li>
+<li><a href="#CHAPTER_IV">THE METHOD OF EXTENSIVE ABSTRACTION</a>  <span class="ralign"><a href="#Page_74">74</a></span></li>
+<li><a href="#CHAPTER_V">SPACE AND MOTION</a>  <span class="ralign"><a href="#Page_99">99</a></span></li>
+<li><a href="#CHAPTER_VI">CONGRUENCE</a>  <span class="ralign"><a href="#Page_120">120</a></span></li>
+<li><a href="#CHAPTER_VII">OBJECTS</a>  <span class="ralign"><a href="#Page_143">143</a></span></li>
+<li><a href="#CHAPTER_VIII">SUMMARY</a>  <span class="ralign"><a href="#Page_164">164</a></span></li>
+<li><a href="#CHAPTER_IX">THE ULTIMATE PHYSICAL CONCEPTS</a>  <span class="ralign"><a href="#Page_185">185</a></span></li>
+<li class="off"><a href="#NOTE1">NOTE: <span class="smcap">On the Greek Concept of a Point</span></a>  <span class="ralign"><a href="#Page_197">197</a></span></li>
+<li class="off"><a href="#NOTE2">NOTE: <span class="smcap">On Significance and Infinite Events</span></a>  <span class="ralign"><a href="#Page_197">197</a></span></li>
+<li class="off"><a href="#INDEX">INDEX</a>  <span class="ralign"><a href="#Page_199">199</a></span></li></ol>
+
+
+
+<hr />
+<h1><a name="THE_CONCEPT_OF_NATURE" id="THE_CONCEPT_OF_NATURE"></a>THE CONCEPT OF NATURE</h1>
+
+
+
+<hr />
+<h2><a name="CHAPTER_I" id="CHAPTER_I"></a><span class="pagenum" title="Page&nbsp;1">&nbsp;</span><a name="Page_1" id="Page_1"></a>CHAPTER I
+<br />
+NATURE AND THOUGHT</h2>
+
+
+<p>The subject-matter of the Tarner lectures is defined by the founder to
+be &lsquo;the Philosophy of the Sciences and the Relations or Want of
+Relations between the different Departments of Knowledge.&rsquo; It is fitting
+at the first lecture of this new foundation to dwell for a few moments
+on the intentions of the donor as expressed in this definition; and I do
+so the more willingly as I shall thereby be enabled to introduce the
+topics to which the present course is to be devoted.</p>
+
+<p>We are justified, I think, in taking the second clause of the definition
+as in part explanatory of the earlier clause. What is the philosophy of
+the sciences? It is not a bad answer to say that it is the study of the
+relations between the different departments of knowledge. Then with
+admirable solicitude for the freedom of learning there is inserted in
+the definition after the word &lsquo;relations&rsquo; the phrase &lsquo;or want of
+relations.&rsquo; A disproof of relations between sciences would in itself
+constitute a philosophy of the sciences. But we could not dispense
+either with the earlier or the later clause. It is not every relation
+between sciences which enters into their philosophy. For example biology
+and physics are connected by the use of the microscope. Still, I may
+safely assert that a technical description of the uses of the microscope
+in biology is not part of the philosophy of the sciences. Again, you
+cannot abandon the later<span class="pagenum" title="Page&nbsp;2">&nbsp;</span><a name="Page_2" id="Page_2"></a> clause of the definition; namely that
+referring to the relations between the sciences, without abandoning the
+explicit reference to an ideal in the absence of which philosophy must
+languish from lack of intrinsic interest. That ideal is the attainment
+of some unifying concept which will set in assigned relationships within
+itself all that there is for knowledge, for feeling, and for emotion.
+That far off ideal is the motive power of philosophic research; and
+claims allegiance even as you expel it. The philosophic pluralist is a
+strict logician; the Hegelian thrives on contradictions by the help of
+his absolute; the Mohammedan divine bows before the creative will of
+Allah; and the pragmatist will swallow anything so long as it &lsquo;works.&rsquo;</p>
+
+<p>The mention of these vast systems and of the age-long controversies from
+which they spring, warns us to concentrate. Our task is the simpler one
+of the philosophy of the sciences. Now a science has already a certain
+unity which is the very reason why that body of knowledge has been
+instinctively recognised as forming a science. The philosophy of a
+science is the endeavour to express explicitly those unifying
+characteristics which pervade that complex of thoughts and make it to be
+a science. The philosophy of the sciences&mdash;conceived as one subject&mdash;is
+the endeavour to exhibit all sciences as one science, or&mdash;in case of
+defeat&mdash;the disproof of such a possibility.</p>
+
+<p>Again I will make a further simplification, and confine attention to the
+natural sciences, that is, to the sciences whose subject-matter is
+nature. By postulating a common subject-matter for this group of
+sciences a unifying philosophy of natural science has been thereby
+presupposed.</p>
+
+<p><span class="pagenum" title="Page&nbsp;3">&nbsp;</span><a name="Page_3" id="Page_3"></a>What do we mean by nature? We have to discuss the philosophy of natural
+science. Natural science is the science of nature. But&mdash;What is nature?</p>
+
+<p>Nature is that which we observe in perception through the senses. In
+this sense-perception we are aware of something which is not thought and
+which is self-contained for thought. This property of being
+self-contained for thought lies at the base of natural science. It means
+that nature can be thought of as a closed system whose mutual relations
+do not require the expression of the fact that they are thought about.</p>
+
+<p>Thus in a sense nature is independent of thought. By this statement no
+metaphysical pronouncement is intended. What I mean is that we can think
+about nature without thinking about thought. I shall say that then we
+are thinking &lsquo;homogeneously&rsquo; about nature.</p>
+
+<p>Of course it is possible to think of nature in conjunction with thought
+about the fact that nature is thought about. In such a case I shall say
+that we are thinking &lsquo;heterogeneously&rsquo; about nature. In fact during the
+last few minutes we have been thinking heterogeneously about nature.
+Natural science is exclusively concerned with homogeneous thoughts about
+nature.</p>
+
+<p>But sense-perception has in it an element which is not thought. It is a
+difficult psychological question whether sense-perception involves
+thought; and if it does involve thought, what is the kind of thought
+which it necessarily involves. Note that it has been stated above that
+sense-perception is an awareness of something which is not thought.
+Namely, nature is not thought. But this is a different question, namely
+that the fact of sense-perception has a factor which is not thought. I
+call this factor &lsquo;sense-awareness.&rsquo; Accord<span class="pagenum" title="Page&nbsp;4">&nbsp;</span><a name="Page_4" id="Page_4"></a>ingly the doctrine that
+natural science is exclusively concerned with homogeneous thoughts about
+nature does not immediately carry with it the conclusion that natural
+science is not concerned with sense-awareness.</p>
+
+<p>However, I do assert this further statement; namely, that though natural
+science is concerned with nature which is the terminus of
+sense-perception, it is not concerned with the sense-awareness itself.</p>
+
+<p>I repeat the main line of this argument, and expand it in certain
+directions.</p>
+
+<p>Thought about nature is different from the sense-perception of nature.
+Hence the fact of sense-perception has an ingredient or factor which is
+not thought. I call this ingredient sense-awareness. It is indifferent
+to my argument whether sense-perception has or has not thought as
+another ingredient. If sense-perception does not involve thought, then
+sense-awareness and sense-perception are identical. But the something
+perceived is perceived as an entity which is the terminus of the
+sense-awareness, something which for thought is beyond the fact of that
+sense-awareness. Also the something perceived certainly does not contain
+other sense-awarenesses which are different from the sense-awareness
+which is an ingredient in that perception. Accordingly nature as
+disclosed in sense-perception is self-contained as against
+sense-awareness, in addition to being self-contained as against thought.
+I will also express this self-containedness of nature by saying that
+nature is closed to mind.</p>
+
+<p>This closure of nature does not carry with it any metaphysical doctrine
+of the disjunction of nature and mind. It means that in sense-perception
+nature is disclosed as a complex of entities whose mutual relations<span class="pagenum" title="Page&nbsp;5">&nbsp;</span><a name="Page_5" id="Page_5"></a> are
+expressible in thought without reference to mind, that is, without
+reference either to sense-awareness or to thought. Furthermore, I do not
+wish to be understood as implying that sense-awareness and thought are
+the only activities which are to be ascribed to mind. Also I am not
+denying that there are relations of natural entities to mind or minds
+other than being the termini of the sense-awarenesses of minds.
+Accordingly I will extend the meaning of the terms &lsquo;homogeneous
+thoughts&rsquo; and &lsquo;heterogeneous thoughts&rsquo; which have already been
+introduced. We are thinking &lsquo;homogeneously&rsquo; about nature when we are
+thinking about it without thinking about thought or about
+sense-awareness, and we are thinking &lsquo;heterogeneously&rsquo; about nature when
+we are thinking about it in conjunction with thinking either about
+thought or about sense-awareness or about both.</p>
+
+<p>I also take the homogeneity of thought about nature as excluding any
+reference to moral or aesthetic values whose apprehension is vivid in
+proportion to self-conscious activity. The values of nature are perhaps
+the key to the metaphysical synthesis of existence. But such a synthesis
+is exactly what I am not attempting. I am concerned exclusively with the
+generalisations of widest scope which can be effected respecting that
+which is known to us as the direct deliverance of sense-awareness.</p>
+
+<p>I have said that nature is disclosed in sense-perception as a complex of
+entities. It is worth considering what we mean by an entity in this
+connexion. &lsquo;Entity&rsquo; is simply the Latin equivalent for &lsquo;thing&rsquo; unless
+some arbitrary distinction is drawn between the words for technical
+purposes. All thought has to be about things. We can gain some idea of
+this necessity of things for<span class="pagenum" title="Page&nbsp;6">&nbsp;</span><a name="Page_6" id="Page_6"></a> thought by examination of the structure of
+a proposition.</p>
+
+<p>Let us suppose that a proposition is being communicated by an expositor
+to a recipient. Such a proposition is composed of phrases; some of these
+phrases may be demonstrative and others may be descriptive.</p>
+
+<p>By a demonstrative phrase I mean a phrase which makes the recipient
+aware of an entity in a way which is independent of the particular
+demonstrative phrase. You will understand that I am here using
+&lsquo;demonstration&rsquo; in the non-logical sense, namely in the sense in which a
+lecturer demonstrates by the aid of a frog and a microscope the
+circulation of the blood for an elementary class of medical students. I
+will call such demonstration &lsquo;speculative&rsquo; demonstration, remembering
+Hamlet&#8217;s use of the word &lsquo;speculation&rsquo; when he says,</p>
+
+<p class="center">There is no speculation in those eyes.</p>
+
+<p style="text-indent:2em;">Thus a demonstrative phrase demonstrates an entity speculatively. It may
+happen that the expositor has meant some other entity&mdash;namely, the
+phrase demonstrates to him an entity which is diverse from the entity
+which it demonstrates to the recipient. In that case there is confusion;
+for there are two diverse propositions, namely the proposition for the
+expositor and the proposition for the recipient. I put this possibility
+aside as irrelevant for our discussion, though in practice it may be
+difficult for two persons to concur in the consideration of exactly the
+same proposition, or even for one person to have determined exactly the
+proposition which he is considering.</p>
+
+<p>Again the demonstrative phrase may fail to demonstrate any entity. In
+that case there is no proposition<span class="pagenum" title="Page&nbsp;7">&nbsp;</span><a name="Page_7" id="Page_7"></a> for the recipient. I think that we
+may assume (perhaps rashly) that the expositor knows what he means.</p>
+
+<p>A demonstrative phrase is a gesture. It is not itself a constituent of
+the proposition, but the entity which it demonstrates is such a
+constituent. You may quarrel with a demonstrative phrase as in some way
+obnoxious to you; but if it demonstrates the right entity, the
+proposition is unaffected though your taste may be offended. This
+suggestiveness of the phraseology is part of the literary quality of the
+sentence which conveys the proposition. This is because a sentence
+directly conveys one proposition, while in its phraseology it suggests a
+penumbra of other propositions charged with emotional value. We are now
+talking of the one proposition directly conveyed in any phraseology.</p>
+
+<p>This doctrine is obscured by the fact that in most cases what is in form
+a mere part of the demonstrative gesture is in fact a part of the
+proposition which it is desired directly to convey. In such a case we
+will call the phraseology of the proposition elliptical. In ordinary
+intercourse the phraseology of nearly all propositions is elliptical.</p>
+
+<p>Let us take some examples. Suppose that the expositor is in London, say
+in Regent&#8217;s Park and in Bedford College, the great women&#8217;s college which
+is situated in that park. He is speaking in the college hall and he
+says,</p>
+
+<blockquote><p>&lsquo;This college building is commodious.&rsquo;</p></blockquote>
+
+<p>The phrase &lsquo;this college building&rsquo; is a demonstrative phrase. Now
+suppose the recipient answers,</p>
+
+<blockquote><p>&lsquo;This is not a college building, it is the lion-house in the Zoo.&rsquo;</p></blockquote>
+
+<p>Then, provided that the expositor&#8217;s original proposi<span class="pagenum" title="Page&nbsp;8">&nbsp;</span><a name="Page_8" id="Page_8"></a>tion has not been
+couched in elliptical phraseology, the expositor sticks to his original
+proposition when he replies,</p>
+
+<blockquote><p>&lsquo;Anyhow, <i>it</i> is commodious.&rsquo;</p></blockquote>
+
+<p>Note that the recipient&#8217;s answer accepts the speculative demonstration
+of the phrase &lsquo;This college building.&rsquo; He does not say, &lsquo;What do you
+mean?&rsquo; He accepts the phrase as demonstrating an entity, but declares
+that same entity to be the lion-house in the Zoo. In his reply, the
+expositor in his turn recognises the success of his original gesture as
+a speculative demonstration, and waives the question of the suitability
+of its mode of suggestiveness with an &lsquo;anyhow.&rsquo; But he is now in a
+position to repeat the original proposition with the aid of a
+demonstrative gesture robbed of any suggestiveness, suitable or
+unsuitable, by saying,</p>
+
+<blockquote><p>&lsquo;<i>It</i> is commodious.&rsquo;</p></blockquote>
+
+<p>The &lsquo;<i>it</i>&rsquo; of this final statement presupposes that thought has seized
+on the entity as a bare objective for consideration.</p>
+
+<p>We confine ourselves to entities disclosed in sense-awareness. The
+entity is so disclosed as a relatum in the complex which is nature. It
+dawns on an observer because of its relations; but it is an objective
+for thought in its own bare individuality. Thought cannot proceed
+otherwise; namely, it cannot proceed without the ideal bare &lsquo;it&rsquo; which
+is speculatively demonstrated. This setting up of the entity as a bare
+objective does not ascribe to it an existence apart from the complex in
+which it has been found by sense-perception. The &lsquo;it&rsquo; for thought is
+essentially a relatum for sense-awareness.</p>
+
+<p>The chances are that the dialogue as to the college building takes
+another form. Whatever the expositor<span class="pagenum" title="Page&nbsp;9">&nbsp;</span><a name="Page_9" id="Page_9"></a> originally meant, he almost
+certainly now takes his former statement as couched in elliptical
+phraseology, and assumes that he was meaning,</p>
+
+<blockquote><p>&lsquo;This is a college building and is commodious.&rsquo;</p></blockquote>
+
+<p>Here the demonstrative phrase or the gesture, which demonstrates the
+&lsquo;it&rsquo; which is commodious, has now been reduced to &lsquo;this&rsquo;; and the
+attenuated phrase, under the circumstances in which it is uttered, is
+sufficient for the purpose of correct demonstration. This brings out the
+point that the verbal form is never the whole phraseology of the
+proposition; this phraseology also includes the general circumstances of
+its production. Thus the aim of a demonstrative phrase is to exhibit a
+definite &lsquo;it&rsquo; as a bare objective for thought; but the <i>modus operandi</i>
+of a demonstrative phrase is to produce an awareness of the entity as a
+particular relatum in an auxiliary complex, chosen merely for the sake
+of the speculative demonstration and irrelevant to the proposition. For
+example, in the above dialogue, colleges and buildings, as related to
+the &lsquo;it&rsquo; speculatively demonstrated by the phrase &lsquo;this college
+building,&rsquo; set that &lsquo;it&rsquo; in an auxiliary complex which is irrelevant to
+the proposition</p>
+
+<blockquote><p>&lsquo;It is commodious.&rsquo;</p></blockquote>
+
+<p>Of course in language every phrase is invariably highly elliptical.
+Accordingly the sentence</p>
+
+<blockquote><p>&lsquo;This college building is commodious&rsquo;</p></blockquote>
+
+<p>means probably</p>
+
+<blockquote><p>&lsquo;This college building is commodious as a college building.&rsquo;</p></blockquote>
+
+<p>But it will be found that in the above discussion we can replace
+&lsquo;commodious&rsquo; by &lsquo;commodious as a college building&rsquo; without altering our
+conclusion; though we can guess that the recipient, who thought<span class="pagenum" title="Page&nbsp;10">&nbsp;</span><a name="Page_10" id="Page_10"></a> he was
+in the lion-house of the Zoo, would be less likely to assent to.</p>
+
+<blockquote><p>&lsquo;Anyhow, it is commodious as a college building.&rsquo;</p></blockquote>
+
+<p>A more obvious instance of elliptical phraseology arises if the
+expositor should address the recipient with the remark,</p>
+
+<blockquote><p>&lsquo;That criminal is your friend.&rsquo;</p></blockquote>
+
+<p>The recipient might answer,</p>
+
+<blockquote><p>&lsquo;He is my friend and you are insulting.&rsquo;</p></blockquote>
+
+<p>Here the recipient assumes that the phrase &lsquo;That criminal&rsquo; is elliptical
+and not merely demonstrative. In fact, pure demonstration is impossible
+though it is the ideal of thought. This practical impossibility of pure
+demonstration is a difficulty which arises in the communication of
+thought and in the retention of thought. Namely, a proposition about a
+particular factor in nature can neither be expressed to others nor
+retained for repeated consideration without the aid of auxiliary
+complexes which are irrelevant to it.</p>
+
+<p>I now pass to descriptive phrases. The expositor says,</p>
+
+<blockquote><p>&lsquo;A college in Regent&#8217;s Park is commodious.&rsquo;</p></blockquote>
+
+<p>The recipient knows Regent&#8217;s Park well. The phrase &lsquo;A college in
+Regent&#8217;s Park&rsquo; is descriptive for him. If its phraseology is not
+elliptical, which in ordinary life it certainly will be in some way or
+other, this proposition simply means,</p>
+
+<blockquote><p>&lsquo;There is an entity which is a college building in Regent&#8217;s Park
+and is commodious.&rsquo;</p></blockquote>
+
+<p>If the recipient rejoins,</p>
+
+<blockquote><p>&lsquo;The lion-house in the Zoo is the only commodious building in
+Regent&#8217;s Park,&rsquo;</p></blockquote>
+
+<p>he now contradicts the expositor, on the assumption that a lion-house in
+a Zoo is not a college building.</p>
+
+<p><span class="pagenum" title="Page&nbsp;11">&nbsp;</span><a name="Page_11" id="Page_11"></a>Thus whereas in the first dialogue the recipient merely quarrelled with
+the expositor without contradicting him, in this dialogue he contradicts
+him. Thus a descriptive phrase is part of the proposition which it helps
+to express, whereas a demonstrative phrase is not part of the
+proposition which it helps to express.</p>
+
+<p>Again the expositor might be standing in Green Park&mdash;where there are no
+college buildings&mdash;and say,</p>
+
+<blockquote><p>&lsquo;This college building is commodious.&rsquo;</p></blockquote>
+
+<p>Probably no proposition will be received by the recipient because the
+demonstrative phrase,</p>
+
+<blockquote><p>&lsquo;This college building&rsquo;</p></blockquote>
+
+<p>has failed to demonstrate owing to the absence of the background of
+sense-awareness which it presupposes.</p>
+
+<p>But if the expositor had said,</p>
+
+<blockquote><p>&lsquo;A college building in Green Park is commodious,&rsquo;</p></blockquote>
+
+<p>the recipient would have received a proposition, but a false one.</p>
+
+<p>Language is usually ambiguous and it is rash to make general assertions
+as to its meanings. But phrases which commence with &lsquo;this&rsquo; or &lsquo;that&rsquo; are
+usually demonstrative, whereas phrases which commence with &lsquo;the&rsquo; or &lsquo;a&rsquo;
+are often descriptive. In studying the theory of propositional
+expression it is important to remember the wide difference between the
+analogous modest words &lsquo;this&rsquo; and &lsquo;that&rsquo; on the one hand and &lsquo;a&rsquo; and
+&lsquo;the&rsquo; on the other hand. The sentence</p>
+
+<blockquote><p>&lsquo;The college building in Regent&#8217;s Park is commodious&rsquo;</p></blockquote>
+
+<p>means, according to the analysis first made by Bertrand Russell, the
+proposition,</p>
+
+<blockquote><p>&lsquo;There is an entity which (i) is a college building in Regent&#8217;s
+Park and (ii) is commodious and (iii) is such
+<span class="pagenum" title="Page&nbsp;12">&nbsp;</span><a name="Page_12" id="Page_12"></a>that any college building in Regent&#8217;s Park is identical with it.&rsquo;</p></blockquote>
+
+<p>The descriptive character of the phrase &lsquo;The college building in
+Regent&#8217;s Park&rsquo; is thus evident. Also the proposition is denied by the
+denial of any one of its three component clauses or by the denial of any
+combination of the component clauses. If we had substituted &lsquo;Green Park&rsquo;
+for &lsquo;Regent&#8217;s Park&rsquo; a false proposition would have resulted. Also the
+erection of a second college in Regent&#8217;s Park would make the proposition
+false, though in ordinary life common sense would politely treat it as
+merely ambiguous.</p>
+
+<p>&lsquo;The Iliad&rsquo; for a classical scholar is usually a demonstrative phrase;
+for it demonstrates to him a well-known poem. But for the majority of
+mankind the phrase is descriptive, namely, it is synonymous with &lsquo;The
+poem named &ldquo;the Iliad&rdquo;.&rsquo;</p>
+
+<p>Names may be either demonstrative or descriptive phrases. For example
+&lsquo;Homer&rsquo; is for us a descriptive phrase, namely, the word with some
+slight difference in suggestiveness means &lsquo;The man who wrote the Iliad.&rsquo;</p>
+
+<p>This discussion illustrates that thought places before itself bare
+objectives, entities as we call them, which the thinking clothes by
+expressing their mutual relations. Sense-awareness discloses fact with
+factors which are the entities for thought. The separate distinction of
+an entity in thought is not a metaphysical assertion, but a method of
+procedure necessary for the finite expression of individual
+propositions. Apart from entities there could be no finite truths; they
+are the means by which the infinitude of irrelevance is kept out of
+thought.</p>
+
+<p>To sum up: the termini for thought are entities,<span class="pagenum" title="Page&nbsp;13">&nbsp;</span><a name="Page_13" id="Page_13"></a> primarily with bare
+individuality, secondarily with properties and relations ascribed to
+them in the procedure of thought; the termini for sense-awareness are
+factors in the fact of nature, primarily relata and only secondarily
+discriminated as distinct individualities.</p>
+
+<p>No characteristic of nature which is immediately posited for knowledge
+by sense-awareness can be explained. It is impenetrable by thought, in
+the sense that its peculiar essential character which enters into
+experience by sense-awareness is for thought merely the guardian of its
+individuality as a bare entity. Thus for thought &lsquo;red&rsquo; is merely a
+definite entity, though for awareness &lsquo;red&rsquo; has the content of its
+individuality. The transition from the &lsquo;red&rsquo; of awareness to the &lsquo;red&rsquo;
+of thought is accompanied by a definite loss of content, namely by the
+transition from the factor &lsquo;red&rsquo; to the entity &lsquo;red.&rsquo; This loss in the
+transition to thought is compensated by the fact that thought is
+communicable whereas sense-awareness is incommunicable.</p>
+
+<p>Thus there are three components in our knowledge of nature, namely,
+fact, factors, and entities. Fact is the undifferentiated terminus of
+sense-awareness; factors are termini of sense-awareness, differentiated
+as elements of fact; entities are factors in their function as the
+termini of thought. The entities thus spoken of are natural entities.
+Thought is wider than nature, so that there are entities for thought
+which are not natural entities.</p>
+
+<p>When we speak of nature as a complex of related entities, the &lsquo;complex&rsquo;
+is fact as an entity for thought, to whose bare individuality is
+ascribed the property of embracing in its complexity the natural
+entities. It is our business to analyse this conception and in the
+course of the analysis space and time should appear. Evidently<span class="pagenum" title="Page&nbsp;14">&nbsp;</span><a name="Page_14" id="Page_14"></a> the
+relations holding between natural entities are themselves natural
+entities, namely they are also factors of fact, there for
+sense-awareness. Accordingly the structure of the natural complex can
+never be completed in thought, just as the factors of fact can never be
+exhausted in sense-awareness. Unexhaustiveness is an essential character
+of our knowledge of nature. Also nature does not exhaust the matter for
+thought, namely there are thoughts which would not occur in any
+homogeneous thinking about nature.</p>
+
+<p>The question as to whether sense-perception involves thought is largely
+verbal. If sense-perception involves a cognition of individuality
+abstracted from the actual position of the entity as a factor in fact,
+then it undoubtedly does involve thought. But if it is conceived as
+sense-awareness of a factor in fact competent to evoke emotion and
+purposeful action without further cognition, then it does not involve
+thought. In such a case the terminus of the sense-awareness is something
+for mind, but nothing for thought. The sense-perception of some lower
+forms of life may be conjectured to approximate to this character
+habitually. Also occasionally our own sense-perception in moments when
+thought-activity has been lulled to quiescence is not far off the
+attainment of this ideal limit.</p>
+
+<p>The process of discrimination in sense-awareness has two distinct sides.
+There is the discrimination of fact into parts, and the discrimination
+of any part of fact as exhibiting relations to entities which are not
+parts of fact though they are ingredients in it. Namely the immediate
+fact for awareness is the whole occurrence of nature. It is nature as an
+event present for sense-awareness, and essentially passing. There is no
+holding<span class="pagenum" title="Page&nbsp;15">&nbsp;</span><a name="Page_15" id="Page_15"></a> nature still and looking at it. We cannot redouble our efforts
+to improve our knowledge of the terminus of our present sense-awareness;
+it is our subsequent opportunity in subsequent sense-awareness which
+gains the benefit of our good resolution. Thus the ultimate fact for
+sense-awareness is an event. This whole event is discriminated by us
+into partial events. We are aware of an event which is our bodily life,
+of an event which is the course of nature within this room, and of a
+vaguely perceived aggregate of other partial events. This is the
+discrimination in sense-awareness of fact into parts.</p>
+
+<p>I shall use the term &lsquo;part&rsquo; in the arbitrarily limited sense of an event
+which is part of the whole fact disclosed in awareness.</p>
+
+<p>Sense-awareness also yields to us other factors in nature which are not
+events. For example, sky-blue is seen as situated in a certain event.
+This relation of situation requires further discussion which is
+postponed to a later lecture. My present point is that sky-blue is found
+in nature with a definite implication in events, but is not an event
+itself. Accordingly in addition to events, there are other factors in
+nature directly disclosed to us in sense-awareness. The conception in
+thought of all the factors in nature as distinct entities with definite
+natural relations is what I have in another place<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a> called the
+&lsquo;diversification of nature.&rsquo;</p>
+
+<div class="footnote"><p><a name="Footnote_1_1" id="Footnote_1_1"></a><span class="label"><a href="#FNanchor_1_1">[1]</a></span> Cf. <i>Enquiry</i>.</p></div>
+
+<p>There is one general conclusion to be drawn from the foregoing
+discussion. It is that the first task of a philosophy of science should
+be some general classification of the entities disclosed to us in
+sense-perception.</p>
+
+<p>Among the examples of entities in addition to &lsquo;events&rsquo; which we have
+used for the purpose of illustration are<span class="pagenum" title="Page&nbsp;16">&nbsp;</span><a name="Page_16" id="Page_16"></a> the buildings of Bedford
+College, Homer, and sky-blue. Evidently these are very different sorts
+of things; and it is likely that statements which are made about one
+kind of entity will not be true about other kinds. If human thought
+proceeded with the orderly method which abstract logic would suggest to
+it, we might go further and say that a classification of natural
+entities should be the first step in science itself. Perhaps you will be
+inclined to reply that this classification has already been effected,
+and that science is concerned with the adventures of material entities
+in space and time.</p>
+
+<p>The history of the doctrine of matter has yet to be written. It is the
+history of the influence of Greek philosophy on science. That influence
+has issued in one long misconception of the metaphysical status of
+natural entities. The entity has been separated from the factor which is
+the terminus of sense-awareness. It has become the substratum for that
+factor, and the factor has been degraded into an attribute of the
+entity. In this way a distinction has been imported into nature which is
+in truth no distinction at all. A natural entity is merely a factor of
+fact, considered in itself. Its disconnexion from the complex of fact is
+a mere abstraction. It is not the substratum of the factor, but the very
+factor itself as bared in thought. Thus what is a mere procedure of mind
+in the translation of sense-awareness into discursive knowledge has been
+transmuted into a fundamental character of nature. In this way matter
+has emerged as being the metaphysical substratum of its properties, and
+the course of nature is interpreted as the history of matter.</p>
+
+<p>Plato and Aristotle found Greek thought preoccupied with the quest for
+the simple substances in terms of<span class="pagenum" title="Page&nbsp;17">&nbsp;</span><a name="Page_17" id="Page_17"></a> which the course of events could be
+expressed. We may formulate this state of mind in the question, What is
+nature made of? The answers which their genius gave to this question,
+and more particularly the concepts which underlay the terms in which
+they framed their answers, have determined the unquestioned
+presuppositions as to time, space and matter which have reigned in
+science.</p>
+
+<p>In Plato the forms of thought are more fluid than in Aristotle, and
+therefore, as I venture to think, the more valuable. Their importance
+consists in the evidence they yield of cultivated thought about nature
+before it had been forced into a uniform mould by the long tradition of
+scientific philosophy. For example in the <i>Timaeus</i> there is a
+presupposition, somewhat vaguely expressed, of a distinction between the
+general becoming of nature and the measurable time of nature. In a later
+lecture I have to distinguish between what I call the passage of nature
+and particular time-systems which exhibit certain characteristics of
+that passage. I will not go so far as to claim Plato in direct support
+of this doctrine, but I do think that the sections of the <i>Timaeus</i>
+which deal with time become clearer if my distinction is admitted.</p>
+
+<p>This is however a digression. I am now concerned with the origin of the
+scientific doctrine of matter in Greek thought. In the <i>Timaeus</i> Plato
+asserts that nature is made of fire and earth with air and water as
+intermediate between them, so that &lsquo;as fire is to air so is air to
+water, and as air is to water so is water to earth.&rsquo; He also suggests a
+molecular hypothesis for these four elements. In this hypothesis
+everything depends on the shape of the atoms; for earth it is cubical
+and for fire<span class="pagenum" title="Page&nbsp;18">&nbsp;</span><a name="Page_18" id="Page_18"></a> it is pyramidal. To-day physicists are again discussing
+the structure of the atom, and its shape is no slight factor in that
+structure. Plato&#8217;s guesses read much more fantastically than does
+Aristotle&#8217;s systematic analysis; but in some ways they are more
+valuable. The main outline of his ideas is comparable with that of
+modern science. It embodies concepts which any theory of natural
+philosophy must retain and in some sense must explain. Aristotle asked
+the fundamental question, What do we mean by &lsquo;substance&rsquo;? Here the
+reaction between his philosophy and his logic worked very unfortunately.
+In his logic, the fundamental type of affirmative proposition is the
+attribution of a predicate to a subject. Accordingly, amid the many
+current uses of the term &lsquo;substance&rsquo; which he analyses, he emphasises
+its meaning as &lsquo;the ultimate substratum which is no longer predicated of
+anything else.&rsquo;</p>
+
+<p>The unquestioned acceptance of the Aristotelian logic has led to an
+ingrained tendency to postulate a substratum for whatever is disclosed
+in sense-awareness, namely, to look below what we are aware of for the
+substance in the sense of the &lsquo;concrete thing.&rsquo; This is the origin of
+the modern scientific concept of matter and of ether, namely they are
+the outcome of this insistent habit of postulation.</p>
+
+<p>Accordingly ether has been invented by modern science as the substratum
+of the events which are spread through space and time beyond the reach
+of ordinary ponderable matter. Personally, I think that predication is a
+muddled notion confusing many different relations under a convenient
+common form of speech. For example, I hold that the relation of green to
+a blade of grass is entirely different from the relation of green<span class="pagenum" title="Page&nbsp;19">&nbsp;</span><a name="Page_19" id="Page_19"></a> to
+the event which is the life history of that blade for some short period,
+and is different from the relation of the blade to that event. In a
+sense I call the event the situation of the green, and in another sense
+it is the situation of the blade. Thus in one sense the blade is a
+character or property which can be predicated of the situation, and in
+another sense the green is a character or property of the same event
+which is also its situation. In this way the predication of properties
+veils radically different relations between entities.</p>
+
+<p>Accordingly &lsquo;substance,&rsquo; which is a correlative term to &lsquo;predication,&rsquo;
+shares in the ambiguity. If we are to look for substance anywhere, I
+should find it in events which are in some sense the ultimate substance
+of nature.</p>
+
+<p>Matter, in its modern scientific sense, is a return to the Ionian effort
+to find in space and time some stuff which composes nature. It has a
+more refined signification than the early guesses at earth and water by
+reason of a certain vague association with the Aristotelian idea of
+substance.</p>
+
+<p>Earth, water, air, fire, and matter, and finally ether are related in
+direct succession so far as concerns their postulated characters of
+ultimate substrata of nature. They bear witness to the undying vitality
+of Greek philosophy in its search for the ultimate entities which are
+the factors of the fact disclosed in sense-awareness. This search is the
+origin of science.</p>
+
+<p>The succession of ideas starting from the crude guesses of the early
+Ionian thinkers and ending in the nineteenth century ether reminds us
+that the scientific doctrine of matter is really a hybrid through which<span class="pagenum" title="Page&nbsp;20">&nbsp;</span><a name="Page_20" id="Page_20"></a>
+philosophy passed on its way to the refined Aristotelian concept of
+substance and to which science returned as it reacted against
+philosophic abstractions. Earth, fire, and water in the Ionic philosophy
+and the shaped elements in the <i>Timaeus</i> are comparable to the matter
+and ether of modern scientific doctrine. But substance represents the
+final philosophic concept of the substratum which underlies any
+attribute. Matter (in the scientific sense) is already in space and
+time. Thus matter represents the refusal to think away spatial and
+temporal characteristics and to arrive at the bare concept of an
+individual entity. It is this refusal which has caused the muddle of
+importing the mere procedure of thought into the fact of nature. The
+entity, bared of all characteristics except those of space and time, has
+acquired a physical status as the ultimate texture of nature; so that
+the course of nature is conceived as being merely the fortunes of matter
+in its adventure through space.</p>
+
+<p>Thus the origin of the doctrine of matter is the outcome of uncritical
+acceptance of space and time as external conditions for natural
+existence. By this I do not mean that any doubt should be thrown on
+facts of space and time as ingredients in nature. What I do mean is &lsquo;the
+unconscious presupposition of space and time as being that within which
+nature is set.&rsquo; This is exactly the sort of presupposition which tinges
+thought in any reaction against the subtlety of philosophical criticism.
+My theory of the formation of the scientific doctrine of matter is that
+first philosophy illegitimately transformed the bare entity, which is
+simply an abstraction necessary for the method of thought, into the
+metaphysical substratum of these factors in nature which in various
+senses are assigned to entities as their<span class="pagenum" title="Page&nbsp;21">&nbsp;</span><a name="Page_21" id="Page_21"></a> attributes; and that, as a
+second step, scientists (including philosophers who were scientists) in
+conscious or unconscious ignoration of philosophy presupposed this
+substratum, <i>qua</i> substratum for attributes, as nevertheless in time and
+space.</p>
+
+<p>This is surely a muddle. The whole being of substance is as a substratum
+for attributes. Thus time and space should be attributes of the
+substance. This they palpably are not, if the matter be the substance of
+nature, since it is impossible to express spatio-temporal truths without
+having recourse to relations involving relata other than bits of matter.
+I waive this point however, and come to another. It is not the substance
+which is in space, but the attributes. What we find in space are the red
+of the rose and the smell of the jasmine and the noise of cannon. We
+have all told our dentists where our toothache is. Thus space is not a
+relation between substances, but between attributes.</p>
+
+<p>Thus even if you admit that the adherents of substance can be allowed to
+conceive substance as matter, it is a fraud to slip substance into space
+on the plea that space expresses relations between substances. On the
+face of it space has nothing to do with substances, but only with their
+attributes. What I mean is, that if you choose&mdash;as I think wrongly&mdash;to
+construe our experience of nature as an awareness of the attributes of
+substances, we are by this theory precluded from finding any analogous
+direct relations between substances as disclosed in our experience. What
+we do find are relations between the attributes of substances. Thus if
+matter is looked on as substance in space, the space in which it finds
+itself has very little to do with the space of our experience.</p>
+
+<p><span class="pagenum" title="Page&nbsp;22">&nbsp;</span><a name="Page_22" id="Page_22"></a>The above argument has been expressed in terms of the relational theory
+of space. But if space be absolute&mdash;namely, if it have a being
+independent of things in it&mdash;the course of the argument is hardly
+changed. For things in space must have a certain fundamental relation to
+space which we will call occupation. Thus the objection that it is the
+attributes which are observed as related to space, still holds.</p>
+
+<p>The scientific doctrine of matter is held in conjunction with an
+absolute theory of time. The same arguments apply to the relations
+between matter and time as apply to the relations between space and
+matter. There is however (in the current philosophy) a difference in the
+connexions of space with matter from those of time with matter, which I
+will proceed to explain.</p>
+
+<p>Space is not merely an ordering of material entities so that any one
+entity bears certain relations to other material entities. The
+occupation of space impresses a certain character on each material
+entity in itself. By reason of its occupation of space matter has
+extension. By reason of its extension each bit of matter is divisible
+into parts, and each part is a numerically distinct entity from every
+other such part. Accordingly it would seem that every material entity is
+not really one entity. It is an essential multiplicity of entities.
+There seems to be no stopping this dissociation of matter into
+multiplicities short of finding each ultimate entity occupying one
+individual point. This essential multiplicity of material entities is
+certainly not what is meant by science, nor does it correspond to
+anything disclosed in sense-awareness. It is absolutely necessary that
+at a certain stage in this dissociation of matter a halt should be
+called, and that the material entities thus obtained<span class="pagenum" title="Page&nbsp;23">&nbsp;</span><a name="Page_23" id="Page_23"></a> should be treated
+as units. The stage of arrest may be arbitrary or may be set by the
+characteristics of nature; but all reasoning in science ultimately drops
+its space-analysis and poses to itself the problem, &lsquo;Here is one
+material entity, what is happening to it as a unit entity?&rsquo; Yet this
+material entity is still retaining its extension, and as thus extended
+is a mere multiplicity. Thus there is an essential atomic property in
+nature which is independent of the dissociation of extension. There is
+something which in itself is one, and which is more than the logical
+aggregate of entities occupying points within the volume which the unit
+occupies. Indeed we may well be sceptical as to these ultimate entities
+at points, and doubt whether there are any such entities at all. They
+have the suspicious character that we are driven to accept them by
+abstract logic and not by observed fact.</p>
+
+<p>Time (in the current philosophy) does not exert the same disintegrating
+effect on matter which occupies it. If matter occupies a duration of
+time, the whole matter occupies every part of that duration. Thus the
+connexion between matter and time differs from the connexion between
+matter and space as expressed in current scientific philosophy. There is
+obviously a greater difficulty in conceiving time as the outcome of
+relations between different bits of matter than there is in the
+analogous conception of space. At an instant distinct volumes of space
+are occupied by distinct bits of matter. Accordingly there is so far no
+intrinsic difficulty in conceiving that space is merely the resultant of
+relations between the bits of matter. But in the one-dimensional time
+the same bit of matter occupies different portions of time. Accordingly
+time would have to be expressible<span class="pagenum" title="Page&nbsp;24">&nbsp;</span><a name="Page_24" id="Page_24"></a> in terms of the relations of a bit of
+matter with itself. My own view is a belief in the relational theory
+both of space and of time, and of disbelief in the current form of the
+relational theory of space which exhibits bits of matter as the relata
+for spatial relations. The true relata are events. The distinction which
+I have just pointed out between time and space in their connexion with
+matter makes it evident that any assimilation of time and space cannot
+proceed along the traditional line of taking matter as a fundamental
+element in space-formation.</p>
+
+<p>The philosophy of nature took a wrong turn during its development by
+Greek thought. This erroneous presupposition is vague and fluid in
+Plato&#8217;s <i>Timaeus.</i> The general groundwork of the thought is still
+uncommitted and can be construed as merely lacking due explanation and
+the guarding emphasis. But in Aristotle&#8217;s exposition the current
+conceptions were hardened and made definite so as to produce a faulty
+analysis of the relation between the matter and the form of nature as
+disclosed in sense-awareness. In this phrase the term &lsquo;matter&rsquo; is not
+used in its scientific sense.</p>
+
+<p>I will conclude by guarding myself against a misapprehension. It is
+evident that the current doctrine of matter enshrines some fundamental
+law of nature. Any simple illustration will exemplify what I mean. For
+example, in a museum some specimen is locked securely in a glass case.
+It stays there for years: it loses its colour, and perhaps falls to
+pieces. But it is the same specimen; and the same chemical elements and
+the same quantities of those elements are present within the case at the
+end as were present at the beginning. Again the engineer and the
+astronomer deal with the motions of real per<span class="pagenum" title="Page&nbsp;25">&nbsp;</span><a name="Page_25" id="Page_25"></a>manences in nature. Any
+theory of nature which for one moment loses sight of these great basic
+facts of experience is simply silly. But it is permissible to point out
+that the scientific expression of these facts has become entangled in a
+maze of doubtful metaphysics; and that, when we remove the metaphysics
+and start afresh on an unprejudiced survey of nature, a new light is
+thrown on many fundamental concepts which dominate science and guide the
+progress of research.</p>
+
+<hr />
+
+<h2><span class="pagenum" title="Page&nbsp;26">&nbsp;</span><a name="Page_26" id="Page_26"></a><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II
+<br />
+THEORIES OF THE BIFURCATION OF NATURE</h2>
+
+
+<p>In my previous lecture I criticised the concept of matter as the
+substance whose attributes we perceive. This way of thinking of matter
+is, I think, the historical reason for its introduction into science,
+and is still the vague view of it at the background of our thoughts
+which makes the current scientific doctrine appear so obvious. Namely we
+conceive ourselves as perceiving attributes of things, and bits of
+matter are the things whose attributes we perceive.</p>
+
+<p>In the seventeenth century the sweet simplicity of this aspect of matter
+received a rude shock. The transmission doctrines of science were then
+in process of elaboration and by the end of the century were
+unquestioned, though their particular forms have since been modified.
+The establishment of these transmission theories marks a turning point
+in the relation between science and philosophy. The doctrines to which I
+am especially alluding are the theories of light and sound. I have no
+doubt that the theories had been vaguely floating about before as
+obvious suggestions of common sense; for nothing in thought is ever
+completely new. But at that epoch they were systematised and made exact,
+and their complete consequences were ruthlessly deduced. It is the
+establishment of this procedure of taking the consequences seriously
+which marks the real discovery of a theory. Systematic doctrines of
+light and sound as being something proceeding from<span class="pagenum" title="Page&nbsp;27">&nbsp;</span><a name="Page_27" id="Page_27"></a> the emitting bodies
+were definitely established, and in particular the connexion of light
+with colour was laid bare by Newton.</p>
+
+<p>The result completely destroyed the simplicity of the &lsquo;substance and
+attribute&rsquo; theory of perception. What we see depends on the light
+entering the eye. Furthermore we do not even perceive what enters the
+eye. The things transmitted are waves or&mdash;as Newton thought&mdash;minute
+particles, and the things seen are colours. Locke met this difficulty by
+a theory of primary and secondary qualities. Namely, there are some
+attributes of the matter which we do perceive. These are the primary
+qualities, and there are other things which we perceive, such as
+colours, which are not attributes of matter, but are perceived by us as
+if they were such attributes. These are the secondary qualities of
+matter.</p>
+
+<p>Why should we perceive secondary qualities? It seems an extremely
+unfortunate arrangement that we should perceive a lot of things that are
+not there. Yet this is what the theory of secondary qualities in fact
+comes to. There is now reigning in philosophy and in science an
+apathetic acquiescence in the conclusion that no coherent account can be
+given of nature as it is disclosed to us in sense-awareness, without
+dragging in its relations to mind. The modern account of nature is not,
+as it should be, merely an account of what the mind knows of nature; but
+it is also confused with an account of what nature does to the mind. The
+result has been disastrous both to science and to philosophy, but
+chiefly to philosophy. It has transformed the grand question of the
+relations between nature and mind into the petty form of the interaction
+between the human body and mind.</p>
+
+<p><span class="pagenum" title="Page&nbsp;28">&nbsp;</span><a name="Page_28" id="Page_28"></a>Berkeley&#8217;s polemic against matter was based on this confusion introduced
+by the transmission theory of light. He advocated, rightly as I think,
+the abandonment of the doctrine of matter in its present form. He had
+however nothing to put in its place except a theory of the relation of
+finite minds to the divine mind.</p>
+
+<p>But we are endeavouring in these lectures to limit ourselves to nature
+itself and not to travel beyond entities which are disclosed in
+sense-awareness.</p>
+
+<p>Percipience in itself is taken for granted. We consider indeed
+conditions for percipience, but only so far as those conditions are
+among the disclosures of perception. We leave to metaphysics the
+synthesis of the knower and the known. Some further explanation and
+defence of this position is necessary, if the line of argument of these
+lectures is to be comprehensible.</p>
+
+<p>The immediate thesis for discussion is that any metaphysical
+interpretation is an illegitimate importation into the philosophy of
+natural science. By a metaphysical interpretation I mean any discussion
+of the how (beyond nature) and of the why (beyond nature) of thought and
+sense-awareness. In the philosophy of science we seek the general
+notions which apply to nature, namely, to what we are aware of in
+perception. It is the philosophy of the thing perceived, and it should
+not be confused with the metaphysics of reality of which the scope
+embraces both perceiver and perceived. No perplexity concerning the
+object of knowledge can be solved by saying that there is a mind knowing
+it<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a>.</p>
+
+<div class="footnote"><p><a name="Footnote_2_2" id="Footnote_2_2"></a><span class="label"><a href="#FNanchor_2_2">[2]</a></span> Cf. <i>Enquiry</i>, preface.</p></div>
+
+<p>In other words, the ground taken is this: sense-awareness is an
+awareness of something. What then is the general character of that
+something of which we<span class="pagenum" title="Page&nbsp;29">&nbsp;</span><a name="Page_29" id="Page_29"></a> are aware? We do not ask about the percipient or
+about the process, but about the perceived. I emphasise this point
+because discussions on the philosophy of science are usually extremely
+metaphysical&mdash;in my opinion, to the great detriment of the subject.</p>
+
+<p>The recourse to metaphysics is like throwing a match into the powder
+magazine. It blows up the whole arena. This is exactly what scientific
+philosophers do when they are driven into a corner and convicted of
+incoherence. They at once drag in the mind and talk of entities in the
+mind or out of the mind as the case may be. For natural philosophy
+everything perceived is in nature. We may not pick and choose. For us
+the red glow of the sunset should be as much part of nature as are the
+molecules and electric waves by which men of science would explain the
+phenomenon. It is for natural philosophy to analyse how these various
+elements of nature are connected.</p>
+
+<p>In making this demand I conceive myself as adopting our immediate
+instinctive attitude towards perceptual knowledge which is only
+abandoned under the influence of theory. We are instinctively willing to
+believe that by due attention, more can be found in nature than that
+which is observed at first sight. But we will not be content with less.
+What we ask from the philosophy of science is some account of the
+coherence of things perceptively known.</p>
+
+<p>This means a refusal to countenance any theory of psychic additions to
+the object known in perception. For example, what is given in perception
+is the green grass. This is an object which we know as an ingredient in
+nature. The theory of psychic additions would treat the greenness as a
+psychic addition furnished by the<span class="pagenum" title="Page&nbsp;30">&nbsp;</span><a name="Page_30" id="Page_30"></a> perceiving mind, and would leave to
+nature merely the molecules and the radiant energy which influence the
+mind towards that perception. My argument is that this dragging in of
+the mind as making additions of its own to the thing posited for
+knowledge by sense-awareness is merely a way of shirking the problem of
+natural philosophy. That problem is to discuss the relations <i>inter se</i>
+of things known, abstracted from the bare fact that they are known.
+Natural philosophy should never ask, what is in the mind and what is in
+nature. To do so is a confession that it has failed to express relations
+between things perceptively known, namely to express those natural
+relations whose expression is natural philosophy. It may be that the
+task is too hard for us, that the relations are too complex and too
+various for our apprehension, or are too trivial to be worth the trouble
+of exposition. It is indeed true that we have gone but a very small way
+in the adequate formulation of such relations. But at least do not let
+us endeavour to conceal failure under a theory of the byplay of the
+perceiving mind.</p>
+
+<p>What I am essentially protesting against is the bifurcation of nature
+into two systems of reality, which, in so far as they are real, are real
+in different senses. One reality would be the entities such as electrons
+which are the study of speculative physics. This would be the reality
+which is there for knowledge; although on this theory it is never known.
+For what is known is the other sort of reality, which is the byplay of
+the mind. Thus there would be two natures, one is the conjecture and the
+other is the dream.</p>
+
+<p>Another way of phrasing this theory which I am arguing against is to
+bifurcate nature into two divisions,<span class="pagenum" title="Page&nbsp;31">&nbsp;</span><a name="Page_31" id="Page_31"></a> namely into the nature apprehended
+in awareness and the nature which is the cause of awareness. The nature
+which is the fact apprehended in awareness holds within it the greenness
+of the trees, the song of the birds, the warmth of the sun, the hardness
+of the chairs, and the feel of the velvet. The nature which is the cause
+of awareness is the conjectured system of molecules and electrons which
+so affects the mind as to produce the awareness of apparent nature. The
+meeting point of these two natures is the mind, the causal nature being
+influent and the apparent nature being effluent.</p>
+
+<p>There are four questions which at once suggest themselves for discussion
+in connexion with this bifurcation theory of nature. They concern (i)
+causality, (ii) time, (iii) space, and (iv) delusions. These questions
+are not really separable. They merely constitute four distinct starting
+points from which to enter upon the discussion of the theory.</p>
+
+<p>Causal nature is the influence on the mind which is the cause of the
+effluence of apparent nature from the mind. This conception of causal
+nature is not to be confused with the distinct conception of one part of
+nature as being the cause of another part. For example, the burning of
+the fire and the passage of heat from it through intervening space is
+the cause of the body, its nerves and its brain, functioning in certain
+ways. But this is not an action of nature on the mind. It is an
+interaction within nature. The causation involved in this interaction is
+causation in a different sense from the influence of this system of
+bodily interactions within nature on the alien mind which thereupon
+perceives redness and warmth.</p>
+
+<p>The bifurcation theory is an attempt to exhibit<span class="pagenum" title="Page&nbsp;32">&nbsp;</span><a name="Page_32" id="Page_32"></a> natural science as an
+investigation of the cause of the fact of knowledge. Namely, it is an
+attempt to exhibit apparent nature as an effluent from the mind because
+of causal nature. The whole notion is partly based on the implicit
+assumption that the mind can only know that which it has itself produced
+and retains in some sense within itself, though it requires an exterior
+reason both as originating and as determining the character of its
+activity. But in considering knowledge we should wipe out all these
+spatial metaphors, such as &lsquo;within the mind&rsquo; and &lsquo;without the mind.&rsquo;
+Knowledge is ultimate. There can be no explanation of the &lsquo;why&rsquo; of
+knowledge; we can only describe the &lsquo;what&rsquo; of knowledge. Namely we can
+analyse the content and its internal relations, but we cannot explain
+why there is knowledge. Thus causal nature is a metaphysical chimera;
+though there is need of a metaphysics whose scope transcends the
+limitation to nature. The object of such a metaphysical science is not
+to explain knowledge, but exhibit in its utmost completeness our concept
+of reality.</p>
+
+<p>However, we must admit that the causality theory of nature has its
+strong suit. The reason why the bifurcation of nature is always creeping
+back into scientific philosophy is the extreme difficulty of exhibiting
+the perceived redness and warmth of the fire in one system of relations
+with the agitated molecules of carbon and oxygen, with the radiant
+energy from them, and with the various functionings of the material
+body. Unless we produce the all-embracing relations, we are faced with a
+bifurcated nature; namely, warmth and redness on one side, and
+molecules, electrons and ether on the other side. Then the two factors
+are explained as being respectively the cause and the mind&#8217;s reaction to
+the cause.</p>
+
+<p><span class="pagenum" title="Page&nbsp;33">&nbsp;</span><a name="Page_33" id="Page_33"></a>Time and space would appear to provide these all-embracing relations
+which the advocates of the philosophy of the unity of nature require.
+The perceived redness of the fire and the warmth are definitely related
+in time and in space to the molecules of the fire and the molecules of
+the body.</p>
+
+<p>It is hardly more than a pardonable exaggeration to say that the
+determination of the meaning of nature reduces itself principally to the
+discussion of the character of time and the character of space. In
+succeeding lectures I shall explain my own view of time and space. I
+shall endeavour to show that they are abstractions from more concrete
+elements of nature, namely, from events. The discussion of the details
+of the process of abstraction will exhibit time and space as
+interconnected, and will finally lead us to the sort of connexions
+between their measurements which occur in the modern theory of
+electromagnetic relativity. But this is anticipating our subsequent line
+of development. At present I wish to consider how the ordinary views of
+time and space help, or fail to help, in unifying our conception of
+nature.</p>
+
+<p>First, consider the absolute theories of time and space. We are to
+consider each, namely both time and space, to be a separate and
+independent system of entities, each system known to us in itself and
+for itself concurrently with our knowledge of the events of nature. Time
+is the ordered succession of durationless instants; and these instants
+are known to us merely as the relata in the serial relation which is the
+time-ordering relation, and the time-ordering relation is merely known
+to us as relating the instants. Namely, the relation and the instants
+are jointly known to us in our apprehension of time, each implying the
+other.</p>
+
+<p><span class="pagenum" title="Page&nbsp;34">&nbsp;</span><a name="Page_34" id="Page_34"></a>This is the absolute theory of time. Frankly, I confess that it seems to
+me to be very unplausible. I cannot in my own knowledge find anything
+corresponding to the bare time of the absolute theory. Time is known to
+me as an abstraction from the passage of events. The fundamental fact
+which renders this abstraction possible is the passing of nature, its
+development, its creative advance, and combined with this fact is
+another characteristic of nature, namely the extensive relation between
+events. These two facts, namely the passage of events and the extension
+of events over each other, are in my opinion the qualities from which
+time and space originate as abstractions. But this is anticipating my
+own later speculations.</p>
+
+<p>Meanwhile, returning to the absolute theory, we are to suppose that time
+is known to us independently of any events in time. What happens in time
+occupies time. This relation of events to the time occupied, namely this
+relation of occupation, is a fundamental relation of nature to time.
+Thus the theory requires that we are aware of two fundamental relations,
+the time-ordering relation between instants, and the time-occupation
+relation between instants of time and states of nature which happen at
+those instants.</p>
+
+<p>There are two considerations which lend powerful support to the reigning
+theory of absolute time. In the first place time extends beyond nature.
+Our thoughts are in time. Accordingly it seems impossible to derive time
+merely from relations between elements of nature. For in that case
+temporal relations could not relate thoughts. Thus, to use a metaphor,
+time would apparently have deeper roots in reality than has nature. For
+we can imagine thoughts related in time without<span class="pagenum" title="Page&nbsp;35">&nbsp;</span><a name="Page_35" id="Page_35"></a> any perception of
+nature. For example we can imagine one of Milton&#8217;s angels with thoughts
+succeeding each other in time, who does not happen to have noticed that
+the Almighty has created space and set therein a material universe. As a
+matter of fact I think that Milton set space on the same absolute level
+as time. But that need not disturb the illustration. In the second place
+it is difficult to derive the true serial character of time from the
+relative theory. Each instant is irrevocable. It can never recur by the
+very character of time. But if on the relative theory an instant of time
+is simply the state of nature at that time, and the time-ordering
+relation is simply the relation between such states, then the
+irrevocableness of time would seem to mean that an actual state of all
+nature can never return. I admit it seems unlikely that there should
+ever be such a recurrence down to the smallest particular. But extreme
+unlikeliness is not the point. Our ignorance is so abysmal that our
+judgments of likeliness and unlikeliness of future events hardly count.
+The real point is that the exact recurrence of a state of nature seems
+merely unlikely, while the recurrence of an instant of time violates our
+whole concept of time-order. The instants of time which have passed, are
+passed, and can never be again.</p>
+
+<p>Any alternative theory of time must reckon with these two considerations
+which are buttresses of the absolute theory. But I will not now continue
+their discussion.</p>
+
+<p>The absolute theory of space is analogous to the corresponding theory of
+time, but the reasons for its maintenance are weaker. Space, on this
+theory, is a system of extensionless points which are the relata in
+space-ordering relations which can technically be com<span class="pagenum" title="Page&nbsp;36">&nbsp;</span><a name="Page_36" id="Page_36"></a>bined into one
+relation. This relation does not arrange the points in one linear series
+analogously to the simple method of the time-ordering relation for
+instants. The essential logical characteristics of this relation from
+which all the properties of space spring are expressed by mathematicians
+in the axioms of geometry. From these axioms<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a> as framed by modern
+mathematicians the whole science of geometry can be deduced by the
+strictest logical reasoning. The details of these axioms do not now
+concern us. The points and the relations are jointly known to us in our
+apprehension of space, each implying the other. What happens in space,
+occupies space. This relation of occupation is not usually stated for
+events but for objects. For example, Pompey&#8217;s statue would be said to
+occupy space, but not the event which was the assassination of Julius
+Caesar. In this I think that ordinary usage is unfortunate, and I hold
+that the relations of events to space and to time are in all respects
+analogous. But here I am intruding my own opinions which are to be
+discussed in subsequent lectures. Thus the theory of absolute space
+requires that we are aware of two fundamental relations, the
+space-ordering relation, which holds between points, and the
+space-occupation relation between points of space and material objects.</p>
+
+<div class="footnote"><p><a name="Footnote_3_3" id="Footnote_3_3"></a><span class="label"><a href="#FNanchor_3_3">[3]</a></span> Cf. (for example) <i>Projective Geometry</i> by Veblen and
+Young, vol.&nbsp;i. 1910, vol.&nbsp;ii. 1917, Ginn and Company, Boston, U.S.A.</p></div>
+
+<p>This theory lacks the two main supports of the corresponding theory of
+absolute time. In the first place space does not extend beyond nature in
+the sense that time seems to do. Our thoughts do not seem to occupy
+space in quite the same intimate way in which they occupy time. For
+example, I have been thinking in a room, and<span class="pagenum" title="Page&nbsp;37">&nbsp;</span><a name="Page_37" id="Page_37"></a> to that extent my thoughts
+are in space. But it seems nonsense to ask how much volume of the room
+they occupied, whether it was a cubic foot or a cubic inch; whereas the
+same thoughts occupy a determinate duration of time, say, from eleven to
+twelve on a certain date.</p>
+
+<p>Thus whereas the relations of a relative theory of time are required to
+relate thoughts, it does not seem so obvious that the relations of a
+relative theory of space are required to relate them. The connexion of
+thought with space seems to have a certain character of indirectness
+which appears to be lacking in the connexion of thought with time.</p>
+
+<p>Again the irrevocableness of time does not seem to have any parallel for
+space. Space, on the relative theory, is the outcome of certain
+relations between objects commonly said to be in space; and whenever
+there are the objects, so related, there is the space. No difficulty
+seems to arise like that of the inconvenient instants of time which
+might conceivably turn up again when we thought that we had done with
+them.</p>
+
+<p>The absolute theory of space is not now generally popular. The knowledge
+of bare space, as a system of entities known to us in itself and for
+itself independently of our knowledge of the events in nature, does not
+seem to correspond to anything in our experience. Space, like time,
+would appear to be an abstraction from events. According to my own
+theory it only differentiates itself from time at a somewhat developed
+stage of the abstractive process. The more usual way of expressing the
+relational theory of space would be to consider space as an abstraction
+from the relations between material objects.</p>
+
+<p>Suppose now we assume absolute time and absolute<span class="pagenum" title="Page&nbsp;38">&nbsp;</span><a name="Page_38" id="Page_38"></a> space. What bearing
+has this assumption on the concept of nature as bifurcated into causal
+nature and apparent nature? Undoubtedly the separation between the two
+natures is now greatly mitigated. We can provide them with two systems
+of relations in common; for both natures can be presumed to occupy the
+same space and the same time. The theory now is this: Causal events
+occupy certain periods of the absolute time and occupy certain positions
+of the absolute space. These events influence a mind which thereupon
+perceives certain apparent events which occupy certain periods in the
+absolute time and occupy certain positions of the absolute space; and
+the periods and positions occupied by the apparent events bear a
+determinate relation to the periods and positions occupied by the causal
+events.</p>
+
+<p>Furthermore definite causal events produce for the mind definite
+apparent events. Delusions are apparent events which appear in temporal
+periods and spatial positions without the intervention of these causal
+events which are proper for influencing of the mind to their perception.</p>
+
+<p>The whole theory is perfectly logical. In these discussions we cannot
+hope to drive an unsound theory to a logical contradiction. A reasoner,
+apart from mere slips, only involves himself in a contradiction when he
+is shying at a <i>reductio ad absurdum</i>. The substantial reason for
+rejecting a philosophical theory is the &lsquo;absurdum&rsquo; to which it reduces
+us. In the case of the philosophy of natural science the &lsquo;absurdum&rsquo; can
+only be that our perceptual knowledge has not the character assigned to
+it by the theory. If our opponent affirms that his knowledge has that
+character, we can only&mdash;after making doubly sure that we understand
+each<span class="pagenum" title="Page&nbsp;39">&nbsp;</span><a name="Page_39" id="Page_39"></a> other&mdash;agree to differ. Accordingly the first duty of an expositor
+in stating a theory in which he disbelieves is to exhibit it as logical.
+It is not there where his trouble lies.</p>
+
+<p>Let me summarise the previously stated objections to this theory of
+nature. In the first place it seeks for the cause of the knowledge of
+the thing known instead of seeking for the character of the thing known:
+secondly it assumes a knowledge of time in itself apart from events
+related in time: thirdly it assumes a knowledge of space in itself apart
+from events related in space. There are in addition to these objections
+other flaws in the theory.</p>
+
+<p>Some light is thrown on the artificial status of causal nature in this
+theory by asking, why causal nature is presumed to occupy time and
+space. This really raises the fundamental question as to what
+characteristics causal nature should have in common with apparent
+nature. Why&mdash;on this theory&mdash;should the cause which influences the mind
+to perception have any characteristics in common with the effluent
+apparent nature? In particular, why should it be in space? Why should it
+be in time? And more generally, What do we know about mind which would
+allow us to infer any particular characteristics of a cause which should
+influence mind to particular effects?</p>
+
+<p>The transcendence of time beyond nature gives some slight reason for
+presuming that causal nature should occupy time. For if the mind
+occupies periods of time, there would seem to be some vague reason for
+assuming that influencing causes occupy the same periods of time, or at
+least, occupy periods which are strictly related to the mental periods.
+But if the mind does not<span class="pagenum" title="Page&nbsp;40">&nbsp;</span><a name="Page_40" id="Page_40"></a> occupy volumes of space, there seems to be no
+reason why causal nature should occupy any volumes of space. Thus space
+would seem to be merely apparent in the same sense as apparent nature is
+merely apparent. Accordingly if science is really investigating causes
+which operate on the mind, it would seem to be entirely on the wrong
+tack in presuming that the causes which it is seeking for have spatial
+relations. Furthermore there is nothing else in our knowledge analogous
+to these causes which influence the mind to perception. Accordingly,
+beyond the rashly presumed fact that they occupy time, there is really
+no ground by which we can determine any point of their character. They
+must remain for ever unknown.</p>
+
+<p>Now I assume as an axiom that science is not a fairy tale. It is not
+engaged in decking out unknowable entities with arbitrary and fantastic
+properties. What then is it that science is doing, granting that it is
+effecting something of importance? My answer is that it is determining
+the character of things known, namely the character of apparent nature.
+But we may drop the term &lsquo;apparent&rsquo;; for there is but one nature, namely
+the nature which is before us in perceptual knowledge. The characters
+which science discerns in nature are subtle characters, not obvious at
+first sight. They are relations of relations and characters of
+characters. But for all their subtlety they are stamped with a certain
+simplicity which makes their consideration essential in unravelling the
+complex relations between characters of more perceptive insistence.</p>
+
+<p>The fact that the bifurcation of nature into causal and apparent
+components does not express what we mean by our knowledge is brought
+before us when we realise<span class="pagenum" title="Page&nbsp;41">&nbsp;</span><a name="Page_41" id="Page_41"></a> our thoughts in any discussion of the causes
+of our perceptions. For example, the fire is burning and we see a red
+coal. This is explained in science by radiant energy from the coal
+entering our eyes. But in seeking for such an explanation we are not
+asking what are the sort of occurrences which are fitted to cause a mind
+to see red. The chain of causation is entirely different. The mind is
+cut out altogether. The real question is, When red is found in nature,
+what else is found there also? Namely we are asking for an analysis of
+the accompaniments in nature of the discovery of red in nature. In a
+subsequent lecture I shall expand this line of thought. I simply draw
+attention to it here in order to point out that the wave-theory of light
+has not been adopted because waves are just the sort of things which
+ought to make a mind perceive colours. This is no part of the evidence
+which has ever been adduced for the wave-theory, yet on the causal
+theory of perception, it is really the only relevant part. In other
+words, science is not discussing the causes of knowledge, but the
+coherence of knowledge. The understanding which is sought by science is
+an understanding of relations within nature.</p>
+
+<p>So far I have discussed the bifurcation of nature in connexion with the
+theories of absolute time and of absolute space. My reason has been that
+the introduction of the relational theories only weakens the case for
+bifurcation, and I wished to discuss this case on its strongest grounds.</p>
+
+<p>For instance, suppose we adopt the relational theory of space. Then the
+space in which apparent nature is set is the expression of certain
+relations between the apparent objects. It is a set of apparent
+relations between<span class="pagenum" title="Page&nbsp;42">&nbsp;</span><a name="Page_42" id="Page_42"></a> apparent relata. Apparent nature is the dream, and
+the apparent relations of space are dream relations, and the space is
+the dream space. Similarly the space in which causal nature is set is
+the expression of certain relations between the causal objects. It is
+the expression of certain facts about the causal activity which is going
+on behind the scenes. Accordingly causal space belongs to a different
+order of reality to apparent space. Hence there is no pointwise
+connexion between the two and it is meaningless to say that the
+molecules of the grass are in any place which has a determinate spatial
+relation to the place occupied by the grass which we see. This
+conclusion is very paradoxical and makes nonsense of all scientific
+phraseology. The case is even worse if we admit the relativity of time.
+For the same arguments apply, and break up time into the dream time and
+causal time which belong to different orders of reality.</p>
+
+<p>I have however been discussing an extreme form of the bifurcation
+theory. It is, as I think, the most defensible form. But its very
+definiteness makes it the more evidently obnoxious to criticism. The
+intermediate form allows that the nature we are discussing is always the
+nature directly known, and so far it rejects the bifurcation theory. But
+it holds that there are psychic additions to nature as thus known, and
+that these additions are in no proper sense part of nature. For example,
+we perceive the red billiard ball at its proper time, in its proper
+place, with its proper motion, with its proper hardness, and with its
+proper inertia. But its redness and its warmth, and the sound of the
+click as a cannon is made off it are psychic additions, namely,
+secondary qualities which are only the mind&#8217;s way of perceiving nature.
+This is not only the vaguely<span class="pagenum" title="Page&nbsp;43">&nbsp;</span><a name="Page_43" id="Page_43"></a> prevalent theory, but is, I believe, the
+historical form of the bifurcation theory in so far as it is derived
+from philosophy. I shall call it the theory of psychic additions.</p>
+
+<p>This theory of psychic additions is a sound common-sense theory which
+lays immense stress on the obvious reality of time, space, solidity and
+inertia, but distrusts the minor artistic additions of colour, warmth
+and sound.</p>
+
+<p>The theory is the outcome of common-sense in retreat. It arose in an
+epoch when the transmission theories of science were being elaborated.
+For example, colour is the result of a transmission from the material
+object to the perceiver&#8217;s eye; and what is thus transmitted is not
+colour. Thus colour is not part of the reality of the material object.
+Similarly for the same reason sounds evaporate from nature. Also warmth
+is due to the transfer of something which is not temperature. Thus we
+are left with spatio-temporal positions, and what I may term the
+&lsquo;pushiness&rsquo; of the body. This lands us to eighteenth and nineteenth
+century materialism, namely, the belief that what is real in nature is
+matter, in time and in space and with inertia.</p>
+
+<p>Evidently a distinction in quality has been presupposed separating off
+some perceptions due to touch from other perceptions. These
+touch-perceptions are perceptions of the real inertia, whereas the other
+perceptions are psychic additions which must be explained on the causal
+theory. This distinction is the product of an epoch in which physical
+science has got ahead of medical pathology and of physiology.
+Perceptions of push are just as much the outcome of transmission as are
+perceptions of colour. When colour is perceived the nerves of the body
+are excited in one way and transmit their message towards the brain, and
+when push is perceived<span class="pagenum" title="Page&nbsp;44">&nbsp;</span><a name="Page_44" id="Page_44"></a> other nerves of the body are excited in another
+way and transmit their message towards the brain. The message of the one
+set is not the conveyance of colour, and the message of the other set is
+not the conveyance of push. But in one case colour is perceived and in
+the other case the push due to the object. If you snip certain nerves,
+there is an end to the perception of colour; and if you snip certain
+other nerves, there is an end to the perception of push. It would appear
+therefore that any reasons which should remove colour from the reality
+of nature should also operate to remove inertia.</p>
+
+<p>Thus the attempted bifurcation of apparent nature into two parts of
+which one part is both causal for its own appearance and for the
+appearance of the other part, which is purely apparent, fails owing to
+the failure to establish any fundamental distinction between our ways of
+knowing about the two parts of nature as thus partitioned. I am not
+denying that the feeling of muscular effort historically led to the
+formulation of the concept of force. But this historical fact does not
+warrant us in assigning a superior reality in nature to material inertia
+over colour or sound. So far as reality is concerned all our
+sense-perceptions are in the same boat, and must be treated on the same
+principle. The evenness of treatment is exactly what this compromise
+theory fails to achieve.</p>
+
+<p>The bifurcation theory however dies hard. The reason is that there
+really is a difficulty to be faced in relating within the same system of
+entities the redness of the fire with the agitation of the molecules. In
+another lecture I will give my own explanation of the origin of the
+difficulty and of its solution.</p>
+
+<p>Another favourite solution, the most attenuated form<span class="pagenum" title="Page&nbsp;45">&nbsp;</span><a name="Page_45" id="Page_45"></a> which the
+bifurcation theory assumes, is to maintain that the molecules and ether
+of science are purely conceptual. Thus there is but one nature, namely
+apparent nature, and atoms and ether are merely names for logical terms
+in conceptual formulae of calculation.</p>
+
+<p>But what is a formula of calculation? It is presumably a statement that
+something or other is true for natural occurrences. Take the simplest of
+all formulae, Two and two make four. This&mdash;so far as it applies to
+nature&mdash;asserts that if you take two natural entities, and then again
+two other natural entities, the combined class contains four natural
+entities. Such formulae which are true for any entities cannot result in
+the production of the concepts of atoms. Then again there are formulae
+which assert that there are entities in nature with such and such
+special properties, say, for example, with the properties of the atoms
+of hydrogen. Now if there are no such entities, I fail to see how any
+statements about them can apply to nature. For example, the assertion
+that there is green cheese in the moon cannot be a premiss in any
+deduction of scientific importance, unless indeed the presence of green
+cheese in the moon has been verified by experiment. The current answer
+to these objections is that, though atoms are merely conceptual, yet
+they are an interesting and picturesque way of saying something else
+which is true of nature. But surely if it is something else that you
+mean, for heaven&#8217;s sake say it. Do away with this elaborate machinery of
+a conceptual nature which consists of assertions about things which
+don&#8217;t exist in order to convey truths about things which do exist. I am
+maintaining the obvious position that scientific laws, if they are true,
+are statements about entities<span class="pagenum" title="Page&nbsp;46">&nbsp;</span><a name="Page_46" id="Page_46"></a> which we obtain knowledge of as being in
+nature; and that, if the entities to which the statements refer are not
+to be found in nature, the statements about them have no relevance to
+any purely natural occurrence. Thus the molecules and electrons of
+scientific theory are, so far as science has correctly formulated its
+laws, each of them factors to be found in nature. The electrons are only
+hypothetical in so far as we are not quite certain that the electron
+theory is true. But their hypothetical character does not arise from the
+essential nature of the theory in itself after its truth has been
+granted.</p>
+
+<p>Thus at the end of this somewhat complex discussion, we return to the
+position which was affirmed at its beginning. The primary task of a
+philosophy of natural science is to elucidate the concept of nature,
+considered as one complex fact for knowledge, to exhibit the fundamental
+entities and the fundamental relations between entities in terms of
+which all laws of nature have to be stated, and to secure that the
+entities and relations thus exhibited are adequate for the expression of
+all the relations between entities which occur in nature.</p>
+
+<p>The third requisite, namely that of adequacy, is the one over which all
+the difficulty occurs. The ultimate data of science are commonly assumed
+to be time, space, material, qualities of material, and relations
+between material objects. But data as they occur in the scientific laws
+do not relate all the entities which present themselves in our
+perception of nature. For example, the wave-theory of light is an
+excellent well-established theory; but unfortunately it leaves out
+colour as perceived. Thus the perceived redness&mdash;or, other colour&mdash;has
+to be cut out of nature and made into the reaction of the mind under the
+impulse of the actual events of<span class="pagenum" title="Page&nbsp;47">&nbsp;</span><a name="Page_47" id="Page_47"></a> nature. In other words this concept of
+the fundamental relations within nature is inadequate. Thus we have to
+bend our energies to the enunciation of adequate concepts.</p>
+
+<p>But in so doing, are we not in fact endeavouring to solve a metaphysical
+problem? I do not think so. We are merely endeavouring to exhibit the
+type of relations which hold between the entities which we in fact
+perceive as in nature. We are not called on to make any pronouncement as
+to the psychological relation of subjects to objects or as to the status
+of either in the realm of reality. It is true that the issue of our
+endeavour may provide material which is relevant evidence for a
+discussion on that question. It can hardly fail to do so. But it is only
+evidence, and is not itself the metaphysical discussion. In order to
+make clear the character of this further discussion which is out of our
+ken, I will set before you two quotations. One is from Schelling and I
+extract the quotation from the work of the Russian philosopher Lossky
+which has recently been so excellently translated into English<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a>&mdash;&lsquo;In
+the &ldquo;Philosophy of Nature&rdquo; I considered the subject-object called nature
+in its activity of self-constructing. In order to understand it, we must
+rise to an intellectual intuition of nature. The empiricist does not
+rise thereto, and for this reason in all his explanations it is always
+<i>he himself</i> that proves to be constructing nature. It is no wonder,
+then, that his construction and that which was to be constructed so
+seldom coincide. A <i>Natur-philosoph</i> raises nature to independence, and
+makes it construct itself, and he never feels, therefore, the necessity
+of opposing nature<span class="pagenum" title="Page&nbsp;48">&nbsp;</span><a name="Page_48" id="Page_48"></a> as constructed (<i>i.e.</i> as experience) to real
+nature, or of correcting the one by means of the other.&rsquo;</p>
+
+<div class="footnote"><p><a name="Footnote_4_4" id="Footnote_4_4"></a><span class="label"><a href="#FNanchor_4_4">[4]</a></span> <i>The Intuitive Basis of Knowledge</i>, by N.&nbsp;O. Lossky,
+transl. by Mrs Duddington, Macmillan and Co., 1919.</p></div>
+
+<p>The other quotation is from a paper read by the Dean of St Paul&#8217;s before
+the Aristotelian Society in May of 1919. Dr Inge&#8217;s paper is entitled
+&lsquo;Platonism and Human Immortality,&rsquo; and in it there occurs the following
+statement: &lsquo;To sum up. The Platonic doctrine of immortality rests on the
+<i>independence</i> of the spiritual world. The spiritual world is not a
+world of unrealised ideals, over against a real world of unspiritual
+fact. It is, on the contrary, the real world, of which we have a true
+though very incomplete knowledge, over against a world of common
+experience which, as a complete whole, is not real, since it is
+compacted out of miscellaneous data, not all on the same level, by the
+help of the imagination. There is no world corresponding to the world of
+our common experience. Nature makes abstractions for us, deciding what
+range of vibrations we are to see and hear, what things we are to notice
+and remember.&rsquo;</p>
+
+<p>I have cited these statements because both of them deal with topics
+which, though they lie outside the range of our discussion, are always
+being confused with it. The reason is that they lie proximate to our
+field of thought, and are topics which are of burning interest to the
+metaphysically minded. It is difficult for a philosopher to realise that
+anyone really is confining his discussion within the limits that I have
+set before you. The boundary is set up just where he is beginning to get
+excited. But I submit to you that among the necessary prolegomena for
+philosophy and for natural science is a thorough understanding of the
+types of entities, and types of relations among those entities, which
+are disclosed to us in our perceptions of nature.</p>
+<hr />
+
+<h2><span class="pagenum" title="Page&nbsp;49">&nbsp;</span><a name="Page_49" id="Page_49"></a><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III
+<br />
+TIME</h2>
+
+
+<p>The two previous lectures of this course have been mainly critical. In
+the present lecture I propose to enter upon a survey of the kinds of
+entities which are posited for knowledge in sense-awareness. My purpose
+is to investigate the sorts of relations which these entities of various
+kinds can bear to each other. A classification of natural entities is
+the beginning of natural philosophy. To-day we commence with the
+consideration of Time.</p>
+
+<p>In the first place there is posited for us a general fact: namely,
+something is going on; there is an occurrence for definition.</p>
+
+<p>This general fact at once yields for our apprehension two factors, which
+I will name, the &lsquo;discerned&rsquo; and the &lsquo;discernible.&rsquo; The discerned is
+comprised of those elements of the general fact which are discriminated
+with their own individual peculiarities. It is the field directly
+perceived. But the entities of this field have relations to other
+entities which are not particularly discriminated in this individual
+way. These other entities are known merely as the relata in relation to
+the entities of the discerned field. Such an entity is merely a
+&lsquo;something&rsquo; which has such-and-such definite relations to some definite
+entity or entities in the discerned field. As being thus related, they
+are&mdash;owing to the particular character of these relations&mdash;known as
+elements of the general fact which is going on. But we are not aware of
+them except as entities fulfilling the functions of relata in these
+relations.</p>
+
+<p>Thus the complete general fact, posited as occurring, comprises both
+sets of entities, namely the entities<span class="pagenum" title="Page&nbsp;50">&nbsp;</span><a name="Page_50" id="Page_50"></a> perceived in their own
+individuality and other entities merely apprehended as relata without
+further definition. This complete general fact is the discernible and it
+comprises the discerned. The discernible is all nature as disclosed in
+that sense-awareness, and extends beyond and comprises all of nature as
+actually discriminated or discerned in that sense-awareness. The
+discerning or discrimination of nature is a peculiar awareness of
+special factors in nature in respect to their peculiar characters. But
+the factors in nature of which we have this peculiar sense-awareness are
+known as not comprising all the factors which together form the whole
+complex of related entities within the general fact there for
+discernment. This peculiarity of knowledge is what I call its
+unexhaustive character. This character may be metaphorically described
+by the statement that nature as perceived always has a ragged edge. For
+example, there is a world beyond the room to which our sight is confined
+known to us as completing the space-relations of the entities discerned
+within the room. The junction of the interior world of the room with the
+exterior world beyond is never sharp. Sounds and subtler factors
+disclosed in sense-awareness float in from the outside. Every type of
+sense has its own set of discriminated entities which are known to be
+relata in relation with entities not discriminated by that sense. For
+example we see something which we do not touch and we touch something
+which we do not see, and we have a general sense of the space-relations
+between the entity disclosed in sight and the entity disclosed in touch.
+Thus in the first place each of these two entities is known as a relatum
+in a general system of space-relations and in the second place the
+particular mutual relation of<span class="pagenum" title="Page&nbsp;51">&nbsp;</span><a name="Page_51" id="Page_51"></a> these two entities as related to each
+other in this general system is determined. But the general system of
+space-relations relating the entity discriminated by sight with that
+discriminated by <a name="err1" id="err1"></a><ins class="correction" title="Transcriber&#8217;s Note: Original read &lsquo;sight&rsquo;.">touch</ins> is not dependent on the peculiar
+character of the other entity as reported by the alternative sense. For
+example, the space-relations of the thing seen would have necessitated
+an entity as a relatum in the place of the thing touched even although
+certain elements of its character had not been disclosed by touch. Thus
+apart from the touch an entity with a certain specific relation to the
+thing seen would have been disclosed by sense-awareness but not
+otherwise discriminated in respect to its individual character. An
+entity merely known as spatially related to some discerned entity is
+what we mean by the bare idea of &lsquo;place.&rsquo; The concept of place marks the
+disclosure in sense-awareness of entities in nature known merely by
+their spatial relations to discerned entities. It is the disclosure of
+the discernible by means of its relations to the discerned.</p>
+
+<p>This disclosure of an entity as a relatum without further specific
+discrimination of quality is the basis of our concept of significance.
+In the above example the thing seen was significant, in that it
+disclosed its spatial relations to other entities not necessarily
+otherwise entering into consciousness. Thus significance is relatedness,
+but it is relatedness with the emphasis on one end only of the relation.</p>
+
+<p>For the sake of simplicity I have confined the argument to spatial
+relations; but the same considerations apply to temporal relations. The
+concept of &lsquo;period of time&rsquo; marks the disclosure in sense-awareness of
+entities in nature known merely by their temporal relations to<span class="pagenum" title="Page&nbsp;52">&nbsp;</span><a name="Page_52" id="Page_52"></a>
+discerned entities. Still further, this separation of the ideas of space
+and time has merely been adopted for the sake of gaining simplicity of
+exposition by conformity to current language. What we discern is the
+specific character of a place through a period of time. This is what I
+mean by an &lsquo;event.&rsquo; We discern some specific character of an event. But
+in discerning an event we are also aware of its significance as a
+relatum in the structure of events. This structure of events is the
+complex of events as related by the two relations of extension and
+cogredience. The most simple expression of the properties of this
+structure are to be found in our spatial and temporal relations. A
+discerned event is known as related in this structure to other events
+whose specific characters are otherwise not disclosed in that immediate
+awareness except so far as that they are relata within the structure.</p>
+
+<p>The disclosure in sense-awareness of the structure of events classifies
+events into those which are discerned in respect to some further
+individual character and those which are not otherwise disclosed except
+as elements of the structure. These signified events must include events
+in the remote past as well as events in the future. We are aware of
+these as the far off periods of unbounded time. But there is another
+classification of events which is also inherent in sense-awareness.
+These are the events which share the immediacy of the immediately
+present discerned events. These are the events whose characters together
+with those of the discerned events comprise all nature present for
+discernment. They form the complete general fact which is all nature now
+present as disclosed in that sense-awareness. It is in this second
+classification of events that the differentiation of space from time
+takes its origin. The germ of<span class="pagenum" title="Page&nbsp;53">&nbsp;</span><a name="Page_53" id="Page_53"></a> space is to be found in the mutual
+relations of events within the immediate general fact which is all
+nature now discernible, namely within the one event which is the
+totality of present nature. The relations of other events to this
+totality of nature form the texture of time.</p>
+
+<p>The unity of this general present fact is expressed by the concept of
+simultaneity. The general fact is the whole simultaneous occurrence of
+nature which is now for sense-awareness. This general fact is what I
+have called the discernible. But in future I will call it a &lsquo;duration,&rsquo;
+meaning thereby a certain whole of nature which is limited only by the
+property of being a simultaneity. Further in obedience to the principle
+of comprising within nature the whole terminus of sense-awareness,
+simultaneity must not be conceived as an irrelevant mental concept
+imposed upon nature. Our sense-awareness posits for immediate
+discernment a certain whole, here called a &lsquo;duration&rsquo;; thus a duration
+is a definite natural entity. A duration is discriminated as a complex
+of partial events, and the natural entities which are components of this
+complex are thereby said to be &lsquo;simultaneous with this duration.&rsquo; Also
+in a derivative sense they are simultaneous with each other in respect
+to this duration. Thus simultaneity is a definite natural relation. The
+word &lsquo;duration&rsquo; is perhaps unfortunate in so far as it suggests a mere
+abstract stretch of time. This is not what I mean. A duration is a
+concrete slab of nature limited by simultaneity which is an essential
+factor disclosed in sense-awareness.</p>
+
+<p>Nature is a process. As in the case of everything directly exhibited in
+sense-awareness, there can be no explanation of this characteristic of
+nature. All that can be done is to use language which may speculatively<span class="pagenum" title="Page&nbsp;54">&nbsp;</span><a name="Page_54" id="Page_54"></a>
+demonstrate it, and also to express the relation of this factor in
+nature to other factors.</p>
+
+<p>It is an exhibition of the process of nature that each duration happens
+and passes. The process of nature can also be termed the passage of
+nature. I definitely refrain at this stage from using the word &lsquo;time,&rsquo;
+since the measurable time of science and of civilised life generally
+merely exhibits some aspects of the more fundamental fact of the passage
+of nature. I believe that in this doctrine I am in full accord with
+Bergson, though he uses &lsquo;time&rsquo; for the fundamental fact which I call the
+&lsquo;passage of nature.&rsquo; Also the passage of nature is exhibited equally in
+spatial transition as well as in temporal transition. It is in virtue of
+its passage that nature is always moving on. It is involved in the
+meaning of this property of &lsquo;moving on&rsquo; that not only is any act of
+sense-awareness just that act and no other, but the terminus of each act
+is also unique and is the terminus of no other act. Sense-awareness
+seizes its only chance and presents for knowledge something which is for
+it alone.</p>
+
+<p>There are two senses in which the terminus of sense-awareness is unique.
+It is unique for the sense-awareness of an individual mind and it is
+unique for the sense-awareness of all minds which are operating under
+natural conditions. There is an important distinction between the two
+cases. (i) For one mind not only is the discerned component of the
+general fact exhibited in any act of sense-awareness distinct from the
+discerned component of the general fact exhibited in any other act of
+sense-awareness of that mind, but the two corresponding durations which
+are respectively related by simultaneity to the two discerned components
+are necessarily distinct. This is an exhibition of the temporal<span class="pagenum" title="Page&nbsp;55">&nbsp;</span><a name="Page_55" id="Page_55"></a> passage
+of nature; namely, one duration has passed into the other. Thus not only
+is the passage of nature an essential character of nature in its <i>r&ocirc;le</i>
+of the terminus of sense-awareness, but it is also essential for
+sense-awareness in itself. It is this truth which makes time appear to
+extend beyond nature. But what extends beyond nature to mind is not the
+serial and measurable time, which exhibits merely the character of
+passage in nature, but the quality of passage itself which is in no way
+measurable except so far as it obtains in nature. That is to say,
+&lsquo;passage&rsquo; is not measurable except as it occurs in nature in connexion
+with extension. In passage we reach a connexion of nature with the
+ultimate metaphysical reality. The quality of passage in durations is a
+particular exhibition in nature of a quality which extends beyond
+nature. For example passage is a quality not only of nature, which is
+the thing known, but also of sense-awareness which is the procedure of
+knowing. Durations have all the reality that nature has, though what
+that may be we need not now determine. The measurableness of time is
+derivative from the properties of durations. So also is the serial
+character of time. We shall find that there are in nature competing
+serial time-systems derived from different families of durations. These
+are a peculiarity of the character of passage as it is found in nature.
+This character has the reality of nature, but we must not necessarily
+transfer natural time to extra-natural entities. (ii) For two minds, the
+discerned components of the general facts exhibited in their respective
+acts of sense-awareness must be different. For each mind, in its
+awareness of nature is aware of a certain complex of related natural
+entities in their relations to the living body as a focus. But the<span class="pagenum" title="Page&nbsp;56">&nbsp;</span><a name="Page_56" id="Page_56"></a>
+associated durations may be identical. Here we are touching on that
+character of the passage nature which issues in the spatial relations of
+simultaneous bodies. This possible identity of the durations in the case
+of the sense-awareness of distinct minds is what binds into one nature
+the private experiences of sentient beings. We are here considering the
+spatial side of the passage of nature. Passage in this aspect of it also
+seems to extend beyond nature to mind.</p>
+
+<p>It is important to distinguish simultaneity from instantaneousness. I
+lay no stress on the mere current usage of the two terms. There are two
+concepts which I want to distinguish, and one I call simultaneity and
+the other instantaneousness. I hope that the words are judiciously
+chosen; but it really does not matter so long as I succeed in explaining
+my meaning. Simultaneity is the property of a group of natural elements
+which in some sense are components of a duration. A duration can be all
+nature present as the immediate fact posited by sense-awareness. A
+duration retains within itself the passage of nature. There are within
+it antecedents and consequents which are also durations which may be the
+complete specious presents of quicker consciousnesses. In other words a
+duration retains temporal thickness. Any concept of all nature as
+immediately known is always a concept of some duration though it may be
+enlarged in its temporal thickness beyond the possible specious present
+of any being known to us as existing within nature. Thus simultaneity is
+an ultimate factor in nature, immediate for sense-awareness.</p>
+
+<p>Instantaneousness is a complex logical concept of a procedure in thought
+by which constructed logical entities are produced for the sake of the
+simple ex<span class="pagenum" title="Page&nbsp;57">&nbsp;</span><a name="Page_57" id="Page_57"></a>pression in thought of properties of nature. Instantaneousness
+is the concept of all nature at an instant, where an instant is
+conceived as deprived of all temporal extension. For example we conceive
+of the distribution of matter in space at an instant. This is a very
+useful concept in science especially in applied mathematics; but it is a
+very complex idea so far as concerns its connexions with the immediate
+facts of sense-awareness. There is no such thing as nature at an instant
+posited by sense-awareness. What sense-awareness delivers over for
+knowledge is nature through a period. Accordingly nature at an instant,
+since it is not itself a natural entity, must be defined in terms of
+genuine natural entities. Unless we do so, our science, which employs
+the concept of instantaneous nature, must abandon all claim to be
+founded upon observation.</p>
+
+<p>I will use the term &lsquo;moment&rsquo; to mean &lsquo;all nature at an instant.&rsquo; A
+moment, in the sense in which the term is here used, has no temporal
+extension, and is in this respect to be contrasted with a duration which
+has such extension. What is directly yielded to our knowledge by
+sense-awareness is a duration. Accordingly we have now to explain how
+moments are derived from durations, and also to explain the purpose
+served by their introduction.</p>
+
+<p>A moment is a limit to which we approach as we confine attention to
+durations of minimum extension. Natural relations among the ingredients
+of a duration gain in complexity as we consider durations of increasing
+temporal extension. Accordingly there is an approach to ideal simplicity
+as we approach an ideal diminution of extension.</p>
+
+<p>The word &lsquo;limit&rsquo; has a precise signification in the logic of number and
+even in the logic of non-numerical<span class="pagenum" title="Page&nbsp;58">&nbsp;</span><a name="Page_58" id="Page_58"></a> one-dimensional series. As used here
+it is so far a mere metaphor, and it is necessary to explain directly
+the concept which it is meant to indicate.</p>
+
+<p>Durations can have the two-termed relational property of extending one
+over the other. Thus the duration which is all nature during a certain
+minute extends over the duration which is all nature during the
+30th&nbsp;second of that minute. This relation of &lsquo;extending
+over&rsquo;&mdash;&lsquo;extension&rsquo; as I shall call it&mdash;is a fundamental natural relation
+whose field comprises more than durations. It is a relation which two
+limited events can have to each other. Furthermore as holding between
+durations the relation appears to refer to the purely temporal
+extension. I shall however maintain that the same relation of extension
+lies at the base both of temporal and spatial extension. This discussion
+can be postponed; and for the present we are simply concerned with the
+relation of extension as it occurs in its temporal aspect for the
+limited field of durations.</p>
+
+<p>The concept of extension exhibits in thought one side of the ultimate
+passage of nature. This relation holds because of the special character
+which passage assumes in nature; it is the relation which in the case of
+durations expresses the properties of &lsquo;passing over.&rsquo; Thus the duration
+which was one definite minute passed over the duration which was its
+30th&nbsp;second. The duration of the 30th&nbsp;second was part of the duration of
+the minute. I shall use the terms &lsquo;whole&rsquo; and &lsquo;part&rsquo; exclusively in this
+sense, that the &lsquo;part&rsquo; is an event which is extended over by the other
+event which is the &lsquo;whole.&rsquo; Thus in my nomenclature &lsquo;whole&rsquo; and &lsquo;part&rsquo;
+refer exclusively to this fundamental relation of extension; and
+accordingly in this technical usage only events can be either wholes or
+parts.</p>
+
+<p><span class="pagenum" title="Page&nbsp;59">&nbsp;</span><a name="Page_59" id="Page_59"></a>The continuity of nature arises from extension. Every event extends over
+other events, and every event is extended over by other events. Thus in
+the special case of durations which are now the only events directly
+under consideration, every duration is part of other durations; and
+every duration has other durations which are parts of it. Accordingly
+there are no maximum durations and no minimum durations. Thus there is
+no atomic structure of durations, and the perfect definition of a
+duration, so as to mark out its individuality and distinguish it from
+highly analogous durations over which it is passing, or which are
+passing over it, is an arbitrary postulate of thought. Sense-awareness
+posits durations as factors in nature but does not clearly enable
+thought to use it as distinguishing the separate individualities of the
+entities of an allied group of slightly differing durations. This is one
+instance of the indeterminateness of sense-awareness. Exactness is an
+ideal of thought, and is only realised in experience by the selection of
+a route of approximation.</p>
+
+<p>The absence of maximum and minimum durations does not exhaust the
+properties of nature which make up its continuity. The passage of nature
+involves the existence of a family of durations. When two durations
+belong to the same family either one contains the other, or they overlap
+each other in a subordinate duration without either containing the
+other; or they are completely separate. The excluded case is that of
+durations overlapping in finite events but not containing a third
+duration as a common part.</p>
+
+<p>It is evident that the relation of extension is transitive; namely as
+applied to durations, if duration <i>A</i> is part of duration <i>B</i>, and
+duration <i>B</i> is part of duration <i>C</i>, then <i>A</i><span class="pagenum" title="Page&nbsp;60">&nbsp;</span><a name="Page_60" id="Page_60"></a> is part of <i>C</i>. Thus the
+first two cases may be combined into one and we can say that two
+durations which belong to the same family <i>either</i> are such that there
+are durations which are parts of both <i>or</i> are completely separate.</p>
+
+<p>Furthermore the converse of this proposition holds; namely, if two
+durations have other durations which are parts of both <i>or</i> if the two
+durations are completely separate, then they belong to the same family.</p>
+
+<p>The further characteristics of the continuity of nature&mdash;so far as
+durations are concerned&mdash;which has not yet been formulated arises in
+connexion with a family of durations. It can be stated in this way:
+There are durations which contain as parts any two durations of the same
+family. For example a week contains as parts any two of its days. It is
+evident that a containing duration satisfies the conditions for
+belonging to the same family as the two contained durations.</p>
+
+<p>We are now prepared to proceed to the definition of a moment of time.
+Consider a set of durations all taken from the same family. Let it have
+the following properties: (i) of any two members of the set one contains
+the other as a part, and (ii) there is no duration which is a common
+part of every member of the set.</p>
+
+<p>Now the relation of whole and part is asymmetrical; and by this I mean
+that if <i>A</i> is part of <i>B</i>, then <i>B</i> is not part of <i>A</i>. Also we have
+already noted that the relation is transitive. Accordingly we can easily
+see that the durations of any set with the properties just enumerated
+must be arranged in a one-dimensional serial order in which as we
+descend the series we progressively reach durations of smaller and
+smaller temporal extension. The series may start with any arbitrarily
+assumed<span class="pagenum" title="Page&nbsp;61">&nbsp;</span><a name="Page_61" id="Page_61"></a> duration of any temporal extension, but in descending the
+series the temporal extension progressively contracts and the successive
+durations are packed one within the other like the nest of boxes of a
+Chinese toy. But the set differs from the toy in this particular: the
+toy has a smallest box which forms the end box of its series; but the
+set of durations can have no smallest duration nor can it converge
+towards a duration as its limit. For the parts either of the end
+duration or of the limit would be parts of all the durations of the set
+and thus the second condition for the set would be violated.</p>
+
+<p>I will call such a set of durations an &lsquo;abstractive set&rsquo; of durations.
+It is evident that an abstractive set as we pass along it converges to
+the ideal of all nature with no temporal extension, namely, to the ideal
+of all nature at an instant. But this ideal is in fact the ideal of a
+nonentity. What the abstractive set is in fact doing is to guide thought
+to the consideration of the progressive simplicity of natural relations
+as we progressively diminish the temporal extension of the duration
+considered. Now the whole point of the procedure is that the
+quantitative expressions of these natural properties do converge to
+limits though the abstractive set does not converge to any limiting
+duration. The laws relating these quantitative limits are the laws of
+nature &lsquo;at an instant,&rsquo; although in truth there is no nature at an
+instant and there is only the abstractive set. Thus an abstractive set
+is effectively the entity meant when we consider an instant of time
+without temporal extension. It subserves all the necessary purposes of
+giving a definite meaning to the concept of the properties of nature at
+an instant. I fully agree that this concept is fundamental in the
+expression of physical science. The<span class="pagenum" title="Page&nbsp;62">&nbsp;</span><a name="Page_62" id="Page_62"></a> difficulty is to express our
+meaning in terms of the immediate deliverances of sense-awareness, and I
+offer the above explanation as a complete solution of the problem.</p>
+
+<p>In this explanation a moment is the set of natural properties reached by
+a route of approximation. An abstractive series is a route of
+approximation. There are different routes of approximation to the same
+limiting set of the properties of nature. In other words there are
+different abstractive sets which are to be regarded as routes of
+approximation to the same moment. Accordingly there is a certain amount
+of technical detail necessary in explaining the relations of such
+abstractive sets with the same convergence and in guarding against
+possible exceptional cases. Such details are not suitable for exposition
+in these lectures, and I have dealt with them fully elsewhere<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a>.</p>
+
+<div class="footnote"><p><a name="Footnote_5_5" id="Footnote_5_5"></a><span class="label"><a href="#FNanchor_5_5">[5]</a></span> Cf. <i>An Enquiry concerning the Principles of Natural
+Knowledge</i>, Cambridge University Press, 1919.</p></div>
+
+<p>It is more convenient for technical purposes to look on a moment as
+being the class of all abstractive sets of durations with the same
+convergence. With this definition (provided that we can successfully
+explain what we mean by the &lsquo;same convergence&rsquo; apart from a detailed
+knowledge of the set of natural properties arrived at by approximation)
+a moment is merely a class of sets of durations whose relations of
+extension in respect to each other have certain definite peculiarities.
+We may term these connexions of the component durations the &lsquo;extrinsic&rsquo;
+properties of a moment; the &lsquo;intrinsic&rsquo; properties of the moment are the
+properties of nature arrived at as a limit as we proceed along any one
+of its abstractive sets. These are the properties of nature &lsquo;at that
+moment,&rsquo; or &lsquo;at that instant.&rsquo;</p>
+
+<p><span class="pagenum" title="Page&nbsp;63">&nbsp;</span><a name="Page_63" id="Page_63"></a>The durations which enter into the composition of a moment all belong to
+one family. Thus there is one family of moments corresponding to one
+family of durations. Also if we take two moments of the same family,
+among the durations which enter into the composition of one moment the
+smaller durations are completely separated from the smaller durations
+which enter into the composition of the other moment. Thus the two
+moments in their intrinsic properties must exhibit the limits of
+completely different states of nature. In this sense the two moments are
+completely separated. I will call two moments of the same family
+&lsquo;parallel.&rsquo;</p>
+
+<p>Corresponding to each duration there are two moments of the associated
+family of moments which are the boundary moments of that duration. A
+&lsquo;boundary moment&rsquo; of a duration can be defined in this way. There are
+durations of the same family as the given duration which overlap it but
+are not contained in it. Consider an abstractive set of such durations.
+Such a set defines a moment which is just as much without the duration
+as within it. Such a moment is a boundary moment of the duration. Also
+we call upon our sense-awareness of the passage of nature to inform us
+that there are two such boundary moments, namely the earlier one and the
+later one. We will call them the initial and the final boundaries.</p>
+
+<p>There are also moments of the same family such that the shorter
+durations in their composition are entirely separated from the given
+duration. Such moments will be said to lie &lsquo;outside&rsquo; the given duration.
+Again other moments of the family are such that the shorter durations in
+their composition are parts of the given duration. Such moments are said
+to lie &lsquo;within&rsquo; the given<span class="pagenum" title="Page&nbsp;64">&nbsp;</span><a name="Page_64" id="Page_64"></a> duration or to &lsquo;inhere&rsquo; in it. The whole
+family of parallel moments is accounted for in this way by reference to
+any given duration of the associated family of durations. Namely, there
+are moments of the family which lie without the given duration, there
+are the two moments which are the boundary moments of the given
+duration, and the moments which lie within the given duration.
+Furthermore any two moments of the same family are the boundary moments
+of some one duration of the associated family of durations.</p>
+
+<p>It is now possible to define the serial relation of temporal order among
+the moments of a family. For let <i>A</i> and <i>C</i> be any two moments of the
+family, these moments are the boundary moments of one duration <i>d</i> of
+the associated family, and any moment <i>B</i> which lies within the duration
+<i>d</i> will be said to lie between the moments <i>A</i> and <i>C</i>. Thus the
+three-termed relation of &lsquo;lying-between&rsquo; as relating three moments <i>A</i>,
+<i>B</i>, and <i>C</i> is completely defined. Also our knowledge of the passage of
+nature assures us that this relation distributes the moments of the
+family into a serial order. I abstain from enumerating the definite
+properties which secure this result, I have enumerated them in my
+recently published book<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a> to which I have already referred. Furthermore
+the passage of nature enables us to know that one direction along the
+series corresponds to passage into the future and the other direction
+corresponds to retrogression towards the past.</p>
+
+<div class="footnote"><p><a name="Footnote_6_6" id="Footnote_6_6"></a><span class="label"><a href="#FNanchor_6_6">[6]</a></span> Cf. <i>Enquiry</i></p></div>
+
+<p>Such an ordered series of moments is what we mean by time defined as a
+series. Each element of the series exhibits an instantaneous state of
+nature. Evidently this serial time is the result of an intellectual
+process of<span class="pagenum" title="Page&nbsp;65">&nbsp;</span><a name="Page_65" id="Page_65"></a> abstraction. What I have done is to give precise definitions
+of the procedure by which the abstraction is effected. This procedure is
+merely a particular case of the general method which in my book I name
+the &lsquo;method of extensive abstraction.&rsquo; This serial time is evidently not
+the very passage of nature itself. It exhibits some of the natural
+properties which flow from it. The state of nature &lsquo;at a moment&rsquo; has
+evidently lost this ultimate quality of passage. Also the temporal
+series of moments only retains it as an extrinsic relation of entities
+and not as the outcome of the essential being of the terms of the
+series.</p>
+
+<p>Nothing has yet been said as to the measurement of time. Such
+measurement does not follow from the mere serial property of time; it
+requires a theory of congruence which will be considered in a later
+lecture.</p>
+
+<p>In estimating the adequacy of this definition of the temporal series as
+a formulation of experience it is necessary to discriminate between the
+crude deliverance of sense-awareness and our intellectual theories. The
+lapse of time is a measurable serial quantity. The whole of scientific
+theory depends on this assumption and any theory of time which fails to
+provide such a measurable series stands self-condemned as unable to
+account for the most salient fact in experience. Our difficulties only
+begin when we ask what it is that is measured. It is evidently something
+so fundamental in experience that we can hardly stand back from it and
+hold it apart so as to view it in its own proportions.</p>
+
+<p>We have first to make up our minds whether time is to be found in nature
+or nature is to be found in time. The difficulty of the latter
+alternative&mdash;namely of making time prior to nature&mdash;is that time then
+becomes<span class="pagenum" title="Page&nbsp;66">&nbsp;</span><a name="Page_66" id="Page_66"></a> a metaphysical enigma. What sort of entities are its instants
+or its periods? The dissociation of time from events discloses to our
+immediate inspection that the attempt to set up time as an independent
+terminus for knowledge is like the effort to find substance in a shadow.
+There is time because there are happenings, and apart from happenings
+there is nothing.</p>
+
+<p>It is necessary however to make a distinction. In some sense time
+extends beyond nature. It is not true that a timeless sense-awareness
+and a timeless thought combine to contemplate a timeful nature.
+Sense-awareness and thought are themselves processes as well as their
+termini in nature. In other words there is a passage of sense-awareness
+and a passage of thought. Thus the reign of the quality of passage
+extends beyond nature. But now the distinction arises between passage
+which is fundamental and the temporal series which is a logical
+abstraction representing some of the properties of nature. A temporal
+series, as we have defined it, represents merely certain properties of a
+family of durations&mdash;properties indeed which durations only possess
+because of their partaking of the character of passage, but on the other
+hand properties which only durations do possess. Accordingly time in the
+sense of a measurable temporal series is a character of nature only, and
+does not extend to the processes of thought and of sense-awareness
+except by a correlation of these processes with the temporal series
+implicated in their procedures.</p>
+
+<p>So far the passage of nature has been considered in connexion with the
+passage of durations; and in this connexion it is peculiarly associated
+with temporal series. We must remember however that the character of
+passage is peculiarly associated with the extension of<span class="pagenum" title="Page&nbsp;67">&nbsp;</span><a name="Page_67" id="Page_67"></a> events, and that
+from this extension spatial transition arises just as much as temporal
+transition. The discussion of this point is reserved for a later lecture
+but it is necessary to remember it now that we are proceeding to discuss
+the application of the concept of passage beyond nature, otherwise we
+shall have too narrow an idea of the essence of passage.</p>
+
+<p>It is necessary to dwell on the subject of sense-awareness in this
+connexion as an example of the way in which time concerns mind, although
+measurable time is a mere abstract from nature and nature is closed to
+mind.</p>
+
+<p>Consider sense-awareness&mdash;not its terminus which is nature, but
+sense-awareness in itself as a procedure of mind. Sense-awareness is a
+relation of mind to nature. Accordingly we are now considering mind as a
+relatum in sense-awareness. For mind there is the immediate
+sense-awareness and there is memory. The distinction between memory and
+the present immediacy has a double bearing. On the one hand it discloses
+that mind is not impartially aware of all those natural durations to
+which it is related by awareness. Its awareness shares in the passage of
+nature. We can imagine a being whose awareness, conceived as his private
+possession, suffers no transition, although the terminus of his
+awareness is our own transient nature. There is no essential reason why
+memory should not be raised to the vividness of the present fact; and
+then from the side of mind, What is the difference between the present
+and the past? Yet with this hypothesis we can also suppose that the
+vivid remembrance and the present fact are posited in awareness as in
+their temporal serial order. Accordingly we must admit that though we
+can imagine that mind in the operation of sense-<span class="pagenum" title="Page&nbsp;68">&nbsp;</span><a name="Page_68" id="Page_68"></a>awareness might be free
+from any character of passage, yet in point of fact our experience of
+sense-awareness exhibits our minds as partaking in this character.</p>
+
+<p>On the other hand the mere fact of memory is an escape from transience.
+In memory the past is present. It is not present as overleaping the
+temporal succession of nature, but it is present as an immediate fact
+for the mind. Accordingly memory is a disengagement of the mind from the
+mere passage of nature; for what has passed for nature has not passed
+for mind.</p>
+
+<p>Furthermore the distinction between memory and the immediate present is
+not so clear as it is conventional to suppose. There is an intellectual
+theory of time as a moving knife-edge, exhibiting a present fact without
+temporal extension. This theory arises from the concept of an ideal
+exactitude of observation. Astronomical observations are successively
+refined to be exact to tenths, to hundredths, and to thousandths of
+seconds. But the final refinements are arrived at by a system of
+averaging, and even then present us with a stretch of time as a margin
+of error. Here error is merely a conventional term to express the fact
+that the character of experience does not accord with the ideal of
+thought. I have already explained how the concept of a moment
+conciliates the observed fact with this ideal; namely, there is a
+limiting simplicity in the quantitative expression of the properties of
+durations, which is arrived at by considering any one of the abstractive
+sets included in the moment. In other words the extrinsic character of
+the moment as an aggregate of durations has associated with it the
+intrinsic character of the moment which is the limiting expression of
+natural properties.</p>
+
+<p><span class="pagenum" title="Page&nbsp;69">&nbsp;</span><a name="Page_69" id="Page_69"></a>Thus the character of a moment and the ideal of exactness which it
+enshrines do not in any way weaken the position that the ultimate
+terminus of awareness is a duration with temporal thickness. This
+immediate duration is not clearly marked out for our apprehension. Its
+earlier boundary is blurred by a fading into memory, and its later
+boundary is blurred by an emergence from anticipation. There is no sharp
+distinction either between memory and the present immediacy or between
+the present immediacy and anticipation. The present is a wavering
+breadth of boundary between the two extremes. Thus our own
+sense-awareness with its extended present has some of the character of
+the sense-awareness of the imaginary being whose mind was free from
+passage and who contemplated all nature as an immediate fact. Our own
+present has its antecedents and its consequents, and for the imaginary
+being all nature has its antecedent and its consequent durations. Thus
+the only difference in this respect between us and the imaginary being
+is that for him all nature shares in the immediacy of our present
+duration.</p>
+
+<p>The conclusion of this discussion is that so far as sense-awareness is
+concerned there is a passage of mind which is distinguishable from the
+passage of nature though closely allied with it. We may speculate, if we
+like, that this alliance of the passage of mind with the passage of
+nature arises from their both sharing in some ultimate character of
+passage which dominates all being. But this is a speculation in which we
+have no concern. The immediate deduction which is sufficient for us is
+that&mdash;so far as sense-awareness is concerned&mdash;mind is not in time or in
+space in the same sense in which the events of nature are in time, but<span class="pagenum" title="Page&nbsp;70">&nbsp;</span><a name="Page_70" id="Page_70"></a>
+that it is derivatively in time and in space by reason of the peculiar
+alliance of its passage with the passage of nature. Thus mind is in time
+and in space in a sense peculiar to itself. This has been a long
+discussion to arrive at a very simple and obvious conclusion. We all
+feel that in some sense our minds are here in this room and at this
+time. But it is not quite in the same sense as that in which the events
+of nature which are the existences of our brains have their spatial and
+temporal positions. The fundamental distinction to remember is that
+immediacy for sense-awareness is not the same as instantaneousness for
+nature. This last conclusion bears on the next discussion with which I
+will terminate this lecture. This question can be formulated thus, Can
+alternative temporal series be found in nature?</p>
+
+<p>A few years ago such a suggestion would have been put aside as being
+fantastically impossible. It would have had no bearing on the science
+then current, and was akin to no ideas which had ever entered into the
+dreams of philosophy. The eighteenth and nineteenth centuries accepted
+as their natural philosophy a certain circle of concepts which were as
+rigid and definite as those of the philosophy of the middle ages, and
+were accepted with as little critical research. I will call this natural
+philosophy &lsquo;materialism.&rsquo; Not only were men of science materialists, but
+also adherents of all schools of philosophy. The idealists only differed
+from the philosophic materialists on question of the alignment of nature
+in reference to mind. But no one had any doubt that the philosophy of
+nature considered in itself was of the type which I have called
+materialism. It is the philosophy which I have already examined in my
+two lectures of this course preceding the present one. It<span class="pagenum" title="Page&nbsp;71">&nbsp;</span><a name="Page_71" id="Page_71"></a> can be
+summarised as the belief that nature is an aggregate of material and
+that this material exists in some sense <i>at</i> each successive member of a
+one-dimensional series of extensionless instants of time. Furthermore
+the mutual relations of the material entities at each instant formed
+these entities into a spatial configuration in an unbounded space. It
+would seem that space&mdash;on this theory&mdash;would be as instantaneous as the
+instants, and that some explanation is required of the relations between
+the successive instantaneous spaces. The materialistic theory is however
+silent on this point; and the succession of instantaneous spaces is
+tacitly combined into one persistent space. This theory is a purely
+intellectual rendering of experience which has had the luck to get
+itself formulated at the dawn of scientific thought. It has dominated
+the language and the imagination of science since science flourished in
+Alexandria, with the result that it is now hardly possible to speak
+without appearing to assume its immediate obviousness.</p>
+
+<p>But when it is distinctly formulated in the abstract terms in which I
+have just stated it, the theory is very far from obvious. The passing
+complex of factors which compose the fact which is the terminus of
+sense-awareness places before us nothing corresponding to the trinity of
+this natural materialism. This trinity is composed (i) of the temporal
+series of extensionless instants, (ii) of the aggregate of material
+entities, and (iii) of space which is the outcome of relations of
+matter.</p>
+
+<p>There is a wide gap between these presuppositions of the intellectual
+theory of materialism and the immediate deliverances of sense-awareness.
+I do not question that this materialistic trinity embodies im<span class="pagenum" title="Page&nbsp;72">&nbsp;</span><a name="Page_72" id="Page_72"></a>portant
+characters of nature. But it is necessary to express these characters in
+terms of the facts of experience. This is exactly what in this lecture I
+have been endeavouring to do so far as time is concerned; and we have
+now come up against the question, Is there only one temporal series? The
+uniqueness of the temporal series is presupposed in the materialist
+philosophy of nature. But that philosophy is merely a theory, like the
+Aristotelian scientific theories so firmly believed in the middle ages.
+If in this lecture I have in any way succeeded in getting behind the
+theory to the immediate facts, the answer is not nearly so certain. The
+question can be transformed into this alternative form, Is there only
+one family of durations? In this question the meaning of a &lsquo;family of
+durations&rsquo; has been defined earlier in this lecture. The answer is now
+not at all obvious. On the materialistic theory the instantaneous
+present is the only field for the creative activity of nature. The past
+is gone and the future is not yet. Thus (on this theory) the immediacy
+of perception is of an instantaneous present, and this unique present is
+the outcome of the past and the promise of the future. But we deny this
+immediately given instantaneous present. There is no such thing to be
+found in nature. As an ultimate fact it is a nonentity. What is
+immediate for sense-awareness is a duration. Now a duration has within
+itself a past and a future; and the temporal breadths of the immediate
+durations of sense-awareness are very indeterminate and dependent on the
+individual percipient. Accordingly there is no unique factor in nature
+which for every percipient is pre-eminently and necessarily the present.
+The passage of nature leaves nothing between the past and the future.<span class="pagenum" title="Page&nbsp;73">&nbsp;</span><a name="Page_73" id="Page_73"></a>
+What we perceive as present is the vivid fringe of memory tinged with
+anticipation. This vividness lights up the discriminated field within a
+duration. But no assurance can thereby be given that the happenings of
+nature cannot be assorted into other durations of alternative families.
+We cannot even know that the series of immediate durations posited by
+the sense-awareness of one individual mind all necessarily belong to the
+same family of durations. There is not the slightest reason to believe
+that this is so. Indeed if my theory of nature be correct, it will not
+be the case.</p>
+
+<p>The materialistic theory has all the completeness of the thought of the
+middle ages, which had a complete answer to everything, be it in heaven
+or in hell or in nature. There is a trimness about it, with its
+instantaneous present, its vanished past, its non-existent future, and
+its inert matter. This trimness is very medieval and ill accords with
+brute fact.</p>
+
+<p>The theory which I am urging admits a greater ultimate mystery and a
+deeper ignorance. The past and the future meet and mingle in the
+ill-defined present. The passage of nature which is only another name
+for the creative force of existence has no narrow ledge of definite
+instantaneous present within which to operate. Its operative presence
+which is now urging nature forward must be sought for throughout the
+whole, in the remotest past as well as in the narrowest breadth of any
+present duration. Perhaps also in the unrealised future. Perhaps also in
+the future which might be as well as the actual future which will be. It
+is impossible to meditate on time and the mystery of the creative
+passage of nature without an overwhelming emotion at the limitations of
+human intelligence.</p>
+
+<hr />
+
+<h2><span class="pagenum" title="Page&nbsp;74">&nbsp;</span><a name="Page_74" id="Page_74"></a><a name="CHAPTER_IV" id="CHAPTER_IV"></a>CHAPTER IV
+<br />
+THE METHOD OF EXTENSIVE ABSTRACTION</h2>
+
+
+<p>To-day&#8217;s lecture must commence with the consideration of limited events.
+We shall then be in a position to enter upon an investigation of the
+factors in nature which are represented by our conception of space.</p>
+
+<p>The duration which is the immediate disclosure of our sense-awareness is
+discriminated into parts. There is the part which is the life of all
+nature within a room, and there is the part which is the life of all
+nature within a table in the room. These parts are limited events. They
+have the endurance of the present duration, and they are parts of it.
+But whereas a duration is an unlimited whole and in a certain limited
+sense is all that there is, a limited event possesses a completely
+defined limitation of extent which is expressed for us in
+spatio-temporal terms.</p>
+
+<p>We are accustomed to associate an event with a certain melodramatic
+quality. If a man is run over, that is an event comprised within certain
+spatio-temporal limits. We are not accustomed to consider the endurance
+of the Great Pyramid throughout any definite day as an event. But the
+natural fact which is the Great Pyramid throughout a day, meaning
+thereby all nature within it, is an event of the same character as the
+man&#8217;s accident, meaning thereby all nature with spatio-temporal
+limitations so as to include the man and the motor during the period
+when they were in contact.</p>
+
+<p><span class="pagenum" title="Page&nbsp;75">&nbsp;</span><a name="Page_75" id="Page_75"></a>We are accustomed to analyse these events into three factors, time,
+space, and material. In fact, we at once apply to them the concepts of
+the materialistic theory of nature. I do not deny the utility of this
+analysis for the purpose of expressing important laws of nature. What I
+am denying is that anyone of these factors is posited for us in
+sense-awareness in concrete independence. We perceive one unit factor in
+nature; and this factor is that something is going on then&mdash;there. For
+example, we perceive the going-on of the Great Pyramid in its relations
+to the goings-on of the surrounding Egyptian events. We are so trained,
+both by language and by formal teaching and by the resulting
+convenience, to express our thoughts in terms of this materialistic
+analysis that intellectually we tend to ignore the true unity of the
+factor really exhibited in sense-awareness. It is this unit factor,
+retaining in itself the passage of nature, which is the primary concrete
+element discriminated in nature. These primary factors are what I mean
+by events.</p>
+
+<p>Events are the field of a two-termed relation, namely the relation of
+extension which was considered in the last lecture. Events are the
+things related by the relation of extension. If an event <i>A</i> extends
+over an event <i>B</i>, then <i>B</i> is &lsquo;part of&rsquo; <i>A</i>, and <i>A</i> is a &lsquo;whole&rsquo; of
+which <i>B</i> is a part. Whole and part are invariably used in these
+lectures in this definite sense. It follows that in reference to this
+relation any two events <i>A</i> and <i>B</i> may have any one of four relations
+to each other, namely (i) <i>A</i> may extend over <i>B</i>, or (ii) <i>B</i> may
+extend over <i>A</i>, or (iii) <i>A</i> and <i>B</i> may both extend over some third
+event <i>C</i>, but neither over the other, or (iv) <i>A</i> and <i>B</i> may be
+entirely separate. These alternatives can<span class="pagenum" title="Page&nbsp;76">&nbsp;</span><a name="Page_76" id="Page_76"></a> obviously be illustrated by
+Euler&#8217;s diagrams as they appear in logical textbooks.</p>
+
+<p>The continuity of nature is the continuity of events. This continuity is
+merely the name for the aggregate of a variety of properties of events
+in connexion with the relation of extension.</p>
+
+<p>In the first place, this relation is transitive; secondly, every event
+contains other events as parts of itself; thirdly every event is a part
+of other events; fourthly given any two finite events there are events
+each of which contains both of them as parts; and fifthly there is a
+special relation between events which I term &lsquo;junction.&rsquo;</p>
+
+<p>Two events have junction when there is a third event of which both
+events are parts, and which is such that no part of it is separated from
+both of the two given events. Thus two events with junction make up
+exactly one event which is in a sense their sum.</p>
+
+<p>Only certain pairs of events have this property. In general any event
+containing two events also contains parts which are separated from both
+events.</p>
+
+<p>There is an alternative definition of the junction of two events which I
+have adopted in my recent book<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a>. Two events have junction when there
+is a third event such that (i) it overlaps both events and (ii) it has
+no part which is separated from both the given events. If either of
+these alternative definitions is adopted as the definition of junction,
+the other definition appears as an axiom respecting the character of
+junction as we know it in nature. But we are not thinking of logical
+definition so much as the formulation of the results of direct
+observation. There is a certain continuity<span class="pagenum" title="Page&nbsp;77">&nbsp;</span><a name="Page_77" id="Page_77"></a> inherent in the observed
+unity of an event, and these two definitions of junction are really
+axioms based on observation respecting the character of this continuity.</p>
+
+<div class="footnote"><p><a name="Footnote_7_7" id="Footnote_7_7"></a><span class="label"><a href="#FNanchor_7_7">[7]</a></span> Cf. <i>Enquiry</i>.</p></div>
+
+<p>The relations of whole and part and of overlapping are particular cases
+of the junction of events. But it is possible for events to have
+junction when they are separate from each other; for example, the upper
+and the lower part of the Great Pyramid are divided by some imaginary
+horizontal plane.</p>
+
+<p>The continuity which nature derives from events has been obscured by the
+illustrations which I have been obliged to give. For example I have
+taken the existence of the Great Pyramid as a fairly well-known fact to
+which I could safely appeal as an illustration. This is a type of event
+which exhibits itself to us as the situation of a recognisable object;
+and in the example chosen the object is so widely recognised that it has
+received a name. An object is an entity of a different type from an
+event. For example, the event which is the life of nature within the
+Great Pyramid yesterday and to-day is divisible into two parts, namely
+the Great Pyramid yesterday and the Great Pyramid to-day. But the
+recognisable object which is also called the Great Pyramid is the same
+object to-day as it was yesterday. I shall have to consider the theory
+of objects in another lecture.</p>
+
+<p>The whole subject is invested with an unmerited air of subtlety by the
+fact that when the event is the situation of a well-marked object, we
+have no language to distinguish the event from the object. In the case
+of the Great Pyramid, the object is the perceived unit entity which as
+perceived remains self-identical through<span class="pagenum" title="Page&nbsp;78">&nbsp;</span><a name="Page_78" id="Page_78"></a>out the ages; while the whole
+dance of molecules and the shifting play of the electromagnetic field
+are ingredients of the event. An object is in a sense out of time. It is
+only derivatively in time by reason of its having the relation to events
+which I term &lsquo;situation.&rsquo; This relation of situation will require
+discussion in a subsequent lecture.</p>
+
+<p>The point which I want to make now is that being the situation of a
+well-marked object is not an inherent necessity for an event. Wherever
+and whenever something is going on, there is an event. Furthermore
+&lsquo;wherever and whenever&rsquo; in themselves presuppose an event, for space and
+time in themselves are abstractions from events. It is therefore a
+consequence of this doctrine that something is always going on
+everywhere, even in so-called empty space. This conclusion is in accord
+with modern physical science which presupposes the play of an
+electromagnetic field throughout space and time. This doctrine of
+science has been thrown into the materialistic form of an all-pervading
+ether. But the ether is evidently a mere idle concept&mdash;in the
+phraseology which Bacon applied to the doctrine of final causes, it is a
+barren virgin. Nothing is deduced from it; and the ether merely
+subserves the purpose of satisfying the demands of the materialistic
+theory. The important concept is that of the shifting facts of the
+fields of force. This is the concept of an ether of events which should
+be substituted for that of a material ether.</p>
+
+<p>It requires no illustration to assure you that an event is a complex
+fact, and the relations between two events form an almost impenetrable
+maze. The clue discovered by the common sense of mankind and
+systematically<span class="pagenum" title="Page&nbsp;79">&nbsp;</span><a name="Page_79" id="Page_79"></a> utilised in science is what I have elsewhere<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a> called
+the law of convergence to simplicity by diminution of extent.</p>
+
+<div class="footnote"><p><a name="Footnote_8_8" id="Footnote_8_8"></a><span class="label"><a href="#FNanchor_8_8">[8]</a></span> Cf. <i>Organisation of Thought</i>, pp.&nbsp;146 et&nbsp;seq. Williams and
+Norgate, 1917.</p></div>
+
+<p>If <i>A</i> and <i>B</i> are two events, and <i>A&#8242;</i> is part of <i>A</i> and <i>B&#8242;</i> is part
+of <i>B</i>, then in many respects the relations between the parts <i>A&#8242;</i> and
+<i>B&#8242;</i> will be simpler than the relations between <i>A</i> and <i>B</i>. This is the
+principle which presides over all attempts at exact observation.</p>
+
+<p>The first outcome of the systematic use of this law has been the
+formulation of the abstract concepts of Time and Space. In the previous
+lecture I sketched how the principle was applied to obtain the
+time-series. I now proceed to consider how the spatial entities are
+obtained by the same method. The systematic procedure is identical in
+principle in both cases, and I have called the general type of procedure
+the &lsquo;method of extensive abstraction.&rsquo;</p>
+
+<p>You will remember that in my last lecture I defined the concept of an
+abstractive set of durations. This definition can be extended so as to
+apply to any events, limited events as well as durations. The only
+change that is required is the substitution of the word &lsquo;event&rsquo; for the
+word &lsquo;duration.&rsquo; Accordingly an abstractive set of events is any set of
+events which possesses the two properties, (i) of any two members of the
+set one contains the other as a part, and (ii) there is no event which
+is a common part of every member of the set. Such a set, as you will
+remember, has the properties of the Chinese toy which is a nest of
+boxes, one within the other, with the difference that the toy has a
+smallest box, while the abstractive class has neither a smallest<span class="pagenum" title="Page&nbsp;80">&nbsp;</span><a name="Page_80" id="Page_80"></a> event
+nor does it converge to a limiting event which is not a member of the
+set.</p>
+
+<p>Thus, so far as the abstractive sets of events are concerned, an
+abstractive set converges to nothing. There is the set with its members
+growing indefinitely smaller and smaller as we proceed in thought
+towards the smaller end of the series; but there is no absolute minimum
+of any sort which is finally reached. In fact the set is just itself and
+indicates nothing else in the way of events, except itself. But each
+event has an intrinsic character in the way of being a situation of
+objects and of having parts which are situations of objects and&mdash;to
+state the matter more generally&mdash;in the way of being a field of the life
+of nature. This character can be defined by quantitative expressions
+expressing relations between various quantities intrinsic to the event
+or between such quantities and other quantities intrinsic to other
+events. In the case of events of considerable spatio-temporal extension
+this set of quantitative expressions is of bewildering complexity. If
+<i>e</i> be an event, let us denote by <i>q</i>(<i>e</i>) the set of quantitative
+expressions defining its character including its connexions with the
+rest of nature. Let <i>e</i><sub>1</sub>, <i>e</i><sub>2</sub>, <i>e</i><sub>3</sub>, etc. be an abstractive
+set, the members being so arranged that each member such as <i>e<sub>n</sub></i>
+extends over all the succeeding members such as <i>e</i><sub><i>n</i>+1</sub>, <i>e</i><sub><i>n</i>+2</sub>
+and so on. Then corresponding to the series</p>
+
+<p class="center">
+<i>e</i><sub>1</sub>, <i>e</i><sub>2</sub>, <i>e</i><sub>3</sub>, &#8230;, <i>e</i><sub><i>n</i></sub>, <i>e</i><sub><i>n</i>+1</sub>, &#8230;,
+</p>
+
+<p>there is the series</p>
+
+<p class="center"><i>q</i>(<i>e</i><sub>1</sub>), <i>q</i>(<i>e</i><sub>2</sub>), <i>q</i>(<i>e</i><sub>3</sub>), &#8230;, <i>q</i>(<i>e</i><sub><i>n</i></sub>), <i>q</i>(<i>e</i><sub><i>n</i>+1</sub>), &#8230;.
+</p>
+
+<p>Call the series of events <i>s</i> and the series of quantitative expressions
+<i>q</i>(<i>s</i>). The series <i>s</i> has no last term and<span class="pagenum" title="Page&nbsp;81">&nbsp;</span><a name="Page_81" id="Page_81"></a> no events which are
+contained in every member of the series. Accordingly the series of
+events converges to nothing. It is just itself. Also the series <i>q</i>(<i>s</i>)
+has no last term. But the sets of homologous quantities running through
+the various terms of the series do converge to definite limits. For
+example if <i>Q</i><sub>1</sub> be a quantitative measurement found in <i>q</i>(<i>e</i><sub>1</sub>),
+and <i>Q</i><sub>2</sub> the homologue to <i>Q</i><sub>1</sub> to be found in <i>q</i>(<i>e</i><sub>2</sub>), and
+<i>Q</i><sub>3</sub> the homologue to <i>Q</i><sub>1</sub> and <i>Q</i><sub>2</sub> to be found in
+<i>q</i>(<i>e</i><sub>3</sub>), and so on, then the series</p>
+
+<p class="center"><i>Q</i><sub>1</sub>, <i>Q</i><sub>2</sub>, <i>Q</i><sub>3</sub>, &#8230;, <i>Q</i><sub><i>n</i></sub>, <i>Q</i><sub><i>n</i>+1</sub>, &#8230;,</p>
+
+<p>though it has no last term, does in general converge to a definite
+limit. Accordingly there is a class of limits <i>l</i>(<i>s</i>) which is the
+class of the limits of those members of <i>q</i>(<i>e</i><sub><i>n</i></sub>) which have
+homologues throughout the series <i>q</i>(<i>s</i>) as <i>n</i> indefinitely increases.
+We can represent this statement diagrammatically by using an arrow (&#8594;)
+to mean &lsquo;converges to.&rsquo; Then</p>
+
+<p class="center"><i>e</i><sub>1</sub>, <i>e</i><sub>2</sub>, <i>e</i><sub>3</sub>, &#8230;, <i>e</i><sub><i>n</i></sub>, <i>e</i><sub><i>n</i>+1</sub>, &#8230; &#8594; nothing,</p>
+
+<p>and</p>
+
+<p class="center"><i>q</i>(<i>e</i><sub>1</sub>), <i>q</i>(<i>e</i><sub>2</sub>), <i>q</i>(<i>e</i><sub>3</sub>), &#8230;, <i>q</i>(<i>e</i><sub><i>n</i></sub>),
+<i>q</i>(<i>e</i><sub><i>n</i>+1</sub>), &#8230; &#8594; <i>l</i>(<i>s</i>).</p>
+
+<p>The mutual relations between the limits in the set <i>l</i>(<i>s</i>), and also
+between these limits and the limits in other sets <i>l</i>(<i>s</i>&#8242;), <i>l</i>(<i>s</i>&#8243;),
+&#8230;, which arise from other abstractive sets <i>s</i>&#8242;, <i>s</i>&#8243;, etc., have a
+peculiar simplicity.</p>
+
+<p>Thus the set <i>s</i> does indicate an ideal simplicity of natural relations,
+though this simplicity is not the character of any actual event in <i>s</i>.
+We can make an approximation to such a simplicity which, as estimated
+numerically, is as close as we like by considering an event which is far
+enough down the series towards the small end. It will be noted that it
+is the infinite series,<span class="pagenum" title="Page&nbsp;82">&nbsp;</span><a name="Page_82" id="Page_82"></a> as it stretches away in unending succession
+towards the small end, which is of importance. The arbitrarily large
+event with which the series starts has no importance at all. We can
+arbitrarily exclude any set of events at the big end of an abstractive
+set without the loss of any important property to the set as thus
+modified.</p>
+
+<p>I call the limiting character of natural relations which is indicated by
+an abstractive set, the &lsquo;intrinsic character&rsquo; of the set; also the
+properties, connected with the relation of whole and part as concerning
+its members, by which an abstractive set is defined together form what I
+call its &lsquo;extrinsic character.&rsquo; The fact that the extrinsic character of
+an abstractive set determines a definite intrinsic character is the
+reason of the importance of the precise concepts of space and time. This
+emergence of a definite intrinsic character from an abstractive set is
+the precise meaning of the law of convergence.</p>
+
+<p>For example, we see a train approaching during a minute. The event which
+is the life of nature within that train during the minute is of great
+complexity and the expression of its relations and of the ingredients of
+its character baffles us. If we take one second of that minute, the more
+limited event which is thus obtained is simpler in respect to its
+ingredients, and shorter and shorter times such as a tenth of that
+second, or a hundredth, or a thousandth&mdash;so long as we have a definite
+rule giving a definite succession of diminishing events&mdash;give events
+whose ingredient characters converge to the ideal simplicity of the
+character of the train at a definite instant. Furthermore there are
+different types of such convergence to simplicity. For example, we can
+converge as above to the limiting character<span class="pagenum" title="Page&nbsp;83">&nbsp;</span><a name="Page_83" id="Page_83"></a> expressing nature at an
+instant within the whole volume of the train at that instant, or to
+nature at an instant within some portion of that volume&mdash;for example
+within the boiler of the engine&mdash;or to nature at an instant on some area
+of surface, or to nature at an instant on some line within the train, or
+to nature at an instant at some point of the train. In the last case the
+simple limiting characters arrived at will be expressed as densities,
+specific gravities, and types of material. Furthermore we need not
+necessarily converge to an abstraction which involves nature at an
+instant. We may converge to the physical ingredients of a certain point
+track throughout the whole minute. Accordingly there are different types
+of extrinsic character of convergence which lead to the approximation to
+different types of intrinsic characters as limits.</p>
+
+<p>We now pass to the investigation of possible connexions between
+abstractive sets. One set may &lsquo;cover&rsquo; another. I define &lsquo;covering&rsquo; as
+follows: An abstractive set <i>p</i> covers an abstractive set <i>q</i> when every
+member of <i>p</i> contains as its parts some members of <i>q</i>. It is evident
+that if any event <i>e</i> contains as a part any member of the set <i>q</i>, then
+owing to the transitive property of extension every succeeding member of
+the small end of <i>q</i> is part of <i>e</i>. In such a case I will say that the
+abstractive set <i>q</i> &lsquo;inheres in&rsquo; the event <i>e</i>. Thus when an abstractive
+set <i>p</i> covers an abstractive set <i>q</i>, the abstractive set <i>q</i> inheres
+in every member of <i>p</i>.</p>
+
+<p>Two abstractive sets may each cover the other. When this is the case I
+shall call the two sets &lsquo;equal in abstractive force.&rsquo; When there is no
+danger of misunderstanding I shall shorten this phrase by simply saying
+that the two abstractive sets are &lsquo;equal.&rsquo; The possibility<span class="pagenum" title="Page&nbsp;84">&nbsp;</span><a name="Page_84" id="Page_84"></a> of this
+equality of abstractive sets arises from the fact that both sets, <i>p</i>
+and <i>q</i>, are infinite series towards their small ends. Thus the equality
+means, that given any event <i>x</i> belonging to <i>p</i>, we can always by
+proceeding far enough towards the small end of <i>q</i> find an event <i>y</i>
+which is part of <i>x</i>, and that then by proceeding far enough towards the
+small end of <i>p</i> we can find an event <i>z</i> which is part of <i>y</i>, and so
+on indefinitely.</p>
+
+<p>The importance of the equality of abstractive sets arises from the
+assumption that the intrinsic characters of the two sets are identical.
+If this were not the case exact observation would be at an end.</p>
+
+<p>It is evident that any two abstractive sets which are equal to a third
+abstractive set are equal to each other. An &lsquo;abstractive element&rsquo; is the
+whole group of abstractive sets which are equal to any one of
+themselves. Thus all abstractive sets belonging to the same element are
+equal and converge to the same intrinsic character. Thus an abstractive
+element is the group of routes of approximation to a definite intrinsic
+character of ideal simplicity to be found as a limit among natural
+facts.</p>
+
+<p>If an abstractive set <i>p</i> covers an abstractive set <i>q</i>, then any
+abstractive set belonging to the abstractive element of which <i>p</i> is a
+member will cover any abstractive set belonging to the element of which
+<i>q</i> is a member. Accordingly it is useful to stretch the meaning of the
+term &lsquo;covering,&rsquo; and to speak of one abstractive element &lsquo;covering&rsquo;
+another abstractive element. If we attempt in like manner to stretch the
+term &lsquo;equal&rsquo; in the sense of &lsquo;equal in abstractive force,&rsquo; it is obvious
+that an abstractive element can only be equal to itself. Thus an
+abstractive element has a unique abstractive force and is the construct
+from events which represents one definite<span class="pagenum" title="Page&nbsp;85">&nbsp;</span><a name="Page_85" id="Page_85"></a> intrinsic character which is
+arrived at as a limit by the use of the principle of convergence to
+simplicity by diminution of extent.</p>
+
+<p>When an abstractive element <i>A</i> covers an abstractive element <i>B</i>, the
+intrinsic character of <i>A</i> in a sense includes the intrinsic character
+of <i>B</i>. It results that statements about the intrinsic character of <i>B</i>
+are in a sense statements about the intrinsic character of <i>A</i>; but the
+intrinsic character of <i>A</i> is more complex than that of <i>B</i>.</p>
+
+<p>The abstractive elements form the fundamental elements of space and
+time, and we now turn to the consideration of the properties involved in
+the formation of special classes of such elements. In my last lecture I
+have already investigated one class of abstractive elements, namely
+moments. Each moment is a group of abstractive sets, and the events
+which are members of these sets are all members of one family of
+durations. The moments of one family form a temporal series; and,
+allowing the existence of different families of moments, there will be
+alternative temporal series in nature. Thus the method of extensive
+abstraction explains the origin of temporal series in terms of the
+immediate facts of experience and at the same time allows for the
+existence of the alternative temporal series which are demanded by the
+modern theory of electromagnetic relativity.</p>
+
+<p>We now turn to space. The first thing to do is to get hold of the class
+of abstractive elements which are in some sense the points of space.
+Such an abstractive element must in some sense exhibit a convergence to
+an absolute minimum of intrinsic character. Euclid has expressed for all
+time the general idea of a point,<span class="pagenum" title="Page&nbsp;86">&nbsp;</span><a name="Page_86" id="Page_86"></a> as being without parts and without
+magnitude. It is this character of being an absolute minimum which we
+want to get at and to express in terms of the extrinsic characters of
+the abstractive sets which make up a point. Furthermore, points which
+are thus arrived at represent the ideal of events without any extension,
+though there are in fact no such entities as these ideal events. These
+points will not be the points of an external timeless space but of
+instantaneous spaces. We ultimately want to arrive at the timeless space
+of physical science, and also of common thought which is now tinged with
+the concepts of science. It will be convenient to reserve the term
+&lsquo;point&rsquo; for these spaces when we get to them. I will therefore use the
+name &lsquo;event-particles&rsquo; for the ideal minimum limits to events. Thus an
+event-particle is an abstractive element and as such is a group of
+abstractive sets; and a point&mdash;namely a point of timeless space&mdash;will be
+a class of event-particles.</p>
+
+<p>Furthermore there is a separate timeless space corresponding to each
+separate temporal series, that is to each separate family of durations.
+We will come back to points in timeless spaces later. I merely mention
+them now that we may understand the stages of our investigation. The
+totality of event-particles will form a four-dimensional manifold, the
+extra dimension arising from time&mdash;in other words&mdash;arising from the
+points of a timeless space being each a class of event-particles.</p>
+
+<p>The required character of the abstractive sets which form
+event-particles would be secured if we could define them as having the
+property of being covered by any abstractive set which they cover. For
+then any other abstractive set which an abstractive set of an
+event-particle covered, would be equal to it, and would<span class="pagenum" title="Page&nbsp;87">&nbsp;</span><a name="Page_87" id="Page_87"></a> therefore be a
+member of the same event-particle. Accordingly an event-particle could
+cover no other abstractive element. This is the definition which I
+originally proposed at a congress in Paris in 1914<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a>. There is however
+a difficulty involved in this definition if adopted without some further
+addition, and I am now not satisfied with the way in which I attempted
+to get over that difficulty in the paper referred to.</p>
+
+<div class="footnote"><p><a name="Footnote_9_9" id="Footnote_9_9"></a><span class="label"><a href="#FNanchor_9_9">[9]</a></span> Cf. &lsquo;La Th&eacute;orie Relationniste de l&#8217;Espace,&rsquo; <i>Rev. de
+M&eacute;taphysique et de Morale</i>, vol.&nbsp;XXIII, 1916.</p></div>
+
+<p>The difficulty is this: When event-particles have once been defined it
+is easy to define the aggregate of event-particles forming the boundary
+of an event; and thence to define the point-contact at their boundaries
+possible for a pair of events of which one is part of the other. We can
+then conceive all the intricacies of tangency. In particular we can
+conceive an abstractive set of which all the members have point-contact
+at the same event-particle. It is then easy to prove that there will be
+no abstractive set with the property of being covered by every
+abstractive set which it covers. I state this difficulty at some length
+because its existence guides the development of our line of argument. We
+have got to annex some condition to the root property of being covered
+by any abstractive set which it covers. When we look into this question
+of suitable conditions we find that in addition to event-particles all
+the other relevant spatial and spatio-temporal abstractive elements can
+be defined in the same way by suitably varying the conditions.
+Accordingly we proceed in a general way suitable for employment beyond
+event-particles.</p>
+
+<p>Let &#963; be the name of any condition which some abstractive sets fulfil. I
+say that an abstractive set is<span class="pagenum" title="Page&nbsp;88">&nbsp;</span><a name="Page_88" id="Page_88"></a> &lsquo;&#963;-prime&rsquo; when it has the two
+properties, (i) that it satisfies the condition &#963; and (ii) that it is
+covered by every abstractive set which both is covered by it and
+satisfies the condition &#963;.</p>
+
+<p>In other words you cannot get any abstractive set satisfying the
+condition &#963; which exhibits intrinsic character more simple than that of
+a &#963;-prime.</p>
+
+<p>There are also the correlative abstractive sets which I call the sets of
+&#963;-antiprimes. An abstractive set is a &#963;-antiprime when it has the two
+properties, (i) that it satisfies the condition &#963; and (ii) that it
+covers every abstractive set which both covers it and satisfies the
+condition &#963;. In other words you cannot get any abstractive set
+satisfying the condition &#963; which exhibits an intrinsic character more
+complex than that of a &#963;-antiprime.</p>
+
+<p>The intrinsic character of a &#963;-prime has a certain minimum of fullness
+among those abstractive sets which are subject to the condition of
+satisfying &#963;; whereas the intrinsic character of a &#963;-antiprime has a
+corresponding maximum of fullness, and includes all it can in the
+circumstances.</p>
+
+<p>Let us first consider what help the notion of antiprimes could give us
+in the definition of moments which we gave in the last lecture. Let the
+condition &#963; be the property of being a class whose members are all
+durations. An abstractive set which satisfies this condition is thus an
+abstractive set composed wholly of durations. It is convenient then to
+define a moment as the group of abstractive sets which are equal to some
+&#963;-antiprime, where the condition &#963; has this special meaning. It will be
+found on consideration (i) that each abstractive set forming a moment is
+a &#963;-antiprime,<span class="pagenum" title="Page&nbsp;89">&nbsp;</span><a name="Page_89" id="Page_89"></a> where &#963; has this special meaning, and (ii) that we have
+excluded from membership of moments abstractive sets of durations which
+all have one common boundary, either the initial boundary or the final
+boundary. We thus exclude special cases which are apt to confuse general
+reasoning. The new definition of a moment, which supersedes our previous
+definition, is (by the aid of the notion of antiprimes) the more
+precisely drawn of the two, and the more useful.</p>
+
+<p>The particular condition which &lsquo;&#963;&rsquo; stood for in the definition of
+moments included something additional to anything which can be derived
+from the bare notion of extension. A duration exhibits for thought a
+totality. The notion of totality is something beyond that of extension,
+though the two are interwoven in the notion of a duration.</p>
+
+<p>In the same way the particular condition &lsquo;&#963;&rsquo; required for the definition
+of an event-particle must be looked for beyond the mere notion of
+extension. The same remark is also true of the particular conditions
+requisite for the other spatial elements. This additional notion is
+obtained by distinguishing between the notion of &lsquo;position&rsquo; and the
+notion of convergence to an ideal zero of extension as exhibited by an
+abstractive set of events.</p>
+
+<p>In order to understand this distinction consider a point of the
+instantaneous space which we conceive as apparent to us in an almost
+instantaneous glance. This point is an event-particle. It has two
+aspects. In one aspect it is there, where it is. This is its position in
+the space. In another aspect it is got at by ignoring the circumambient
+space, and by concentrating attention on the smaller and smaller set of
+events which approximate to it. This is its extrinsic character. Thus a
+point has<span class="pagenum" title="Page&nbsp;90">&nbsp;</span><a name="Page_90" id="Page_90"></a> three characters, namely, its position in the whole
+instantaneous space, its extrinsic character, and its intrinsic
+character. The same is true of any other spatial element. For example an
+instantaneous volume in instantaneous space has three characters,
+namely, its position, its extrinsic character as a group of abstractive
+sets, and its intrinsic character which is the limit of natural
+properties which is indicated by any one of these abstractive sets.</p>
+
+<p>Before we can talk about position in instantaneous space, we must
+evidently be quite clear as to what we mean by instantaneous space in
+itself. Instantaneous space must be looked for as a character of a
+moment. For a moment is all nature at an instant. It cannot be the
+intrinsic character of the moment. For the intrinsic character tells us
+the limiting character of nature in space at that instant. Instantaneous
+space must be an assemblage of abstractive elements considered in their
+mutual relations. Thus an instantaneous space is the assemblage of
+abstractive elements covered by some one moment, and it is the
+instantaneous space of that moment.</p>
+
+<p>We have now to ask what character we have found in nature which is
+capable of according to the elements of an instantaneous space different
+qualities of position. This question at once brings us to the
+intersection of moments, which is a topic not as yet considered in these
+lectures.</p>
+
+<p>The locus of intersection of two moments is the assemblage of
+abstractive elements covered by both of them. Now two moments of the
+same temporal series cannot intersect. Two moments respectively of
+different families necessarily intersect. Accordingly in the
+in<span class="pagenum" title="Page&nbsp;91">&nbsp;</span><a name="Page_91" id="Page_91"></a>stantaneous space of a moment we should expect the fundamental
+properties to be marked by the intersections with moments of other
+families. If <i>M</i> be a given moment, the intersection of <i>M</i> with another
+moment <i>A</i> is an instantaneous plane in the instantaneous space of <i>M</i>;
+and if <i>B</i> be a third moment intersecting both <i>M</i> and <i>A</i>, the
+intersection of <i>M</i> and <i>B</i> is another plane in the space <i>M</i>. Also the
+common intersection of <i>A</i>, <i>B</i>, and <i>M</i> is the intersection of the two
+planes in the space <i>M</i>, namely it is a straight line in the space <i>M</i>.
+An exceptional case arises if <i>B</i> and <i>M</i> intersect in the same plane as
+<i>A</i> and <i>M</i>. Furthermore if <i>C</i> be a fourth moment, then apart from
+special cases which we need not consider, it intersects <i>M</i> in a plane
+which the straight line (<i>A</i>, <i>B</i>, <i>M</i>) meets. Thus there is in general
+a common intersection of four moments of different families. This common
+intersection is an assemblage of abstractive elements which are each
+covered (or &lsquo;lie in&rsquo;) all four moments. The three-dimensional property
+of instantaneous space comes to this, that (apart from special relations
+between the four moments) any fifth moment either contains the whole of
+their common intersection or none of it. No further subdivision of the
+common intersection is possible by means of moments. The &lsquo;all or none&rsquo;
+principle holds. This is not an <i>&agrave;&nbsp;priori</i> truth but an empirical fact
+of nature.</p>
+
+<p>It will be convenient to reserve the ordinary spatial terms &lsquo;plane,&rsquo;
+&lsquo;straight line,&rsquo; &lsquo;point&rsquo; for the elements of the timeless space of a
+time-system. Accordingly an instantaneous plane in the instantaneous
+space of a moment will be called a &lsquo;level,&rsquo; an instantaneous straight
+line will be called a &lsquo;rect,&rsquo; and an instantaneous point<span class="pagenum" title="Page&nbsp;92">&nbsp;</span><a name="Page_92" id="Page_92"></a> will be called
+a &lsquo;punct.&rsquo; Thus a punct is the assemblage of abstractive elements which
+lie in each of four moments whose families have no special relations to
+each other. Also if <i>P</i> be any moment, either every abstractive element
+belonging to a given punct lies in <i>P</i>, or no abstractive element of
+that punct lies in <i>P</i>.</p>
+
+<p>Position is the quality which an abstractive element possesses in virtue
+of the moments in which it lies. The abstractive elements which lie in
+the instantaneous space of a given moment <i>M</i> are differentiated from
+each other by the various other moments which intersect <i>M</i> so as to
+contain various selections of these abstractive elements. It is this
+differentiation of the elements which constitutes their differentiation
+of position. An abstractive element which belongs to a punct has the
+simplest type of position in <i>M</i>, an abstractive element which belongs
+to a rect but not to a punct has a more complex quality of position, an
+abstractive element which belongs to a level and not to a rect has a
+still more complex quality of position, and finally the most complex
+quality of position belongs to an abstractive element which belongs to a
+volume and not to a level. A volume however has not yet been defined.
+This definition will be given in the next lecture.</p>
+
+<p>Evidently levels, rects, and puncts in their capacity as infinite
+aggregates cannot be the termini of sense-awareness, nor can they be
+limits which are approximated to in sense-awareness. Any one member of a
+level has a certain quality arising from its character as also belonging
+to a certain set of moments, but the level as a whole is a mere logical
+notion without any route of approximation along entities posited in
+sense-awareness.</p>
+
+<p>On the other hand an event-particle is defined so as<span class="pagenum" title="Page&nbsp;93">&nbsp;</span><a name="Page_93" id="Page_93"></a> to exhibit this
+character of being a route of approximation marked out by entities
+posited in sense-awareness. A definite event-particle is defined in
+reference to a definite punct in the following manner: Let the condition
+&#963; mean the property of covering all the abstractive elements which are
+members of that punct; so that an abstractive set which satisfies the
+condition &#963; is an abstractive set which covers every abstractive element
+belonging to the punct. Then the definition of the event-particle
+associated with the punct is that it is the group of all the &#963;-primes,
+where &#963; has this particular meaning.</p>
+
+<p>It is evident that&mdash;with this meaning of &#963;&mdash;every abstractive set equal
+to a &#963;-prime is itself a &#963;-prime. Accordingly an event-particle as thus
+defined is an abstractive element, namely it is the group of those
+abstractive sets which are each equal to some given abstractive set. If
+we write out the definition of the event-particle associated with some
+given punct, which we will call &#960;, it is as follows: The event-particle
+associated with &#960; is the group of abstractive classes each of which has
+the two properties (i) that it covers every abstractive set in &#960; and
+(ii) that all the abstractive sets which also satisfy the former
+condition as to &#960; and which it covers, also cover it.</p>
+
+<p>An event-particle has position by reason of its association with a
+punct, and conversely the punct gains its derived character as a route
+of approximation from its association with the event-particle. These two
+characters of a point are always recurring in any treatment of the
+derivation of a point from the observed facts of nature, but in general
+there is no clear recognition of their distinction.</p>
+
+<p><span class="pagenum" title="Page&nbsp;94">&nbsp;</span><a name="Page_94" id="Page_94"></a>The peculiar simplicity of an instantaneous point has a twofold origin,
+one connected with position, that is to say with its character as a
+punct, and the other connected with its character as an event-particle.
+The simplicity of the punct arises from its indivisibility by a moment.</p>
+
+<p>The simplicity of an event-particle arises from the indivisibility of
+its intrinsic character. The intrinsic character of an event-particle is
+indivisible in the sense that every abstractive set covered by it
+exhibits the same intrinsic character. It follows that, though there are
+diverse abstractive elements covered by event-particles, there is no
+advantage to be gained by considering them since we gain no additional
+simplicity in the expression of natural properties.</p>
+
+<p>These two characters of simplicity enjoyed respectively by
+event-particles and puncts define a meaning for Euclid&#8217;s phrase,
+&lsquo;without parts and without magnitude.&rsquo;</p>
+
+<p>It is obviously convenient to sweep away out of our thoughts all these
+stray abstractive sets which are covered by event-particles without
+themselves being members of them. They give us nothing new in the way of
+intrinsic character. Accordingly we can think of rects and levels as
+merely loci of event-particles. In so doing we are also cutting out
+those abstractive elements which cover sets of event-particles, without
+these elements being event-particles themselves. There are classes of
+these abstractive elements which are of great importance. I will
+consider them later on in this and in other lectures. Meanwhile we will
+ignore them. Also I will always speak of &lsquo;event-particles&rsquo; in preference
+to &lsquo;puncts,&rsquo; the latter being an artificial word for which I have no
+great affection.</p>
+
+<p><span class="pagenum" title="Page&nbsp;95">&nbsp;</span><a name="Page_95" id="Page_95"></a>Parallelism among rects and levels is now explicable.</p>
+
+<p>Consider the instantaneous space belonging to a moment <i>A</i>, and let <i>A</i>
+belong to the temporal series of moments which I will call &#945;. Consider
+any other temporal series of moments which I will call &#946;. The moments of
+&#946; do not intersect each other and they intersect the moment <i>A</i> in a
+family of levels. None of these levels can intersect, and they form a
+family of parallel instantaneous planes in the instantaneous space of
+moment <i>A</i>. Thus the parallelism of moments in a temporal series begets
+the parallelism of levels in an instantaneous space, and thence&mdash;as it
+is easy to see&mdash;the parallelism of rects. Accordingly the Euclidean
+property of space arises from the parabolic property of time. It may be
+that there is reason to adopt a hyperbolic theory of time and a
+corresponding hyperbolic theory of space. Such a theory has not been
+worked out, so it is not possible to judge as to the character of the
+evidence which could be brought forward in its favour.</p>
+
+<p>The theory of order in an instantaneous space is immediately derived
+from time-order. For consider the space of a moment <i>M</i>. Let &#945; be the
+name of a time-system to which <i>M</i> does not belong. Let <i>A<sub>1</sub></i>,
+<i>A<sub>2</sub></i>, <i>A<sub>3</sub></i> etc. be moments of &#945; in the order of their occurrences.
+Then <i>A<sub>1</sub></i>, <i>A<sub>2</sub></i>, <i>A<sub>3</sub></i>, etc. intersect <i>M</i> in parallel levels
+<i>l<sub>1</sub></i>, <i>l<sub>2</sub></i>, <i>l<sub>3</sub></i>, etc. Then the relative order of the parallel
+levels in the space of <i>M</i> is the same as the relative order of the
+corresponding moments in the time-system &#945;. Any rect in <i>M</i> which
+intersects all these levels in its set of puncts, thereby receives for
+its puncts an order of position on it. So spatial order is derivative
+from temporal order. Furthermore there are alternative time-systems, but
+there is only one definite spatial order in each instan<span class="pagenum" title="Page&nbsp;96">&nbsp;</span><a name="Page_96" id="Page_96"></a>taneous space.
+Accordingly the various modes of deriving spatial order from diverse
+time-systems must harmonise with one spatial order in each instantaneous
+space. In this way also diverse time-orders are comparable.</p>
+
+<p>We have two great questions still on hand to be settled before our
+theory of space is fully adjusted. One of these is the question of the
+determination of the methods of measurement within the space, in other
+words, the congruence-theory of the space. The measurement of space will
+be found to be closely connected with the measurement of time, with
+respect to which no principles have as yet been determined. Thus our
+congruence-theory will be a theory both for space and for time. Secondly
+there is the determination of the timeless space which corresponds to
+any particular time-system with its infinite set of instantaneous spaces
+in its successive moments. This is the space&mdash;or rather, these are the
+spaces&mdash;of physical science. It is very usual to dismiss this space by
+saying that this is conceptual. I do not understand the virtue of these
+phrases. I suppose that it is meant that the space is the conception of
+something in nature. Accordingly if the space of physical science is to
+be called conceptual, I ask, What in nature is it the conception of? For
+example, when we speak of a point in the timeless space of physical
+science, I suppose that we are speaking of something in nature. If we
+are not so speaking, our scientists are exercising their wits in the
+realms of pure fantasy, and this is palpably not the case. This demand
+for a definite Habeas Corpus Act for the production of the relevant
+entities in nature applies whether space be relative or absolute. On the
+theory of relative<span class="pagenum" title="Page&nbsp;97">&nbsp;</span><a name="Page_97" id="Page_97"></a> space, it may perhaps be argued that there is no
+timeless space for physical science, and that there is only the
+momentary series of instantaneous spaces.</p>
+
+<p>An explanation must then be asked for the meaning of the very common
+statement that such and such a man walked four miles in some definite
+hour. How can you measure distance from one space into another space? I
+understand walking out of the sheet of an ordnance map. But the meaning
+of saying that Cambridge at 10&nbsp;o&#8217;clock this morning in the appropriate
+instantaneous space for that instant is 52&nbsp;miles from London at
+11&nbsp;o&#8217;clock this morning in the appropriate instantaneous space for that
+instant beats me entirely. I think that, by the time a meaning has been
+produced for this statement, you will find that you have constructed
+what is in fact a timeless space. What I cannot understand is how to
+produce an explanation of meaning without in effect making some such
+construction. Also I may add that I do not know how the instantaneous
+spaces are thus correlated into one space by any method which is
+available on the current theories of space.</p>
+
+<p>You will have noticed that by the aid of the assumption of alternative
+time-systems, we are arriving at an explanation of the character of
+space. In natural science &lsquo;to explain&rsquo; means merely to discover
+&lsquo;interconnexions.&rsquo; For example, in one sense there is no explanation of
+the red which you see. It is red, and there is nothing else to be said
+about it. Either it is posited before you in sense-awareness or you are
+ignorant of the entity red. But science has explained red. Namely it has
+discovered interconnexions between red as a factor in nature and other
+factors in nature, for example waves of light which are waves of
+electromagnetic disturbances.<span class="pagenum" title="Page&nbsp;98">&nbsp;</span><a name="Page_98" id="Page_98"></a> There are also various pathological
+states of the body which lead to the seeing of red without the
+occurrence of light waves. Thus connexions have been discovered between
+red as posited in sense-awareness and various other factors in nature.
+The discovery of these connexions constitutes the scientific explanation
+of our vision of colour. In like manner the dependence of the character
+of space on the character of time constitutes an explanation in the
+sense in which science seeks to explain. The systematising intellect
+abhors bare facts. The character of space has hitherto been presented as
+a collection of bare facts, ultimate and disconnected. The theory which
+I am expounding sweeps away this disconnexion of the facts of space.</p>
+<hr />
+
+<h2><span class="pagenum" title="Page&nbsp;99">&nbsp;</span><a name="Page_99" id="Page_99"></a><a name="CHAPTER_V" id="CHAPTER_V"></a>CHAPTER V
+<br />
+SPACE AND MOTION</h2>
+
+
+<p>The topic for this lecture is the continuation of the task of explaining
+the construction of spaces as abstracts from the facts of nature. It was
+noted at the close of the previous lecture that the question of
+congruence had not been considered, nor had the construction of a
+timeless space which should correlate the successive momentary spaces of
+a given time-system. Furthermore it was also noted that there were many
+spatial abstractive elements which we had not yet defined. We will first
+consider the definition of some of these abstractive elements, namely
+the definitions of solids, of areas, and of routes. By a &lsquo;route&rsquo; I mean
+a linear segment, whether straight or curved. The exposition of these
+definitions and the preliminary explanations necessary will, I hope,
+serve as a general explanation of the function of event-particles in the
+analysis of nature.</p>
+
+<p>We note that event-particles have &lsquo;position&rsquo; in respect to each other.
+In the last lecture I explained that &lsquo;position&rsquo; was quality gained by a
+spatial element in virtue of the intersecting moments which covered it.
+Thus each event-particle has position in this sense. The simplest mode
+of expressing the position in nature of an event-particle is by first
+fixing on any definite time-system. Call it &#945;. There will be one moment
+of the temporal series of &#945; which covers the given event-particle. Thus
+the position of the event-particle in the temporal series &#945; is defined
+by this moment, which we<span class="pagenum" title="Page&nbsp;100">&nbsp;</span><a name="Page_100" id="Page_100"></a> will call <i>M</i>. The position of the particle in
+the space of <i>M</i> is then fixed in the ordinary way by three levels which
+intersect in it and in it only. This procedure of fixing the position of
+an event-particle shows that the aggregate of event-particles forms a
+four-dimensional manifold. A finite event occupies a limited chunk of
+this manifold in a sense which I now proceed to explain.</p>
+
+<p>Let <i>e</i> be any given event. The manifold of event-particles falls into
+three sets in reference to <i>e</i>. Each event-particle is a group of equal
+abstractive sets and each abstractive set towards its small-end is
+composed of smaller and smaller finite events. When we select from these
+finite events which enter into the make-up of a given event-particle
+those which are small enough, one of three cases must occur. Either (i)
+all of these small events are entirely separate from the given event
+<i>e</i>, or (ii) all of these small events are parts of the event <i>e</i>, or
+(iii) all of these small events overlap the event <i>e</i> but are not parts
+of it. In the first case the event-particle will be said to &lsquo;lie
+outside&rsquo; the event <i>e</i>, in the second case the event-particle will be
+said to &lsquo;lie inside&rsquo; the event <i>e</i>, and in the third case the
+event-particle will be said to be a &lsquo;boundary-particle&rsquo; of the event
+<i>e</i>. Thus there are three sets of particles, namely the set of those
+which lie outside the event <i>e</i>, the set of those which lie inside the
+event <i>e</i>, and the boundary of the event <i>e</i> which is the set of
+boundary-particles of <i>e</i>. Since an event is four-dimensional, the
+boundary of an event is a three-dimensional manifold. For a finite event
+there is a continuity of boundary; for a duration the boundary consists
+of those event-particles which are covered by either of the two bounding
+moments. Thus the boundary of a duration consists of two momentary
+three-dimen<span class="pagenum" title="Page&nbsp;101">&nbsp;</span><a name="Page_101" id="Page_101"></a>sional spaces. An event will be said to &lsquo;occupy&rsquo; the
+aggregate of event-particles which lie within it.</p>
+
+<p>Two events which have &lsquo;junction&rsquo; in the sense in which junction was
+described in my last lecture, and yet are separated so that neither
+event either overlaps or is part of the other event, are said to be
+&lsquo;adjoined.&rsquo;</p>
+
+<p>This relation of adjunction issues in a peculiar relation between the
+boundaries of the two events. The two boundaries must have a common
+portion which is in fact a continuous three-dimensional locus of
+event-particles in the four-dimensional manifold.</p>
+
+<p>A three-dimensional locus of event-particles which is the common portion
+of the boundary of two adjoined events will be called a &lsquo;solid.&rsquo; A solid
+may or may not lie completely in one moment. A solid which does not lie
+in one moment will be called &lsquo;vagrant.&rsquo; A solid which does lie in one
+moment will be called a volume. A volume may be defined as the locus of
+the event-particles in which a moment intersects an event, provided that
+the two do intersect. The intersection of a moment and an event will
+evidently consist of those event-particles which are covered by the
+moment and lie in the event. The identity of the two definitions of a
+volume is evident when we remember that an intersecting moment divides
+the event into two adjoined events.</p>
+
+<p>A solid as thus defined, whether it be vagrant or be a volume, is a mere
+aggregate of event-particles illustrating a certain quality of position.
+We can also define a solid as an abstractive element. In order to do so
+we recur to the theory of primes explained in the preceding lecture. Let
+the condition named &#963; stand for the fact that each of the events of any
+abstractive set satisfying it has all the event-particles of some
+particular solid lying<span class="pagenum" title="Page&nbsp;102">&nbsp;</span><a name="Page_102" id="Page_102"></a> in it. Then the group of all the &#963;-primes is the
+abstractive element which is associated with the given solid. I will
+call this abstractive element the solid as an abstractive element, and I
+will call the aggregate of event-particles the solid as a locus. The
+instantaneous volumes in instantaneous space which are the ideals of our
+sense-perception are volumes as abstractive elements. What we really
+perceive with all our efforts after exactness are small events far
+enough down some abstractive set belonging to the volume as an
+abstractive element.</p>
+
+<p>It is difficult to know how far we approximate to any perception of
+vagrant solids. We certainly do not think that we make any such
+approximation. But then our thoughts&mdash;in the case of people who do think
+about such topics&mdash;are so much under the control of the materialistic
+theory of nature that they hardly count for evidence. If Einstein&#8217;s
+theory of gravitation has any truth in it, vagrant solids are of great
+importance in science. The whole boundary of a finite event may be
+looked on as a particular example of a vagrant solid as a locus. Its
+particular property of being closed prevents it from being definable as
+an abstractive element.</p>
+
+<p>When a moment intersects an event, it also intersects the boundary of
+that event. This locus, which is the portion of the boundary contained
+in the moment, is the bounding surface of the corresponding volume of
+that event contained in the moment. It is a two-dimensional locus.</p>
+
+<p>The fact that every volume has a bounding surface is the origin of the
+Dedekindian continuity of space.</p>
+
+<p>Another event may be cut by the same moment in another volume and this
+volume will also have its boundary. These two volumes in the
+instantaneous<span class="pagenum" title="Page&nbsp;103">&nbsp;</span><a name="Page_103" id="Page_103"></a> space of one moment may mutually overlap in the familiar
+way which I need not describe in detail and thus cut off portions from
+each other&#8217;s surfaces. These portions of surfaces are &lsquo;momental areas.&rsquo;</p>
+
+<p>It is unnecessary at this stage to enter into the complexity of a
+definition of vagrant areas. Their definition is simple enough when the
+four-dimensional manifold of event-particles has been more fully
+explored as to its properties.</p>
+
+<p>Momental areas can evidently be defined as abstractive elements by
+exactly the same method as applied to solids. We have merely to
+substitute &lsquo;area&rsquo; for a &lsquo;solid&rsquo; in the words of the definition already
+given. Also, exactly as in the analogous case of a solid, what we
+perceive as an approximation to our ideal of an area is a small event
+far enough down towards the small end of one of the equal abstractive
+sets which belongs to the area as an abstractive element.</p>
+
+<p>Two momental areas lying in the same moment can cut each other in a
+momental segment which is not necessarily rectilinear. Such a segment
+can also be defined as an abstractive element. It is then called a
+&lsquo;momental route.&rsquo; We will not delay over any general consideration of
+these momental routes, nor is it important for us to proceed to the
+still wider investigation of vagrant routes in general. There are
+however two simple sets of routes which are of vital importance. One is
+a set of momental routes and the other of vagrant routes. Both sets can
+be classed together as straight routes. We proceed to define them
+without any reference to the definitions of volumes and surfaces.</p>
+
+<p>The two types of straight routes will be called rectilinear routes and
+stations. Rectilinear routes are<span class="pagenum" title="Page&nbsp;104">&nbsp;</span><a name="Page_104" id="Page_104"></a> momental routes and stations are
+vagrant routes. Rectilinear routes are routes which in a sense lie in
+rects. Any two event-particles on a rect define the set of
+event-particles which lie between them on that rect. Let the
+satisfaction of the condition &#963; by an abstractive set mean that the two
+given event-particles and the event-particles lying between them on the
+rect all lie in every event belonging to the abstractive set. The group
+of &#963;-primes, where &#963; has this meaning, form an abstractive element. Such
+abstractive elements are rectilinear routes. They are the segments of
+instantaneous straight lines which are the ideals of exact perception.
+Our actual perception, however exact, will be the perception of a small
+event sufficiently far down one of the abstractive sets of the
+abstractive element.</p>
+
+<p>A station is a vagrant route and no moment can intersect any station in
+more than one event-particle. Thus a station carries with it a
+comparison of the positions in their respective moments of the
+event-particles covered by it. Rects arise from the intersection of
+moments. But as yet no properties of events have been mentioned by which
+any analogous vagrant loci can be found out.</p>
+
+<p>The general problem for our investigation is to determine a method of
+comparison of position in one instantaneous space with positions in
+other instantaneous spaces. We may limit ourselves to the spaces of the
+parallel moments of one time-system. How are positions in these various
+spaces to be compared? In other words, What do we mean by motion? It is
+the fundamental question to be asked of any theory of relative space,
+and like many other fundamental questions it is apt to be left
+unanswered. It is not an answer to reply, that<span class="pagenum" title="Page&nbsp;105">&nbsp;</span><a name="Page_105" id="Page_105"></a> we all know what we mean
+by motion. Of course we do, so far as sense-awareness is concerned. I am
+asking that your theory of space should provide nature with something to
+be observed. You have not settled the question by bringing forward a
+theory according to which there is nothing to be observed, and by then
+reiterating that nevertheless we do observe this non-existent fact.
+Unless motion is something as a fact in nature, kinetic energy and
+momentum and all that depends on these physical concepts evaporate from
+our list of physical realities. Even in this revolutionary age my
+conservatism resolutely opposes the identification of momentum and
+moonshine.</p>
+
+<p>Accordingly I assume it as an axiom, that motion is a physical fact. It
+is something that we perceive as in nature. Motion presupposes rest.
+Until theory arose to vitiate immediate intuition, that is to say to
+vitiate the uncriticised judgments which immediately arise from
+sense-awareness, no one doubted that in motion you leave behind that
+which is at rest. Abraham in his wanderings left his birthplace where it
+had ever been. A theory of motion and a theory of rest are the same
+thing viewed from different aspects with altered emphasis.</p>
+
+<p>Now you cannot have a theory of rest without in some sense admitting a
+theory of absolute position. It is usually assumed that relative space
+implies that there is no absolute position. This is, according to my
+creed, a mistake. The assumption arises from the failure to make another
+distinction; namely, that there may be alternative definitions of
+absolute position. This possibility enters with the admission of
+alternative time-systems. Thus the series of spaces in the parallel<span class="pagenum" title="Page&nbsp;106">&nbsp;</span><a name="Page_106" id="Page_106"></a>
+moments of one temporal series may have their own definition of absolute
+position correlating sets of event-particles in these successive spaces,
+so that each set consists of event-particles, one from each space, all
+with the property of possessing the same absolute position in that
+series of spaces. Such a set of event-particles will form a point in the
+timeless space of that time-system. Thus a point is really an absolute
+position in the timeless space of a given time-system.</p>
+
+<p>But there are alternative time-systems, and each time-system has its own
+peculiar group of points&mdash;that is to say, its own peculiar definition of
+absolute position. This is exactly the theory which I will elaborate.</p>
+
+<p>In looking to nature for evidence of absolute position it is of no use
+to recur to the four-dimensional manifold of event-particles. This
+manifold has been obtained by the extension of thought beyond the
+immediacy of observation. We shall find nothing in it except what we
+have put there to represent the ideas in thought which arise from our
+direct sense-awareness of nature. To find evidence of the properties
+which are to be found
+in the manifold of event-particles we must always recur to the
+observation of relations between events. Our problem is to determine
+those relations between events which issue in the property of absolute
+position in a timeless space. This is in fact the problem of the
+determination of the very meaning of the timeless spaces of physical
+science.</p>
+
+<p>In reviewing the factors of nature as immediately disclosed in
+sense-awareness, we should note the fundamental character of the percept
+of &lsquo;being here.&rsquo; We discern an event merely as a factor in a determinate
+complex in which each factor has its own peculiar share.</p>
+
+<p><span class="pagenum" title="Page&nbsp;107">&nbsp;</span><a name="Page_107" id="Page_107"></a>There are two factors which are always ingredient in this complex, one
+is the duration which is represented in thought by the concept of all
+nature that is present now, and the other is the peculiar <i>locus standi</i>
+for mind involved in the sense-awareness. This <i>locus standi</i> in nature
+is what is represented in thought by the concept of &lsquo;here,&rsquo; namely of an
+&lsquo;event here.&rsquo;</p>
+
+<p>This is the concept of a definite factor in nature. This factor is an
+event in nature which is the focus in nature for that act of awareness,
+and the other events are perceived as referred to it. This event is part
+of the associated duration. I call it the &lsquo;percipient event.&rsquo; This event
+is not the mind, that is to say, not the percipient. It is that in
+nature from which the mind perceives. The complete foothold of the mind
+in nature is represented by the pair of events, namely, the present
+duration which marks the &lsquo;when&rsquo; of awareness and the percipient event
+which marks the &lsquo;where&rsquo; of awareness and the &lsquo;how&rsquo; of awareness. This
+percipient event is roughly speaking the bodily life of the incarnate
+mind. But this identification is only a rough one. For the functions of
+the body shade off into those of other events in nature; so that for
+some purposes the percipient event is to be reckoned as merely part of
+the bodily life and for other purposes it may even be reckoned as more
+than the bodily life. In many respects the demarcation is purely
+arbitrary, depending upon where in a sliding scale you choose to draw
+the line.</p>
+
+<p>I have already in my previous lecture on Time discussed the association
+of mind with nature. The difficulty of the discussion lies in the
+liability of constant factors to be overlooked. We never note them by
+contrast with their absences. The purpose of a discussion of such<span class="pagenum" title="Page&nbsp;108">&nbsp;</span><a name="Page_108" id="Page_108"></a>
+factors may be described as being to make obvious things look odd. We
+cannot envisage them unless we manage to invest them with some of the
+freshness which is due to strangeness.</p>
+
+<p>It is because of this habit of letting constant factors slip from
+consciousness that we constantly fall into the error of thinking of the
+sense-awareness of a particular factor in nature as being a two-termed
+relation between the mind and the factor. For example, I perceive a
+green leaf. Language in this statement suppresses all reference to any
+factors other than the percipient mind and the green leaf and the
+relation of sense-awareness. It discards the obvious inevitable factors
+which are essential elements in the perception. I am here, the leaf is
+there; and the event here and the event which is the life of the leaf
+there are both embedded in a totality of nature which is now, and within
+this totality there are other discriminated factors which it is
+irrelevant to mention. Thus language habitually sets before the mind a
+misleading abstract of the indefinite complexity of the fact of
+sense-awareness.</p>
+
+<p>What I now want to discuss is the special relation of the percipient
+event which is &lsquo;here&rsquo; to the duration which is &lsquo;now.&rsquo; This relation is a
+fact in nature, namely the mind is aware of nature as being with these
+two factors in this relation.</p>
+
+<p>Within the short present duration the &lsquo;here&rsquo; of the percipient event has
+a definite meaning of some sort. This meaning of &lsquo;here&rsquo; is the content
+of the special relation of the percipient event to its associated
+duration. I will call this relation &lsquo;cogredience.&rsquo; Accordingly I ask for
+a description of the character of the relation of cogredience. The
+present snaps into a past and a present<span class="pagenum" title="Page&nbsp;109">&nbsp;</span><a name="Page_109" id="Page_109"></a> when the &lsquo;here&rsquo; of cogredience
+loses its single determinate meaning. There has been a passage of nature
+from the &lsquo;here&rsquo; of perception within the past duration to the different
+&lsquo;here&rsquo; of perception within the present duration. But the two &lsquo;heres&rsquo; of
+sense-awareness within neighbouring durations may be indistinguishable.
+In this case there has been a passage from the past to the present, but
+a more retentive perceptive force might have retained the passing nature
+as one complete present instead of letting the earlier duration slip
+into the past. Namely, the sense of rest helps the integration of
+durations into a prolonged present, and the sense of motion
+differentiates nature into a succession of shortened durations. As we
+look out of a railway carriage in an express train, the present is past
+before reflexion can seize it. We live in snippits too quick for
+thought. On the other hand the immediate present is prolonged according
+as nature presents itself to us in an aspect of unbroken rest. Any
+change in nature provides ground for a differentiation among durations
+so as to shorten the present. But there is a great distinction between
+self-change in nature and change in external nature. Self-change in
+nature is change in the quality of the standpoint of the percipient
+event. It is the break up of the &lsquo;here&rsquo; which necessitates the break up
+of the present duration. Change in external nature is compatible with a
+prolongation of the present of contemplation rooted in a given
+standpoint. What I want to bring out is that the preservation of a
+peculiar relation to a duration is a necessary condition for the
+function of that duration as a present duration for sense-awareness.
+This peculiar relation is the relation of cogredience between the
+percipient event and the duration.<span class="pagenum" title="Page&nbsp;110">&nbsp;</span><a name="Page_110" id="Page_110"></a> Cogredience is the preservation of
+unbroken quality of standpoint within the duration. It is the
+continuance of identity of station within the whole of nature which is
+the terminus of sense-awareness. The duration may comprise change within
+itself, but cannot&mdash;so far as it is one present duration&mdash;comprise
+change in the quality of its peculiar relation to the contained
+percipient event.</p>
+
+<p>In other words, perception is always &lsquo;here,&rsquo; and a duration can only be
+posited as present for sense-awareness on condition that it affords one
+unbroken meaning of &lsquo;here&rsquo; in its relation to the percipient event. It
+is only in the past that you can have been &lsquo;there&rsquo; with a standpoint
+distinct from your present &lsquo;here.&rsquo;</p>
+
+<p>Events there and events here are facts of nature, and the qualities of
+being &lsquo;there&rsquo; and &lsquo;here&rsquo; are not merely qualities of awareness as a
+relation between nature and mind. The quality of determinate station in
+the duration which belongs to an event which is &lsquo;here&rsquo; in one
+determinate sense of &lsquo;here&rsquo; is the same kind of quality of station which
+belongs to an event which is &lsquo;there&rsquo; in one determinate sense of
+&lsquo;there.&rsquo; Thus cogredience has nothing to do with any biological
+character of the event which is related by it to the associated
+duration. This biological character is apparently a further condition
+for the peculiar connexion of a percipient event with the percipience of
+mind; but it has nothing to do with the relation of the percipient event
+to the duration which is the present whole of nature posited as the
+disclosure of the percipience.</p>
+
+<p>Given the requisite biological character, the event in its character of
+a percipient event selects that duration with which the operative past
+of the event is practically cogredient within the limits of the
+exactitude of<span class="pagenum" title="Page&nbsp;111">&nbsp;</span><a name="Page_111" id="Page_111"></a> observation. Namely, amid the alternative time-systems
+which nature offers there will be one with a duration giving the best
+average of cogredience for all the subordinate parts of the percipient
+event. This duration will be the whole of nature which is the terminus
+posited by sense-awareness. Thus the character of the percipient event
+determines the time-system immediately evident in nature. As the
+character of the percipient event changes with the passage of
+nature&mdash;or, in other words, as the percipient mind in its passage
+correlates itself with the passage of the percipient event into another
+percipient event&mdash;the time-system correlated with the percipience of
+that mind may change. When the bulk of the events perceived are
+cogredient in a duration other than that of the percipient event, the
+percipience may include a double consciousness of cogredience, namely
+the consciousness of the whole within which the observer in the train is
+&lsquo;here,&rsquo; and the consciousness of the whole within which the trees and
+bridges and telegraph posts are definitely &lsquo;there.&rsquo; Thus in perceptions
+under certain circumstances the events discriminated assert their own
+relations of cogredience. This assertion of cogredience is peculiarly
+evident when the duration to which the perceived event is cogredient is
+the same as the duration which is the present whole of nature&mdash;in other
+words, when the event and the percipient event are both cogredient to
+the same duration.</p>
+
+<p>We are now prepared to consider the meaning of stations in a duration,
+where stations are a peculiar kind of routes, which define absolute
+position in the associated timeless space.</p>
+
+<p>There are however some preliminary explanations. A finite event will be
+said to extend throughout a<span class="pagenum" title="Page&nbsp;112">&nbsp;</span><a name="Page_112" id="Page_112"></a> duration when it is part of the duration
+and is intersected by any moment which lies in the duration. Such an
+event begins with the duration and ends with it. Furthermore every event
+which begins with the duration and ends with it, extends throughout the
+duration. This is an axiom based on the continuity of events. By
+beginning with a duration and ending with it, I mean (i) that the event
+is part of the duration, and (ii) that both the initial and final
+boundary moments of the duration cover some event-particles on the
+boundary of the event.</p>
+
+<p>Every event which is cogredient with a duration extends throughout that
+duration.</p>
+
+<p>It is not true that all the parts of an event cogredient with a duration
+are also cogredient with the duration. The relation of cogredience may
+fail in either of two ways. One reason for failure may be that the part
+does not extend throughout the duration. In this case the part may be
+cogredient with another duration which is part of the given duration,
+though it is not cogredient with the given duration itself. Such a part
+would be cogredient if its existence were sufficiently prolonged in that
+time-system. The other reason for failure arises from the
+four-dimensional extension of events so that there is no determinate
+route of transition of events in linear series. For example, the tunnel
+of a tube railway is an event at rest in a certain time-system, that is
+to say, it is cogredient with a certain duration. A train travelling in
+it is part of that tunnel, but is not itself at rest.</p>
+
+<p>If an event <i>e</i> be cogredient with a duration <i>d</i>, and <i>d&#8242;</i> be any
+duration which is part of <i>d</i>. Then <i>d&#8242;</i> belongs to the same time-system
+as <i>d</i>. Also <i>d&#8242;</i> intersects <i>e</i> in an event <i>e&#8242;</i> which is part of <i>e</i>
+and is cogredient with <i>d&#8242;</i>.</p>
+
+<p><span class="pagenum" title="Page&nbsp;113">&nbsp;</span><a name="Page_113" id="Page_113"></a>Let <i>P</i> be any event-particle lying in a given duration <i>d</i>. Consider
+the aggregate of events in which <i>P</i> lies and which are also cogredient
+with <i>d</i>. Each of these events occupies its own aggregate of
+event-particles. These aggregates will have a common portion, namely the
+class of event-particle lying in all of them. This class of
+event-particles is what I call the &lsquo;station&rsquo; of the event-particle <i>P</i>
+in the duration <i>d</i>. This is the station in the character of a locus. A
+station can also be defined in the character of an abstractive element.
+Let the property &#963; be the name of the property which an abstractive set
+possesses when (i) each of its events is cogredient with the duration
+<i>d</i> and (ii) the event-particle <i>P</i> lies in each of its events. Then the
+group of &#963;-primes, where &#963; has this meaning, is an abstractive element
+and is the station of <i>P</i> in <i>d</i> as an abstractive element. The locus of
+event-particles covered by the station of <i>P</i> in <i>d</i> as an abstractive
+element is the station of <i>P</i> in <i>d</i> as a locus. A station has
+accordingly the usual three characters, namely, its character of
+position, its extrinsic character as an abstractive element, and its
+intrinsic character.</p>
+
+<p>It follows from the peculiar properties of rest that two stations
+belonging to the same duration cannot intersect. Accordingly every
+event-particle on a station of a duration has that station as its
+station in the duration. Also every duration which is part of a given
+duration intersects the stations of the given duration in loci which are
+its own stations. By means of these properties we can utilise the
+overlappings of the durations of one family&mdash;that is, of one
+time-system&mdash;to prolong stations indefinitely backwards and forwards.
+Such a prolonged station will be called a point-track. A point-track is
+a<span class="pagenum" title="Page&nbsp;114">&nbsp;</span><a name="Page_114" id="Page_114"></a> locus of event-particles. It is defined by reference to one
+particular time-system, &#945; say. Corresponding to any other time-system
+these will be a different group of point-tracks. Every event-particle
+will lie on one and only one point-track of the group belonging to any
+one time-system. The group of point-tracks of the time-system &#945; is the
+group of points of the timeless space of &#945;. Each such point indicates a
+certain quality of absolute position in reference to the durations of
+the family associated with &#945;, and thence in reference to the successive
+instantaneous spaces lying in the successive moments of &#945;. Each moment
+of &#945; will intersect a point-track in one and only one event-particle.</p>
+
+<p>This property of the unique intersection of a moment and a point-track
+is not confined to the case when the moment and the point-track belong
+to the same time-system. Any two event-particles on a point-track are
+sequential, so that they cannot lie in the same moment. Accordingly no
+moment can intersect a point-track more than once, and every moment
+intersects a point-track in one event-particle.</p>
+
+<p>Anyone who at the successive moments of &#945; should be at the
+event-particles where those moments intersect a given point of &#945; will be
+at rest in the timeless space of time-system &#945;. But in any other
+timeless space belonging to another time-system he will be at a
+different point at each succeeding moment of that time-system. In other
+words he will be moving. He will be moving in a straight line with
+uniform velocity. We might take this as the definition of a straight
+line. Namely, a straight line in the space of time-system &#946; is the locus
+of those points of &#946; which all intersect some one point-track which is a
+point in the space of some<span class="pagenum" title="Page&nbsp;115">&nbsp;</span><a name="Page_115" id="Page_115"></a> other time-system. Thus each point in the
+space of a time-system &#945; is associated with one and only one straight
+line of the space of any other time-system &#946;. Furthermore the set of
+straight lines in space &#946; which are thus associated with points in space
+&#945; form a complete family of parallel straight lines in space &#946;. Thus
+there is a one-to-one correlation of points in space &#945; with the straight
+lines of a certain definite family of parallel straight lines in space
+&#946;. Conversely there is an analogous one-to-one correlation of the points
+in space &#946; with the straight lines of a certain family of parallel
+straight lines in space &#945;. These families will be called respectively
+the family of parallels in &#946; associated with &#945;, and the family of
+parallels in &#945; associated with &#946;. The direction in the space of &#946;
+indicated by the family of parallels in &#946; will be called the direction
+of &#945; in space &#946;, and the family of parallels in &#945; is the direction of &#946;
+in space &#945;. Thus a being at rest at a point of space &#945; will be moving
+uniformly along a line in space &#946; which is in the direction of &#945; in
+space &#946;, and a being at rest at a point of space &#946; will be moving
+uniformly along a line in space &#945; which is in the direction of &#946; in
+space &#945;.</p>
+
+<p>I have been speaking of the timeless spaces which are associated with
+time-systems. These are the spaces of physical science and of any
+concept of space as eternal and unchanging. But what we actually
+perceive is an approximation to the instantaneous space indicated by
+event-particles which lie within some moment of the time-system
+associated with our awareness. The points of such an instantaneous space
+are event-particles and the straight lines are rects. Let the
+time-system be named &#945;, and let the moment of time-system &#945; to which our
+quick perception of nature approximates be<span class="pagenum" title="Page&nbsp;116">&nbsp;</span><a name="Page_116" id="Page_116"></a> called <i>M</i>. Any straight
+line <i>r</i> in space &#945; is a locus of points and each point is a point-track
+which is a locus of event-particles. Thus in the four-dimensional
+geometry of all event-particles there is a two-dimensional locus which
+is the locus of all event-particles on points lying on the straight line
+<i>r</i>. I will call this locus of event-particles the matrix of the
+straight line <i>r</i>. A matrix intersects any moment in a rect. Thus the
+matrix of <i>r</i> intersects the moment <i>M</i> in a rect &#961;. Thus &#961; is the
+instantaneous rect in <i>M</i> which occupies at the moment <i>M</i> the straight
+line <i>r</i> in the space of &#945;. Accordingly when one sees instantaneously a
+moving being and its path ahead of it, what one really sees is the being
+at some event-particle <i>A</i> lying in the rect &#961; which is the apparent
+path on the assumption of uniform motion. But the actual rect &#961; which is
+a locus of event-particles is never traversed by the being. These
+event-particles are the instantaneous facts which pass with the
+instantaneous moment. What is really traversed are other event-particles
+which at succeeding instants occupy the same points of space &#945; as those
+occupied by the event-particles of the rect &#961;. For example, we see a
+stretch of road and a lorry moving along it. The instantaneously seen
+road is a portion of the rect &#961;&mdash;of course only an approximation to it.
+The lorry is the moving object. But the road as seen is never traversed.
+It is thought of as being traversed because the intrinsic characters of
+the later events are in general so similar to those of the instantaneous
+road that we do not trouble to discriminate. But suppose a land mine
+under the road has been exploded before the lorry gets there. Then it is
+fairly obvious that the lorry does not traverse what we saw at first.
+Suppose the lorry is at rest in<span class="pagenum" title="Page&nbsp;117">&nbsp;</span><a name="Page_117" id="Page_117"></a> space &#946;. Then the straight line <i>r</i> of
+space &#945; is in the direction of &#946; in space &#945;, and the rect &#961; is the
+representative in the moment <i>M</i> of the line <i>r</i> of space &#945;. The
+direction of &#961; in the instantaneous space of the moment <i>M</i> is the
+direction of &#946; in <i>M</i>, where <i>M</i> is a moment of time-system &#945;. Again the
+matrix of the line <i>r</i> of space &#945; will also be the matrix of some line
+<i>s</i> of space &#946; which will be in the direction of &#945; in space &#946;. Thus if
+the lorry halts at some point <i>P</i> of space &#945; which lies on the line <i>r</i>,
+it is now moving along the line <i>s</i> of space &#946;. This is the theory of
+relative motion; the common matrix is the bond which connects the motion
+of &#946; in space &#945; with the motions of &#945; in space &#946;.</p>
+
+<p>Motion is essentially a relation between some object of nature and the
+one timeless space of a time-system. An instantaneous space is static,
+being related to the static nature at an instant. In perception when we
+see things moving in an approximation to an instantaneous space, the
+future lines of motion as immediately perceived are rects which are
+never traversed. These approximate rects are composed of small events,
+namely approximate routes and event-particles, which are passed away
+before the moving objects reach them. Assuming that our forecasts of
+rectilinear motion are correct, these rects occupy the straight lines in
+timeless space which are traversed. Thus the rects are symbols in
+immediate sense-awareness of a future which can only be expressed in
+terms of timeless space.</p>
+
+<p>We are now in a position to explore the fundamental character of
+perpendicularity. Consider the two time-systems &#945; and &#946;, each with its
+own timeless space and its own family of instantaneous moments with
+their instantaneous spaces. Let <i>M</i> and <i>N</i> be respectively a<span class="pagenum" title="Page&nbsp;118">&nbsp;</span><a name="Page_118" id="Page_118"></a> moment of
+&#945; and a moment of &#946;. In <i>M</i> there is the direction of &#946; and in <i>N</i> there
+is the direction of &#945;. But <i>M</i> and <i>N</i>, being moments of different
+time-systems, intersect in a level. Call this level &#955;. Then &#955; is an
+instantaneous plane in the instantaneous space of <i>M</i> and also in the
+instantaneous space of <i>N</i>. It is the locus of all the event-particles
+which lie both in <i>M</i> and in <i>N</i>.</p>
+
+<p>In the instantaneous space of <i>M</i> the level &#955; is perpendicular to the
+direction of &#946; in <i>M</i>, and in the instantaneous space of <i>N</i> the level &#955;
+is perpendicular to the direction of &#945; in <i>N</i>. This is the fundamental
+property which forms the definition of perpendicularity. The symmetry of
+perpendicularity is a particular instance of the symmetry of the mutual
+relations between two time-systems. We shall find in the next lecture
+that it is from this symmetry that the theory of congruence is deduced.</p>
+
+<p>The theory of perpendicularity in the timeless space of any time-system
+&#945; follows immediately from this theory of perpendicularity in each of
+its instantaneous spaces. Let &#961; be any rect in the moment <i>M</i> of &#945; and
+let &#955; be a level in <i>M</i> which is perpendicular to &#961;. The locus of those
+points of the space of &#945; which intersect <i>M</i> in event-particles on &#961; is
+the straight line <i>r</i> of space &#945;, and the locus of those points of the
+space of &#945; which intersect <i>M</i> in event-particles on &#955; is the plane <i>l</i>
+of space &#945;. Then the plane <i>l</i> is perpendicular to the line <i>r</i>.</p>
+
+<p>In this way we have pointed out unique and definite properties in nature
+which correspond to perpendicularity. We shall find that this discovery
+of definite unique properties defining perpendicularity is of critical
+importance in the theory of congruence which is the topic for the next
+lecture.</p>
+
+<p><span class="pagenum" title="Page&nbsp;119">&nbsp;</span><a name="Page_119" id="Page_119"></a>I regret that it has been necessary for me in this lecture to administer
+such a large dose of four-dimensional geometry. I do not apologise,
+because I am really not responsible for the fact that nature in its most
+fundamental aspect is four-dimensional. Things are what they are; and it
+is useless to disguise the fact that &lsquo;what things are&rsquo; is often very
+difficult for our intellects to follow. It is a mere evasion of the
+ultimate problems to shirk such obstacles.</p>
+
+<hr />
+<h2><span class="pagenum" title="Page&nbsp;120">&nbsp;</span><a name="Page_120" id="Page_120"></a><a name="CHAPTER_VI" id="CHAPTER_VI"></a>CHAPTER VI
+<br />
+CONGRUENCE</h2>
+
+
+<p>The aim of this lecture is to establish a theory of congruence. You must
+understand at once that congruence is a controversial question. It is
+the theory of measurement in space and in time. The question seems
+simple. In fact it is simple enough for a standard procedure to have
+been settled by act of parliament; and devotion to metaphysical
+subtleties is almost the only crime which has never been imputed to any
+English parliament. But the procedure is one thing and its meaning is
+another.</p>
+
+<p>First let us fix attention on the purely mathematical question. When the
+segment between two points <i>A</i> and <i>B</i> is congruent to that between the
+two points <i>C</i> and <i>D</i>, the quantitative measurements of the two
+segments are equal. The equality of the numerical measures and the
+congruence of the two segments are not always clearly discriminated, and
+are lumped together under the term equality. But the procedure of
+measurement presupposes congruence. For example, a yard measure is
+applied successively to measure two distances between two pairs of
+points on the floor of a room. It is of the essence of the procedure of
+measurement that the yard measure remains unaltered as it is transferred
+from one position to another. Some objects can palpably alter as they
+move&mdash;for example, an elastic thread; but a yard measure does not alter
+if made of the proper material. What is this but a judgment of
+congruence applied to the train of successive positions of the yard<span class="pagenum" title="Page&nbsp;121">&nbsp;</span><a name="Page_121" id="Page_121"></a>
+measure? We know that it does not alter because we judge it to be
+congruent to itself in various positions. In the case of the thread we
+can observe the loss of self-congruence. Thus immediate judgments of
+congruence are presupposed in measurement, and the process of
+measurement is merely a procedure to extend the recognition of
+congruence to cases where these immediate judgments are not available.
+Thus we cannot define congruence by measurement.</p>
+
+<p>In modern expositions of the axioms of geometry certain conditions are
+laid down which the relation of congruence between segments is to
+satisfy. It is supposed that we have a complete theory of points,
+straight lines, planes, and the order of points on planes&mdash;in fact, a
+complete theory of non-metrical geometry. We then enquire about
+congruence and lay down the set of conditions&mdash;or axioms as they are
+called&mdash;which this relation satisfies. It has then been proved that
+there are alternative relations which satisfy these conditions equally
+well and that there is nothing intrinsic in the theory of space to lead
+us to adopt any one of these relations in preference to any other as the
+relation of congruence which we adopt. In other words there are
+alternative metrical geometries which all exist by an equal right so far
+as the intrinsic theory of space is concerned.</p>
+
+<p>Poincar&eacute;, the great French mathematician, held that our actual choice
+among these geometries is guided purely by convention, and that the
+effect of a change of choice would be simply to alter our expression of
+the physical laws of nature. By &lsquo;convention&rsquo; I understand Poincar&eacute; to
+mean that there is nothing inherent in nature itself giving any peculiar
+<i>r&ocirc;le</i> to one of these<span class="pagenum" title="Page&nbsp;122">&nbsp;</span><a name="Page_122" id="Page_122"></a> congruence relations, and that the choice of one
+particular relation is guided by the volitions of the mind at the other
+end of the sense-awareness. The principle of guidance is intellectual
+convenience and not natural fact.</p>
+
+<p>This position has been misunderstood by many of Poincar&eacute;&#8217;s expositors.
+They have muddled it up with another question, namely that owing to the
+inexactitude of observation it is impossible to make an exact statement
+in the comparison of measures. It follows that a certain subset of
+closely allied congruence relations can be assigned of which each member
+equally well agrees with that statement of observed congruence when the
+statement is properly qualified with its limits of error.</p>
+
+<p>This is an entirely different question and it presupposes a rejection of
+Poincar&eacute;&#8217;s position. The absolute indetermination of nature in respect
+of all the relations of congruence is replaced by the indetermination of
+observation with respect to a small subgroup of these relations.</p>
+
+<p>Poincar&eacute;&#8217;s position is a strong one. He in effect challenges anyone to
+point out any factor in nature which gives a preeminent status to the
+congruence relation which mankind has actually adopted. But undeniably
+the position is very paradoxical. Bertrand Russell had a controversy
+with him on this question, and pointed out that on Poincar&eacute;&#8217;s principles
+there was nothing in nature to determine whether the earth is larger or
+smaller than some assigned billiard ball. Poincar&eacute; replied that the
+attempt to find reasons in nature for the selection of a definite
+congruence relation in space is like trying to determine the position of
+a<span class="pagenum" title="Page&nbsp;123">&nbsp;</span><a name="Page_123" id="Page_123"></a> ship in the ocean by counting the crew and observing the colour of
+the captain&#8217;s eyes.</p>
+
+<p>In my opinion both disputants were right, assuming the grounds on which
+the discussion was based. Russell in effect pointed out that apart from
+minor inexactitudes a determinate congruence relation is among the
+factors in nature which our sense-awareness posits for us. Poincar&eacute; asks
+for information as to the factor in nature which might lead any
+particular congruence relation to play a preeminent <i>r&ocirc;le</i> among the
+factors posited in sense-awareness. I cannot see the answer to either of
+these contentions provided that you admit the materialistic theory of
+nature. With this theory nature at an instant in space is an independent
+fact. Thus we have to look for our preeminent congruence relation amid
+nature in instantaneous space; and Poincar&eacute; is undoubtedly right in
+saying that nature on this hypothesis gives us no help in finding it.</p>
+
+<p>On the other hand Russell is in an equally strong position when he
+asserts that, as a fact of observation, we do find it, and what is more
+agree in finding the same congruence relation. On this basis it is one
+of the most extraordinary facts of human experience that all mankind
+without any assignable reason should agree in fixing attention on just
+one congruence relation amid the indefinite number of indistinguishable
+competitors for notice. One would have expected disagreement on this
+fundamental choice to have divided nations and to have rent families.
+But the difficulty was not even discovered till the close of the
+nineteenth century by a few mathematical philosophers and philosophic
+mathematicians. The case is not like that of our agreement on some
+fundamental fact of nature such as the three<span class="pagenum" title="Page&nbsp;124">&nbsp;</span><a name="Page_124" id="Page_124"></a> dimensions of space. If
+space has only three dimensions we should expect all mankind to be aware
+of the fact, as they are aware of it. But in the case of congruence,
+mankind agree in an arbitrary interpretation of sense-awareness when
+there is nothing in nature to guide it.</p>
+
+<p>I look on it as no slight recommendation of the theory of nature which I
+am expounding to you that it gives a solution of this difficulty by
+pointing out the factor in nature which issues in the preeminence of one
+congruence relation over the indefinite herd of other such relations.</p>
+
+<p>The reason for this result is that nature is no longer confined within
+space at an instant. Space and time are now interconnected; and this
+peculiar factor of time which is so immediately distinguished among the
+deliverances of our sense-awareness, relates itself to one particular
+congruence relation in space.</p>
+
+<p>Congruence is a particular example of the fundamental fact of
+recognition. In perception we recognise. This recognition does not
+merely concern the comparison of a factor of nature posited by memory
+with a factor posited by immediate sense-awareness. Recognition takes
+place within the present without any intervention of pure memory. For
+the present fact is a duration with its antecedent and consequent
+durations which are parts of itself. The discrimination in
+sense-awareness of a finite event with its quality of passage is also
+accompanied by the discrimination of other factors of nature which do
+not share in the passage of events. Whatever passes is an event. But we
+find entities in nature which do not pass; namely we recognise
+samenesses in nature. Recognition is not primarily an intellectual act
+of comparison; it is in its essence merely<span class="pagenum" title="Page&nbsp;125">&nbsp;</span><a name="Page_125" id="Page_125"></a> sense-awareness in its
+capacity of positing before us factors in nature which do not pass. For
+example, green is perceived as situated in a certain finite event within
+the present duration. This green preserves its self-identity throughout,
+whereas the event passes and thereby obtains the property of breaking
+into parts. The green patch has parts. But in talking of the green patch
+we are speaking of the event in its sole capacity of being for us the
+situation of green. The green itself is numerically one self-identical
+entity, without parts because it is without passage.</p>
+
+<p>Factors in nature which are without passage will be called objects.
+There are radically different kinds of objects which will be considered
+in the succeeding lecture.</p>
+
+<p>Recognition is reflected into the intellect as comparison. The
+recognised objects of one event are compared with the recognised objects
+of another event. The comparison may be between two events in the
+present, or it may be between two events of which one is posited by
+memory-awareness and the other by immediate sense-awareness. But it is
+not the events which are compared. For each event is essentially unique
+and incomparable. What are compared are the objects and relations of
+objects situated in events. The event considered as a relation between
+objects has lost its passage and in this aspect is itself an object.
+This object is not the event but only an intellectual abstraction. The
+same object can be situated in many events; and in this sense even the
+whole event, viewed as an object, can recur, though not the very event
+itself with its passage and its relations to other events.</p>
+
+<p>Objects which are not posited by sense-awareness may be known to the
+intellect. For example, relations<span class="pagenum" title="Page&nbsp;126">&nbsp;</span><a name="Page_126" id="Page_126"></a> between objects and relations between
+relations may be factors in nature not disclosed in sense-awareness but
+known by logical inference as necessarily in being. Thus objects for our
+knowledge may be merely logical abstractions. For example, a complete
+event is never disclosed in sense-awareness, and thus the object which
+is the sum total of objects situated in an event as thus inter-related
+is a mere abstract concept. Again a right-angle is a perceived object
+which can be situated in many events; but, though rectangularity is
+posited by sense-awareness, the majority of geometrical relations are
+not so posited. Also rectangularity is in fact often not perceived when
+it can be proved to have been there for perception. Thus an object is
+often known merely as an abstract relation not directly posited in
+sense-awareness although it is there in nature.</p>
+
+<p>The identity of quality between congruent segments is generally of this
+character. In certain special cases this identity of quality can be
+directly perceived. But in general it is inferred by a process of
+measurement depending on our direct sense-awareness of selected cases
+and a logical inference from the transitive character of congruence.</p>
+
+<p>Congruence depends on motion, and thereby is generated the connexion
+between spatial congruence and temporal congruence. Motion along a
+straight line has a symmetry round that line. This symmetry is expressed
+by the symmetrical geometrical relations of the line to the family of
+planes normal to it.</p>
+
+<p>Also another symmetry in the theory of motion arises from the fact that
+rest in the points of &#946; corresponds to uniform motion along a definite
+family of parallel straight lines in the space of &#945;. We must note the
+three<span class="pagenum" title="Page&nbsp;127">&nbsp;</span><a name="Page_127" id="Page_127"></a> characteristics, (i) of the uniformity of the motion
+corresponding to any point of &#946; along its correlated straight line in &#945;,
+and (ii) of the equality in magnitude of the velocities along the
+various lines of &#945; correlated to rest in the various points of &#946;, and
+(iii) of the parallelism of the lines of this family.</p>
+
+<p>We are now in possession of a theory of parallels and a theory of
+perpendiculars and a theory of motion, and from these theories the
+theory of congruence can be constructed. It will be remembered that a
+family of parallel levels in any moment is the family of levels in which
+that moment is intersected by the family of moments of some other
+time-system. Also a family of parallel moments is the family of moments
+of some one time-system. Thus we can enlarge our concept of a family of
+parallel levels so as to include levels in different moments of one
+time-system. With this enlarged concept we say that a complete family of
+parallel levels in a time-system &#945; is the complete family of levels in
+which the moments of &#945; intersect the moments of &#946;. This complete family
+of parallel levels is also evidently a family lying in the moments of
+the time-system &#946;. By introducing a third time-system &#947;, parallel rects
+are obtained. Also all the points of any one time-system form a family
+of parallel point-tracks. Thus there are three types of parallelograms
+in the four-dimensional manifold of event-particles.</p>
+
+<p>In parallelograms of the first type the two pairs of parallel sides are
+both of them pairs of rects. In parallelograms of the second type one
+pair of parallel sides is a pair of rects and the other pair is a pair
+of point-tracks. In parallelograms of the third type the two pairs of
+parallel sides are both of them pairs of point-tracks.</p>
+
+<p><span class="pagenum" title="Page&nbsp;128">&nbsp;</span><a name="Page_128" id="Page_128"></a>The first axiom of congruence is that the opposite sides of any
+parallelogram are congruent. This axiom enables us to compare the
+lengths of any two segments either respectively on parallel rects or on
+the same rect. Also it enables us to compare the lengths of any two
+segments either respectively on parallel point-tracks or on the same
+point-track. It follows from this axiom that two objects at rest in any
+two points of a time-system &#946; are moving with equal velocities in any
+other time-system &#945; along parallel lines. Thus we can speak of the
+velocity in &#945; due to the time-system &#946; without specifying any particular
+point in &#946;. The axiom also enables us to measure time in any
+time-system; but does not enable us to compare times in different
+time-systems.</p>
+
+<p>The second axiom of congruence concerns parallelograms on congruent
+bases and between the same parallels, which have also their other pairs
+of sides parallel. The axiom asserts that the rect joining the two
+event-particles of intersection of the diagonals is parallel to the rect
+on which the bases lie. By the aid of this axiom it easily follows that
+the diagonals of a parallelogram bisect each other.</p>
+
+<p>Congruence is extended in any space beyond parallel rects to all rects
+by two axioms depending on perpendicularity. The first of these axioms,
+which is the third axiom of congruence, is that if <i>ABC</i> is a triangle
+of rects in any moment and <i>D</i> is the middle event-particle of the base
+<i>BC</i>, then the level through <i>D</i> perpendicular to <i>BC</i> contains <i>A</i> when
+and only when <i>AB</i> is congruent to <i>AC</i>. This axiom evidently expresses
+the symmetry of perpendicularity, and is the essence of the famous pons
+asinorum expressed as an axiom.</p>
+
+<p>The second axiom depending on perpendicularity,<span class="pagenum" title="Page&nbsp;129">&nbsp;</span><a name="Page_129" id="Page_129"></a> and the fourth axiom of
+congruence, is that if <i>r</i> and <i>A</i> be a rect and an event-particle in
+the same moment and <i>AB</i> and <i>AC</i> be a pair of rectangular rects
+intersecting <i>r</i> in <i>B</i> and <i>C</i>, and <i>AD</i> and <i>AE</i> be another pair of
+rectangular rects intersecting <i>r</i> in <i>D</i> and <i>E</i>, then either <i>D</i> or
+<i>E</i> lies in the segment <i>BC</i> and the other one of the two does not lie
+in this segment. Also as a particular case of this axiom, if <i>AB</i> be
+perpendicular to <i>r</i> and in consequence <i>AC</i> be parallel to <i>r</i>, then
+<i>D</i> and <i>E</i> lie on opposite sides of <i>B</i> respectively. By the aid of
+these two axioms the theory of congruence can be extended so as to
+compare lengths of segments on any two rects. Accordingly Euclidean
+metrical geometry in space is completely established and lengths in the
+spaces of different time-systems are comparable as the result of
+definite properties of nature which indicate just that particular method
+of comparison.</p>
+
+<p>The comparison of time-measurements in diverse time-systems requires two
+other axioms. The first of these axioms, forming the fifth axiom of
+congruence, will be called the axiom of &lsquo;kinetic symmetry.&rsquo; It expresses
+the symmetry of the quantitative relations between two time-systems when
+the times and lengths in the two systems are measured in congruent
+units.</p>
+
+<p>The axiom can be explained as follows: Let &#945; and &#946; be the names of two
+time-systems. The directions of motion in the space of &#945; due to rest in
+a point of &#946; is called the &lsquo;&#946;-direction in &#945;&rsquo; and the direction of
+motion in the space of &#946; due to rest in a point of &#945; is called the
+&lsquo;&#945;-direction in &#946;.&rsquo; Consider a motion in the space of &#945; consisting of a
+certain velocity in the &#946;-direction of &#945; and a certain velocity at
+right-angles to it. This motion represents rest in the space of another
+time-system<span class="pagenum" title="Page&nbsp;130">&nbsp;</span><a name="Page_130" id="Page_130"></a>&mdash;call it &#960;. Rest in &#960; will also be represented in the space
+of &#946; by a certain velocity in the &#945;-direction in &#946; and a certain
+velocity at right-angles to this &#945;-direction. Thus a certain motion in
+the space of &#945; is correlated to a certain motion in the space of &#946;, as
+both representing the same fact which can also be represented by rest in
+&#960;. Now another time-system, which I will name &#963;, can be found which is
+such that rest in its space is represented by the same magnitudes of
+velocities along and perpendicular to the &#945;-direction in &#946; as those
+velocities in &#945;, along and perpendicular to the &#946;-direction, which
+represent rest in &#960;. The required axiom of kinetic symmetry is that rest
+in &#963; will be represented in &#945; by the same velocities along and
+perpendicular to the &#946;-direction in &#945; as those velocities in &#946; along and
+perpendicular to the &#945;-direction which represent rest in &#960;.</p>
+
+<p>A particular case of this axiom is that relative velocities are equal
+and opposite. Namely rest in &#945; is represented in &#946; by a velocity along
+the &#945;-direction which is equal to the velocity along the &#946;-direction in
+&#945; which represents rest in &#946;.</p>
+
+<p>Finally the sixth axiom of congruence is that the relation of congruence
+is transitive. So far as this axiom applies to space, it is superfluous.
+For the property follows from our previous axioms. It is however
+necessary for time as a supplement to the axiom of kinetic symmetry. The
+meaning of the axiom is that if the time-unit of system &#945; is congruent
+to the time-unit of system &#946;, and the time-unit of system &#946; is congruent
+to the time-unit of system &#947;, then the time-units of &#945; and &#947; are also
+congruent.</p>
+
+<p>By means of these axioms formulae for the trans<span class="pagenum" title="Page&nbsp;131">&nbsp;</span><a name="Page_131" id="Page_131"></a>formation of
+measurements made in one time-system to measurements of the same facts
+of nature made in another time-system can be deduced. These formulae
+will be found to involve one arbitrary constant which I will call <i>k</i>.</p>
+
+<p>It is of the dimensions of the square of a velocity. Accordingly four
+cases arise. In the first case <i>k</i> is zero. This case produces
+nonsensical results in opposition to the elementary deliverances of
+experience. We put this case aside.</p>
+
+<p>In the second case <i>k</i> is infinite. This case yields the ordinary
+formulae for transformation in relative motion, namely those formulae
+which are to be found in every elementary book on dynamics.</p>
+
+<p>In the third case, <i>k</i> is negative. Let us call it &minus;<i>c</i><sup>2</sup>, where <i>c</i>
+will be of the dimensions of a velocity. This case yields the formulae
+of transformation which Larmor discovered for the transformation of
+Maxwell&#8217;s equations of the electromagnetic field. These formulae were
+extended by H.&nbsp;A. Lorentz, and used by Einstein and Minkowski as the
+basis of their novel theory of relativity. I am not now speaking of
+Einstein&#8217;s more recent theory of general relativity by which he deduces
+his modification of the law of gravitation. If this be the case which
+applies to nature, then <i>c</i> must be a close approximation to the
+velocity of light <i>in vacuo</i>. Perhaps it is this actual velocity. In
+this connexion &lsquo;<i>in vacuo</i>&rsquo; must not mean an absence of events, namely
+the absence of the all-pervading ether of events. It must mean the
+absence of certain types of objects.</p>
+
+<p>In the fourth case, <i>k</i> is positive. Let us call it <i>h</i><sup>2</sup>, where <i>h</i>
+will be of the dimensions of a velocity. This gives a perfectly possible
+type of transformation formulae,<span class="pagenum" title="Page&nbsp;132">&nbsp;</span><a name="Page_132" id="Page_132"></a> but not one which explains any facts
+of experience. It has also another disadvantage. With the assumption of
+this fourth case the distinction between space and time becomes unduly
+blurred. The whole object of these lectures has been to enforce the
+doctrine that space and time spring from a common root, and that the
+ultimate fact of experience is a space-time fact. But after all mankind
+does distinguish very sharply between space and time, and it is owing to
+this sharpness of distinction that the doctrine of these lectures is
+somewhat of a paradox. Now in the third assumption this sharpness of
+distinction is adequately preserved. There is a fundamental distinction
+between the metrical properties of point-tracks and rects. But in the
+fourth assumption this fundamental distinction vanishes.</p>
+
+<p>Neither the third nor the fourth assumption can agree with experience
+unless we assume that the velocity <i>c</i> of the third assumption, and the
+velocity <i>h</i> of the fourth assumption, are extremely large compared to
+the velocities of ordinary experience. If this be the case the formulae
+of both assumptions will obviously reduce to a close approximation to
+the formulae of the second assumption which are the ordinary formulae of
+dynamical textbooks. For the sake of a name, I will call these textbook
+formulae the &lsquo;orthodox&rsquo; formulae.</p>
+
+<p>There can be no question as to the general approximate correctness of
+the orthodox formulae. It would be merely silly to raise doubts on this
+point. But the determination of the status of these formulae is by no
+means settled by this admission. The independence of time and space is
+an unquestioned presupposition of the orthodox thought which has
+produced the orthodox formulae. With this presupposition and given the<span class="pagenum" title="Page&nbsp;133">&nbsp;</span><a name="Page_133" id="Page_133"></a>
+absolute points of one absolute space, the orthodox formulae are
+immediate deductions. Accordingly, these formulae are presented to our
+imaginations as facts which cannot be otherwise, time and space being
+what they are. The orthodox formulae have therefore attained to the
+status of necessities which cannot be questioned in science. Any attempt
+to replace these formulae by others was to abandon the <i>r&ocirc;le</i> of
+physical explanation and to have recourse to mere mathematical formulae.</p>
+
+<p>But even in physical science difficulties have accumulated round the
+orthodox formulae. In the first place Maxwell&#8217;s equations of the
+electromagnetic field are not invariant for the transformations of the
+orthodox formulae; whereas they are invariant for the transformations of
+the formulae arising from the third of the four cases mentioned above,
+provided that the velocity <i>c</i> is identified with a famous
+electromagnetic constant quantity.</p>
+
+<p>Again the null results of the delicate experiments to detect the earth&#8217;s
+variations of motion through the ether in its orbital path are explained
+immediately by the formulae of the third case. But if we assume the
+orthodox formulae we have to make a special and arbitrary assumption as
+to the contraction of matter during motion. I mean the
+Fitzgerald-Lorentz assumption.</p>
+
+<p>Lastly Fresnel&#8217;s coefficient of drag which represents the variation of
+the velocity of light in a moving medium is explained by the formulae of
+the third case, and requires another arbitrary assumption if we use the
+orthodox formulae.</p>
+
+<p>It appears therefore that on the mere basis of physical explanation
+there are advantages in the formulae<span class="pagenum" title="Page&nbsp;134">&nbsp;</span><a name="Page_134" id="Page_134"></a> of the third case as compared with
+the orthodox formulae. But the way is blocked by the ingrained belief
+that these latter formulae possess a character of necessity. It is
+therefore an urgent requisite for physical science and for philosophy to
+examine critically the grounds for this supposed necessity. The only
+satisfactory method of scrutiny is to recur to the first principles of
+our knowledge of nature. This is exactly what I am endeavouring to do in
+these lectures. I ask what it is that we are aware of in our
+sense-perception of nature. I then proceed to examine those factors in
+nature which lead us to conceive nature as occupying space and
+persisting through time. This procedure has led us to an investigation
+of the characters of space and time. It results from these
+investigations that the formulae of the third case and the orthodox
+formulae are on a level as possible formulae resulting from the basic
+character of our knowledge of nature. The orthodox formulae have thus
+lost any advantage as to necessity which they enjoyed over the serial
+group. The way is thus open to adopt whichever of the two groups best
+accords with observation.</p>
+
+<p>I take this opportunity of pausing for a moment from the course of my
+argument, and of reflecting on the general character which my doctrine
+ascribes to some familiar concepts of science. I have no doubt that some
+of you have felt that in certain aspects this character is very
+paradoxical.</p>
+
+<p>This vein of paradox is partly due to the fact that educated language
+has been made to conform to the prevalent orthodox theory. We are thus,
+in expounding an alternative doctrine, driven to the use of either
+strange terms or of familiar words with unusual meanings. This<span class="pagenum" title="Page&nbsp;135">&nbsp;</span><a name="Page_135" id="Page_135"></a> victory
+of the orthodox theory over language is very natural. Events are named
+after the prominent objects situated in them, and thus both in language
+and in thought the event sinks behind the object, and becomes the mere
+play of its relations. The theory of space is then converted into a
+theory of the relations of objects instead of a theory of the relations
+of events. But objects have not the passage of events. Accordingly space
+as a relation between objects is devoid of any connexion with time. It
+is space at an instant without any determinate relations between the
+spaces at successive instants. It cannot be one timeless space because
+the relations between objects change.</p>
+
+<p>A few minutes ago in speaking of the deduction of the orthodox formulae
+for relative motion I said that they followed as an immediate deduction
+from the assumption of absolute points in absolute space. This reference
+to absolute space was not an oversight. I know that the doctrine of the
+relativity of space at present holds the field both in science and
+philosophy. But I do not think that its inevitable consequences are
+understood. When we really face them the paradox of the presentation of
+the character of space which I have elaborated is greatly mitigated. If
+there is no absolute position, a point must cease to be a simple entity.
+What is a point to one man in a balloon with his eyes fixed on an
+instrument is a track of points to an observer on the earth who is
+watching the balloon through a telescope, and is another track of points
+to an observer in the sun who is watching the balloon through some
+instrument suited to such a being. Accordingly if I am reproached with
+the paradox of my theory of points as classes of event-particles, and of
+my theory of event-particles as<span class="pagenum" title="Page&nbsp;136">&nbsp;</span><a name="Page_136" id="Page_136"></a> groups of abstractive sets, I ask my
+critic to explain exactly what he means by a point. While you explain
+your meaning about anything, however simple, it is always apt to look
+subtle and fine spun. I have at least explained exactly what I do mean
+by a point, what relations it involves and what entities are the relata.
+If you admit the relativity of space, you also must admit that points
+are complex entities, logical constructs involving other entities and
+their relations. Produce your theory, not in a few vague phrases of
+indefinite meaning, but explain it step by step in definite terms
+referring to assigned relations and assigned relata. Also show that your
+theory of points issues in a theory of space. Furthermore note that the
+example of the man in the balloon, the observer on earth, and the
+observer in the sun, shows that every assumption of relative rest
+requires a timeless space with radically different points from those
+which issue from every other such assumption. The theory of the
+relativity of space is inconsistent with any doctrine of one unique set
+of points of one timeless space.</p>
+
+<p>The fact is that there is no paradox in my doctrine of the nature of
+space which is not in essence inherent in the theory of the relativity
+of space. But this doctrine has never really been accepted in science,
+whatever people say. What appears in our dynamical treatises is Newton&#8217;s
+doctrine of relative motion based on the doctrine of differential motion
+in absolute space. When you once admit that the points are radically
+different entities for differing assumptions of rest, then the orthodox
+formulae lose all their obviousness. They were only obvious because you
+were really thinking of something else. When discussing this topic you
+can<span class="pagenum" title="Page&nbsp;137">&nbsp;</span><a name="Page_137" id="Page_137"></a> only avoid paradox by taking refuge from the flood of criticism in
+the comfortable ark of no meaning.</p>
+
+<p>The new theory provides a definition of the congruence of periods of
+time. The prevalent view provides no such definition. Its position is
+that if we take such time-measurements so that certain familiar
+velocities which seem to us to be uniform are uniform, then the laws of
+motion are true. Now in the first place no change could appear either as
+uniform or non-uniform without involving a definite determination of the
+congruence for time-periods. So in appealing to familiar phenomena it
+allows that there is some factor in nature which we can intellectually
+construct as a congruence theory. It does not however say anything about
+it except that the laws of motion are then true. Suppose that with some
+expositors we cut out the reference to familiar velocities such as the
+rate of rotation of the earth. We are then driven to admit that there is
+no meaning in temporal congruence except that certain assumptions make
+the laws of motion true. Such a statement is historically false. King
+Alfred the Great was ignorant of the laws of motion, but knew very well
+what he meant by the measurement of time, and achieved his purpose by
+means of burning candles. Also no one in past ages justified the use of
+sand in hour-glasses by saying that some centuries later interesting
+laws of motion would be discovered which would give a meaning to the
+statement that the sand was emptied from the bulbs in equal times.
+Uniformity in change is directly perceived, and it follows that mankind
+perceives in nature factors from which a theory of temporal congruence
+can be formed. The prevalent theory entirely fails to produce such
+factors.</p>
+
+<p><span class="pagenum" title="Page&nbsp;138">&nbsp;</span><a name="Page_138" id="Page_138"></a>The mention of the laws of motion raises another point where the
+prevalent theory has nothing to say and the new theory gives a complete
+explanation. It is well known that the laws of motion are not valid for
+any axes of reference which you may choose to take fixed in any rigid
+body. You must choose a body which is not rotating and has no
+acceleration. For example they do not really apply to axes fixed in the
+earth because of the diurnal rotation of that body. The law which fails
+when you assume the wrong axes as at rest is the third law, that action
+and reaction are equal and opposite. With the wrong axes uncompensated
+centrifugal forces and uncompensated composite centrifugal forces
+appear, due to rotation. The influence of these forces can be
+demonstrated by many facts on the earth&#8217;s surface, Foucault&#8217;s pendulum,
+the shape of the earth, the fixed directions of the rotations of
+cyclones and anticyclones. It is difficult to take seriously the
+suggestion that these domestic phenomena on the earth are due to the
+influence of the fixed stars. I cannot persuade myself to believe that a
+little star in its twinkling turned round Foucault&#8217;s pendulum in the
+Paris Exhibition of 1861. Of course anything is believable when a
+definite physical connexion has been demonstrated, for example the
+influence of sunspots. Here all demonstration is lacking in the form of
+any coherent theory. According to the theory of these lectures the axes
+to which motion is to be referred are axes at rest in the space of some
+time-system. For example, consider the space of a time-system &#945;. There
+are sets of axes at rest in the space of &#945;. These are suitable dynamical
+axes. Also a set of axes in this space which is moving with uniform
+velocity without rotation is<span class="pagenum" title="Page&nbsp;139">&nbsp;</span><a name="Page_139" id="Page_139"></a> another suitable set. All the moving
+points fixed in these moving axes are really tracing out parallel lines
+with one uniform velocity. In other words they are the reflections in
+the space of &#945; of a set of fixed axes in the space of some other
+time-system &#946;. Accordingly the group of dynamical axes required for
+Newton&#8217;s Laws of Motion is the outcome of the necessity of referring
+motion to a body at rest in the space of some one time-system in order
+to obtain a coherent account of physical properties. If we do not do so
+the meaning of the motion of one portion of our physical configuration
+is different from the meaning of the motion of another portion of the
+same configuration. Thus the meaning of motion being what it is, in
+order to describe the motion of any system of objects without changing
+the meaning of your terms as you proceed with your description, you are
+bound to take one of these sets of axes as axes of reference; though you
+may choose their reflections into the space of any time-system which you
+wish to adopt. A definite physical reason is thereby assigned for the
+peculiar property of the dynamical group of axes.</p>
+
+<p>On the orthodox theory the position of the equations of motion is most
+ambiguous. The space to which they refer is completely undetermined and
+so is the measurement of the lapse of time. Science is simply setting
+out on a fishing expedition to see whether it cannot find some procedure
+which it can call the measurement of space and some procedure which it
+can call the measurement of time, and something which it can call a
+system of forces, and something which it can call masses, so that these
+formulae may be satisfied. The only reason&mdash;on this theory&mdash;why anyone
+should want to satisfy these formulae is a sentimental regard for
+Galileo,<span class="pagenum" title="Page&nbsp;140">&nbsp;</span><a name="Page_140" id="Page_140"></a> Newton, Euler and Lagrange. The theory, so far from founding
+science on a sound observational basis, forces everything to conform to
+a mere mathematical preference for certain simple formulae.</p>
+
+<p>I do not for a moment believe that this is a true account of the real
+status of the Laws of Motion. These equations want some slight
+adjustment for the new formulae of relativity. But with these
+adjustments, imperceptible in ordinary use, the laws deal with
+fundamental physical quantities which we know very well and wish to
+correlate.</p>
+
+<p>The measurement of time was known to all civilised nations long before
+the laws were thought of. It is this time as thus measured that the laws
+are concerned with. Also they deal with the space of our daily life.
+When we approach to an accuracy of measurement beyond that of
+observation, adjustment is allowable. But within the limits of
+observation we know what we mean when we speak of measurements of space
+and measurements of time and uniformity of change. It is for science to
+give an intellectual account of what is so evident in sense-awareness.
+It is to me thoroughly incredible that the ultimate fact beyond which
+there is no deeper explanation is that mankind has really been swayed by
+an unconscious desire to satisfy the mathematical formulae which we call
+the Laws of Motion, formulae completely unknown till the seventeenth
+century of our epoch.</p>
+
+<p>The correlation of the facts of sense-experience effected by the
+alternative account of nature extends beyond the physical properties of
+motion and the properties of congruence. It gives an account of the
+meaning of the geometrical entities such as points, straight lines, and
+volumes, and connects the kindred<span class="pagenum" title="Page&nbsp;141">&nbsp;</span><a name="Page_141" id="Page_141"></a>" ideas of extension in time and
+extension in space. The theory satisfies the true purpose of an
+intellectual explanation in the sphere of natural philosophy. This
+purpose is to exhibit the interconnexions of nature, and to show that
+one set of ingredients in nature requires for the exhibition of its
+character the presence of the other sets of ingredients.</p>
+
+<p>The false idea which we have to get rid of is that of nature as a mere
+aggregate of independent entities, each capable of isolation. According
+to this conception these entities, whose characters are capable of
+isolated definition, come together and by their accidental relations
+form the system of nature. This system is thus thoroughly accidental;
+and, even if it be subject to a mechanical fate, it is only accidentally
+so subject.</p>
+
+<p>With this theory space might be without time, and time might be without
+space. The theory admittedly breaks down when we come to the relations
+of matter and space. The relational theory of space is an admission that
+we cannot know space without matter or matter without space. But the
+seclusion of both from time is still jealously guarded. The relations
+between portions of matter in space are accidental facts owing to the
+absence of any coherent account of how space springs from matter or how
+matter springs from space. Also what we really observe in nature, its
+colours and its sounds and its touches are secondary qualities; in other
+words, they are not in nature at all but are accidental products of the
+relations between nature and mind.</p>
+
+<p>The explanation of nature which I urge as an alternative ideal to this
+accidental view of nature, is that nothing in nature could be what it is
+except as an<span class="pagenum" title="Page&nbsp;142">&nbsp;</span><a name="Page_142" id="Page_142"></a> ingredient in nature as it is. The whole which is present
+for discrimination is posited in sense-awareness as necessary for the
+discriminated parts. An isolated event is not an event, because every
+event is a factor in a larger whole and is significant of that whole.
+There can be no time apart from space; and no space apart from time; and
+no space and no time apart from the passage of the events of nature. The
+isolation of an entity in thought, when we think of it as a bare &lsquo;it,&rsquo;
+has no counterpart in any corresponding isolation in nature. Such
+isolation is merely part of the procedure of intellectual knowledge.</p>
+
+<p>The laws of nature are the outcome of the characters of the entities
+which we find in nature. The entities being what they are, the laws must
+be what they are; and conversely the entities follow from the laws. We
+are a long way from the attainment of such an ideal; but it remains as
+the abiding goal of theoretical science.</p>
+
+<hr />
+<h2><span class="pagenum" title="Page&nbsp;143">&nbsp;</span><a name="Page_143" id="Page_143"></a><a name="CHAPTER_VII" id="CHAPTER_VII"></a>CHAPTER VII
+<br />
+OBJECTS</h2>
+
+
+<p>The ensuing lecture is concerned with the theory of objects. Objects are
+elements in nature which do not pass. The awareness of an object as some
+factor not sharing in the passage of nature is what I call
+&lsquo;recognition.&rsquo; It is impossible to recognise an event, because an event
+is essentially distinct from every other event. Recognition is an
+awareness of sameness. But to call recognition an awareness of sameness
+implies an intellectual act of comparison accompanied with judgment. I
+use recognition for the non-intellectual relation of sense-awareness
+which connects the mind with a factor of nature without passage. On the
+intellectual side of the mind&#8217;s experience there are comparisons of
+things recognised and consequent judgments of sameness or diversity.
+Probably &lsquo;sense-recognition&rsquo; would be a better term for what I mean by
+&lsquo;recognition.&rsquo; I have chosen the simpler term because I think that I
+shall be able to avoid the use of &lsquo;recognition&rsquo; in any other meaning
+than that of &lsquo;sense-recognition.&rsquo; I am quite willing to believe that
+recognition, in my sense of the term, is merely an ideal limit, and that
+there is in fact no recognition without intellectual accompaniments of
+comparison and judgment. But recognition is that relation of the mind to
+nature which provides the material for the intellectual activity.</p>
+
+<p>An object is an ingredient in the character of some event. In fact the
+character of an event is nothing but the objects which are ingredient in
+it and the ways in<span class="pagenum" title="Page&nbsp;144">&nbsp;</span><a name="Page_144" id="Page_144"></a> which those objects make their ingression into the
+event. Thus the theory of objects is the theory of the comparison of
+events. Events are only comparable because they body forth permanences.
+We are comparing objects in events whenever we can say, &lsquo;There it is
+again.&rsquo; Objects are the elements in nature which can &lsquo;be again.&rsquo;</p>
+
+<p>Sometimes permanences can be proved to exist which evade recognition in
+the sense in which I am using that term. The permanences which evade
+recognition appear to us as abstract properties either of events or of
+objects. All the same they are there for recognition although
+undiscriminated in our sense-awareness. The demarcation of events, the
+splitting of nature up into parts is effected by the objects which we
+recognise as their ingredients. The discrimination of nature is the
+recognition of objects amid passing events. It is a compound of the
+awareness of the passage of nature, of the consequent partition of
+nature, and of the definition of certain parts of nature by the modes of
+the ingression of objects into them.</p>
+
+<p>You may have noticed that I am using the term &lsquo;ingression&rsquo; to denote the
+general relation of objects to events. The ingression of an object into
+an event is the way the character of the event shapes itself in virtue
+of the being of the object. Namely the event is what it is, because the
+object is what it is; and when I am thinking of this modification of the
+event by the object, I call the relation between the two &lsquo;the ingression
+of the object into the event.&rsquo; It is equally true to say that objects
+are what they are because events are what they are. Nature is such that
+there can be no events and no objects without the ingression of objects
+into events.<span class="pagenum" title="Page&nbsp;145">&nbsp;</span><a name="Page_145" id="Page_145"></a> Although there are events such that the ingredient objects
+evade our recognition. These are the events in empty space. Such events
+are only analysed for us by the intellectual probing of science.</p>
+
+<p>Ingression is a relation which has various modes. There are obviously
+very various kinds of objects; and no one kind of object can have the
+same sort of relations to events as objects of another kind can have. We
+shall have to analyse out some of the different modes of ingression
+which different kinds of objects have into events.</p>
+
+<p>But even if we stick to one and the same kind of objects, an object of
+that kind has different modes of ingression into different events.
+Science and philosophy have been apt to entangle themselves in a
+simple-minded theory that an object is at one place at any definite
+time, and is in no sense anywhere else. This is in fact the attitude of
+common sense thought, though it is not the attitude of language which is
+na&iuml;vely expressing the facts of experience. Every other sentence in a
+work of literature which is endeavouring truly to interpret the facts of
+experience expresses differences in surrounding events due to the
+presence of some object. An object is ingredient throughout its
+neighbourhood, and its neighbourhood is indefinite. Also the
+modification of events by ingression is susceptible of quantitative
+differences. Finally therefore we are driven to admit that each object
+is in some sense ingredient throughout nature; though its ingression may
+be quantitatively irrelevant in the expression of our individual
+experiences.</p>
+
+<p>This admission is not new either in philosophy or science. It is
+obviously a necessary axiom for those<span class="pagenum" title="Page&nbsp;146">&nbsp;</span><a name="Page_146" id="Page_146"></a> philosophers who insist that
+reality is a system. In these lectures we are keeping off the profound
+and vexed question as to what we mean by &lsquo;reality.&rsquo; I am maintaining the
+humbler thesis that nature is a system. But I suppose that in this case
+the less follows from the greater, and that I may claim the support of
+these philosophers. The same doctrine is essentially interwoven in all
+modern physical speculation. As long ago as 1847 Faraday in a paper in
+the <i>Philosophical Magazine</i> remarked that his theory of tubes of force
+implies that in a sense an electric charge is everywhere. The
+modification of the electromagnetic field at every point of space at
+each instant owing to the past history of each electron is another way
+of stating the same fact. We can however illustrate the doctrine by the
+more familiar facts of life without recourse to the abstruse
+speculations of theoretical physics.</p>
+
+<p>The waves as they roll on to the Cornish coast tell of a gale in
+mid-Atlantic; and our dinner witnesses to the ingression of the cook
+into the dining room. It is evident that the ingression of objects into
+events includes the theory of causation. I prefer to neglect this aspect
+of ingression, because causation raises the memory of discussions based
+upon theories of nature which are alien to my own. Also I think that
+some new light may be thrown on the subject by viewing it in this fresh
+aspect.</p>
+
+<p>The examples which I have given of the ingression of objects into events
+remind us that ingression takes a peculiar form in the case of some
+events; in a sense, it is a more concentrated form. For example, the
+electron has a certain position in space and a certain shape. Perhaps it
+is an extremely small sphere in a certain<span class="pagenum" title="Page&nbsp;147">&nbsp;</span><a name="Page_147" id="Page_147"></a> test-tube. The storm is a
+gale situated in mid-Atlantic with a certain latitude and longitude, and
+the cook is in the kitchen. I will call this special form of ingression
+the &lsquo;relation of situation&rsquo;; also, by a double use of the word
+&lsquo;situation,&rsquo; I will call the event in which an object is situated &lsquo;the
+situation of the object.&rsquo; Thus a situation is an event which is a
+relatum in the relation of situation. Now our first impression is that
+at last we have come to the simple plain fact of where the object really
+is; and that the vaguer relation which I call ingression should not be
+muddled up with the relation of situation, as if including it as a
+particular case. It seems so obvious that any object is in such and such
+a position, and that it is influencing other events in a totally
+different sense. Namely, in a sense an object is the character of the
+event which is its situation, but it only influences the character of
+other events. Accordingly the relations of situation and influencing are
+not generally the same sort of relation, and should not be subsumed
+under the same term &lsquo;ingression.&rsquo; I believe that this notion is a
+mistake, and that it is impossible to draw a clear distinction between
+the two relations.</p>
+
+<p>For example, Where was your toothache? You went to a dentist and pointed
+out the tooth to him. He pronounced it perfectly sound, and cured you by
+stopping another tooth. Which tooth was the situation of the toothache?
+Again, a man has an arm amputated, and experiences sensations in the
+hand which he has lost. The situation of the imaginary hand is in fact
+merely thin air. You look into a mirror and see a fire. The flames that
+you see are situated behind the mirror. Again at night you watch the
+sky; if some of the stars had vanished from existence hours ago, you
+would not be any the<span class="pagenum" title="Page&nbsp;148">&nbsp;</span><a name="Page_148" id="Page_148"></a> wiser. Even the situations of the planets differ
+from those which science would assign to them.</p>
+
+<p>Anyhow you are tempted to exclaim, the cook is in the kitchen. If you
+mean her mind, I will not agree with you on the point; for I am only
+talking of nature. Let us think only of her bodily presence. What do you
+mean by this notion? We confine ourselves to typical manifestations of
+it. You can see her, touch her, and hear her. But the examples which I
+have given you show that the notions of the situations of what you see,
+what you touch, and what you hear are not so sharply separated out as to
+defy further questioning. You cannot cling to the idea that we have two
+sets of experiences of nature, one of primary qualities which belong to
+the objects perceived, and one of secondary qualities which are the
+products of our mental excitements. All we know of nature is in the same
+boat, to sink or swim together. The constructions of science are merely
+expositions of the characters of things perceived. Accordingly to affirm
+that the cook is a certain dance of molecules and electrons is merely to
+affirm that the things about her which are perceivable have certain
+characters. The situations of the perceived manifestations of her bodily
+presence have only a very general relation to the situations of the
+molecules, to be determined by discussion of the circumstances of
+perception.</p>
+
+<p>In discussing the relations of situation in particular and of ingression
+in general, the first requisite is to note that objects are of radically
+different types. For each type &lsquo;situation&rsquo; and &lsquo;ingression&rsquo; have their
+own special meanings which are different from their meanings for other
+types, though connexions can be pointed out.<span class="pagenum" title="Page&nbsp;149">&nbsp;</span><a name="Page_149" id="Page_149"></a> It is necessary therefore
+in discussing them to determine what type of objects are under
+consideration. There are, I think, an indefinite number of types of
+objects. Happily we need not think of them all. The idea of situation
+has its peculiar importance in reference to three types of objects which
+I call sense-objects, perceptual objects and scientific objects. The
+suitability of these names for the three types is of minor importance,
+so long as I can succeed in explaining what I mean by them.</p>
+
+<p>These three types form an ascending hierarchy, of which each member
+presupposes the type below. The base of the hierarchy is formed by the
+sense-objects. These objects do not presuppose any other type of
+objects. A sense-object is a factor of nature posited by sense-awareness
+which (i), in that it is an object, does not share in the passage of
+nature and (ii) is not a relation between other factors of nature. It
+will of course be a relatum in relations which also implicate other
+factors of nature. But it is always a relatum and never the relation
+itself. Examples of sense-objects are a particular sort of colour, say
+Cambridge blue, or a particular sort of sound, or a particular sort of
+smell, or a particular sort of feeling. I am not talking of a particular
+patch of blue as seen during a particular second of time at a definite
+date. Such a patch is an event where Cambridge blue is situated.
+Similarly I am not talking of any particular concert-room as filled with
+the note. I mean the note itself and not the patch of volume filled by
+the sound for a tenth of a second. It is natural for us to think of the
+note in itself, but in the case of colour we are apt to think of it
+merely as a property of the patch. No one thinks of the note as a<span class="pagenum" title="Page&nbsp;150">&nbsp;</span><a name="Page_150" id="Page_150"></a>
+property of the concert-room. We see the blue and we hear the note. Both
+the blue and the note are immediately posited by the discrimination of
+sense-awareness which relates the mind to nature. The blue is posited as
+in nature related to other factors in nature. In particular it is
+posited as in the relation of being situated in the event which is its
+situation.</p>
+
+<p>The difficulties which cluster around the relation of situation arise
+from the obstinate refusal of philosophers to take seriously the
+ultimate fact of multiple relations. By a multiple relation I mean a
+relation which in any concrete instance of its occurrence necessarily
+involves more than two relata. For example, when John likes Thomas there
+are only two relata, John and Thomas. But when John gives that book to
+Thomas there are three relata, John, that book, and Thomas.</p>
+
+<p>Some schools of philosophy, under the influence of the Aristotelian
+logic and the Aristotelian philosophy, endeavour to get on without
+admitting any relations at all except that of substance and attribute.
+Namely all apparent relations are to be resolvable into the concurrent
+existence of substances with contrasted attributes. It is fairly obvious
+that the Leibnizian monadology is the necessary outcome of any such
+philosophy. If you dislike pluralism, there will be only one monad.</p>
+
+<p>Other schools of philosophy admit relations but obstinately refuse to
+contemplate relations with more than two relata. I do not think that
+this limitation is based on any set purpose or theory. It merely arises
+from the fact that more complicated relations are a bother to people
+without adequate mathematical training, when they are admitted into the
+reasoning.</p>
+
+<p>I must repeat that we have nothing to do in these<span class="pagenum" title="Page&nbsp;151">&nbsp;</span><a name="Page_151" id="Page_151"></a> lectures with the
+ultimate character of reality. It is quite possible that in the true
+philosophy of reality there are only individual substances with
+attributes, or that there are only relations with pairs of relata. I do
+not believe that such is the case; but I am not concerned to argue about
+it now. Our theme is Nature. So long as we confine ourselves to the
+factors posited in the sense-awareness of nature, it seems to me that
+there certainly are instances of multiple relations between these
+factors, and that the relation of situation for sense-objects is one
+example of such multiple relations.</p>
+
+<p>Consider a blue coat, a flannel coat of Cambridge blue belonging to some
+athlete. The coat itself is a perceptual object and its situation is not
+what I am talking about. We are talking of someone&#8217;s definite
+sense-awareness of Cambridge blue as situated in some event of nature.
+He may be looking at the coat directly. He then sees Cambridge blue as
+situated practically in the same event as the coat at that instant. It
+is true that the blue which he sees is due to light which left the coat
+some inconceivably small fraction of a second before. This difference
+would be important if he were looking at a star whose colour was
+Cambridge blue. The star might have ceased to exist days ago, or even
+years ago. The situation of the blue will not then be very intimately
+connected with the situation (in another sense of &lsquo;situation&rsquo;) of any
+perceptual object. This disconnexion of the situation of the blue and
+the situation of some associated perceptual object does not require a
+star for its exemplification. Any looking glass will suffice. Look at
+the coat through a looking glass. Then blue is seen as situated behind
+the mirror. The event which is its situation depends upon the position
+of the observer.</p>
+
+<p><span class="pagenum" title="Page&nbsp;152">&nbsp;</span><a name="Page_152" id="Page_152"></a>The sense-awareness of the blue as situated in a certain event which I
+call the situation, is thus exhibited as the sense-awareness of a
+relation between the blue, the percipient event of the observer, the
+situation, and intervening events. All nature is in fact required,
+though only certain intervening events require their characters to be of
+certain definite sorts. The ingression of blue into the events of nature
+is thus exhibited as systematically correlated. The awareness of the
+observer depends on the position of the percipient event in this
+systematic correlation. I will use the term &lsquo;ingression into nature&rsquo; for
+this systematic correlation of the blue with nature. Thus the ingression
+of blue into any definite event is a part statement of the fact of the
+ingression of blue into nature.</p>
+
+<p>In respect to the ingression of blue into nature events may be roughly
+put into four classes which overlap and are not very clearly separated.
+These classes are (i) the percipient events, (ii) the situations, (iii)
+the active conditioning events, (iv) the passive conditioning events. To
+understand this classification of events in the general fact of the
+ingression of blue into nature, let us confine attention to one
+situation for one percipient event and to the consequent <i>r&ocirc;les</i> of the
+conditioning events for the ingression as thus limited. The percipient
+event is the relevant bodily state of the observer. The situation is
+where he sees the blue, say, behind the mirror. The active conditioning
+events are the events whose characters are particularly relevant for the
+event (which is the situation) to be the situation for that percipient
+event, namely the coat, the mirror, and the state of the room as to
+light and atmosphere. The passive conditioning events are the events of
+the rest of nature.</p>
+
+<p><span class="pagenum" title="Page&nbsp;153">&nbsp;</span><a name="Page_153" id="Page_153"></a>In general the situation is an active conditioning event; namely the
+coat itself, when there is no mirror or other such contrivance to
+produce abnormal effects. But the example of the mirror shows us that
+the situation may be one of the passive conditioning events. We are then
+apt to say that our senses have been cheated, because we demand as a
+right that the situation should be an active condition in the
+ingression.</p>
+
+<p>This demand is not so baseless as it may seem when presented as I have
+put it. All we know of the characters of the events of nature is based
+on the analysis of the relations of situations to percipient events. If
+situations were not in general active conditions, this analysis would
+tell us nothing. Nature would be an unfathomable enigma to us and there
+could be no science. Accordingly the incipient discontent when a
+situation is found to be a passive condition is in a sense justifiable;
+because if that sort of thing went on too often, the <i>r&ocirc;le</i> of the
+intellect would be ended.</p>
+
+<p>Furthermore the mirror is itself the situation of other sense-objects
+either for the same observer with the same percipient event, or for
+other observers with other percipient events. Thus the fact that an
+event is a situation in the ingression of one set of sense-objects into
+nature is presumptive evidence that that event is an active condition in
+the ingression of other sense-objects into nature which may have other
+situations.</p>
+
+<p>This is a fundamental principle of science which it has derived from
+common sense.</p>
+
+<p>I now turn to perceptual objects. When we look at the coat, we do not in
+general say, There is a patch of Cambridge blue; what naturally occurs
+to us is, There is a coat. Also the judgment that what we have seen is<span class="pagenum" title="Page&nbsp;154">&nbsp;</span><a name="Page_154" id="Page_154"></a>
+a garment of man&#8217;s attire is a detail. What we perceive is an object
+other than a mere sense-object. It is not a mere patch of colour, but
+something more; and it is that something more which we judge to be a
+coat. I will use the word &lsquo;coat&rsquo; as the name for that crude object which
+is more than a patch of colour, and without any allusion to the
+judgments as to its usefulness as an article of attire either in the
+past or the future. The coat which is perceived&mdash;in this sense of the
+word &lsquo;coat&rsquo;&mdash;is what I call a perceptual object. We have to investigate
+the general character of these perceptual objects.</p>
+
+<p>It is a law of nature that in general the situation of a sense-object is
+not only the situation of that sense-object for one definite percipient
+event, but is the situation of a variety of sense-objects for a variety
+of percipient events. For example, for any one percipient event, the
+situation of a sense-object of sight is apt also to be the situations of
+sense-objects of sight, of touch, of smell, and of sound. Furthermore
+this concurrence in the situations of sense-objects has led to the
+body&mdash;<i>i.e.</i> the percipient event&mdash;so adapting itself that the
+perception of one sense-object in a certain situation leads to a
+subconscious sense-awareness of other sense-objects in the same
+situation. This interplay is especially the case between touch and
+sight. There is a certain correlation between the ingressions of
+sense-objects of touch and sense-objects of sight into nature, and in a
+slighter degree between the ingressions of other pairs of sense-objects.
+I call this sort of correlation the &lsquo;conveyance&rsquo; of one sense-object by
+another. When you see the blue flannel coat you subconsciously feel
+yourself wearing it or otherwise touching it. If you are a smoker, you
+may also subconsciously be aware of the<span class="pagenum" title="Page&nbsp;155">&nbsp;</span><a name="Page_155" id="Page_155"></a> faint aroma of tobacco. The
+peculiar fact, posited by this sense-awareness of the concurrence of
+subconscious sense-objects along with one or more dominating
+sense-objects in the same situation, is the sense-awareness of the
+perceptual object. The perceptual object is not primarily the issue of a
+judgment. It is a factor of nature directly posited in sense-awareness.
+The element of judgment comes in when we proceed to classify the
+particular perceptual object. For example, we say, That is flannel, and
+we think of the properties of flannel and the uses of athletes&#8217; coats.
+But that all takes place after we have got hold of the perceptual
+object. Anticipatory judgments affect the perceptual object perceived by
+focussing and diverting attention.</p>
+
+<p>The perceptual object is the outcome of the habit of experience.
+Anything which conflicts with this habit hinders the sense-awareness of
+such an object. A sense-object is not the product of the association of
+intellectual ideas; it is the product of the association of
+sense-objects in the same situation. This outcome is not intellectual;
+it is an object of peculiar type with its own particular ingression into
+nature.</p>
+
+<p>There are two kinds of perceptual objects, namely, &lsquo;delusive perceptual
+objects&rsquo; and &lsquo;physical objects.&rsquo; The situation of a delusive perceptual
+object is a passive condition in the ingression of that object into
+nature. Also the event which is the situation will have the relation of
+situation to the object only for one particular percipient event. For
+example, an observer sees the image of the blue coat in a mirror. It is
+a blue coat that he sees and not a mere patch of colour. This shows that
+the active conditions for the conveyance of a group of subconscious
+sense-objects by a dominating<span class="pagenum" title="Page&nbsp;156">&nbsp;</span><a name="Page_156" id="Page_156"></a> sense-object are to be found in the
+percipient event. Namely we are to look for them in the investigations
+of medical psychologists. The ingression into nature of the delusive
+sense-object is conditioned by the adaptation of bodily events to the
+more normal occurrence, which is the ingression of the physical object.</p>
+
+<p>A perceptual object is a physical object when (i) its situation is an
+active conditioning event for the ingression of any of its component
+sense-objects, and (ii) the same event can be the situation of the
+perceptual object for an indefinite number of possible percipient
+events. Physical objects are the ordinary objects which we perceive when
+our senses are not cheated, such as chairs, tables and trees. In a way
+physical objects have more insistent perceptive power than
+sense-objects. Attention to the fact of their occurrence in nature is
+the first condition for the survival of complex living organisms. The
+result of this high perceptive power of physical objects is the
+scholastic philosophy of nature which looks on the sense-objects as mere
+attributes of the physical objects. This scholastic point of view is
+directly contradicted by the wealth of sense-objects which enter into
+our experience as situated in events without any connexion with physical
+objects. For example, stray smells, sounds, colours and more subtle
+nameless sense-objects. There is no perception of physical objects
+without perception of sense-objects. But the converse does not hold:
+namely, there is abundant perception of sense-objects unaccompanied by
+any perception of physical objects. This lack of reciprocity in the
+relations between sense-objects and physical objects is fatal to the
+scholastic natural philosophy.</p>
+
+<p><span class="pagenum" title="Page&nbsp;157">&nbsp;</span><a name="Page_157" id="Page_157"></a>There is a great difference in the <i>r&ocirc;les</i> of the situations of
+sense-objects and physical objects. The situations of a physical object
+are conditioned by uniqueness and continuity. The uniqueness is an ideal
+limit to which we approximate as we proceed in thought along an
+abstractive set of durations, considering smaller and smaller durations
+in the approach to the ideal limit of the moment of time. In other
+words, when the duration is small enough, the situation of the physical
+object within that duration is practically unique.</p>
+
+<p>The identification of the same physical object as being situated in
+distinct events in distinct durations is effected by the condition of
+continuity. This condition of continuity is the condition that a
+continuity of passage of events, each event being a situation of the
+object in its corresponding duration, can be found from the earlier to
+the later of the two given events. So far as the two events are
+practically adjacent in one specious present, this continuity of passage
+may be directly perceived. Otherwise it is a matter of judgment and
+inference.</p>
+
+<p>The situations of a sense-object are not conditioned by any such
+conditions either of uniqueness or of continuity. In any durations
+however small a sense-object may have any number of situations separated
+from each other. Thus two situations of a sense-object, either in the
+same duration or in different durations, are not necessarily connected
+by any continuous passage of events which are also situations of that
+sense-object.</p>
+
+<p>The characters of the conditioning events involved in the ingression of
+a sense-object into nature can be largely expressed in terms of the
+physical objects which are situated in those events. In one respect this
+is also a tautology. For the physical object is nothing else than<span class="pagenum" title="Page&nbsp;158">&nbsp;</span><a name="Page_158" id="Page_158"></a> the
+habitual concurrence of a certain set of sense-objects in one situation.
+Accordingly when we know all about the physical object, we thereby know
+its component sense-objects. But a physical object is a condition for
+the occurrence of sense-objects other than those which are its
+components. For example, the atmosphere causes the events which are its
+situations to be active conditioning events in the transmission of
+sound. A mirror which is itself a physical object is an active condition
+for the situation of a patch of colour behind it, due to the reflection
+of light in it.</p>
+
+<p>Thus the origin of scientific knowledge is the endeavour to express in
+terms of physical objects the various <i>r&ocirc;les</i> of events as active
+conditions in the ingression of sense-objects into nature. It is in the
+progress of this investigation that scientific objects emerge. They
+embody those aspects of the character of the situations of the physical
+objects which are most permanent and are expressible without reference
+to a multiple relation including a percipient event. Their relations to
+each other are also characterised by a certain simplicity and
+uniformity. Finally the characters of the observed physical objects and
+sense-objects can be expressed in terms of these scientific objects. In
+fact the whole point of the search for scientific objects is the
+endeavour to obtain this simple expression of the characters of events.
+These scientific objects are not themselves merely formulae for
+calculation; because formulae must refer to things in nature, and the
+scientific objects are the things in nature to which the formulae refer.</p>
+
+<p>A scientific object such as a definite electron is a systematic
+correlation of the characters of all events throughout all nature. It is
+an aspect of the systematic<span class="pagenum" title="Page&nbsp;159">&nbsp;</span><a name="Page_159" id="Page_159"></a> character of nature. The electron is not
+merely where its charge is. The charge is the quantitative character of
+certain events due to the ingression of the electron into nature. The
+electron is its whole field of force. Namely the electron is the
+systematic way in which all events are modified as the expression of its
+ingression. The situation of an electron in any small duration may be
+defined as that event which has the quantitative character which is the
+charge of the electron. We may if we please term the mere charge the
+electron. But then another name is required for the scientific object
+which is the full entity which concerns science, and which I have called
+the electron.</p>
+
+<p>According to this conception of scientific objects, the rival theories
+of action at a distance and action by transmission through a medium are
+both incomplete expressions of the true process of nature. The stream of
+events which form the continuous series of situations of the electron is
+entirely self-determined, both as regards having the intrinsic character
+of being the series of situations of that electron and as regards the
+time-systems with which its various members are cogredient, and the flux
+of their positions in their corresponding durations. This is the
+foundation of the denial of action at a distance; namely the progress of
+the stream of the situations of a scientific object can be determined by
+an analysis of the stream itself.</p>
+
+<p>On the other hand the ingression of every electron into nature modifies
+to some extent the character of every event. Thus the character of the
+stream of events which we are considering bears marks of the existence
+of every other electron throughout the universe. If we like to think of
+the electrons as being merely what I call<span class="pagenum" title="Page&nbsp;160">&nbsp;</span><a name="Page_160" id="Page_160"></a> their charges, then the
+charges act at a distance. But this action consists in the modification
+of the situation of the other electron under consideration. This
+conception of a charge acting at a distance is a wholly artificial one.
+The conception which most fully expresses the character of nature is
+that of each event as modified by the ingression of each electron into
+nature. The ether is the expression of this systematic modification of
+events throughout space and throughout time. The best expression of the
+character of this modification is for physicists to find out. My theory
+has nothing to do with that and is ready to accept any outcome of
+physical research.</p>
+
+<p>The connexion of objects with space requires elucidation. Objects are
+situated in events. The relation of situation is a different relation
+for each type of object, and in the case of sense-objects it cannot be
+expressed as a two-termed relation. It would perhaps be better to use a
+different word for these different types of the relation of situation.
+It has not however been necessary to do so for our purposes in these
+lectures. It must be understood however that, when situation is spoken
+of, some one definite type is under discussion, and it may happen that
+the argument may not apply to situation of another type. In all cases
+however I use situation to express a relation between objects and events
+and not between objects and abstractive elements. There is a derivative
+relation between objects and spatial elements which I call the relation
+of location; and when this relation holds, I say that the object is
+located in the abstractive element. In this sense, an object may be
+located in a moment of time, in a volume of space, an area, a line, or a
+point. There will be a peculiar type of location corresponding to each
+type of situation; and<span class="pagenum" title="Page&nbsp;161">&nbsp;</span><a name="Page_161" id="Page_161"></a> location is in each case derivative from the
+corresponding relation of situation in a way which I will proceed to
+explain.</p>
+
+<p>Also location in the timeless space of some time-system is a relation
+derivative from location in instantaneous spaces of the same
+time-system. Accordingly location in an instantaneous space is the
+primary idea which we have to explain. Great confusion has been
+occasioned in natural philosophy by the neglect to distinguish between
+the different types of objects, the different types of situation, the
+different types of location, and the difference between location and
+situation. It is impossible to reason accurately in the vague concerning
+objects and their positions without keeping these distinctions in view.
+An object is located in an abstractive element, when an abstractive set
+belonging to that element can be found such that each event belonging to
+that set is a situation of the object. It will be remembered that an
+abstractive element is a certain group of abstractive sets, and that
+each abstractive set is a set of events. This definition defines the
+location of an element in any type of abstractive element. In this sense
+we can talk of the existence of an object at an instant, meaning thereby
+its location in some definite moment. It may also be located in some
+spatial element of the instantaneous space of that moment.</p>
+
+<p>A quantity can be said to be located in an abstractive element when an
+abstractive set belonging to the element can be found such that the
+quantitative expressions of the corresponding characters of its events
+converge to the measure of the given quantity as a limit when we pass
+along the abstractive set towards its converging end.</p>
+
+<p><span class="pagenum" title="Page&nbsp;162">&nbsp;</span><a name="Page_162" id="Page_162"></a>By these definitions location in elements of instantaneous spaces is
+defined. These elements occupy corresponding elements of timeless
+spaces. An object located in an element of an instantaneous space will
+also be said to be located at that moment in the timeless element of the
+timeless space which is occupied by that instantaneous element.</p>
+
+<p>It is not every object which can be located in a moment. An object which
+can be located in every moment of some duration will be called a
+&lsquo;uniform&rsquo; object throughout that duration. Ordinary physical objects
+appear to us to be uniform objects, and we habitually assume that
+scientific objects such as electrons are uniform. But some sense-objects
+certainly are not uniform. A tune is an example of a non-uniform object.
+We have perceived it as a whole in a certain duration; but the tune as a
+tune is not at any moment of that duration though one of the individual
+notes may be located there.</p>
+
+<p>It is possible therefore that for the existence of certain sorts of
+objects, <i>e.g.</i> electrons, minimum quanta of time are requisite. Some
+such postulate is apparently indicated by the modern quantum theory and
+it is perfectly consistent with the doctrine of objects maintained in
+these lectures.</p>
+
+<p>Also the instance of the distinction between the electron as the mere
+quantitative electric charge of its situation and the electron as
+standing for the ingression of an object throughout nature illustrates
+the indefinite number of types of objects which exist in nature. We can
+intellectually distinguish even subtler and subtler types of objects.
+Here I reckon subtlety as meaning seclusion from the immediate
+apprehension of sense-awareness. Evolution in the complexity of life
+means an<span class="pagenum" title="Page&nbsp;163">&nbsp;</span><a name="Page_163" id="Page_163"></a> increase in the types of objects directly sensed. Delicacy of
+sense-apprehension means perceptions of objects as distinct entities
+which are mere subtle ideas to cruder sensibilities. The phrasing of
+music is a mere abstract subtlety to the unmusical; it is a direct
+sense-apprehension to the initiated. For example, if we could imagine
+some lowly type of organic being thinking and aware of our thoughts, it
+would wonder at the abstract subtleties in which we indulge as we think
+of stones and bricks and drops of water and plants. It only knows of
+vague undifferentiated feelings in nature. It would consider us as given
+over to the play of excessively abstract intellects. But then if it
+could think, it would anticipate; and if it anticipated, it would soon
+perceive for itself.</p>
+
+<p>In these lectures we have been scrutinising the foundations of natural
+philosophy. We are stopping at the very point where a boundless ocean of
+enquiries opens out for our questioning.</p>
+
+<p>I agree that the view of Nature which I have maintained in these
+lectures is not a simple one. Nature appears as a complex system whose
+factors are dimly discerned by us. But, as I ask you, Is not this the
+very truth? Should we not distrust the jaunty assurance with which every
+age prides itself that it at last has hit upon the ultimate concepts in
+which all that happens can be formulated? The aim of science is to seek
+the simplest explanations of complex facts. We are apt to fall into the
+error of thinking that the facts are simple because simplicity is the
+goal of our quest. The guiding motto in the life of every natural
+philosopher should be, Seek simplicity and distrust it.</p>
+
+<hr />
+<h2><span class="pagenum" title="Page&nbsp;164">&nbsp;</span><a name="Page_164" id="Page_164"></a><a name="CHAPTER_VIII" id="CHAPTER_VIII"></a>CHAPTER VIII
+<br />
+SUMMARY</h2>
+
+
+<p>There is a general agreement that Einstein&#8217;s investigations have one
+fundamental merit irrespective of any criticisms which we may feel
+inclined to pass on them. They have made us think. But when we have
+admitted so far, we are most of us faced with a distressing perplexity.
+What is it that we ought to think about? The purport of my lecture this
+afternoon will be to meet this difficulty and, so far as I am able, to
+set in a clear light the changes in the background of our scientific
+thought which are necessitated by any acceptance, however qualified, of
+Einstein&#8217;s main positions. I remember that I am lecturing to the members
+of a chemical society who are not for the most part versed in advanced
+mathematics. The first point that I would urge upon you is that what
+immediately concerns you is not so much the detailed deductions of the
+new theory as this general change in the background of scientific
+conceptions which will follow from its acceptance. Of course, the
+detailed deductions are important, because unless our colleagues the
+astronomers and the physicists find these predictions to be verified we
+can neglect the theory altogether. But we may now take it as granted
+that in many striking particulars these deductions have been found to be
+in agreement with observation. Accordingly the theory has to be taken
+seriously and we are anxious to know what will be the consequences of
+its final acceptance. Furthermore during the last few weeks<span class="pagenum" title="Page&nbsp;165">&nbsp;</span><a name="Page_165" id="Page_165"></a> the
+scientific journals and the lay press have been filled with articles as
+to the nature of the crucial experiments which have been made and as to
+some of the more striking expressions of the outcome of the new theory.
+&lsquo;Space caught bending&rsquo; appeared on the news-sheet of a well-known
+evening paper. This rendering is a terse but not inapt translation of
+Einstein&#8217;s own way of interpreting his results. I should say at once
+that I am a heretic as to this explanation and that I shall expound to
+you another explanation based upon some work of my own, an explanation
+which seems to me to be more in accordance with our scientific ideas and
+with the whole body of facts which have to be explained. We have to
+remember that a new theory must take account of the old well-attested
+facts of science just as much as of the very latest experimental results
+which have led to its production.</p>
+
+<p>To put ourselves in the position to assimilate and to criticise any
+change in ultimate scientific conceptions we must begin at the
+beginning. So you must bear with me if I commence by making some simple
+and obvious reflections. Let us consider three statements, (i)
+&lsquo;Yesterday a man was run over on the Chelsea Embankment,&rsquo; (ii)
+&lsquo;Cleopatra&#8217;s Needle is on the Charing Cross Embankment,&rsquo; and (iii)
+&lsquo;There are dark lines in the Solar Spectrum.&rsquo; The first statement about
+the accident to the man is about what we may term an &lsquo;occurrence,&rsquo; a
+&lsquo;happening,&rsquo; or an &lsquo;event.&rsquo; I will use the term &lsquo;event&rsquo; because it is
+the shortest. In order to specify an observed event, the place, the
+time, and character of the event are necessary. In specifying the place
+and the time you are really stating the relation of the assigned event
+to the general structure of other observed events. For<span class="pagenum" title="Page&nbsp;166">&nbsp;</span><a name="Page_166" id="Page_166"></a> example, the man
+was run over between your tea and your dinner and adjacently to a
+passing barge in the river and the traffic in the Strand. The point
+which I want to make is this: Nature is known to us in our experience as
+a complex of passing events. In this complex we discern definite mutual
+relations between component events, which we may call their relative
+positions, and these positions we express partly in terms of space and
+partly in terms of time. Also in addition to its mere relative position
+to other events, each particular event has its own peculiar character.
+In other words, nature is a structure of events and each event has its
+position in this structure and its own peculiar character or quality.</p>
+
+<p>Let us now examine the other two statements in the light of this general
+principle as to the meaning of nature. Take the second statement,
+&lsquo;Cleopatra&#8217;s Needle is on the Charing Cross Embankment.&rsquo; At first sight
+we should hardly call this an event. It seems to lack the element of
+time or transitoriness. But does it? If an angel had made the remark
+some hundreds of millions of years ago, the earth was not in existence,
+twenty millions of years ago there was no Thames, eighty years ago there
+was no Thames Embankment, and when I was a small boy Cleopatra&#8217;s Needle
+was not there. And now that it is there, we none of us expect it to be
+eternal. The static timeless element in the relation of Cleopatra&#8217;s
+Needle to the Embankment is a pure illusion generated by the fact that
+for purposes of daily intercourse its emphasis is needless. What it
+comes to is this: Amidst the structure of events which form the medium
+within which the daily life of Londoners is passed we know how to
+identify a certain<span class="pagenum" title="Page&nbsp;167">&nbsp;</span><a name="Page_167" id="Page_167"></a> stream of events which maintain permanence of
+character, namely the character of being the situations of Cleopatra&#8217;s
+Needle. Day by day and hour by hour we can find a certain chunk in the
+transitory life of nature and of that chunk we say, &lsquo;There is
+Cleopatra&#8217;s Needle.&rsquo; If we define the Needle in a sufficiently abstract
+manner we can say that it never changes. But a physicist who looks on
+that part of the life of nature as a dance of electrons, will tell you
+that daily it has lost some molecules and gained others, and even the
+plain man can see that it gets dirtier and is occasionally washed. Thus
+the question of change in the Needle is a mere matter of definition. The
+more abstract your definition, the more permanent the Needle. But
+whether your Needle change or be permanent, all you mean by stating that
+it is situated on the Charing Cross Embankment, is that amid the
+structure of events you know of a certain continuous limited stream of
+events, such that any chunk of that stream, during any hour, or any day,
+or any second, has the character of being the situation of Cleopatra&#8217;s
+Needle.</p>
+
+<p>Finally, we come to the third statement, &lsquo;There are dark lines in the
+Solar Spectrum.&rsquo; This is a law of nature. But what does that mean? It
+means merely this. If any event has the character of being an exhibition
+of the solar spectrum under certain assigned circumstances, it will also
+have the character of exhibiting dark lines in that spectrum.</p>
+
+<p>This long discussion brings us to the final conclusion that the concrete
+facts of nature are events exhibiting a certain structure in their
+mutual relations and certain characters of their own. The aim of science
+is to express the relations between their characters in terms of the<span class="pagenum" title="Page&nbsp;168">&nbsp;</span><a name="Page_168" id="Page_168"></a>
+mutual structural relations between the events thus characterised. The
+mutual structural relations between events are both spatial and
+temporal. If you think of them as merely spatial you are omitting the
+temporal element, and if you think of them as merely temporal you are
+omitting the spatial element. Thus when you think of space alone, or of
+time alone, you are dealing in abstractions, namely, you are leaving out
+an essential element in the life of nature as known to you in the
+experience of your senses. Furthermore there are different ways of
+making these abstractions which we think of as space and as time; and
+under some circumstances we adopt one way and under other circumstances
+we adopt another way. Thus there is no paradox in holding that what we
+mean by space under one set of circumstances is not what we mean by
+space under another set of circumstances. And equally what we mean by
+time under one set of circumstances is not what we mean by time under
+another set of circumstances. By saying that space and time are
+abstractions, I do not mean that they do not express for us real facts
+about nature. What I mean is that there are no spatial facts or temporal
+facts apart from physical nature, namely that space and time are merely
+ways of expressing certain truths about the relations between events.
+Also that under different circumstances there are different sets of
+truths about the universe which are naturally presented to us as
+statements about space. In such a case what a being under the one set of
+circumstances means by space will be different from that meant by a
+being under the other set of circumstances. Accordingly when we are
+comparing two observations made under different circumstances we have to
+ask &lsquo;Do the<span class="pagenum" title="Page&nbsp;169">&nbsp;</span><a name="Page_169" id="Page_169"></a> two observers mean the same thing by space and the same
+thing by time?&rsquo; The modern theory of relativity has arisen because
+certain perplexities as to the concordance of certain delicate
+observations such as the motion of the earth through the ether, the
+perihelion of mercury, and the positions of the stars in the
+neighbourhood of the sun, have been solved by reference to this purely
+relative significance of space and time.</p>
+
+<p>I want now to recall your attention to Cleopatra&#8217;s Needle, which I have
+not yet done with. As you are walking along the Embankment you suddenly
+look up and say, &lsquo;Hullo, there&#8217;s the Needle.&rsquo; In other words, you
+recognise it. You cannot recognise an event; because when it is gone, it
+is gone. You may observe another event of analogous character, but the
+actual chunk of the life of nature is inseparable from its unique
+occurrence. But a character of an event can be recognised. We all know
+that if we go to the Embankment near Charing Cross we shall observe an
+event having the character which we recognise as Cleopatra&#8217;s Needle.
+Things which we thus recognise I call objects. An object is situated in
+those events or in that stream of events of which it expresses the
+character. There are many sorts of objects. For example, the colour
+green is an object according to the above definition. It is the purpose
+of science to trace the laws which govern the appearance of objects in
+the various events in which they are found to be situated. For this
+purpose we can mainly concentrate on two types of objects, which I will
+call material physical objects and scientific objects. A material
+physical object is an ordinary bit of matter, Cleopatra&#8217;s Needle for
+example. This is a much more complicated type of object than a mere
+colour, such as<span class="pagenum" title="Page&nbsp;170">&nbsp;</span><a name="Page_170" id="Page_170"></a> the colour of the Needle. I call these simple objects,
+such as colours or sounds, sense-objects. An artist will train himself
+to attend more particularly to sense-objects where the ordinary person
+attends normally to material objects. Thus if you were walking with an
+artist, when you said &lsquo;There&#8217;s Cleopatra&#8217;s Needle,&rsquo; perhaps he
+simultaneously exclaimed &lsquo;There&#8217;s a nice bit of colour.&rsquo; Yet you were
+both expressing your recognition of different component characters of
+the same event. But in science we have found out that when we know all
+about the adventures amid events of material physical objects and of
+scientific objects we have most of the relevant information which will
+enable us to predict the conditions under which we shall perceive
+sense-objects in specific situations. For example, when we know that
+there is a blazing fire (<i>i.e.</i> material and scientific objects
+undergoing various exciting adventures amid events) and opposite to it a
+mirror (which is another material object) and the positions of a man&#8217;s
+face and eyes gazing into the mirror, we know that he can perceive the
+redness of the flame situated in an event behind the mirror&mdash;thus, to a
+large extent, the appearance of sense-objects is conditioned by the
+adventures of material objects. The analysis of these adventures makes
+us aware of another character of events, namely their characters as
+fields of activity which determine the subsequent events to which they
+will pass on the objects situated in them. We express these fields of
+activity in terms of gravitational, electromagnetic, or chemical forces
+and attractions. But the exact expression of the nature of these fields
+of activity forces us intellectually to acknowledge a less obvious type
+of objects as situated in events. I mean molecules<span class="pagenum" title="Page&nbsp;171">&nbsp;</span><a name="Page_171" id="Page_171"></a> and electrons. These
+objects are not recognised in isolation. We cannot well miss Cleopatra&#8217;s
+Needle, if we are in its neighbourhood; but no one has seen a single
+molecule or a single electron, yet the characters of events are only
+explicable to us by expressing them in terms of these scientific
+objects. Undoubtedly molecules and electrons are abstractions. But then
+so is Cleopatra&#8217;s Needle. The concrete facts are the events
+themselves&mdash;I have already explained to you that to be an abstraction
+does not mean that an entity is nothing. It merely means that its
+existence is only one factor of a more concrete element of nature. So an
+electron is abstract because you cannot wipe out the whole structure of
+events and yet retain the electron in existence. In the same way the
+grin on the cat is abstract; and the molecule is really in the event in
+the same sense as the grin is really on the cat&#8217;s face. Now the more
+ultimate sciences such as Chemistry or Physics cannot express their
+ultimate laws in terms of such vague objects as the sun, the earth,
+Cleopatra&#8217;s Needle, or a human body. Such objects more properly belong
+to Astronomy, to Geology, to Engineering, to Archaeology, or to Biology.
+Chemistry and Physics only deal with them as exhibiting statistical
+complexes of the effects of their more intimate laws. In a certain
+sense, they only enter into Physics and Chemistry as technological
+applications. The reason is that they are too vague. Where does
+Cleopatra&#8217;s Needle begin and where does it end? Is the soot part of it?
+Is it a different object when it sheds a molecule or when its surface
+enters into chemical combination with the acid of a London fog? The
+definiteness and permanence of the Needle is nothing to the possible
+permanent definiteness<span class="pagenum" title="Page&nbsp;172">&nbsp;</span><a name="Page_172" id="Page_172"></a> of a molecule as conceived by science, and the
+permanent definiteness of a molecule in its turn yields to that of an
+electron. Thus science in its most ultimate formulation of law seeks
+objects with the most permanent definite simplicity of character and
+expresses its final laws in terms of them.</p>
+
+<p>Again when we seek definitely to express the relations of events which
+arise from their spatio-temporal structure, we approximate to simplicity
+by progressively diminishing the extent (both temporal and spatial) of
+the events considered. For example, the event which is the life of the
+chunk of nature which is the Needle during one minute has to the life of
+nature within a passing barge during the same minute a very complex
+spatio-temporal relation. But suppose we progressively diminish the time
+considered to a second, to a hundredth of a second, to a thousandth of a
+second, and so on. As we pass along such a series we approximate to an
+ideal simplicity of structural relations of the pairs of events
+successively considered, which ideal we call the spatial relations of
+the Needle to the barge at some instant. Even these relations are too
+complicated for us, and we consider smaller and smaller bits of the
+Needle and of the barge. Thus we finally reach the ideal of an event so
+restricted in its extension as to be without extension in space or
+extension in time. Such an event is a mere spatial point-flash of
+instantaneous duration. I call such an ideal event an &lsquo;event-particle.&rsquo;
+You must not think of the world as ultimately built up of
+event-particles. That is to put the cart before the horse. The world we
+know is a continuous stream of occurrence which we can discriminate into
+finite events forming by their overlappings and containings of each
+other and<span class="pagenum" title="Page&nbsp;173">&nbsp;</span><a name="Page_173" id="Page_173"></a> separations a spatio-temporal structure. We can express the
+properties of this structure in terms of the ideal limits to routes of
+approximation, which I have termed event-particles. Accordingly
+event-particles are abstractions in their relations to the more concrete
+events. But then by this time you will have comprehended that you cannot
+analyse concrete nature without abstracting. Also I repeat, the
+abstractions of science are entities which are truly in nature, though
+they have no meaning in isolation from nature.</p>
+
+<p>The character of the spatio-temporal structure of events can be fully
+expressed in terms of relations between these more abstract
+event-particles. The advantage of dealing with event-particles is that
+though they are abstract and complex in respect to the finite events
+which we directly observe, they are simpler than finite events in
+respect to their mutual relations. Accordingly they express for us the
+demands of an ideal accuracy, and of an ideal simplicity in the
+exposition of relations. These event-particles are the ultimate elements
+of the four-dimensional space-time manifold which the theory of
+relativity presupposes. You will have observed that each event-particle
+is as much an instant of time as it is a point of space. I have called
+it an instantaneous point-flash. Thus in the structure of this
+space-time manifold space is not finally discriminated from time, and
+the possibility remains open for diverse modes of discrimination
+according to the diverse circumstances of observers. It is this
+possibility which makes the fundamental distinction between the new way
+of conceiving the universe and the old way. The secret of understanding
+relativity is to understand this. It is of no use rushing in with
+picturesque paradoxes, such as<span class="pagenum" title="Page&nbsp;174">&nbsp;</span><a name="Page_174" id="Page_174"></a> &lsquo;Space caught bending,&rsquo; if you have not
+mastered this fundamental conception which underlies the whole theory.
+When I say that it underlies the whole theory, I mean that in my opinion
+it ought to underlie it, though I may confess some doubts as to how far
+all expositions of the theory have really understood its implications
+and its premises.</p>
+
+<p>Our measurements when they are expressed in terms of an ideal accuracy
+are measurements which express properties of the space-time manifold.
+Now there are measurements of different sorts. You can measure lengths,
+or angles, or areas, or volumes, or times. There are also other sorts of
+measures such as measurements of intensity of illumination, but I will
+disregard these for the moment and will confine attention to those
+measurements which particularly interest us as being measurements of
+space or of time. It is easy to see that four such measurements of the
+proper characters are necessary to determine the position of an
+event-particle in the space-time manifold in its relation to the rest of
+the manifold. For example, in a rectangular field you start from one
+corner at a given time, you measure a definite distance along one side,
+you then strike out into the field at right angles, and then measure a
+definite distance parallel to the other pair of sides, you then rise
+vertically a definite height and take the time. At the point and at the
+time which you thus reach there is occurring a definite instantaneous
+point-flash of nature. In other words, your four measurements have
+determined a definite event-particle belonging to the four-dimension
+space-time manifold. These measurements have appeared to be very simple
+to the land-surveyor and raise in his mind no philosophic difficulties.
+But<span class="pagenum" title="Page&nbsp;175">&nbsp;</span><a name="Page_175" id="Page_175"></a> suppose there are beings on Mars sufficiently advanced in
+scientific invention to be able to watch in detail the operations of
+this survey on earth. Suppose that they construe the operations of the
+English land-surveyors in reference to the space natural to a being on
+Mars, namely a Martio-centric space in which that planet is fixed. The
+earth is moving relatively to Mars and is rotating. To the beings on
+Mars the operations, construed in this fashion, effect measurements of
+the greatest complication. Furthermore, according to the relativistic
+doctrine, the operation of time-measurement on earth will not correspond
+quite exactly to any time-measurement on Mars.</p>
+
+<p>I have discussed this example in order to make you realise that in
+thinking of the possibilities of measurement in the space-time manifold,
+we must not confine ourselves merely to those minor variations which
+might seem natural to human beings on the earth. Let us make therefore
+the general statement that four measurements, respectively of
+independent types (such as measurements of lengths in three directions
+and a time), can be found such that a definite event-particle is
+determined by them in its relations to other parts of the manifold.</p>
+
+<p>If (<i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>, <i>p</i><sub>3</sub>, <i>p</i><sub>4</sub>) be a set of measurements of this
+system, then the event-particle which is thus determined will be said to
+have <i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>, <i>p</i><sub>3</sub>, <i>p</i><sub>4</sub> as its co-ordinates in this
+system of measurement. Suppose that we name it the <i>p</i>-system of
+measurement. Then in the same <i>p</i>-system by properly varying (<i>p</i><sub>1</sub>,
+<i>p</i><sub>2</sub>, <i>p</i><sub>3</sub>, <i>p</i><sub>4</sub>) every event-particle that has been, or will
+be, or instantaneously is now, can be indicated. Furthermore, according
+to any system of measurement that is natural to us,<span class="pagenum" title="Page&nbsp;176">&nbsp;</span><a name="Page_176" id="Page_176"></a> three of the
+co-ordinates will be measurements of space and one will be a measurement
+of time. Let us always take the last co-ordinate to represent the
+time-measurement. Then we should naturally say that (<i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>,
+<i>p</i><sub>3</sub>) determined a point in space and that the event-particle
+happened at that point at the time <i>p</i><sub>4</sub>. But we must not make the
+mistake of thinking that there is a space in addition to the space-time
+manifold. That manifold is all that there is for the determination of
+the meaning of space and time. We have got to determine the meaning of a
+space-point in terms of the event-particles of the four-dimensional
+manifold. There is only one way to do this. Note that if we vary the
+time and take times with the same three space co-ordinates, then the
+event-particles, thus indicated, are all at the same point. But seeing
+that there is nothing else except the event-particles, this can only
+mean that the point (<i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>, <i>p</i><sub>3</sub>) of the space in the
+<i>p</i>-system is merely the collection of event-particles (<i>p</i><sub>1</sub>,
+<i>p</i><sub>2</sub>, <i>p</i><sub>3</sub>, [<i>p</i><sub>4</sub>]), where <i>p</i><sub>4</sub> is varied and (<i>p</i><sub>1</sub>,
+<i>p</i><sub>2</sub>, <i>p</i><sub>3</sub>) is kept fixed. It is rather disconcerting to find that
+a point in space is not a simple entity; but it is a conclusion which
+follows immediately from the relative theory of space.</p>
+
+<p>Furthermore the inhabitant of Mars determines event-particles by another
+system of measurements. Call his system the <i>q</i>-system. According to him
+(<i>q</i><sub>1</sub>, <i>q</i><sub>2</sub>, <i>q</i><sub>3</sub>, <i>q</i><sub>4</sub>) determines an event-particle, and
+(<i>q</i><sub>1</sub>, <i>q</i><sub>2</sub>, <i>q</i><sub>3</sub>) determines a point and <i>q</i><sub>4</sub> a time. But
+the collection of event-particles which he thinks of as a point is
+entirely different from any such collection which the man on earth
+thinks of as a point. Thus the <i>q</i>-space for the man on Mars is quite
+different from the <i>p</i>-space for the land-surveyor on earth.</p>
+
+<p><span class="pagenum" title="Page&nbsp;177">&nbsp;</span><a name="Page_177" id="Page_177"></a>So far in speaking of space we have been talking of the timeless space
+of physical science, namely, of our concept of eternal space in which
+the world adventures. But the space which we see as we look about is
+instantaneous space. Thus if our natural perceptions are adjustable to
+the <i>p</i>-system of measurements we see instantaneously all the
+event-particles at some definite time <i>p</i><sub>4</sub>, and observe a succession
+of such spaces as time moves on. The timeless space is achieved by
+stringing together all these instantaneous spaces. The points of an
+instantaneous space are event-particles, and the points of an eternal
+space are strings of event-particles occurring in succession. But the
+man on Mars will never perceive the same instantaneous spaces as the man
+on the earth. This system of instantaneous spaces will cut across the
+earth-man&#8217;s system. For the earth-man there is one instantaneous space
+which is the instantaneous present, there are the past spaces and the
+future spaces. But the present space of the man on Mars cuts across the
+present space of the man on the earth. So that of the event-particles
+which the earth-man thinks of as happening now in the present, the man
+on Mars thinks that some are already past and are ancient history, that
+others are in the future, and others are in the immediate present. This
+break-down in the neat conception of a past, a present, and a future is
+a serious paradox. I call two event-particles which on some or other
+system of measurement are in the same instantaneous space &lsquo;co-present&rsquo;
+event-particles. Then it is possible that <i>A</i> and <i>B</i> may be co-present,
+and that <i>A</i> and <i>C</i> may be co-present, but that <i>B</i> and <i>C</i> may not be
+co-present. For example, at some inconceivable distance from us there
+are events co-present with us<span class="pagenum" title="Page&nbsp;178">&nbsp;</span><a name="Page_178" id="Page_178"></a> now and also co-present with the birth of
+Queen Victoria. If <i>A</i> and <i>B</i> are co-present there will be some systems
+in which <i>A</i> precedes <i>B</i> and some in which <i>B</i> precedes <i>A</i>. Also there
+can be no velocity quick enough to carry a material particle from <i>A</i> to
+<i>B</i> or from <i>B</i> to <i>A</i>. These different measure-systems with their
+divergences of time-reckoning are puzzling, and to some extent affront
+our common sense. It is not the usual way in which we think of the
+Universe. We think of one necessary time-system and one necessary space.
+According to the new theory, there are an indefinite number of
+discordant time-series and an indefinite number of distinct spaces. Any
+correlated pair, a time-system and a space-system, will do in which to
+fit our description of the Universe. We find that under given conditions
+our measurements are necessarily made in some one pair which together
+form our natural measure-system. The difficulty as to discordant
+time-systems is partly solved by distinguishing between what I call the
+creative advance of nature, which is not properly serial at all, and any
+one time series. We habitually muddle together this creative advance,
+which we experience and know as the perpetual transition of nature into
+novelty, with the single-time series which we naturally employ for
+measurement. The various time-series each measure some aspect of the
+creative advance, and the whole bundle of them express all the
+properties of this advance which are measurable. The reason why we have
+not previously noted this difference of time-series is the very small
+difference of properties between any two such series. Any observable
+phenomena due to this cause depend on the square of the ratio of any
+velocity entering into the observation to<span class="pagenum" title="Page&nbsp;179">&nbsp;</span><a name="Page_179" id="Page_179"></a> the velocity of light. Now
+light takes about fifty minutes to get round the earth&#8217;s orbit; and the
+earth takes rather more than 17,531&nbsp;half-hours to do the same. Hence all
+the effects due to this motion are of the order of the ratio of one to
+the square of 10,000. Accordingly an earth-man and a sun-man have only
+neglected effects whose quantitative magnitudes all contain the factor
+1/10<sup>8</sup>. Evidently such effects can only be noted by means of the most
+refined observations. They have been observed however. Suppose we
+compare two observations on the velocity of light made with the same
+apparatus as we turn it through a right angle. The velocity of the earth
+relatively to the sun is in one direction, the velocity of light
+relatively to the ether should be the same in all directions. Hence if
+space when we take the ether as at rest means the same thing as space
+when we take the earth as at rest, we ought to find that the velocity of
+light relatively to the earth varies according to the direction from
+which it comes.</p>
+
+<p>These observations on earth constitute the basic principle of the famous
+experiments designed to detect the motion of the earth through the
+ether. You all know that, quite unexpectedly, they gave a null result.
+This is completely explained by the fact that, the space-system and the
+time-system which we are using are in certain minute ways different from
+the space and the time relatively to the sun or relatively to any other
+body with respect to which it is moving.</p>
+
+<p>All this discussion as to the nature of time and space has lifted above
+our horizon a great difficulty which affects the formulation of all the
+ultimate laws of physics&mdash;for example, the laws of the electromagnetic
+field, and the law of gravitation. Let us take the law of<span class="pagenum" title="Page&nbsp;180">&nbsp;</span><a name="Page_180" id="Page_180"></a> gravitation
+as an example. Its formulation is as follows: Two material bodies
+attract each other with a force proportional to the product of their
+masses and <a name="err2" id="err2"></a><ins class="correction" title="Transcriber&#8217;s Note: Original read &lsquo;universely&rsquo;.">inversely</ins> proportional to the square of their distances.
+In this statement the bodies are supposed to be small enough to be
+treated as material particles in relation to their distances; and we
+need not bother further about that minor point. The difficulty to which
+I want to draw your attention is this: In the formulation of the law one
+definite time and one definite space are presupposed. The two masses are
+assumed to be in simultaneous positions.</p>
+
+<p>But what is simultaneous in one time-system may not be simultaneous in
+another time-system. So according to our new views the law is in this
+respect not formulated so as to have any exact meaning. Furthermore an
+analogous difficulty arises over the question of distance. The distance
+between two instantaneous positions, <i>i.e.</i> between two event-particles,
+is different in different space-systems. What space is to be chosen?
+Thus again the law lacks precise formulation, if relativity is accepted.
+Our problem is to seek a fresh interpretation of the law of gravity in
+which these difficulties are evaded. In the first place we must avoid
+the abstractions of space and time in the formulation of our fundamental
+ideas and must recur to the ultimate facts of nature, namely to events.
+Also in order to find the ideal simplicity of expressions of the
+relations between events, we restrict ourselves to event-particles. Thus
+the life of a material particle is its adventure amid a track of
+event-particles strung out as a continuous series or path in the
+four-dimensional space-time manifold. These event-particles are the
+various situations of the material particle. We<span class="pagenum" title="Page&nbsp;181">&nbsp;</span><a name="Page_181" id="Page_181"></a> usually express this
+fact by adopting our natural space-time system and by talking of the
+path in space of the material particle as it exists at successive
+instants of time.</p>
+
+<p>We have to ask ourselves what are the laws of nature which lead the
+material particle to adopt just this path among event-particles and no
+other. Think of the path as a whole. What characteristic has that path
+got which would not be shared by any other slightly varied path? We are
+asking for more than a law of gravity. We want laws of motion and a
+general idea of the way to formulate the effects of physical forces.</p>
+
+<p>In order to answer our question we put the idea of the attracting masses
+in the background and concentrate attention on the field of activity of
+the events in the neighbourhood of the path. In so doing we are acting
+in conformity with the whole trend of scientific thought during the last
+hundred years, which has more and more concentrated attention on the
+field of force as the immediate agent in directing motion, to the
+exclusion of the consideration of the immediate mutual influence between
+two distant bodies. We have got to find the way of expressing the field
+of activity of events in the neighbourhood of some definite
+event-particle <i>E</i> of the four-dimensional manifold. I bring in a
+fundamental physical idea which I call the &lsquo;impetus&rsquo; to express this
+physical field. The event-particle <i>E</i> is related to any neighbouring
+event-particle <i>P</i> by an element of impetus. The assemblage of all the
+elements of impetus relating <i>E</i> to the assemblage of event-particles in
+the neighbourhood of <i>E</i> expresses the character of the field of
+activity in the neighbourhood of <i>E</i>. Where I differ from Einstein is
+that he conceives this quantity which I call the impetus as merely
+expressing the characters of the space and<span class="pagenum" title="Page&nbsp;182">&nbsp;</span><a name="Page_182" id="Page_182"></a> time to be adopted and thus
+ends by talking of the gravitational field expressing a curvature in the
+space-time manifold. I cannot attach any clear conception to his
+interpretation of space and time. My formulae differ slightly from his,
+though they agree in those instances where his results have been
+verified. I need hardly say that in this particular of the formulation
+of the law of gravitation I have drawn on the general method of
+procedure which constitutes his great discovery.</p>
+
+<p>Einstein showed how to express the characters of the assemblage of
+elements of impetus of the field surrounding an event-particle <i>E</i> in
+terms of ten quantities which I will call <i>J</i><sub>11</sub>, <i>J</i><sub>12</sub>
+(=<i>J</i><sub>21</sub>), <i>J</i><sub>22</sub>, <i>J</i><sub>23</sub>(=<i>J</i><sub>32</sub>), etc. It will be noted that
+there are four spatio-temporal measurements relating <i>E</i> to its
+neighbour <i>P</i>, and that there are ten pairs of such measurements if we
+are allowed to take any one measurement twice over to make one such
+pair. The ten <i>J</i>&#8217;s depend merely on the position of <i>E</i> in the
+four-dimensional manifold, and the element of impetus between <i>E</i> and
+<i>P</i> can be expressed in terms of the ten <i>J</i>&#8217;s and the ten pairs of the
+four spatio-temporal measurements relating <i>E</i> and <i>P</i>. The numerical
+values of the <i>J</i>&#8217;s will depend on the system of measurement adopted,
+but are so adjusted to each particular system that the same value is
+obtained for the element of impetus between <i>E</i> and <i>P</i>, whatever be the
+system of measurement adopted. This fact is expressed by saying that the
+ten <i>J</i>&#8217;s form a &lsquo;tensor.&rsquo; It is not going too far to say that the
+announcement that physicists would have in future to study the theory of
+tensors created a veritable panic among them when the verification of
+Einstein&#8217;s predictions was first announced.</p>
+
+<p><span class="pagenum" title="Page&nbsp;183">&nbsp;</span><a name="Page_183" id="Page_183"></a>The ten <i>J</i>&#8217;s at any event-particle <i>E</i> can be expressed in terms of two
+functions which I call the potential and the &lsquo;associate-potential&rsquo; at
+<i>E</i>. The potential is practically what is meant by the ordinary
+gravitation potential, when we express ourselves in terms of the
+Euclidean space in reference to which the attracting mass is at rest.
+The associate-potential is defined by the modification of substituting
+the direct distance for the inverse distance in the definition of the
+potential, and its calculation can easily be made to depend on that of
+the old-fashioned potential. Thus the calculation of the <i>J</i>&#8217;s&mdash;the
+coefficients of impetus, as I will call them&mdash;does not involve anything
+very revolutionary in the mathematical knowledge of physicists. We now
+return to the path of the attracted particle. We add up all the elements
+of impetus in the whole path, and obtain thereby what I call the
+&lsquo;integral impetus.&rsquo; The characteristic of the actual path as compared
+with neighbouring alternative paths is that in the actual paths the
+integral impetus would neither gain nor lose, if the particle wobbled
+out of it into a small extremely near alternative path. Mathematicians
+would express this by saying, that the integral impetus is stationary
+for an infinitesimal displacement. In this statement of the law of
+motion I have neglected the existence of other forces. But that would
+lead me too far afield.</p>
+
+<p>The electromagnetic theory has to be modified to allow for the presence
+of a gravitational field. Thus Einstein&#8217;s investigations lead to the
+first discovery of any relation between gravity and other physical
+phenomena. In the form in which I have put this modification, we deduce
+Einstein&#8217;s fundamental principle, as to the motion of light along its
+rays, as a first approximation<span class="pagenum" title="Page&nbsp;184">&nbsp;</span><a name="Page_184" id="Page_184"></a> which is absolutely true for infinitely
+short waves. Einstein&#8217;s principle, thus partially verified, stated in my
+language is that a ray of light always follows a path such that the
+integral impetus along it is zero. This involves that every element of
+impetus along it is zero.</p>
+
+<p>In conclusion, I must apologise. In the first place I have considerably
+toned down the various exciting peculiarities of the original theory and
+have reduced it to a greater conformity with the older physics. I do not
+allow that physical phenomena are due to oddities of space. Also I have
+added to the dullness of the lecture by my respect for the audience. You
+would have enjoyed a more popular lecture with illustrations of
+delightful paradoxes. But I know also that you are serious students who
+are here because you really want to know how the new theories may affect
+your scientific researches.</p>
+
+<hr />
+<h2><span class="pagenum" title="Page&nbsp;185">&nbsp;</span><a name="Page_185" id="Page_185"></a><a name="CHAPTER_IX" id="CHAPTER_IX"></a>CHAPTER IX
+<br />
+THE ULTIMATE PHYSICAL CONCEPTS</h2>
+
+
+<p>The second chapter of this book lays down the first principle to be
+guarded in framing our physical concept. We must avoid vicious
+bifurcation. Nature is nothing else than the deliverance of
+sense-awareness. We have no principles whatever to tell us what could
+stimulate mind towards sense-awareness. Our sole task is to exhibit in
+one system the characters and inter-relations of all that is observed.
+Our attitude towards nature is purely &lsquo;behaviouristic,&rsquo; so far as
+concerns the formulation of physical concepts.</p>
+
+<p>Our knowledge of nature is an experience of activity (or passage). The
+things previously observed are active entities, the &lsquo;events.&rsquo; They are
+chunks in the life of nature. These events have to each other relations
+which in our knowledge differentiate themselves into space-relations and
+time-relations. But this differentiation between space and time, though
+inherent in nature, is comparatively superficial; and space and time are
+each partial expressions of one fundamental relation between events
+which is neither spatial nor temporal. This relation I call &lsquo;extension.&rsquo;
+The relation of &lsquo;extending over&rsquo; is the relation of &lsquo;including,&rsquo; either
+in a spatial or in a temporal sense, or in both. But the mere
+&lsquo;inclusion&rsquo; is more fundamental than either alternative and does not
+require any spatio-temporal differentiation. In respect to extension two
+events are mutually related so that either (i) one includes the other,
+or (ii) one overlaps the other without complete inclusion, or (iii)
+they<span class="pagenum" title="Page&nbsp;186">&nbsp;</span><a name="Page_186" id="Page_186"></a> are entirely separate. But great care is required in the
+definition of spatial and temporal elements from this basis in order to
+avoid tacit limitations really depending on undefined relations and
+properties.</p>
+
+<p>Such fallacies can be avoided by taking account of two elements in our
+experience, namely, (i) our observational &lsquo;present,&rsquo; and (ii) our
+&lsquo;percipient event.&rsquo;</p>
+
+<p>Our observational &lsquo;present&rsquo; is what I call a &lsquo;duration.&rsquo; It is the whole
+of nature apprehended in our immediate observation. It has therefore the
+nature of an event, but possesses a peculiar completeness which marks
+out such durations as a special type of events inherent in nature. A
+duration is not instantaneous. It is all that there is of nature with
+certain temporal limitations. In contradistinction to other events a
+duration will be called infinite and the other events are finite<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a>. In
+our knowledge of a duration we distinguish (i) certain included events
+which are particularly discriminated as to their peculiar
+individualities, and (ii) the remaining included events which are only
+known as necessarily in being by reason of their relations to the
+discriminated events and to the whole duration. The duration as a whole
+is signified<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a> by that quality of relatedness (in respect to
+extension) possessed by the part which is immediately under observation;
+namely, by the fact that there is essentially a beyond to whatever is
+observed. I mean by this that every event is known as being related to
+other events which it does not include. This fact, that every event is
+known as possessing the quality of exclusion, shows that exclusion is as
+positive a relation as inclusion. There are of course no merely
+negative<span class="pagenum" title="Page&nbsp;187">&nbsp;</span><a name="Page_187" id="Page_187"></a> relations in nature, and exclusion is not the mere negative of
+inclusion, though the two relations are contraries. Both relations are
+concerned solely with events, and exclusion is capable of logical
+definition in terms of inclusion.</p>
+
+<div class="footnote"><p><a name="Footnote_10_10" id="Footnote_10_10"></a><span class="label"><a href="#FNanchor_10_10">[10]</a></span> Cf. note on &lsquo;significance,&rsquo; pp.&nbsp;<a href="#Page_197">197</a>, <a href="#Page_198">198</a>.</p></div>
+
+<div class="footnote"><p><a name="Footnote_11_11" id="Footnote_11_11"></a><span class="label"><a href="#FNanchor_11_11">[11]</a></span> Cf. Ch.&nbsp;<a href="#CHAPTER_III">III</a>, pp.&nbsp;<a href="#Page_51">51</a> et&nbsp;seq.</p></div>
+
+<p>Perhaps the most obvious exhibition of significance is to be found in
+our knowledge of the geometrical character of events inside an opaque
+material object. For example we know that an opaque sphere has a centre.
+This knowledge has nothing to do with the material; the sphere may be a
+solid uniform billiard ball or a hollow lawn-tennis ball. Such knowledge
+is essentially the product of significance, since the general character
+of the external discriminated events has informed us that there are
+events within the sphere and has also informed us of their geometrical
+structure.</p>
+
+<p>Some criticisms on &lsquo;The Principles of Natural Knowledge&rsquo; show that
+difficulty has been found in apprehending durations as real
+stratifications of nature. I think that this hesitation arises from the
+unconscious influence of the vicious principle of bifurcation, so deeply
+embedded in modern philosophical thought. We observe nature as extended
+in an immediate present which is simultaneous but not instantaneous, and
+therefore the whole which is immediately discerned or signified as an
+inter-related system forms a stratification of nature which is a
+physical fact. This conclusion immediately follows unless we admit
+bifurcation in the form of the principle of psychic additions, here
+rejected.</p>
+
+<p>Our &lsquo;percipient event&rsquo; is that event included in our observational
+present which we distinguish as being in some peculiar way our
+standpoint for perception. It is roughly speaking that event which is
+our bodily life<span class="pagenum" title="Page&nbsp;188">&nbsp;</span><a name="Page_188" id="Page_188"></a> within the present duration. The theory of perception
+as evolved by medical psychology is based on significance. The distant
+situation of a perceived object is merely known to us as signified by
+our bodily state, <i>i.e.</i> by our percipient event. In fact perception
+requires sense-awareness of the significations of our percipient event
+together with sense-awareness of a peculiar relation (situation) between
+certain objects and the events thus signified. Our percipient event is
+saved by being the whole of nature by this fact of its significations.
+This is the meaning of calling the percipient event our standpoint for
+perception. The course of a ray of light is only derivatively connected
+with perception. What we do perceive are objects as related to events
+signified by the bodily states excited by the ray. These signified
+events (as is the case of images seen behind a mirror) may have very
+little to do with the actual course of the ray. In the course of
+evolution those animals have survived whose sense-awareness is
+concentrated on those significations of their bodily states which are on
+the average important for their welfare. The whole world of events is
+signified, but there are some which exact the death penalty for
+inattention.</p>
+
+<p>The percipient event is always here and now in the associated present
+duration. It has, what may be called, an absolute position in that
+duration. Thus one definite duration is associated with a definite
+percipient event, and we are thus aware of a peculiar relation which
+finite events can bear to durations. I call this relation &lsquo;cogredience.&rsquo;
+The notion of rest is derivative from that of cogredience, and the
+notion of motion is derivative from that of inclusion within a duration
+without cogredience with it. In fact motion is a relation (of varying<span class="pagenum" title="Page&nbsp;189">&nbsp;</span><a name="Page_189" id="Page_189"></a>
+character) between an observed event and an observed duration, and
+cogredience is the most simple character or subspecies of motion. To sum
+up, a duration and a percipient event are essentially involved in the
+general character of each observation of nature, and the percipient
+event is cogredient with the duration.</p>
+
+<p>Our knowledge of the peculiar characters of different events depends
+upon our power of comparison. I call the exercise of this factor in our
+knowledge &lsquo;recognition,&rsquo; and the requisite sense-awareness of the
+comparable characters I call &lsquo;sense-recognition.&rsquo; Recognition and
+abstraction essentially involve each other. Each of them exhibits an
+entity for knowledge which is less than the concrete fact, but is a real
+factor in that fact. The most concrete fact capable of separate
+discrimination is the event. We cannot abstract without recognition, and
+we cannot recognise without abstraction. Perception involves
+apprehension of the event and recognition of the factors of its
+character.</p>
+
+<p>The things recognised are what I call &lsquo;objects.&rsquo; In this general sense
+of the term the relation of extension is itself an object. In practice
+however I restrict the term to those objects which can in some sense or
+other be said to have a situation in an event; namely, in the phrase
+&lsquo;There it is again&rsquo; I restrict the &lsquo;there&rsquo; to be the indication of a
+special event which is the situation of the object. Even so, there are
+different types of objects, and statements which are true of objects of
+one type are not in general true of objects of other types. The objects
+with which we are here concerned in the formulation of physical laws are
+material objects, such as bits of matter, molecules and electrons. An
+object of one of these types has relations to events other than those<span class="pagenum" title="Page&nbsp;190">&nbsp;</span><a name="Page_190" id="Page_190"></a>
+belonging to the stream of its situations. The fact of its situations
+within this stream has impressed on all other events certain
+modifications of their characters. In truth the object in its
+completeness may be conceived as a specific set of correlated
+modifications of the characters of all events, with the property that
+these modifications attain to a certain focal property for those events
+which belong to the stream of its situations. The total assemblage of
+the modifications of the characters of events due to the existence of an
+object in a stream of situations is what I call the &lsquo;physical field&rsquo; due
+to the object. But the object cannot really be separated from its field.
+The object is in fact nothing else than the systematically adjusted set
+of modifications of the field. The conventional limitation of the object
+to the focal stream of events in which it is said to be &lsquo;situated&rsquo; is
+convenient for some purposes, but it obscures the ultimate fact of
+nature. From this point of view the antithesis between action at a
+distance and action by transmission is meaningless. The doctrine of this
+paragraph is nothing else than another way of expressing the
+unresolvable multiple relation of an object to events.</p>
+
+<p>A complete time-system is formed by any one family of parallel
+durations. Two durations are parallel if either (i) one includes the
+other, or (ii) they overlap so as to include a third duration common to
+both, or (iii) are entirely separate. The excluded case is that of two
+durations overlapping so as to include in common an aggregate of finite
+events but including in common no other complete duration. The
+recognition of the fact of an indefinite number of families of parallel
+durations is what differentiates the concept of nature here put forward
+from the older orthodox concept of<span class="pagenum" title="Page&nbsp;191">&nbsp;</span><a name="Page_191" id="Page_191"></a> the essentially unique time-systems.
+Its divergence from Einstein&#8217;s concept of nature will be briefly
+indicated later.</p>
+
+<p>The instantaneous spaces of a given time-system are the ideal
+(non-existent) durations of zero temporal thickness indicated by routes
+of approximation along series formed by durations of the associated
+family. Each such instantaneous space represents the ideal of nature at
+an instant and is also a moment of time. Each time-system thus possesses
+an aggregate of moments belonging to it alone. Each event-particle lies
+in one and only one moment of a given time-system. An event-particle has
+three characters<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a>: (i) its extrinsic character which is its character
+as a definite route of convergence among events, (ii) its intrinsic
+character which is the peculiar quality of nature in its neighbourhood,
+namely, the character of the physical field in the neighbourhood, and
+(iii) its position.</p>
+
+<div class="footnote"><p><a name="Footnote_12_12" id="Footnote_12_12"></a><span class="label"><a href="#FNanchor_12_12">[12]</a></span> Cf. pp.&nbsp;<a href="#Page_82">82</a> et&nbsp;seq.</p></div>
+
+<p>The position of an event-particle arises from the aggregate of moments
+(no two of the same family) in which it lies. We fix our attention on
+one of these moments which is approximated to by the short duration of
+our immediate experience, and we express position as the position in
+this moment. But the event-particle receives its position in moment <i>M</i>
+in virtue of the whole aggregate of other moments <i>M</i>&#8242;, <i>M</i>&#8243;, etc.,
+in which it also lies. The differentiation of <i>M</i> into a geometry of
+event-particles (instantaneous points) expresses the differentiation of
+<i>M</i> by its intersections with moments of alien time-systems. In this way
+planes and straight lines and event-particles themselves find their
+being. Also the parallelism of planes and straight lines arises from the
+parallelism of the moments of one and<span class="pagenum" title="Page&nbsp;192">&nbsp;</span><a name="Page_192" id="Page_192"></a> the same time-system intersecting
+<i>M</i>. Similarly the order of parallel planes and of event-particles on
+straight lines arises from the time-order of these intersecting moments.
+The explanation is not given here<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a>. It is sufficient now merely to
+mention the sources from which the whole of geometry receives its
+physical explanation.</p>
+
+<div class="footnote"><p><a name="Footnote_13_13" id="Footnote_13_13"></a><span class="label"><a href="#FNanchor_13_13">[13]</a></span> Cf. <i>Principles of Natural Knowledge</i>, and previous
+chapters of the present work.</p></div>
+
+<p>The correlation of the various momentary spaces of one time-system is
+achieved by the relation of cogredience. Evidently motion in an
+instantaneous space is unmeaning. Motion expresses a comparison between
+position in one instantaneous space with positions in other
+instantaneous spaces of the same time-system. Cogredience yields the
+simplest outcome of such comparison, namely, rest.</p>
+
+<p>Motion and rest are immediately observed facts. They are relative in the
+sense that they depend on the time-system which is fundamental for the
+observation. A string of event-particles whose successive occupation
+means rest in the given time-system forms a timeless point in the
+timeless space of that time-system. In this way each time-system
+possesses its own permanent timeless space peculiar to it alone, and
+each such space is composed of timeless points which belong to that
+time-system and to no other. The paradoxes of relativity arise from
+neglecting the fact that different assumptions as to rest involve the
+expression of the facts of physical science in terms of radically
+different spaces and times, in which points and moments have different
+meanings.</p>
+
+<p>The source of order has already been indicated and that of congruence is
+now found. It depends on motion.<span class="pagenum" title="Page&nbsp;193">&nbsp;</span><a name="Page_193" id="Page_193"></a> From cogredience, perpendicularity
+arises; and from perpendicularity in conjunction with the reciprocal
+symmetry between the relations of any two time-systems congruence both
+in time and space is completely defined (cf. <i>loc. cit.</i>).</p>
+
+<p>The resulting formulae are those for the electromagnetic theory of
+relativity, or, as it is now termed, the restricted theory. But there is
+this vital difference: the critical velocity <i>c</i> which occurs in these
+formulae has now no connexion whatever with light or with any other fact
+of the physical field (in distinction from the extensional structure of
+events). It simply marks the fact that our congruence determination
+embraces both times and spaces in one universal system, and therefore if
+two arbitrary units are chosen, one for all spaces and one for all
+times, their ratio will be a velocity which is a fundamental property of
+nature expressing the fact that times and spaces are really comparable.</p>
+
+<p>The physical properties of nature are expressed in terms of material
+objects (electrons, etc.). The physical character of an event arises
+from the fact that it belongs to the field of the whole complex of such
+objects. From another point of view we can say that these objects are
+nothing else than our way of expressing the mutual correlation of the
+physical characters of events.</p>
+
+<p>The spatio-temporal measurableness of nature arises from (i) the
+relation of extension between events, and (ii) the stratified character
+of nature arising from each of the alternative time-systems, and (iii)
+rest and motion, as exhibited in the relations of finite events to
+time-systems. None of these sources of measurement depend on the
+physical characters of finite events as exhibited by the situated
+objects. They are completely signified<span class="pagenum" title="Page&nbsp;194">&nbsp;</span><a name="Page_194" id="Page_194"></a> for events whose physical
+characters are unknown. Thus the spatio-temporal measurements are
+independent of the objectival physical characters. Furthermore the
+character of our knowledge of a whole duration, which is essentially
+derived from the significance of the part within the immediate field of
+discrimination, constructs it for us as a uniform whole independent, so
+far as its extension is concerned, of the unobserved characters of
+remote events. Namely, there is a definite whole of nature,
+simultaneously now present, whatever may be the character of its remote
+events. This consideration reinforces the previous conclusion. This
+conclusion leads to the assertion of the essential uniformity of the
+momentary spaces of the various time-systems, and thence to the
+uniformity of the timeless spaces of which there is one to each
+time-system.</p>
+
+<p>The analysis of the general character of observed nature set forth above
+affords explanations of various fundamental observational facts: (&#945;) It
+explains the differentiation of the one quality of extension into time
+and space. (&#946;) It gives a meaning to the observed facts of geometrical
+and temporal position, of geometrical and temporal order, and of
+geometrical straightness and planeness. (&#947;) It selects one definite
+system of congruence embracing both space and time, and thus explains
+the concordance as to measurement which is in practice attained. (&#948;) It
+explains (consistently with the theory of relativity) the observed
+phenomena of rotation, <i>e.g.</i> Foucault&#8217;s pendulum, the equatorial bulge
+of the earth, the fixed senses of rotation of cyclones and anticyclones,
+and the gyro-compass. It does this by its admission of definite
+stratifications of nature which are disclosed by the very character of
+our knowledge of it. (&#949;) Its ex<span class="pagenum" title="Page&nbsp;195">&nbsp;</span><a name="Page_195" id="Page_195"></a>planations of motion are more
+fundamental than those expressed in (&#948;); for it explains what is meant
+by motion itself. The observed motion of an extended object is the
+relation of its various situations to the stratification of nature
+expressed by the time-system fundamental to the observation. This motion
+expresses a real relation of the object to the rest of nature. The
+quantitative expression of this relation will vary according to the
+time-system selected for its expression.</p>
+
+<p>This theory accords no peculiar character to light beyond that accorded
+to other physical phenomena such as sound. There is no ground for such a
+differentiation. Some objects we know by sight only, and other objects
+we know by sound only, and other objects we observe neither by light nor
+by sound but by touch or smell or otherwise. The velocity of light
+varies according to its medium and so does that of sound. Light moves in
+curved paths under certain conditions and so does sound. Both light and
+sound are waves of disturbance in the physical characters of events; and
+(as has been stated above, p.&nbsp;<a href="#Page_188">188</a>) the actual course of the light is of
+no more importance for perception than is the actual course of the
+sound. To base the whole philosophy of nature upon light is a baseless
+assumption. The Michelson-Morley and analogous experiments show that
+within the limits of our inexactitude of observation the velocity of
+light is an approximation to the critical velocity &lsquo;<i>c</i>&rsquo; which expresses
+the relation between our space and time units. It is provable that the
+assumption as to light by which these experiments and the influence of
+the gravitational field on the light-rays are explained is deducible <i>as
+an approximation</i> from the equations of the electromagnetic field. This<span class="pagenum" title="Page&nbsp;196">&nbsp;</span><a name="Page_196" id="Page_196"></a>
+completely disposes of any necessity for differentiating light from
+other physical phenomena as possessing any peculiar fundamental
+character.</p>
+
+<p>It is to be observed that the measurement of extended nature by means of
+extended objects is meaningless apart from some observed fact of
+simultaneity inherent in nature and not merely a play of thought.
+Otherwise there is no meaning to the concept of one presentation of your
+extended measuring rod <i>AB</i>. Why not <i>AB&#8242;</i> where <i>B&#8242;</i> is the end <i>B</i>
+five minutes later? Measurement presupposes for its possibility nature
+as a simultaneity, and an observed object present then and present now.
+In other words, measurement of extended nature requires some inherent
+character in nature affording a rule of presentation of events.
+Furthermore congruence cannot be defined by the permanence of the
+measuring rod. The permanence is itself meaningless apart from some
+immediate judgment of self-congruence. Otherwise how is an elastic
+string differentiated from a rigid measuring rod? Each remains the same
+self-identical object. Why is one a possible measuring rod and the other
+not so? The meaning of congruence lies beyond the self-identity of the
+object. In other words measurement presupposes the measurable, and the
+theory of the measurable is the theory of congruence.</p>
+
+<p>Furthermore the admission of stratifications of nature bears on the
+formulation of the laws of nature. It has been laid down that these laws
+are to be expressed in differential equations which, as expressed in any
+general system of measurement, should bear no reference to any other
+particular measure-system. This requirement is purely arbitrary. For a
+measure-system measures something inherent in nature; otherwise it has
+no<span class="pagenum" title="Page&nbsp;197">&nbsp;</span><a name="Page_197" id="Page_197"></a> connexion with nature at all. And that something which is measured
+by a particular measure-system may have a special relation to the
+phenomenon whose law is being formulated. For example the gravitational
+field due to a material object at rest in a certain time-system may be
+expected to exhibit in its formulation particular reference to spatial
+and temporal quantities of that time-system. The field can of course be
+expressed in any measure-systems, but the particular reference will
+remain as the simple physical explanation.</p>
+
+
+<h3><a name="NOTE1" id="NOTE1"></a>NOTE: ON THE GREEK CONCEPT OF A POINT</h3>
+
+<p>The preceding pages had been passed for press before I had the pleasure
+of seeing Sir T.&nbsp;L. Heath&#8217;s <i>Euclid in Greek</i><a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a>. In the original
+Euclid&#8217;s first definition is</p>
+
+<p class="center"><ins class="info" title="Greek: s&ecirc;meion estin, ou meros outhen.">&#963;&#951;&#956;&#949;&#953;&#959;&#957; &#949;&#963;&#964;&#953;&#957;, &#959;&#965; &#956;&#949;&#961;&#959;&#962; &#959;&#965;&#952;&#949;&#957;.</ins>
+</p>
+
+<p>I have quoted it on p.&nbsp;<a href="#Page_86">86</a> in the expanded form taught to me in
+childhood, &lsquo;without parts and without magnitude.&rsquo; I should have
+consulted Heath&#8217;s English edition&mdash;a classic from the moment of its
+issue&mdash;before committing myself to a statement about Euclid. This is
+however a trivial correction not affecting sense and not worth a note. I
+wish here to draw attention to Heath&#8217;s own note to this definition in
+his <i>Euclid in Greek</i>. He summarises Greek thought on the nature of a
+point, from the Pythagoreans, through Plato and Aristotle, to Euclid. My
+analysis of the requisite character of a point on pp.&nbsp;<a href="#Page_89">89</a> and <a href="#Page_90">90</a> is in
+complete agreement with the outcome of the Greek discussion.</p>
+
+<div class="footnote"><p><a name="Footnote_14_14" id="Footnote_14_14"></a><span class="label"><a href="#FNanchor_14_14">[14]</a></span> Camb. Univ. Press, 1920.</p></div>
+
+
+<h3><a name="NOTE2" id="NOTE2"></a>NOTE: ON SIGNIFICANCE AND INFINITE EVENTS</h3>
+
+<p>The theory of significance has been expanded and made more definite in
+the present volume. It had already been introduced in the <i>Principles of
+Natural Knowledge</i> (cf. subarticles&nbsp;3.3 to 3.8 and 16.1, 16.2, 19.4, and
+articles&nbsp;20, 21). In reading over the proofs of the present volume, I
+come to the conclusion that in the<span class="pagenum" title="Page&nbsp;198">&nbsp;</span><a name="Page_198" id="Page_198"></a> light of this development my
+limitation of infinite events to durations is untenable. This limitation
+is stated in article&nbsp;33 of the <i>Principles</i> and at the beginning of
+<a href="#CHAPTER_IV">Chapter&nbsp;IV</a> (p.&nbsp;<a href="#Page_74">74</a>) of this book. There is not only a significance of the
+discerned events embracing the whole present duration, but there is a
+significance of a cogredient event involving its extension through a
+whole time-system backwards and forwards. In other words the essential
+&lsquo;beyond&rsquo; in nature is a definite beyond in time as well as in space [cf.
+pp.&nbsp;<a href="#Page_53">53</a>, <a href="#Page_194">194</a>]. This follows from my whole thesis as to the assimilation
+of time and space and their origin in extension. It also has the same
+basis in the analysis of the character of our knowledge of nature. It
+follows from this admission that it is possible to define point-tracks
+[<i>i.e.</i> the points of timeless spaces] as abstractive elements. This is
+a great improvement as restoring the balance between moments and points.
+I still hold however to the statement in subarticle&nbsp;35.4 of the
+<i>Principles</i> that the intersection of a pair of non-parallel durations
+does not present itself to us as one event. This correction does not
+affect any of the subsequent reasoning in the two books.</p>
+
+<p>I may take this opportunity of pointing out that the &lsquo;stationary events&rsquo;
+of article&nbsp;57 of the <i>Principles</i> are merely cogredient events got at
+from an abstract mathematical point of view.</p>
+
+<hr />
+<h2><span class="pagenum" title="Page&nbsp;199">&nbsp;</span><a name="Page_199" id="Page_199"></a><a name="INDEX" id="INDEX"></a>INDEX</h2>
+
+<p><i>In the case of terms of frequent occurrence, only those occurrences are
+indexed which are of peculiar importance for the elucidation of
+meaning.</i></p>
+<table class="az" border="1" summary="Alphabetic jump-table for the index">
+        <tr>
+            <td><a href="#IX_A">A</a></td>
+            <td><a href="#IX_B">B</a></td>
+            <td><a href="#IX_C">C</a></td>
+            <td><a href="#IX_D">D</a></td>
+            <td><a href="#IX_E">E</a></td>
+            <td><a href="#IX_F">F</a></td>
+            <td><a href="#IX_G">G</a></td>
+            <td><a href="#IX_H">H</a></td>
+            <td><a href="#IX_I">I</a></td>
+            <td><a href="#IX_J">J</a></td>
+            <td><a href="#IX_K">K</a></td>
+            <td><a href="#IX_L">L</a></td>
+            <td><a href="#IX_M">M</a></td>
+        </tr>
+        <tr>
+            <td><a href="#IX_N">N</a></td>
+            <td><a href="#IX_O">O</a></td>
+            <td><a href="#IX_P">P</a></td>
+            <td><a href="#IX_Q">Q</a></td>
+            <td><a href="#IX_R">R</a></td>
+            <td><a href="#IX_S">S</a></td>
+            <td><a href="#IX_T">T</a></td>
+            <td><a href="#IX_U">U</a></td>
+            <td><a href="#IX_V">V</a></td>
+            <td><a href="#IX_W">W</a></td>
+            <td>X</td>
+            <td><a href="#IX_Y">Y</a></td>
+            <td>Z</td>
+        </tr>
+</table>
+
+<ul class="IX">
+<li><a name="IX_A" id="IX_A"></a>A [<i>or</i> an], <a href="#Page_11">11</a></li>
+<li>Abraham, <a href="#Page_105">105</a></li>
+<li>Absolute position, <a href="#Page_105">105</a>, <a href="#Page_106">106</a>, <a href="#Page_114">114</a>, <a href="#Page_188">188</a></li>
+<li>Abstraction, <a href="#Page_33">33</a>, <a href="#Page_37">37</a>, <a href="#Page_168">168</a>, <a href="#Page_171">171</a>, <a href="#Page_173">173</a>;
+<ul class="IX">
+<li>extensive, <a href="#Page_65">65</a>, <a href="#Page_79">79</a>, <a href="#Page_85">85</a></li></ul></li>
+<li>Abstractive element, <a href="#Page_84">84</a>;
+<ul class="IX">
+<li>set, <a href="#Page_61">61</a>, <a href="#Page_79">79</a></li></ul></li>
+<li>Action at a distance, <a href="#Page_159">159</a>, <a href="#Page_190">190</a></li>
+<li>Action by transmission, <a href="#Page_159">159</a>, <a href="#Page_190">190</a></li>
+<li>Active conditions, <a href="#Page_158">158</a></li>
+<li>Activity, field of, <a href="#Page_170">170</a>, <a href="#Page_181">181</a></li>
+<li>Adjunction, <a href="#Page_101">101</a></li>
+<li>Aggregate, <a href="#Page_23">23</a></li>
+<li>Alexander, Prof., <a href="#Page_viii">viii</a></li>
+<li>Alexandria, <a href="#Page_71">71</a></li>
+<li>Alfred the Great, <a href="#Page_137">137</a></li>
+<li>Anticipation, <a href="#Page_69">69</a></li>
+<li>Anti-prime, <a href="#Page_88">88</a></li>
+<li>Apparent nature, <a href="#Page_31">31</a>, <a href="#Page_39">39</a></li>
+<li>Area, <a href="#Page_99">99</a>;
+<ul class="IX">
+<li>momental, <a href="#Page_103">103</a>;</li>
+<li>vagrant, <a href="#Page_103">103</a></li></ul></li>
+<li>Aristotelian logic, <a href="#Page_150">150</a></li>
+<li>Aristotle, <a href="#Page_16">16</a>, <a href="#Page_17">17</a>, <a href="#Page_18">18</a>, <a href="#Page_24">24</a>, <a href="#Page_197">197</a></li>
+<li>Associate-potential, <a href="#Page_183">183</a></li>
+<li>Atom, <a href="#Page_17">17</a></li>
+<li>Attribute, <a href="#Page_21">21</a>, <a href="#Page_26">26</a>, <a href="#Page_150">150</a></li>
+<li>Awareness, <a href="#Page_3">3</a></li>
+<li>Axiom, <a href="#Page_36">36</a>, <a href="#Page_121">121</a></li>
+<li>Axioms of congruence, <a href="#Page_128">128</a> et&nbsp;seqq.</li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_B" id="IX_B"></a>Bacon, Francis, <a href="#Page_78">78</a></li>
+<li>Behaviouristic, <a href="#Page_185">185</a></li>
+<li>Bergson, <a href="#Page_54">54</a></li>
+<li>Berkeley, <a href="#Page_28">28</a></li>
+<li>Between, <a href="#Page_64">64</a></li>
+<li>Beyond, <a href="#Page_186">186</a>, <a href="#Page_198">198</a></li>
+<li>Bifurcation, <a href="#Page_vi">vi</a>, <a href="#Page_30">30</a>, <a href="#Page_185">185</a>, <a href="#Page_187">187</a></li>
+<li>Boundary, <a href="#Page_100">100</a>;
+<ul class="IX">
+<li>moment, <a href="#Page_63">63</a>;</li>
+<li>particle, <a href="#Page_100">100</a></li></ul></li>
+<li>Broad, C.&nbsp;D., <a href="#Page_viii">viii</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_C" id="IX_C"></a>Calculation, formula of, <a href="#Page_45">45</a>, <a href="#Page_158">158</a></li>
+<li>Cambridge, <a href="#Page_97">97</a></li>
+<li>Causal nature, <a href="#Page_31">31</a>, <a href="#Page_39">39</a></li>
+<li>Causation, <a href="#Page_31">31</a>, <a href="#Page_146">146</a></li>
+<li>Centrifugal force, <a href="#Page_138">138</a></li>
+<li>Change, uniformity of, <a href="#Page_140">140</a></li>
+<li>Character, extrinsic, <a href="#Page_82">82</a>, <a href="#Page_89">89</a>, <a href="#Page_90">90</a>, <a href="#Page_113">113</a>, <a href="#Page_191">191</a>;
+<ul class="IX">
+<li>intrinsic, <a href="#Page_80">80</a>, <a href="#Page_82">82</a>, <a href="#Page_90">90</a>, <a href="#Page_113">113</a>, <a href="#Page_191">191</a></li></ul></li>
+<li>Charge, <a href="#Page_160">160</a></li>
+<li>Closure of nature, <a href="#Page_4">4</a></li>
+<li>Coefficient of drag, <a href="#Page_133">133</a></li>
+<li>Coefficients of impetus, <a href="#Page_183">183</a></li>
+<li>Cogredience, <a href="#Page_110">110</a>, <a href="#Page_188">188</a></li>
+<li>Coherence, <a href="#Page_29">29</a></li>
+<li>Comparison, <a href="#Page_124">124</a>, <a href="#Page_125">125</a>, <a href="#Page_143">143</a>, <a href="#Page_189">189</a></li>
+<li>Complex, <a href="#Page_13">13</a></li>
+<li>Conceptual nature, <a href="#Page_45">45</a>;
+<ul class="IX">
+<li>space, <a href="#Page_96">96</a></li></ul></li>
+<li>Concrete facts, <a href="#Page_167">167</a>, <a href="#Page_171">171</a>, <a href="#Page_189">189</a></li>
+<li>Conditioning events, <a href="#Page_152">152</a></li>
+<li>Conditions, active, <a href="#Page_158">158</a></li>
+<li>Congruence, <a href="#Page_65">65</a>, <a href="#Page_96">96</a>, <a href="#Page_118">118</a>, <a href="#Page_120">120</a>, <a href="#Page_127">127</a>, <a href="#Page_196">196</a></li>
+<li>Continuity, <a href="#Page_157">157</a>;
+<ul class="IX">
+<li>Dedekindian, <a href="#Page_102">102</a>;</li>
+<li>of events, <a href="#Page_76">76</a>;</li>
+<li>of nature, <a href="#Page_59">59</a>, <a href="#Page_76">76</a></li></ul></li>
+<li>Convention, <a href="#Page_121">121</a></li>
+<li>Convergence, <a href="#Page_62">62</a>, <a href="#Page_79">79</a>;
+<ul class="IX">
+<li>law of, <a href="#Page_82">82</a></li></ul></li>
+<li>Conveyance, <a href="#Page_154">154</a>, <a href="#Page_155">155</a></li>
+<li>Co-present, <a href="#Page_177">177</a></li>
+<li>Covering, <a href="#Page_83">83</a></li>
+<li>Creative advance, <a href="#Page_178">178</a></li>
+<li>Critical velocity, <a href="#Page_193">193</a>, <a href="#Page_195">195</a></li>
+<li>Curvature of space-time, <a href="#Page_182">182</a></li>
+<li>Cyclone, <a href="#Page_194">194</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_D" id="IX_D"></a>Dedekindian continuity, <a href="#Page_102">102</a></li>
+<li>Definite, <a href="#Page_53">53</a>, <a href="#Page_194">194</a>, <a href="#Page_198">198</a></li>
+<li>Delusions, <a href="#Page_31">31</a>, <a href="#Page_38">38</a></li>
+<li>Delusive perceptual object, <a href="#Page_153">153</a></li>
+<li>Demarcation of events, <a href="#Page_144">144</a></li>
+<li>Demonstrative phrase, <a href="#Page_6">6</a></li>
+<li>Descriptive phrase, <a href="#Page_6">6</a>, <a href="#Page_10">10</a></li>
+<li>Differential equations, <a href="#Page_196">196</a></li>
+<li>Discrimination, <a href="#Page_14">14</a>, <a href="#Page_50">50</a>, <a href="#Page_144">144</a></li>
+<li>Diversification of nature, <a href="#Page_15">15</a></li>
+<li>Duddington, Mrs, <a href="#Page_47">47</a></li>
+<li>Duration, <a href="#Page_37">37</a>, <a href="#Page_53">53</a>, <a href="#Page_55">55</a>, <a href="#Page_186">186</a></li>
+<li>Durations, families of, <a href="#Page_59">59</a>, <a href="#Page_73">73</a>, <a href="#Page_190">190</a></li>
+<li>Dynamical axes, <a href="#Page_138">138</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_E" id="IX_E"></a>Einstein, <a href="#Page_vii">vii</a>, <a href="#Page_102">102</a>, <a href="#Page_131">131</a>, <a href="#Page_164">164</a>, <a href="#Page_165">165</a>, <a href="#Page_181">181</a>, <a href="#Page_182">182</a>, <a href="#Page_183">183</a>, <a href="#Page_184">184</a>, <a href="#Page_191">191</a></li>
+<li>Electromagnetic field, <a href="#Page_179">179</a></li>
+<li>Electron, <a href="#Page_30">30</a>, <a href="#Page_146">146</a>, <a href="#Page_158">158</a>, <a href="#Page_171">171</a></li>
+<li>Element, <a href="#Page_17">17</a>;
+<ul class="IX">
+<li>abstractive, <a href="#Page_84">84</a></li></ul></li>
+<li>Elliptical phraseology, <a href="#Page_7">7</a></li>
+<li><span class="pagenum" title="Page&nbsp;200">&nbsp;</span><a name="Page_200" id="Page_200"></a>Empty space, <a href="#Page_145">145</a></li>
+<li>Entity, <a href="#Page_5">5</a>, <a href="#Page_13">13</a></li>
+<li>Equal in abstractive force, <a href="#Page_83">83</a></li>
+<li>Error, <a href="#Page_68">68</a></li>
+<li>Ether, <a href="#Page_18">18</a>, <a href="#Page_78">78</a>, <a href="#Page_160">160</a>;
+<ul class="IX">
+<li>material, <a href="#Page_78">78</a>;</li>
+<li>of events, <a href="#Page_78">78</a></li></ul></li>
+<li>Euclid, <a href="#Page_85">85</a>, <a href="#Page_94">94</a>, <a href="#Page_197">197</a></li>
+<li>Euler, <a href="#Page_140">140</a></li>
+<li>Event, <a href="#Page_15">15</a>, <a href="#Page_52">52</a>, <a href="#Page_75">75</a>, <a href="#Page_165">165</a>;
+<ul class="IX">
+<li>percipient, <a href="#Page_107">107</a>, <a href="#Page_152">152</a>, <a href="#Page_186">186</a></li></ul></li>
+<li>Event-particle, <a href="#Page_86">86</a>, <a href="#Page_93">93</a>, <a href="#Page_94">94</a>, <a href="#Page_172">172</a>, <a href="#Page_191">191</a></li>
+<li>Events, conditioning, <a href="#Page_152">152</a>;
+<ul class="IX">
+<li>continuity of, <a href="#Page_76">76</a>;</li>
+<li>demarcation of, <a href="#Page_144">144</a>;</li>
+<li>ether of, <a href="#Page_78">78</a>;</li>
+<li>infinite, <a href="#Page_197">197</a>, <a href="#Page_198">198</a>;</li>
+<li>limited, <a href="#Page_74">74</a>;</li>
+<li>passage of, <a href="#Page_34">34</a>;</li>
+<li>signified, <a href="#Page_52">52</a>;</li>
+<li>stationary, <a href="#Page_198">198</a>;</li>
+<li>stream of, <a href="#Page_167">167</a>;</li>
+<li>structure of, <a href="#Page_52">52</a>, <a href="#Page_166">166</a></li></ul></li>
+<li>Exclusion, <a href="#Page_186">186</a></li>
+<li>Explanation, <a href="#Page_97">97</a>, <a href="#Page_141">141</a></li>
+<li>Extended nature, <a href="#Page_196">196</a></li>
+<li>Extension, <a href="#Page_22">22</a>, <a href="#Page_58">58</a>, <a href="#Page_75">75</a>, <a href="#Page_185">185</a></li>
+<li>Extensive abstraction, <a href="#Page_65">65</a>, <a href="#Page_79">79</a>, <a href="#Page_85">85</a></li>
+<li>Extrinsic character, <a href="#Page_82">82</a>, <a href="#Page_89">89</a>, <a href="#Page_90">90</a>, <a href="#Page_113">113</a>, <a href="#Page_191">191</a>;
+<ul class="IX">
+<li>properties, <a href="#Page_62">62</a></li></ul></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_F" id="IX_F"></a>Fact, <a href="#Page_12">12</a>, <a href="#Page_13">13</a></li>
+<li>Factors, <a href="#Page_12">12</a>, <a href="#Page_13">13</a>, <a href="#Page_15">15</a></li>
+<li>Facts, concrete, <a href="#Page_167">167</a>, <a href="#Page_171">171</a></li>
+<li>Family of durations, <a href="#Page_59">59</a>, <a href="#Page_63">63</a>, <a href="#Page_73">73</a>;
+<ul class="IX">
+<li>of moments, <a href="#Page_63">63</a></li></ul></li>
+<li>Faraday, <a href="#Page_146">146</a></li>
+<li>Field, gravitational, <a href="#Page_197">197</a>;
+<ul class="IX">
+<li>of activity, <a href="#Page_170">170</a>, <a href="#Page_181">181</a>;</li>
+<li>physical, <a href="#Page_190">190</a></li></ul></li>
+<li>Finite truths, <a href="#Page_12">12</a></li>
+<li>Fitzgerald, <a href="#Page_133">133</a></li>
+<li>Formula of calculation, <a href="#Page_45">45</a>, <a href="#Page_158">158</a></li>
+<li>Foucault, <a href="#Page_138">138</a>, <a href="#Page_194">194</a></li>
+<li>Four-dimensional manifold, <a href="#Page_86">86</a></li>
+<li>Fresnel, <a href="#Page_133">133</a></li>
+<li>Future, the, <a href="#Page_72">72</a>, <a href="#Page_177">177</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_G" id="IX_G"></a>Galileo, <a href="#Page_139">139</a></li>
+<li>Geometrical order, <a href="#Page_194">194</a></li>
+<li>Geometry, <a href="#Page_36">36</a>;
+<ul class="IX">
+<li>metrical, <a href="#Page_129">129</a></li></ul></li>
+<li>Gravitation, <a href="#Page_179">179</a> et&nbsp;seqq.</li>
+<li>Gravitational field, <a href="#Page_197">197</a></li>
+<li>Greek philosophy, <a href="#Page_16">16</a>;
+<ul class="IX">
+<li>thought, <a href="#Page_197">197</a></li></ul></li>
+<li>Gyro-compass, <a href="#Page_194">194</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_H" id="IX_H"></a>Heath, Sir T.&nbsp;L., <a href="#Page_197">197</a></li>
+<li>Here, <a href="#Page_107">107</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_I" id="IX_I"></a>Idealists, <a href="#Page_70">70</a></li>
+<li>Immediacy, <a href="#Page_52">52</a>;
+<ul class="IX">
+<li>of perception, <a href="#Page_72">72</a></li></ul></li>
+<li>Impetus, <a href="#Page_181">181</a>, <a href="#Page_182">182</a>;
+<ul class="IX">
+<li>coefficients of, <a href="#Page_183">183</a>;</li>
+<li>integral, <a href="#Page_183">183</a></li></ul></li>
+<li>Inclusion, <a href="#Page_186">186</a></li>
+<li>Individuality, <a href="#Page_13">13</a></li>
+<li>Infinite events, <a href="#Page_197">197</a>, <a href="#Page_198">198</a></li>
+<li>Inge, Dr, <a href="#Page_48">48</a></li>
+<li>Ingredient, <a href="#Page_14">14</a></li>
+<li>Ingression, <a href="#Page_144">144</a>, <a href="#Page_145">145</a>, <a href="#Page_148">148</a>, <a href="#Page_152">152</a></li>
+<li>Inherence, <a href="#Page_83">83</a></li>
+<li>Inside, <a href="#Page_106">106</a></li>
+<li>Instant, <a href="#Page_33">33</a>, <a href="#Page_35">35</a>, <a href="#Page_57">57</a></li>
+<li>Instantaneous plane, <a href="#Page_91">91</a>;
+<ul class="IX">
+<li>present, <a href="#Page_72">72</a>;</li>
+<li>spaces, <a href="#Page_86">86</a>, <a href="#Page_90">90</a>, <a href="#Page_177">177</a></li></ul></li>
+<li>Instantaneousness, <a href="#Page_56">56</a>, <a href="#Page_57">57</a></li>
+<li>Intersection, locus of, <a href="#Page_90">90</a></li>
+<li>Intrinsic character, <a href="#Page_80">80</a>, <a href="#Page_82">82</a>, <a href="#Page_90">90</a>, <a href="#Page_113">113</a>, <a href="#Page_191">191</a>;
+<ul class="IX">
+<li>properties, <a href="#Page_62">62</a></li></ul></li>
+<li>Ionian thinkers, <a href="#Page_19">19</a></li>
+<li>Irrelevance, infinitude of, <a href="#Page_12">12</a></li>
+<li>Irrevocableness, <a href="#Page_35">35</a>, <a href="#Page_37">37</a></li>
+<li>It, <a href="#Page_8">8</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_J" id="IX_J"></a>Julius Caesar, <a href="#Page_36">36</a></li>
+<li>Junction, <a href="#Page_76">76</a>, <a href="#Page_101">101</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_K" id="IX_K"></a>Kinetic energy, <a href="#Page_105">105</a>;
+<ul class="IX">
+<li>symmetry, <a href="#Page_129">129</a></li></ul></li>
+<li>Knowledge, <a href="#Page_28">28</a>, <a href="#Page_32">32</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_L" id="IX_L"></a>Lagrange, <a href="#Page_140">140</a></li>
+<li>Larmor, <a href="#Page_131">131</a></li>
+<li>Law of convergence, <a href="#Page_82">82</a></li>
+<li>Laws of motion, <a href="#Page_137">137</a>, <a href="#Page_139">139</a>;
+<ul class="IX">
+<li>of nature, <a href="#Page_196">196</a></li></ul></li>
+<li>Leibnizian monadology, <a href="#Page_150">150</a></li>
+<li>Level, <a href="#Page_91">91</a>, <a href="#Page_92">92</a></li>
+<li>Light, <a href="#Page_195">195</a>;
+<ul class="IX">
+<li>ray of, <a href="#Page_188">188</a>;</li>
+<li>velocity of, <a href="#Page_131">131</a></li></ul></li>
+<li>Limit, <a href="#Page_57">57</a></li>
+<li>Limited events, <a href="#Page_74">74</a></li>
+<li>Location, <a href="#Page_160">160</a>, <a href="#Page_161">161</a></li>
+<li>Locke, <a href="#Page_27">27</a></li>
+<li>Locus, <a href="#Page_102">102</a>;
+<ul class="IX">
+<li>of intersection, <a href="#Page_90">90</a></li></ul></li>
+<li>London, <a href="#Page_97">97</a></li>
+<li>Lorentz, H.&nbsp;A., <a href="#Page_131">131</a>, <a href="#Page_133">133</a></li>
+<li>Lossky, <a href="#Page_47">47</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_M" id="IX_M"></a>Manifold, four-dimensional, <a href="#Page_86">86</a>;
+<ul class="IX">
+<li>space-time, <a href="#Page_173">173</a></li></ul></li>
+<li>Material ether, <a href="#Page_78">78</a>;
+<ul class="IX">
+<li>object, <a href="#Page_169">169</a></li></ul></li>
+<li>Materialism, <a href="#Page_43">43</a>, <a href="#Page_70">70</a></li>
+<li>Matrix, <a href="#Page_116">116</a></li>
+<li>Matter, <a href="#Page_16">16</a>, <a href="#Page_17">17</a>, <a href="#Page_19">19</a>, <a href="#Page_20">20</a>, <a href="#Page_26">26</a></li>
+<li>Maxwell, <a href="#Page_131">131</a>, <a href="#Page_133">133</a></li>
+<li>Measurableness, <a href="#Page_196">196</a>;
+<ul class="IX">
+<li>of nature, <a href="#Page_193">193</a></li></ul></li>
+<li>Measurement, <a href="#Page_96">96</a>, <a href="#Page_120">120</a>, <a href="#Page_174">174</a>, <a href="#Page_196">196</a>;
+<ul class="IX">
+<li>of time, <a href="#Page_65">65</a>, <a href="#Page_140">140</a></li></ul></li>
+<li>Measure-system, <a href="#Page_196">196</a></li>
+<li>Memory, <a href="#Page_68">68</a></li>
+<li>Metaphysics, <a href="#Page_28">28</a>, <a href="#Page_32">32</a></li>
+<li>Metrical geometry, <a href="#Page_129">129</a></li>
+<li>Michelson-Morley, <a href="#Page_195">195</a></li>
+<li>Milton, <a href="#Page_35">35</a></li>
+<li>Mind, <a href="#Page_27">27</a>, <a href="#Page_28">28</a></li>
+<li><span class="pagenum" title="Page&nbsp;201">&nbsp;</span><a name="Page_201" id="Page_201"></a>Minkowski, <a href="#Page_viii">viii</a>, <a href="#Page_131">131</a></li>
+<li>Molecule, <a href="#Page_32">32</a>, <a href="#Page_171">171</a></li>
+<li>Moment, <a href="#Page_57">57</a>, <a href="#Page_60">60</a>, <a href="#Page_88">88</a></li>
+<li>Momental area, <a href="#Page_103">103</a>;
+<ul class="IX">
+<li>route, <a href="#Page_103">103</a></li></ul></li>
+<li>Momentum, <a href="#Page_105">105</a></li>
+<li>Motion, <a href="#Page_105">105</a>, <a href="#Page_114">114</a>, <a href="#Page_117">117</a>, <a href="#Page_127">127</a>, <a href="#Page_188">188</a>, <a href="#Page_192">192</a></li>
+<li>Multiplicity, <a href="#Page_22">22</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_N" id="IX_N"></a>Natural philosophy, <a href="#Page_29">29</a>, <a href="#Page_30">30</a></li>
+<li>Natural science, philosophy of, <a href="#Page_46">46</a></li>
+<li>Nature, <a href="#Page_3">3</a>;
+<ul class="IX">
+<li>apparent, <a href="#Page_31">31</a>, <a href="#Page_39">39</a>;</li>
+<li>causal, <a href="#Page_31">31</a>, <a href="#Page_39">39</a>;</li>
+<li>conceptual, <a href="#Page_45">45</a>;</li>
+<li>continuity of, <a href="#Page_59">59</a>, <a href="#Page_76">76</a>;</li>
+<li>discrimination of, <a href="#Page_144">144</a>;</li>
+<li>extended, <a href="#Page_196">196</a>;</li>
+<li>laws of, <a href="#Page_196">196</a>;</li>
+<li>passage of, <a href="#Page_54">54</a>;</li>
+<li>stratification of, <a href="#Page_194">194</a>, <a href="#Page_196">196</a>;</li>
+<li>system of, <a href="#Page_146">146</a></li></ul></li>
+<li>Newton, <a href="#Page_27">27</a>, <a href="#Page_136">136</a>, <a href="#Page_139">139</a>, <a href="#Page_140">140</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_O" id="IX_O"></a>Object, <a href="#Page_77">77</a>, <a href="#Page_125">125</a>, <a href="#Page_143">143</a>, <a href="#Page_169">169</a>, <a href="#Page_189">189</a>;
+<ul class="IX">
+<li>delusive perceptual, <a href="#Page_155">155</a>;</li>
+<li>material, <a href="#Page_169">169</a>;</li>
+<li>perceptual, <a href="#Page_153">153</a>;</li>
+<li>physical, <a href="#Page_155">155</a>, <a href="#Page_157">157</a>;</li>
+<li>scientific, <a href="#Page_158">158</a>, <a href="#Page_169">169</a>;</li>
+<li>uniform, <a href="#Page_162">162</a></li></ul></li>
+<li>Occupation, <a href="#Page_22">22</a>, <a href="#Page_34">34</a>, <a href="#Page_36">36</a>, <a href="#Page_100">100</a>, <a href="#Page_101">101</a></li>
+<li>Order, source of, <a href="#Page_192">192</a>;
+<ul class="IX">
+<li>spatial, <a href="#Page_95">95</a>, <a href="#Page_194">194</a>;</li>
+<li>temporal, <a href="#Page_64">64</a>, <a href="#Page_95">95</a>, <a href="#Page_194">194</a></li></ul></li>
+<li>Organisation of thought, <a href="#Page_79">79</a></li>
+<li>Outside, <a href="#Page_63">63</a>, <a href="#Page_100">100</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_P" id="IX_P"></a>Paradox, <a href="#Page_192">192</a></li>
+<li>Parallel, <a href="#Page_63">63</a>, <a href="#Page_127">127</a>;
+<ul class="IX">
+<li>durations, <a href="#Page_190">190</a></li></ul></li>
+<li>Parallelism, <a href="#Page_95">95</a>, <a href="#Page_191">191</a></li>
+<li>Parallelogram, <a href="#Page_127">127</a></li>
+<li>Paris, <a href="#Page_87">87</a>, <a href="#Page_138">138</a></li>
+<li>Parliament, <a href="#Page_120">120</a></li>
+<li>Part, <a href="#Page_14">14</a>, <a href="#Page_15">15</a>, <a href="#Page_58">58</a></li>
+<li>Passage of events, <a href="#Page_34">34</a>;
+<ul class="IX">
+<li>of nature, <a href="#Page_54">54</a></li></ul></li>
+<li>Past, the, <a href="#Page_72">72</a>, <a href="#Page_177">177</a></li>
+<li>Perception, <a href="#Page_3">3</a></li>
+<li>Perceptual objects, <a href="#Page_149">149</a>, <a href="#Page_153">153</a></li>
+<li>Percipience, <a href="#Page_28">28</a></li>
+<li>Percipient event, <a href="#Page_107">107</a>, <a href="#Page_152">152</a>, <a href="#Page_186">186</a>, <a href="#Page_187">187</a></li>
+<li>Period of time, <a href="#Page_51">51</a></li>
+<li>Permanence, <a href="#Page_144">144</a></li>
+<li>Perpendicularity, <a href="#Page_117">117</a>, <a href="#Page_127">127</a>, <a href="#Page_193">193</a></li>
+<li>Philosophy, <a href="#Page_1">1</a>;
+<ul class="IX">
+<li>natural, <a href="#Page_29">29</a>, <a href="#Page_30">30</a>;</li>
+<li>of natural science, <a href="#Page_46">46</a>;</li>
+<li>of the sciences, <a href="#Page_2">2</a></li></ul></li>
+<li>Physical field, <a href="#Page_190">190</a>;
+<ul class="IX">
+<li>object, <a href="#Page_155">155</a>, <a href="#Page_156">156</a>, <a href="#Page_157">157</a></li></ul></li>
+<li>Physics, speculative, <a href="#Page_30">30</a></li>
+<li>Place, <a href="#Page_51">51</a></li>
+<li>Plane, <a href="#Page_191">191</a>;
+<ul class="IX">
+<li>instantaneous, <a href="#Page_91">91</a></li></ul></li>
+<li>Plato, <a href="#Page_16">16</a>, <a href="#Page_17">17</a>, <a href="#Page_18">18</a>, <a href="#Page_24">24</a>, <a href="#Page_197">197</a></li>
+<li>Poincar&eacute;, <a href="#Page_121">121</a>, <a href="#Page_122">122</a>, <a href="#Page_123">123</a></li>
+<li>Point, <a href="#Page_35">35</a>, <a href="#Page_89">89</a>, <a href="#Page_91">91</a>, <a href="#Page_114">114</a>, <a href="#Page_173">173</a>, <a href="#Page_176">176</a></li>
+<li>Point-flash, <a href="#Page_172">172</a>, <a href="#Page_173">173</a></li>
+<li>Point of space, <a href="#Page_85">85</a></li>
+<li>Point, timeless, <a href="#Page_192">192</a></li>
+<li>Point-track, <a href="#Page_113">113</a>, <a href="#Page_198">198</a></li>
+<li>Pompey, <a href="#Page_36">36</a></li>
+<li>Position, <a href="#Page_89">89</a>, <a href="#Page_90">90</a>, <a href="#Page_92">92</a>, <a href="#Page_93">93</a>, <a href="#Page_99">99</a>, <a href="#Page_113">113</a>, <a href="#Page_191">191</a>;
+<ul class="IX">
+<li>absolute, <a href="#Page_105">105</a>, <a href="#Page_106">106</a>, <a href="#Page_114">114</a>, <a href="#Page_188">188</a></li></ul></li>
+<li>Potential, <a href="#Page_183">183</a>;
+<ul class="IX">
+<li>associate-, <a href="#Page_183">183</a></li></ul></li>
+<li>Predicate, <a href="#Page_18">18</a></li>
+<li>Predication, <a href="#Page_18">18</a></li>
+<li>Present, the, <a href="#Page_69">69</a>, <a href="#Page_72">72</a>, <a href="#Page_177">177</a>;
+<ul class="IX">
+<li>instantaneous, <a href="#Page_72">72</a>;</li>
+<li>observational, <a href="#Page_186">186</a></li></ul></li>
+<li>Primary qualities, <a href="#Page_27">27</a></li>
+<li>Prime, <a href="#Page_88">88</a></li>
+<li>Process, <a href="#Page_53">53</a>, <a href="#Page_54">54</a>;
+<ul class="IX">
+<li>of nature, <a href="#Page_54">54</a></li></ul></li>
+<li>Psychic additions, <a href="#Page_29">29</a>, <a href="#Page_187">187</a></li>
+<li>Punct, <a href="#Page_92">92</a>, <a href="#Page_93">93</a>, <a href="#Page_94">94</a></li>
+<li>Pythagoreans, <a href="#Page_197">197</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_Q" id="IX_Q"></a>Quality, <a href="#Page_27">27</a></li>
+<li>Quantum of time, <a href="#Page_162">162</a></li>
+<li>Quantum theory, <a href="#Page_162">162</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_R" id="IX_R"></a>Ray of light, <a href="#Page_188">188</a></li>
+<li>Reality, <a href="#Page_30">30</a>;
+<ul class="IX">
+<li>of durations, <a href="#Page_55">55</a>, <a href="#Page_187">187</a></li></ul></li>
+<li>Recognition, <a href="#Page_124">124</a>, <a href="#Page_143">143</a>, <a href="#Page_189">189</a></li>
+<li>Rect, <a href="#Page_91">91</a>, <a href="#Page_92">92</a></li>
+<li>Recurrence, <a href="#Page_35">35</a></li>
+<li>Relative motion, <a href="#Page_117">117</a>;
+<ul class="IX">
+<li>velocity, <a href="#Page_130">130</a></li></ul></li>
+<li>Relativity, <a href="#Page_169">169</a>;
+<ul class="IX">
+<li>restricted theory of, <a href="#Page_193">193</a></li></ul></li>
+<li>Rest, <a href="#Page_105">105</a>, <a href="#Page_114">114</a>, <a href="#Page_188">188</a>, <a href="#Page_192">192</a></li>
+<li>Rotation, <a href="#Page_138">138</a>, <a href="#Page_194">194</a></li>
+<li>Route, <a href="#Page_99">99</a>;
+<ul class="IX">
+<li>momental, <a href="#Page_103">103</a>;</li>
+<li>straight, <a href="#Page_103">103</a></li></ul></li>
+<li>Russell, Bertrand, <a href="#Page_11">11</a>, <a href="#Page_122">122</a>, <a href="#Page_123">123</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_S" id="IX_S"></a>Schelling, <a href="#Page_47">47</a></li>
+<li>Science, <a href="#Page_2">2</a>;
+<ul class="IX">
+<li>metaphysical, <a href="#Page_32">32</a></li></ul></li>
+<li>Scientific objects, <a href="#Page_149">149</a>, <a href="#Page_158">158</a>, <a href="#Page_169">169</a></li>
+<li>Secondary qualities, <a href="#Page_27">27</a></li>
+<li>Self-congruence, <a href="#Page_196">196</a></li>
+<li>Self-containedness of nature, <a href="#Page_4">4</a></li>
+<li>Sense-awareness, <a href="#Page_3">3</a>, <a href="#Page_67">67</a></li>
+<li>Sense-object, <a href="#Page_149">149</a>, <a href="#Page_170">170</a></li>
+<li>Sense-perception, <a href="#Page_3">3</a>, <a href="#Page_14">14</a></li>
+<li>Sense-recognition, <a href="#Page_143">143</a>, <a href="#Page_189">189</a></li>
+<li>Series, temporal, <a href="#Page_66">66</a>, <a href="#Page_70">70</a>, <a href="#Page_85">85</a>, <a href="#Page_178">178</a></li>
+<li>Set, abstractive, <a href="#Page_61">61</a>, <a href="#Page_79">79</a></li>
+<li>Significance, <a href="#Page_51">51</a>, <a href="#Page_186">186</a>, <a href="#Page_187">187</a>, <a href="#Page_188">188</a>, <a href="#Page_194">194</a>, <a href="#Page_197">197</a>, <a href="#Page_198">198</a></li>
+<li>Signified events, <a href="#Page_52">52</a></li>
+<li>Simplicity, <a href="#Page_163">163</a>, <a href="#Page_173">173</a></li>
+<li>Simultaneity, <a href="#Page_53">53</a>, <a href="#Page_56">56</a>, <a href="#Page_196">196</a></li>
+<li>Situation, <a href="#Page_15">15</a>, <a href="#Page_78">78</a>, <a href="#Page_147">147</a>, <a href="#Page_148">148</a>, <a href="#Page_152">152</a>, <a href="#Page_160">160</a>, <a href="#Page_189">189</a></li>
+<li>Solid, <a href="#Page_99">99</a>, <a href="#Page_101">101</a>, <a href="#Page_102">102</a>;
+<ul class="IX">
+<li>vagrant, <a href="#Page_101">101</a></li></ul></li>
+<li>Sound, <a href="#Page_195">195</a></li>
+<li>Space, <a href="#Page_16">16</a>, <a href="#Page_17">17</a>, <a href="#Page_31">31</a>, <a href="#Page_33">33</a>, <a href="#Page_79">79</a>;
+<ul class="IX">
+<li>empty, <a href="#Page_145">145</a>;</li>
+<li>timeless, <a href="#Page_86">86</a>, <a href="#Page_106">106</a>, <a href="#Page_114">114</a>;</li>
+<li>uniformity of, <a href="#Page_194">194</a></li></ul></li>
+<li>Spaces, instantaneous, <a href="#Page_86">86</a>, <a href="#Page_90">90</a></li>
+<li><span class="pagenum" title="Page&nbsp;202">&nbsp;</span><a name="Page_202" id="Page_202"></a>Space-system, <a href="#Page_179">179</a></li>
+<li>Space-time manifold, <a href="#Page_173">173</a></li>
+<li>Spatial-order, <a href="#Page_95">95</a></li>
+<li>Spatio-temporal structure, <a href="#Page_173">173</a></li>
+<li>Speculative demonstration, <a href="#Page_6">6</a></li>
+<li>Speculative physics, <a href="#Page_30">30</a></li>
+<li>Standpoint for perception, <a href="#Page_107">107</a>, <a href="#Page_188">188</a></li>
+<li>Station, <a href="#Page_103">103</a>, <a href="#Page_104">104</a>, <a href="#Page_113">113</a></li>
+<li>Stationary events, <a href="#Page_198">198</a></li>
+<li>Straight line, <a href="#Page_91">91</a>, <a href="#Page_114">114</a>, <a href="#Page_191">191</a>;
+<ul class="IX">
+<li>route, <a href="#Page_103">103</a></li></ul></li>
+<li>Stratification of nature, <a href="#Page_187">187</a>, <a href="#Page_194">194</a>, <a href="#Page_196">196</a></li>
+<li>Stream of events, <a href="#Page_167">167</a></li>
+<li>Structure of events, <a href="#Page_52">52</a>, <a href="#Page_166">166</a></li>
+<li>Structure, spatio-temporal, <a href="#Page_173">173</a></li>
+<li>Subject, <a href="#Page_18">18</a></li>
+<li>Substance, <a href="#Page_16">16</a>, <a href="#Page_18">18</a>, <a href="#Page_19">19</a>, <a href="#Page_150">150</a></li>
+<li>Substratum, <a href="#Page_16">16</a>, <a href="#Page_18">18</a>, <a href="#Page_21">21</a></li>
+<li>Symmetry, <a href="#Page_118">118</a>, <a href="#Page_126">126</a>;
+<ul class="IX">
+<li>kinetic, <a href="#Page_129">129</a></li></ul></li>
+<li>System of nature, <a href="#Page_146">146</a></li>
+<li>System, time-, <a href="#Page_192">192</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_T" id="IX_T"></a>Tarner, Edward, <a href="#Page_v">v</a>, <a href="#Page_1">1</a></li>
+<li>Temporal order, <a href="#Page_64">64</a>, <a href="#Page_95">95</a>, <a href="#Page_194">194</a></li>
+<li>Temporal series, <a href="#Page_66">66</a>, <a href="#Page_70">70</a>, <a href="#Page_85">85</a></li>
+<li>Tensor, <a href="#Page_182">182</a></li>
+<li>Terminus, <a href="#Page_4">4</a></li>
+<li>The, <a href="#Page_11">11</a></li>
+<li>Theory, quantum, <a href="#Page_162">162</a></li>
+<li>There, <a href="#Page_110">110</a>, <a href="#Page_189">189</a></li>
+<li>This, <a href="#Page_11">11</a></li>
+<li>Thought, <a href="#Page_3">3</a>, <a href="#Page_14">14</a></li>
+<li>Timaeus, the, <a href="#Page_17">17</a>, <a href="#Page_20">20</a>, <a href="#Page_24">24</a></li>
+<li>Time, <a href="#Page_16">16</a>, <a href="#Page_17">17</a>, <a href="#Page_31">31</a>, <a href="#Page_33">33</a>, <a href="#Page_49">49</a>, <a href="#Page_79">79</a>;
+<ul class="IX">
+<li>measurement of, <a href="#Page_140">140</a>;</li>
+<li>quantum of, <a href="#Page_162">162</a>;</li>
+<li>transcendence of, <a href="#Page_39">39</a></li></ul></li>
+<li>Time-series, <a href="#Page_178">178</a>, also cf. Temporal series</li>
+<li>Time-system, see Time-series, also <a href="#Page_91">91</a>, <a href="#Page_97">97</a>, <a href="#Page_104">104</a>, <a href="#Page_179">179</a>, <a href="#Page_192">192</a></li>
+<li>Timeless point, <a href="#Page_192">192</a>;
+<ul class="IX">
+<li>space, <a href="#Page_86">86</a>, <a href="#Page_106">106</a>, <a href="#Page_114">114</a>, <a href="#Page_177">177</a></li></ul></li>
+<li>Totality, <a href="#Page_89">89</a></li>
+<li>Transcendence of time, <a href="#Page_39">39</a></li>
+<li>Transmission, <a href="#Page_26">26</a>, <a href="#Page_28">28</a>;
+<ul class="IX">
+<li>action by, <a href="#Page_159">159</a>, <a href="#Page_190">190</a></li></ul></li>
+<li>Tubes of force, <a href="#Page_146">146</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_U" id="IX_U"></a>Unexhaustiveness, <a href="#Page_50">50</a></li>
+<li>Uniform object, <a href="#Page_162">162</a></li>
+<li>Uniformity of change, <a href="#Page_140">140</a>;
+<ul class="IX">
+<li>of space, <a href="#Page_194">194</a></li></ul></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_V" id="IX_V"></a>Vagrant area, <a href="#Page_103">103</a>;
+<ul class="IX">
+<li>solid, <a href="#Page_101">101</a></li></ul></li>
+<li>Veblen and Young, <a href="#Page_36">36</a></li>
+<li>Velocity, critical, <a href="#Page_193">193</a>, <a href="#Page_195">195</a>;
+<ul class="IX">
+<li>of light, <a href="#Page_131">131</a>, <a href="#Page_195">195</a>;</li>
+<li>relative, <a href="#Page_130">130</a></li></ul></li>
+<li>Volume, <a href="#Page_92">92</a>, <a href="#Page_101">101</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_W" id="IX_W"></a>When, <a href="#Page_107">107</a></li>
+<li>Where, <a href="#Page_107">107</a></li>
+<li>Whole, <a href="#Page_58">58</a></li>
+<li>Within, <a href="#Page_63">63</a></li>
+</ul>
+
+<ul class="IX">
+<li><a name="IX_Y" id="IX_Y"></a>Young, Veblen and, <a href="#Page_36">36</a></li>
+</ul>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of Project Gutenberg's The Concept of Nature, by Alfred North Whitehead
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+Project Gutenberg's The Concept of Nature, by Alfred North Whitehead
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: The Concept of Nature
+       The Tarner Lectures Delivered in Trinity College, November 1919
+
+Author: Alfred North Whitehead
+
+Release Date: July 16, 2006 [EBook #18835]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK THE CONCEPT OF NATURE ***
+
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+
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+Produced by Janet Kegg, Laura Wisewell and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
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+  +------------------------------------------------------------------+
+  |                                                                  |
+  | Transcriber's Note: In the parts containing mathematical         |
+  | notation, superscripts are denoted using a carat and subscripts  |
+  | using underscores, for example x^2, e_1, e_{n+1}. Greek          |
+  | letters used as symbols are written out, for example {sigma},    |
+  | but the one Greek phrase has been transliterated. All of these   |
+  | special characters are preserved in the UTF-8 and HTML versions  |
+  | of this ebook.                                                   |
+  |                                                                  |
+  | Italicised words are marked using underscores _like this_, but   |
+  | the letters used in the mathematics (which were all in italic    |
+  | font) have not been marked, to aid legibility and to avoid       |
+  | confusion with the subscripts.                                   |
+  |                                                                  |
+  | Two printer errors have been corrected. These are:               |
+  |                                                                  |
+  | "...relating the entity discriminated by sight with that         |
+  | discriminated by [sight]..." sight has been changed to touch as  |
+  | suggested by the sense.                                          |
+  |                                                                  |
+  | "...[universely] proportional to..." universely has been changed |
+  | to inversely.                                                    |
+  |                                                                  |
+  +------------------------------------------------------------------+
+
+
+
+
+                            The Concept of
+
+
+                                NATURE
+
+
+                         THE TARNER LECTURES
+                     DELIVERED IN TRINITY COLLEGE
+                            NOVEMBER 1919
+
+
+                        Alfred North Whitehead
+
+
+
+
+PREFACE
+
+
+The contents of this book were originally delivered at Trinity College
+in the autumn of 1919 as the inaugural course of Tarner lectures. The
+Tarner lectureship is an occasional office founded by the liberality of
+Mr Edward Tarner. The duty of each of the successive holders of the post
+will be to deliver a course on 'the Philosophy of the Sciences and the
+Relations or Want of Relations between the different Departments of
+Knowledge.' The present book embodies the endeavour of the first
+lecturer of the series to fulfil his task.
+
+The chapters retain their original lecture form and remain as delivered
+with the exception of minor changes designed to remove obscurities of
+expression. The lecture form has the advantage of suggesting an audience
+with a definite mental background which it is the purpose of the lecture
+to modify in a specific way. In the presentation of a novel outlook with
+wide ramifications a single line of communications from premises to
+conclusions is not sufficient for intelligibility. Your audience will
+construe whatever you say into conformity with their pre-existing
+outlook. For this reason the first two chapters and the last two
+chapters are essential for intelligibility though they hardly add to the
+formal completeness of the exposition. Their function is to prevent the
+reader from bolting up side tracks in pursuit of misunderstandings. The
+same reason dictates my avoidance of the existing technical terminology
+of philosophy. The modern natural philosophy is shot through and
+through with the fallacy of bifurcation which is discussed in the second
+chapter of this work. Accordingly all its technical terms in some subtle
+way presuppose a misunderstanding of my thesis. It is perhaps as well to
+state explicitly that if the reader indulges in the facile vice of
+bifurcation not a word of what I have here written will be intelligible.
+
+The last two chapters do not properly belong to the special course.
+Chapter VIII is a lecture delivered in the spring of 1920 before the
+Chemical Society of the students of the Imperial College of Science and
+Technology. It has been appended here as conveniently summing up and
+applying the doctrine of the book for an audience with one definite type
+of outlook.
+
+This volume on 'the Concept of Nature' forms a companion book to my
+previous work _An Enquiry concerning the Principles of Natural
+Knowledge_. Either book can be read independently, but they supplement
+each other. In part the present book supplies points of view which were
+omitted from its predecessor; in part it traverses the same ground with
+an alternative exposition. For one thing, mathematical notation has been
+carefully avoided, and the results of mathematical deductions are
+assumed. Some of the explanations have been improved and others have
+been set in a new light. On the other hand important points of the
+previous work have been omitted where I have had nothing fresh to say
+about them. On the whole, whereas the former work based itself chiefly
+on ideas directly drawn from mathematical physics, the present book
+keeps closer to certain fields of philosophy and physics to the
+exclusion of mathematics. The two works meet in their discussions of
+some details of space and time.
+
+I am not conscious that I have in any way altered my views. Some
+developments have been made. Those that are capable of a
+non-mathematical exposition have been incorporated in the text. The
+mathematical developments are alluded to in the last two chapters. They
+concern the adaptation of the principles of mathematical physics to the
+form of the relativity principle which is here maintained. Einstein's
+method of using the theory of tensors is adopted, but the application is
+worked out on different lines and from different assumptions. Those of
+his results which have been verified by experience are obtained also by
+my methods. The divergence chiefly arises from the fact that I do not
+accept his theory of non-uniform space or his assumption as to the
+peculiar fundamental character of light-signals. I would not however be
+misunderstood to be lacking in appreciation of the value of his recent
+work on general relativity which has the high merit of first disclosing
+the way in which mathematical physics should proceed in the light of the
+principle of relativity. But in my judgment he has cramped the
+development of his brilliant mathematical method in the narrow bounds of
+a very doubtful philosophy.
+
+The object of the present volume and of its predecessor is to lay the
+basis of a natural philosophy which is the necessary presupposition of a
+reorganised speculative physics. The general assimilation of space and
+time which dominates the constructive thought can claim the independent
+support of Minkowski from the side of science and also of succeeding
+relativists, while on the side of philosophers it was, I believe, one
+theme of Prof. Alexander's Gifford lectures delivered some few years ago
+but not yet published. He also summarised his conclusions on this
+question in a lecture to the Aristotelian Society in the July of 1918.
+Since the publication of _An Enquiry concerning the Principles of
+Natural Knowledge_ I have had the advantage of reading Mr C. D. Broad's
+_Perception, Physics, and Reality_ [Camb. Univ. Press, 1914]. This
+valuable book has assisted me in my discussion in Chapter II, though I
+am unaware as to how far Mr Broad would assent to any of my arguments as
+there stated.
+
+It remains for me to thank the staff of the University Press, its
+compositors, its proof-readers, its clerks, and its managing officials,
+not only for the technical excellence of their work, but for the way
+they have co-operated so as to secure my convenience.
+
+A. N. W.
+
+    IMPERIAL COLLEGE OF SCIENCE
+        AND TECHNOLOGY.
+            _April_, 1920.
+
+
+
+
+CONTENTS
+
+
+   CHAP.                                                  PAGE
+
+       I NATURE AND THOUGHT                                  1
+
+      II THEORIES OF THE BIFURCATION OF NATURE              26
+
+     III TIME                                               49
+
+      IV THE METHOD OF EXTENSIVE ABSTRACTION                74
+
+       V SPACE AND MOTION                                   99
+
+      VI CONGRUENCE                                        120
+
+     VII OBJECTS                                           143
+
+    VIII SUMMARY                                           164
+
+      IX THE ULTIMATE PHYSICAL CONCEPTS                    185
+
+         NOTE: ON THE GREEK CONCEPT OF A POINT             197
+
+         NOTE: ON SIGNIFICANCE AND INFINITE EVENTS         197
+
+         INDEX                                             199
+
+
+
+
+THE CONCEPT OF NATURE
+
+
+
+
+CHAPTER I
+
+NATURE AND THOUGHT
+
+
+The subject-matter of the Tarner lectures is defined by the founder to
+be 'the Philosophy of the Sciences and the Relations or Want of
+Relations between the different Departments of Knowledge.' It is fitting
+at the first lecture of this new foundation to dwell for a few moments
+on the intentions of the donor as expressed in this definition; and I do
+so the more willingly as I shall thereby be enabled to introduce the
+topics to which the present course is to be devoted.
+
+We are justified, I think, in taking the second clause of the definition
+as in part explanatory of the earlier clause. What is the philosophy of
+the sciences? It is not a bad answer to say that it is the study of the
+relations between the different departments of knowledge. Then with
+admirable solicitude for the freedom of learning there is inserted in
+the definition after the word 'relations' the phrase 'or want of
+relations.' A disproof of relations between sciences would in itself
+constitute a philosophy of the sciences. But we could not dispense
+either with the earlier or the later clause. It is not every relation
+between sciences which enters into their philosophy. For example biology
+and physics are connected by the use of the microscope. Still, I may
+safely assert that a technical description of the uses of the microscope
+in biology is not part of the philosophy of the sciences. Again, you
+cannot abandon the later clause of the definition; namely that
+referring to the relations between the sciences, without abandoning the
+explicit reference to an ideal in the absence of which philosophy must
+languish from lack of intrinsic interest. That ideal is the attainment
+of some unifying concept which will set in assigned relationships within
+itself all that there is for knowledge, for feeling, and for emotion.
+That far off ideal is the motive power of philosophic research; and
+claims allegiance even as you expel it. The philosophic pluralist is a
+strict logician; the Hegelian thrives on contradictions by the help of
+his absolute; the Mohammedan divine bows before the creative will of
+Allah; and the pragmatist will swallow anything so long as it 'works.'
+
+The mention of these vast systems and of the age-long controversies from
+which they spring, warns us to concentrate. Our task is the simpler one
+of the philosophy of the sciences. Now a science has already a certain
+unity which is the very reason why that body of knowledge has been
+instinctively recognised as forming a science. The philosophy of a
+science is the endeavour to express explicitly those unifying
+characteristics which pervade that complex of thoughts and make it to be
+a science. The philosophy of the sciences--conceived as one subject--is
+the endeavour to exhibit all sciences as one science, or--in case of
+defeat--the disproof of such a possibility.
+
+Again I will make a further simplification, and confine attention to the
+natural sciences, that is, to the sciences whose subject-matter is
+nature. By postulating a common subject-matter for this group of
+sciences a unifying philosophy of natural science has been thereby
+presupposed.
+
+What do we mean by nature? We have to discuss the philosophy of natural
+science. Natural science is the science of nature. But--What is nature?
+
+Nature is that which we observe in perception through the senses. In
+this sense-perception we are aware of something which is not thought and
+which is self-contained for thought. This property of being
+self-contained for thought lies at the base of natural science. It means
+that nature can be thought of as a closed system whose mutual relations
+do not require the expression of the fact that they are thought about.
+
+Thus in a sense nature is independent of thought. By this statement no
+metaphysical pronouncement is intended. What I mean is that we can think
+about nature without thinking about thought. I shall say that then we
+are thinking 'homogeneously' about nature.
+
+Of course it is possible to think of nature in conjunction with thought
+about the fact that nature is thought about. In such a case I shall say
+that we are thinking 'heterogeneously' about nature. In fact during the
+last few minutes we have been thinking heterogeneously about nature.
+Natural science is exclusively concerned with homogeneous thoughts about
+nature.
+
+But sense-perception has in it an element which is not thought. It is a
+difficult psychological question whether sense-perception involves
+thought; and if it does involve thought, what is the kind of thought
+which it necessarily involves. Note that it has been stated above that
+sense-perception is an awareness of something which is not thought.
+Namely, nature is not thought. But this is a different question, namely
+that the fact of sense-perception has a factor which is not thought. I
+call this factor 'sense-awareness.' Accordingly the doctrine that
+natural science is exclusively concerned with homogeneous thoughts about
+nature does not immediately carry with it the conclusion that natural
+science is not concerned with sense-awareness.
+
+However, I do assert this further statement; namely, that though natural
+science is concerned with nature which is the terminus of
+sense-perception, it is not concerned with the sense-awareness itself.
+
+I repeat the main line of this argument, and expand it in certain
+directions.
+
+Thought about nature is different from the sense-perception of nature.
+Hence the fact of sense-perception has an ingredient or factor which is
+not thought. I call this ingredient sense-awareness. It is indifferent
+to my argument whether sense-perception has or has not thought as
+another ingredient. If sense-perception does not involve thought, then
+sense-awareness and sense-perception are identical. But the something
+perceived is perceived as an entity which is the terminus of the
+sense-awareness, something which for thought is beyond the fact of that
+sense-awareness. Also the something perceived certainly does not contain
+other sense-awarenesses which are different from the sense-awareness
+which is an ingredient in that perception. Accordingly nature as
+disclosed in sense-perception is self-contained as against
+sense-awareness, in addition to being self-contained as against thought.
+I will also express this self-containedness of nature by saying that
+nature is closed to mind.
+
+This closure of nature does not carry with it any metaphysical doctrine
+of the disjunction of nature and mind. It means that in sense-perception
+nature is disclosed as a complex of entities whose mutual relations are
+expressible in thought without reference to mind, that is, without
+reference either to sense-awareness or to thought. Furthermore, I do not
+wish to be understood as implying that sense-awareness and thought are
+the only activities which are to be ascribed to mind. Also I am not
+denying that there are relations of natural entities to mind or minds
+other than being the termini of the sense-awarenesses of minds.
+Accordingly I will extend the meaning of the terms 'homogeneous
+thoughts' and 'heterogeneous thoughts' which have already been
+introduced. We are thinking 'homogeneously' about nature when we are
+thinking about it without thinking about thought or about
+sense-awareness, and we are thinking 'heterogeneously' about nature when
+we are thinking about it in conjunction with thinking either about
+thought or about sense-awareness or about both.
+
+I also take the homogeneity of thought about nature as excluding any
+reference to moral or aesthetic values whose apprehension is vivid in
+proportion to self-conscious activity. The values of nature are perhaps
+the key to the metaphysical synthesis of existence. But such a synthesis
+is exactly what I am not attempting. I am concerned exclusively with the
+generalisations of widest scope which can be effected respecting that
+which is known to us as the direct deliverance of sense-awareness.
+
+I have said that nature is disclosed in sense-perception as a complex of
+entities. It is worth considering what we mean by an entity in this
+connexion. 'Entity' is simply the Latin equivalent for 'thing' unless
+some arbitrary distinction is drawn between the words for technical
+purposes. All thought has to be about things. We can gain some idea of
+this necessity of things for thought by examination of the structure of
+a proposition.
+
+Let us suppose that a proposition is being communicated by an expositor
+to a recipient. Such a proposition is composed of phrases; some of these
+phrases may be demonstrative and others may be descriptive.
+
+By a demonstrative phrase I mean a phrase which makes the recipient
+aware of an entity in a way which is independent of the particular
+demonstrative phrase. You will understand that I am here using
+'demonstration' in the non-logical sense, namely in the sense in which a
+lecturer demonstrates by the aid of a frog and a microscope the
+circulation of the blood for an elementary class of medical students. I
+will call such demonstration 'speculative' demonstration, remembering
+Hamlet's use of the word 'speculation' when he says,
+
+    There is no speculation in those eyes.
+
+Thus a demonstrative phrase demonstrates an entity speculatively. It may
+happen that the expositor has meant some other entity--namely, the
+phrase demonstrates to him an entity which is diverse from the entity
+which it demonstrates to the recipient. In that case there is confusion;
+for there are two diverse propositions, namely the proposition for the
+expositor and the proposition for the recipient. I put this possibility
+aside as irrelevant for our discussion, though in practice it may be
+difficult for two persons to concur in the consideration of exactly the
+same proposition, or even for one person to have determined exactly the
+proposition which he is considering.
+
+Again the demonstrative phrase may fail to demonstrate any entity. In
+that case there is no proposition for the recipient. I think that we
+may assume (perhaps rashly) that the expositor knows what he means.
+
+A demonstrative phrase is a gesture. It is not itself a constituent of
+the proposition, but the entity which it demonstrates is such a
+constituent. You may quarrel with a demonstrative phrase as in some way
+obnoxious to you; but if it demonstrates the right entity, the
+proposition is unaffected though your taste may be offended. This
+suggestiveness of the phraseology is part of the literary quality of the
+sentence which conveys the proposition. This is because a sentence
+directly conveys one proposition, while in its phraseology it suggests a
+penumbra of other propositions charged with emotional value. We are now
+talking of the one proposition directly conveyed in any phraseology.
+
+This doctrine is obscured by the fact that in most cases what is in form
+a mere part of the demonstrative gesture is in fact a part of the
+proposition which it is desired directly to convey. In such a case we
+will call the phraseology of the proposition elliptical. In ordinary
+intercourse the phraseology of nearly all propositions is elliptical.
+
+Let us take some examples. Suppose that the expositor is in London, say
+in Regent's Park and in Bedford College, the great women's college which
+is situated in that park. He is speaking in the college hall and he
+says,
+
+    'This college building is commodious.'
+
+The phrase 'this college building' is a demonstrative phrase. Now
+suppose the recipient answers,
+
+    'This is not a college building, it is the lion-house in the Zoo.'
+
+Then, provided that the expositor's original proposition has not been
+couched in elliptical phraseology, the expositor sticks to his original
+proposition when he replies,
+
+    'Anyhow, _it_ is commodious.'
+
+Note that the recipient's answer accepts the speculative demonstration
+of the phrase 'This college building.' He does not say, 'What do you
+mean?' He accepts the phrase as demonstrating an entity, but declares
+that same entity to be the lion-house in the Zoo. In his reply, the
+expositor in his turn recognises the success of his original gesture as
+a speculative demonstration, and waives the question of the suitability
+of its mode of suggestiveness with an 'anyhow.' But he is now in a
+position to repeat the original proposition with the aid of a
+demonstrative gesture robbed of any suggestiveness, suitable or
+unsuitable, by saying,
+
+    '_It_ is commodious.'
+
+The '_it_' of this final statement presupposes that thought has seized
+on the entity as a bare objective for consideration.
+
+We confine ourselves to entities disclosed in sense-awareness. The
+entity is so disclosed as a relatum in the complex which is nature. It
+dawns on an observer because of its relations; but it is an objective
+for thought in its own bare individuality. Thought cannot proceed
+otherwise; namely, it cannot proceed without the ideal bare 'it' which
+is speculatively demonstrated. This setting up of the entity as a bare
+objective does not ascribe to it an existence apart from the complex in
+which it has been found by sense-perception. The 'it' for thought is
+essentially a relatum for sense-awareness.
+
+The chances are that the dialogue as to the college building takes
+another form. Whatever the expositor originally meant, he almost
+certainly now takes his former statement as couched in elliptical
+phraseology, and assumes that he was meaning,
+
+    'This is a college building and is commodious.'
+
+Here the demonstrative phrase or the gesture, which demonstrates the
+'it' which is commodious, has now been reduced to 'this'; and the
+attenuated phrase, under the circumstances in which it is uttered, is
+sufficient for the purpose of correct demonstration. This brings out the
+point that the verbal form is never the whole phraseology of the
+proposition; this phraseology also includes the general circumstances of
+its production. Thus the aim of a demonstrative phrase is to exhibit a
+definite 'it' as a bare objective for thought; but the _modus operandi_
+of a demonstrative phrase is to produce an awareness of the entity as a
+particular relatum in an auxiliary complex, chosen merely for the sake
+of the speculative demonstration and irrelevant to the proposition. For
+example, in the above dialogue, colleges and buildings, as related to
+the 'it' speculatively demonstrated by the phrase 'this college
+building,' set that 'it' in an auxiliary complex which is irrelevant to
+the proposition
+
+    'It is commodious.'
+
+Of course in language every phrase is invariably highly elliptical.
+Accordingly the sentence
+
+    'This college building is commodious'
+
+means probably
+
+    'This college building is commodious as a college building.'
+
+But it will be found that in the above discussion we can replace
+'commodious' by 'commodious as a college building' without altering our
+conclusion; though we can guess that the recipient, who thought he was
+in the lion-house of the Zoo, would be less likely to assent to.
+
+    'Anyhow, it is commodious as a college building.'
+
+A more obvious instance of elliptical phraseology arises if the
+expositor should address the recipient with the remark,
+
+    'That criminal is your friend.'
+
+The recipient might answer,
+
+    'He is my friend and you are insulting.'
+
+Here the recipient assumes that the phrase 'That criminal' is elliptical
+and not merely demonstrative. In fact, pure demonstration is impossible
+though it is the ideal of thought. This practical impossibility of pure
+demonstration is a difficulty which arises in the communication of
+thought and in the retention of thought. Namely, a proposition about a
+particular factor in nature can neither be expressed to others nor
+retained for repeated consideration without the aid of auxiliary
+complexes which are irrelevant to it.
+
+I now pass to descriptive phrases. The expositor says,
+
+    'A college in Regent's Park is commodious.'
+
+The recipient knows Regent's Park well. The phrase 'A college in
+Regent's Park' is descriptive for him. If its phraseology is not
+elliptical, which in ordinary life it certainly will be in some way or
+other, this proposition simply means,
+
+    'There is an entity which is a college building in Regent's Park
+    and is commodious.'
+
+If the recipient rejoins,
+
+    'The lion-house in the Zoo is the only commodious building in
+    Regent's Park,'
+
+he now contradicts the expositor, on the assumption that a lion-house in
+a Zoo is not a college building.
+
+Thus whereas in the first dialogue the recipient merely quarrelled with
+the expositor without contradicting him, in this dialogue he contradicts
+him. Thus a descriptive phrase is part of the proposition which it helps
+to express, whereas a demonstrative phrase is not part of the
+proposition which it helps to express.
+
+Again the expositor might be standing in Green Park--where there are no
+college buildings--and say,
+
+    'This college building is commodious.'
+
+Probably no proposition will be received by the recipient because the
+demonstrative phrase,
+
+    'This college building'
+
+has failed to demonstrate owing to the absence of the background of
+sense-awareness which it presupposes.
+
+But if the expositor had said,
+
+    'A college building in Green Park is commodious,'
+
+the recipient would have received a proposition, but a false one.
+
+Language is usually ambiguous and it is rash to make general assertions
+as to its meanings. But phrases which commence with 'this' or 'that' are
+usually demonstrative, whereas phrases which commence with 'the' or 'a'
+are often descriptive. In studying the theory of propositional
+expression it is important to remember the wide difference between the
+analogous modest words 'this' and 'that' on the one hand and 'a' and
+'the' on the other hand. The sentence
+
+    'The college building in Regent's Park is commodious'
+
+means, according to the analysis first made by Bertrand Russell, the
+proposition,
+
+   'There is an entity which (i) is a college building in Regent's
+   Park and (ii) is commodious and (iii) is such that any college
+   building in Regent's Park is identical with it.'
+
+The descriptive character of the phrase 'The college building in
+Regent's Park' is thus evident. Also the proposition is denied by the
+denial of any one of its three component clauses or by the denial of any
+combination of the component clauses. If we had substituted 'Green Park'
+for 'Regent's Park' a false proposition would have resulted. Also the
+erection of a second college in Regent's Park would make the proposition
+false, though in ordinary life common sense would politely treat it as
+merely ambiguous.
+
+'The Iliad' for a classical scholar is usually a demonstrative phrase;
+for it demonstrates to him a well-known poem. But for the majority of
+mankind the phrase is descriptive, namely, it is synonymous with 'The
+poem named "the Iliad".'
+
+Names may be either demonstrative or descriptive phrases. For example
+'Homer' is for us a descriptive phrase, namely, the word with some
+slight difference in suggestiveness means 'The man who wrote the Iliad.'
+
+This discussion illustrates that thought places before itself bare
+objectives, entities as we call them, which the thinking clothes by
+expressing their mutual relations. Sense-awareness discloses fact with
+factors which are the entities for thought. The separate distinction of
+an entity in thought is not a metaphysical assertion, but a method of
+procedure necessary for the finite expression of individual
+propositions. Apart from entities there could be no finite truths; they
+are the means by which the infinitude of irrelevance is kept out of
+thought.
+
+To sum up: the termini for thought are entities, primarily with bare
+individuality, secondarily with properties and relations ascribed to
+them in the procedure of thought; the termini for sense-awareness are
+factors in the fact of nature, primarily relata and only secondarily
+discriminated as distinct individualities.
+
+No characteristic of nature which is immediately posited for knowledge
+by sense-awareness can be explained. It is impenetrable by thought, in
+the sense that its peculiar essential character which enters into
+experience by sense-awareness is for thought merely the guardian of its
+individuality as a bare entity. Thus for thought 'red' is merely a
+definite entity, though for awareness 'red' has the content of its
+individuality. The transition from the 'red' of awareness to the 'red'
+of thought is accompanied by a definite loss of content, namely by the
+transition from the factor 'red' to the entity 'red.' This loss in the
+transition to thought is compensated by the fact that thought is
+communicable whereas sense-awareness is incommunicable.
+
+Thus there are three components in our knowledge of nature, namely,
+fact, factors, and entities. Fact is the undifferentiated terminus of
+sense-awareness; factors are termini of sense-awareness, differentiated
+as elements of fact; entities are factors in their function as the
+termini of thought. The entities thus spoken of are natural entities.
+Thought is wider than nature, so that there are entities for thought
+which are not natural entities.
+
+When we speak of nature as a complex of related entities, the 'complex'
+is fact as an entity for thought, to whose bare individuality is
+ascribed the property of embracing in its complexity the natural
+entities. It is our business to analyse this conception and in the
+course of the analysis space and time should appear. Evidently the
+relations holding between natural entities are themselves natural
+entities, namely they are also factors of fact, there for
+sense-awareness. Accordingly the structure of the natural complex can
+never be completed in thought, just as the factors of fact can never be
+exhausted in sense-awareness. Unexhaustiveness is an essential character
+of our knowledge of nature. Also nature does not exhaust the matter for
+thought, namely there are thoughts which would not occur in any
+homogeneous thinking about nature.
+
+The question as to whether sense-perception involves thought is largely
+verbal. If sense-perception involves a cognition of individuality
+abstracted from the actual position of the entity as a factor in fact,
+then it undoubtedly does involve thought. But if it is conceived as
+sense-awareness of a factor in fact competent to evoke emotion and
+purposeful action without further cognition, then it does not involve
+thought. In such a case the terminus of the sense-awareness is something
+for mind, but nothing for thought. The sense-perception of some lower
+forms of life may be conjectured to approximate to this character
+habitually. Also occasionally our own sense-perception in moments when
+thought-activity has been lulled to quiescence is not far off the
+attainment of this ideal limit.
+
+The process of discrimination in sense-awareness has two distinct sides.
+There is the discrimination of fact into parts, and the discrimination
+of any part of fact as exhibiting relations to entities which are not
+parts of fact though they are ingredients in it. Namely the immediate
+fact for awareness is the whole occurrence of nature. It is nature as an
+event present for sense-awareness, and essentially passing. There is no
+holding nature still and looking at it. We cannot redouble our efforts
+to improve our knowledge of the terminus of our present sense-awareness;
+it is our subsequent opportunity in subsequent sense-awareness which
+gains the benefit of our good resolution. Thus the ultimate fact for
+sense-awareness is an event. This whole event is discriminated by us
+into partial events. We are aware of an event which is our bodily life,
+of an event which is the course of nature within this room, and of a
+vaguely perceived aggregate of other partial events. This is the
+discrimination in sense-awareness of fact into parts.
+
+I shall use the term 'part' in the arbitrarily limited sense of an event
+which is part of the whole fact disclosed in awareness.
+
+Sense-awareness also yields to us other factors in nature which are not
+events. For example, sky-blue is seen as situated in a certain event.
+This relation of situation requires further discussion which is
+postponed to a later lecture. My present point is that sky-blue is found
+in nature with a definite implication in events, but is not an event
+itself. Accordingly in addition to events, there are other factors in
+nature directly disclosed to us in sense-awareness. The conception in
+thought of all the factors in nature as distinct entities with definite
+natural relations is what I have in another place[1] called the
+'diversification of nature.'
+
+[1] Cf. _Enquiry_.
+
+There is one general conclusion to be drawn from the foregoing
+discussion. It is that the first task of a philosophy of science should
+be some general classification of the entities disclosed to us in
+sense-perception.
+
+Among the examples of entities in addition to 'events' which we have
+used for the purpose of illustration are the buildings of Bedford
+College, Homer, and sky-blue. Evidently these are very different sorts
+of things; and it is likely that statements which are made about one
+kind of entity will not be true about other kinds. If human thought
+proceeded with the orderly method which abstract logic would suggest to
+it, we might go further and say that a classification of natural
+entities should be the first step in science itself. Perhaps you will be
+inclined to reply that this classification has already been effected,
+and that science is concerned with the adventures of material entities
+in space and time.
+
+The history of the doctrine of matter has yet to be written. It is the
+history of the influence of Greek philosophy on science. That influence
+has issued in one long misconception of the metaphysical status of
+natural entities. The entity has been separated from the factor which is
+the terminus of sense-awareness. It has become the substratum for that
+factor, and the factor has been degraded into an attribute of the
+entity. In this way a distinction has been imported into nature which is
+in truth no distinction at all. A natural entity is merely a factor of
+fact, considered in itself. Its disconnexion from the complex of fact is
+a mere abstraction. It is not the substratum of the factor, but the very
+factor itself as bared in thought. Thus what is a mere procedure of mind
+in the translation of sense-awareness into discursive knowledge has been
+transmuted into a fundamental character of nature. In this way matter
+has emerged as being the metaphysical substratum of its properties, and
+the course of nature is interpreted as the history of matter.
+
+Plato and Aristotle found Greek thought preoccupied with the quest for
+the simple substances in terms of which the course of events could be
+expressed. We may formulate this state of mind in the question, What is
+nature made of? The answers which their genius gave to this question,
+and more particularly the concepts which underlay the terms in which
+they framed their answers, have determined the unquestioned
+presuppositions as to time, space and matter which have reigned in
+science.
+
+In Plato the forms of thought are more fluid than in Aristotle, and
+therefore, as I venture to think, the more valuable. Their importance
+consists in the evidence they yield of cultivated thought about nature
+before it had been forced into a uniform mould by the long tradition of
+scientific philosophy. For example in the _Timaeus_ there is a
+presupposition, somewhat vaguely expressed, of a distinction between the
+general becoming of nature and the measurable time of nature. In a later
+lecture I have to distinguish between what I call the passage of nature
+and particular time-systems which exhibit certain characteristics of
+that passage. I will not go so far as to claim Plato in direct support
+of this doctrine, but I do think that the sections of the _Timaeus_
+which deal with time become clearer if my distinction is admitted.
+
+This is however a digression. I am now concerned with the origin of the
+scientific doctrine of matter in Greek thought. In the _Timaeus_ Plato
+asserts that nature is made of fire and earth with air and water as
+intermediate between them, so that 'as fire is to air so is air to
+water, and as air is to water so is water to earth.' He also suggests a
+molecular hypothesis for these four elements. In this hypothesis
+everything depends on the shape of the atoms; for earth it is cubical
+and for fire it is pyramidal. To-day physicists are again discussing
+the structure of the atom, and its shape is no slight factor in that
+structure. Plato's guesses read much more fantastically than does
+Aristotle's systematic analysis; but in some ways they are more
+valuable. The main outline of his ideas is comparable with that of
+modern science. It embodies concepts which any theory of natural
+philosophy must retain and in some sense must explain. Aristotle asked
+the fundamental question, What do we mean by 'substance'? Here the
+reaction between his philosophy and his logic worked very unfortunately.
+In his logic, the fundamental type of affirmative proposition is the
+attribution of a predicate to a subject. Accordingly, amid the many
+current uses of the term 'substance' which he analyses, he emphasises
+its meaning as 'the ultimate substratum which is no longer predicated of
+anything else.'
+
+The unquestioned acceptance of the Aristotelian logic has led to an
+ingrained tendency to postulate a substratum for whatever is disclosed
+in sense-awareness, namely, to look below what we are aware of for the
+substance in the sense of the 'concrete thing.' This is the origin of
+the modern scientific concept of matter and of ether, namely they are
+the outcome of this insistent habit of postulation.
+
+Accordingly ether has been invented by modern science as the substratum
+of the events which are spread through space and time beyond the reach
+of ordinary ponderable matter. Personally, I think that predication is a
+muddled notion confusing many different relations under a convenient
+common form of speech. For example, I hold that the relation of green to
+a blade of grass is entirely different from the relation of green to
+the event which is the life history of that blade for some short period,
+and is different from the relation of the blade to that event. In a
+sense I call the event the situation of the green, and in another sense
+it is the situation of the blade. Thus in one sense the blade is a
+character or property which can be predicated of the situation, and in
+another sense the green is a character or property of the same event
+which is also its situation. In this way the predication of properties
+veils radically different relations between entities.
+
+Accordingly 'substance,' which is a correlative term to 'predication,'
+shares in the ambiguity. If we are to look for substance anywhere, I
+should find it in events which are in some sense the ultimate substance
+of nature.
+
+Matter, in its modern scientific sense, is a return to the Ionian effort
+to find in space and time some stuff which composes nature. It has a
+more refined signification than the early guesses at earth and water by
+reason of a certain vague association with the Aristotelian idea of
+substance.
+
+Earth, water, air, fire, and matter, and finally ether are related in
+direct succession so far as concerns their postulated characters of
+ultimate substrata of nature. They bear witness to the undying vitality
+of Greek philosophy in its search for the ultimate entities which are
+the factors of the fact disclosed in sense-awareness. This search is the
+origin of science.
+
+The succession of ideas starting from the crude guesses of the early
+Ionian thinkers and ending in the nineteenth century ether reminds us
+that the scientific doctrine of matter is really a hybrid through which
+philosophy passed on its way to the refined Aristotelian concept of
+substance and to which science returned as it reacted against
+philosophic abstractions. Earth, fire, and water in the Ionic philosophy
+and the shaped elements in the _Timaeus_ are comparable to the matter
+and ether of modern scientific doctrine. But substance represents the
+final philosophic concept of the substratum which underlies any
+attribute. Matter (in the scientific sense) is already in space and
+time. Thus matter represents the refusal to think away spatial and
+temporal characteristics and to arrive at the bare concept of an
+individual entity. It is this refusal which has caused the muddle of
+importing the mere procedure of thought into the fact of nature. The
+entity, bared of all characteristics except those of space and time, has
+acquired a physical status as the ultimate texture of nature; so that
+the course of nature is conceived as being merely the fortunes of matter
+in its adventure through space.
+
+Thus the origin of the doctrine of matter is the outcome of uncritical
+acceptance of space and time as external conditions for natural
+existence. By this I do not mean that any doubt should be thrown on
+facts of space and time as ingredients in nature. What I do mean is 'the
+unconscious presupposition of space and time as being that within which
+nature is set.' This is exactly the sort of presupposition which tinges
+thought in any reaction against the subtlety of philosophical criticism.
+My theory of the formation of the scientific doctrine of matter is that
+first philosophy illegitimately transformed the bare entity, which is
+simply an abstraction necessary for the method of thought, into the
+metaphysical substratum of these factors in nature which in various
+senses are assigned to entities as their attributes; and that, as a
+second step, scientists (including philosophers who were scientists) in
+conscious or unconscious ignoration of philosophy presupposed this
+substratum, _qua_ substratum for attributes, as nevertheless in time and
+space.
+
+This is surely a muddle. The whole being of substance is as a substratum
+for attributes. Thus time and space should be attributes of the
+substance. This they palpably are not, if the matter be the substance of
+nature, since it is impossible to express spatio-temporal truths without
+having recourse to relations involving relata other than bits of matter.
+I waive this point however, and come to another. It is not the substance
+which is in space, but the attributes. What we find in space are the red
+of the rose and the smell of the jasmine and the noise of cannon. We
+have all told our dentists where our toothache is. Thus space is not a
+relation between substances, but between attributes.
+
+Thus even if you admit that the adherents of substance can be allowed to
+conceive substance as matter, it is a fraud to slip substance into space
+on the plea that space expresses relations between substances. On the
+face of it space has nothing to do with substances, but only with their
+attributes. What I mean is, that if you choose--as I think wrongly--to
+construe our experience of nature as an awareness of the attributes of
+substances, we are by this theory precluded from finding any analogous
+direct relations between substances as disclosed in our experience. What
+we do find are relations between the attributes of substances. Thus if
+matter is looked on as substance in space, the space in which it finds
+itself has very little to do with the space of our experience.
+
+The above argument has been expressed in terms of the relational theory
+of space. But if space be absolute--namely, if it have a being
+independent of things in it--the course of the argument is hardly
+changed. For things in space must have a certain fundamental relation to
+space which we will call occupation. Thus the objection that it is the
+attributes which are observed as related to space, still holds.
+
+The scientific doctrine of matter is held in conjunction with an
+absolute theory of time. The same arguments apply to the relations
+between matter and time as apply to the relations between space and
+matter. There is however (in the current philosophy) a difference in the
+connexions of space with matter from those of time with matter, which I
+will proceed to explain.
+
+Space is not merely an ordering of material entities so that any one
+entity bears certain relations to other material entities. The
+occupation of space impresses a certain character on each material
+entity in itself. By reason of its occupation of space matter has
+extension. By reason of its extension each bit of matter is divisible
+into parts, and each part is a numerically distinct entity from every
+other such part. Accordingly it would seem that every material entity is
+not really one entity. It is an essential multiplicity of entities.
+There seems to be no stopping this dissociation of matter into
+multiplicities short of finding each ultimate entity occupying one
+individual point. This essential multiplicity of material entities is
+certainly not what is meant by science, nor does it correspond to
+anything disclosed in sense-awareness. It is absolutely necessary that
+at a certain stage in this dissociation of matter a halt should be
+called, and that the material entities thus obtained should be treated
+as units. The stage of arrest may be arbitrary or may be set by the
+characteristics of nature; but all reasoning in science ultimately drops
+its space-analysis and poses to itself the problem, 'Here is one
+material entity, what is happening to it as a unit entity?' Yet this
+material entity is still retaining its extension, and as thus extended
+is a mere multiplicity. Thus there is an essential atomic property in
+nature which is independent of the dissociation of extension. There is
+something which in itself is one, and which is more than the logical
+aggregate of entities occupying points within the volume which the unit
+occupies. Indeed we may well be sceptical as to these ultimate entities
+at points, and doubt whether there are any such entities at all. They
+have the suspicious character that we are driven to accept them by
+abstract logic and not by observed fact.
+
+Time (in the current philosophy) does not exert the same disintegrating
+effect on matter which occupies it. If matter occupies a duration of
+time, the whole matter occupies every part of that duration. Thus the
+connexion between matter and time differs from the connexion between
+matter and space as expressed in current scientific philosophy. There is
+obviously a greater difficulty in conceiving time as the outcome of
+relations between different bits of matter than there is in the
+analogous conception of space. At an instant distinct volumes of space
+are occupied by distinct bits of matter. Accordingly there is so far no
+intrinsic difficulty in conceiving that space is merely the resultant of
+relations between the bits of matter. But in the one-dimensional time
+the same bit of matter occupies different portions of time. Accordingly
+time would have to be expressible in terms of the relations of a bit of
+matter with itself. My own view is a belief in the relational theory
+both of space and of time, and of disbelief in the current form of the
+relational theory of space which exhibits bits of matter as the relata
+for spatial relations. The true relata are events. The distinction which
+I have just pointed out between time and space in their connexion with
+matter makes it evident that any assimilation of time and space cannot
+proceed along the traditional line of taking matter as a fundamental
+element in space-formation.
+
+The philosophy of nature took a wrong turn during its development by
+Greek thought. This erroneous presupposition is vague and fluid in
+Plato's _Timaeus_. The general groundwork of the thought is still
+uncommitted and can be construed as merely lacking due explanation and
+the guarding emphasis. But in Aristotle's exposition the current
+conceptions were hardened and made definite so as to produce a faulty
+analysis of the relation between the matter and the form of nature as
+disclosed in sense-awareness. In this phrase the term 'matter' is not
+used in its scientific sense.
+
+I will conclude by guarding myself against a misapprehension. It is
+evident that the current doctrine of matter enshrines some fundamental
+law of nature. Any simple illustration will exemplify what I mean. For
+example, in a museum some specimen is locked securely in a glass case.
+It stays there for years: it loses its colour, and perhaps falls to
+pieces. But it is the same specimen; and the same chemical elements and
+the same quantities of those elements are present within the case at the
+end as were present at the beginning. Again the engineer and the
+astronomer deal with the motions of real permanences in nature. Any
+theory of nature which for one moment loses sight of these great basic
+facts of experience is simply silly. But it is permissible to point out
+that the scientific expression of these facts has become entangled in a
+maze of doubtful metaphysics; and that, when we remove the metaphysics
+and start afresh on an unprejudiced survey of nature, a new light is
+thrown on many fundamental concepts which dominate science and guide the
+progress of research.
+
+
+
+
+CHAPTER II
+
+THEORIES OF THE BIFURCATION OF NATURE
+
+
+In my previous lecture I criticised the concept of matter as the
+substance whose attributes we perceive. This way of thinking of matter
+is, I think, the historical reason for its introduction into science,
+and is still the vague view of it at the background of our thoughts
+which makes the current scientific doctrine appear so obvious. Namely we
+conceive ourselves as perceiving attributes of things, and bits of
+matter are the things whose attributes we perceive.
+
+In the seventeenth century the sweet simplicity of this aspect of matter
+received a rude shock. The transmission doctrines of science were then
+in process of elaboration and by the end of the century were
+unquestioned, though their particular forms have since been modified.
+The establishment of these transmission theories marks a turning point
+in the relation between science and philosophy. The doctrines to which I
+am especially alluding are the theories of light and sound. I have no
+doubt that the theories had been vaguely floating about before as
+obvious suggestions of common sense; for nothing in thought is ever
+completely new. But at that epoch they were systematised and made exact,
+and their complete consequences were ruthlessly deduced. It is the
+establishment of this procedure of taking the consequences seriously
+which marks the real discovery of a theory. Systematic doctrines of
+light and sound as being something proceeding from the emitting bodies
+were definitely established, and in particular the connexion of light
+with colour was laid bare by Newton.
+
+The result completely destroyed the simplicity of the 'substance and
+attribute' theory of perception. What we see depends on the light
+entering the eye. Furthermore we do not even perceive what enters the
+eye. The things transmitted are waves or--as Newton thought--minute
+particles, and the things seen are colours. Locke met this difficulty by
+a theory of primary and secondary qualities. Namely, there are some
+attributes of the matter which we do perceive. These are the primary
+qualities, and there are other things which we perceive, such as
+colours, which are not attributes of matter, but are perceived by us as
+if they were such attributes. These are the secondary qualities of
+matter.
+
+Why should we perceive secondary qualities? It seems an extremely
+unfortunate arrangement that we should perceive a lot of things that are
+not there. Yet this is what the theory of secondary qualities in fact
+comes to. There is now reigning in philosophy and in science an
+apathetic acquiescence in the conclusion that no coherent account can be
+given of nature as it is disclosed to us in sense-awareness, without
+dragging in its relations to mind. The modern account of nature is not,
+as it should be, merely an account of what the mind knows of nature; but
+it is also confused with an account of what nature does to the mind. The
+result has been disastrous both to science and to philosophy, but
+chiefly to philosophy. It has transformed the grand question of the
+relations between nature and mind into the petty form of the interaction
+between the human body and mind.
+
+Berkeley's polemic against matter was based on this confusion introduced
+by the transmission theory of light. He advocated, rightly as I think,
+the abandonment of the doctrine of matter in its present form. He had
+however nothing to put in its place except a theory of the relation of
+finite minds to the divine mind.
+
+But we are endeavouring in these lectures to limit ourselves to nature
+itself and not to travel beyond entities which are disclosed in
+sense-awareness.
+
+Percipience in itself is taken for granted. We consider indeed
+conditions for percipience, but only so far as those conditions are
+among the disclosures of perception. We leave to metaphysics the
+synthesis of the knower and the known. Some further explanation and
+defence of this position is necessary, if the line of argument of these
+lectures is to be comprehensible.
+
+The immediate thesis for discussion is that any metaphysical
+interpretation is an illegitimate importation into the philosophy of
+natural science. By a metaphysical interpretation I mean any discussion
+of the how (beyond nature) and of the why (beyond nature) of thought and
+sense-awareness. In the philosophy of science we seek the general
+notions which apply to nature, namely, to what we are aware of in
+perception. It is the philosophy of the thing perceived, and it should
+not be confused with the metaphysics of reality of which the scope
+embraces both perceiver and perceived. No perplexity concerning the
+object of knowledge can be solved by saying that there is a mind knowing
+it[2].
+
+[2] Cf. _Enquiry_, preface.
+
+In other words, the ground taken is this: sense-awareness is an
+awareness of something. What then is the general character of that
+something of which we are aware? We do not ask about the percipient or
+about the process, but about the perceived. I emphasise this point
+because discussions on the philosophy of science are usually extremely
+metaphysical--in my opinion, to the great detriment of the subject.
+
+The recourse to metaphysics is like throwing a match into the powder
+magazine. It blows up the whole arena. This is exactly what scientific
+philosophers do when they are driven into a corner and convicted of
+incoherence. They at once drag in the mind and talk of entities in the
+mind or out of the mind as the case may be. For natural philosophy
+everything perceived is in nature. We may not pick and choose. For us
+the red glow of the sunset should be as much part of nature as are the
+molecules and electric waves by which men of science would explain the
+phenomenon. It is for natural philosophy to analyse how these various
+elements of nature are connected.
+
+In making this demand I conceive myself as adopting our immediate
+instinctive attitude towards perceptual knowledge which is only
+abandoned under the influence of theory. We are instinctively willing to
+believe that by due attention, more can be found in nature than that
+which is observed at first sight. But we will not be content with less.
+What we ask from the philosophy of science is some account of the
+coherence of things perceptively known.
+
+This means a refusal to countenance any theory of psychic additions to
+the object known in perception. For example, what is given in perception
+is the green grass. This is an object which we know as an ingredient in
+nature. The theory of psychic additions would treat the greenness as a
+psychic addition furnished by the perceiving mind, and would leave to
+nature merely the molecules and the radiant energy which influence the
+mind towards that perception. My argument is that this dragging in of
+the mind as making additions of its own to the thing posited for
+knowledge by sense-awareness is merely a way of shirking the problem of
+natural philosophy. That problem is to discuss the relations _inter se_
+of things known, abstracted from the bare fact that they are known.
+Natural philosophy should never ask, what is in the mind and what is in
+nature. To do so is a confession that it has failed to express relations
+between things perceptively known, namely to express those natural
+relations whose expression is natural philosophy. It may be that the
+task is too hard for us, that the relations are too complex and too
+various for our apprehension, or are too trivial to be worth the trouble
+of exposition. It is indeed true that we have gone but a very small way
+in the adequate formulation of such relations. But at least do not let
+us endeavour to conceal failure under a theory of the byplay of the
+perceiving mind.
+
+What I am essentially protesting against is the bifurcation of nature
+into two systems of reality, which, in so far as they are real, are real
+in different senses. One reality would be the entities such as electrons
+which are the study of speculative physics. This would be the reality
+which is there for knowledge; although on this theory it is never known.
+For what is known is the other sort of reality, which is the byplay of
+the mind. Thus there would be two natures, one is the conjecture and the
+other is the dream.
+
+Another way of phrasing this theory which I am arguing against is to
+bifurcate nature into two divisions, namely into the nature apprehended
+in awareness and the nature which is the cause of awareness. The nature
+which is the fact apprehended in awareness holds within it the greenness
+of the trees, the song of the birds, the warmth of the sun, the hardness
+of the chairs, and the feel of the velvet. The nature which is the cause
+of awareness is the conjectured system of molecules and electrons which
+so affects the mind as to produce the awareness of apparent nature. The
+meeting point of these two natures is the mind, the causal nature being
+influent and the apparent nature being effluent.
+
+There are four questions which at once suggest themselves for discussion
+in connexion with this bifurcation theory of nature. They concern (i)
+causality, (ii) time, (iii) space, and (iv) delusions. These questions
+are not really separable. They merely constitute four distinct starting
+points from which to enter upon the discussion of the theory.
+
+Causal nature is the influence on the mind which is the cause of the
+effluence of apparent nature from the mind. This conception of causal
+nature is not to be confused with the distinct conception of one part of
+nature as being the cause of another part. For example, the burning of
+the fire and the passage of heat from it through intervening space is
+the cause of the body, its nerves and its brain, functioning in certain
+ways. But this is not an action of nature on the mind. It is an
+interaction within nature. The causation involved in this interaction is
+causation in a different sense from the influence of this system of
+bodily interactions within nature on the alien mind which thereupon
+perceives redness and warmth.
+
+The bifurcation theory is an attempt to exhibit natural science as an
+investigation of the cause of the fact of knowledge. Namely, it is an
+attempt to exhibit apparent nature as an effluent from the mind because
+of causal nature. The whole notion is partly based on the implicit
+assumption that the mind can only know that which it has itself produced
+and retains in some sense within itself, though it requires an exterior
+reason both as originating and as determining the character of its
+activity. But in considering knowledge we should wipe out all these
+spatial metaphors, such as 'within the mind' and 'without the mind.'
+Knowledge is ultimate. There can be no explanation of the 'why' of
+knowledge; we can only describe the 'what' of knowledge. Namely we can
+analyse the content and its internal relations, but we cannot explain
+why there is knowledge. Thus causal nature is a metaphysical chimera;
+though there is need of a metaphysics whose scope transcends the
+limitation to nature. The object of such a metaphysical science is not
+to explain knowledge, but exhibit in its utmost completeness our concept
+of reality.
+
+However, we must admit that the causality theory of nature has its
+strong suit. The reason why the bifurcation of nature is always creeping
+back into scientific philosophy is the extreme difficulty of exhibiting
+the perceived redness and warmth of the fire in one system of relations
+with the agitated molecules of carbon and oxygen, with the radiant
+energy from them, and with the various functionings of the material
+body. Unless we produce the all-embracing relations, we are faced with a
+bifurcated nature; namely, warmth and redness on one side, and
+molecules, electrons and ether on the other side. Then the two factors
+are explained as being respectively the cause and the mind's reaction to
+the cause.
+
+Time and space would appear to provide these all-embracing relations
+which the advocates of the philosophy of the unity of nature require.
+The perceived redness of the fire and the warmth are definitely related
+in time and in space to the molecules of the fire and the molecules of
+the body.
+
+It is hardly more than a pardonable exaggeration to say that the
+determination of the meaning of nature reduces itself principally to the
+discussion of the character of time and the character of space. In
+succeeding lectures I shall explain my own view of time and space. I
+shall endeavour to show that they are abstractions from more concrete
+elements of nature, namely, from events. The discussion of the details
+of the process of abstraction will exhibit time and space as
+interconnected, and will finally lead us to the sort of connexions
+between their measurements which occur in the modern theory of
+electromagnetic relativity. But this is anticipating our subsequent line
+of development. At present I wish to consider how the ordinary views of
+time and space help, or fail to help, in unifying our conception of
+nature.
+
+First, consider the absolute theories of time and space. We are to
+consider each, namely both time and space, to be a separate and
+independent system of entities, each system known to us in itself and
+for itself concurrently with our knowledge of the events of nature. Time
+is the ordered succession of durationless instants; and these instants
+are known to us merely as the relata in the serial relation which is the
+time-ordering relation, and the time-ordering relation is merely known
+to us as relating the instants. Namely, the relation and the instants
+are jointly known to us in our apprehension of time, each implying the
+other.
+
+This is the absolute theory of time. Frankly, I confess that it seems to
+me to be very unplausible. I cannot in my own knowledge find anything
+corresponding to the bare time of the absolute theory. Time is known to
+me as an abstraction from the passage of events. The fundamental fact
+which renders this abstraction possible is the passing of nature, its
+development, its creative advance, and combined with this fact is
+another characteristic of nature, namely the extensive relation between
+events. These two facts, namely the passage of events and the extension
+of events over each other, are in my opinion the qualities from which
+time and space originate as abstractions. But this is anticipating my
+own later speculations.
+
+Meanwhile, returning to the absolute theory, we are to suppose that time
+is known to us independently of any events in time. What happens in time
+occupies time. This relation of events to the time occupied, namely this
+relation of occupation, is a fundamental relation of nature to time.
+Thus the theory requires that we are aware of two fundamental relations,
+the time-ordering relation between instants, and the time-occupation
+relation between instants of time and states of nature which happen at
+those instants.
+
+There are two considerations which lend powerful support to the reigning
+theory of absolute time. In the first place time extends beyond nature.
+Our thoughts are in time. Accordingly it seems impossible to derive time
+merely from relations between elements of nature. For in that case
+temporal relations could not relate thoughts. Thus, to use a metaphor,
+time would apparently have deeper roots in reality than has nature. For
+we can imagine thoughts related in time without any perception of
+nature. For example we can imagine one of Milton's angels with thoughts
+succeeding each other in time, who does not happen to have noticed that
+the Almighty has created space and set therein a material universe. As a
+matter of fact I think that Milton set space on the same absolute level
+as time. But that need not disturb the illustration. In the second place
+it is difficult to derive the true serial character of time from the
+relative theory. Each instant is irrevocable. It can never recur by the
+very character of time. But if on the relative theory an instant of time
+is simply the state of nature at that time, and the time-ordering
+relation is simply the relation between such states, then the
+irrevocableness of time would seem to mean that an actual state of all
+nature can never return. I admit it seems unlikely that there should
+ever be such a recurrence down to the smallest particular. But extreme
+unlikeliness is not the point. Our ignorance is so abysmal that our
+judgments of likeliness and unlikeliness of future events hardly count.
+The real point is that the exact recurrence of a state of nature seems
+merely unlikely, while the recurrence of an instant of time violates our
+whole concept of time-order. The instants of time which have passed, are
+passed, and can never be again.
+
+Any alternative theory of time must reckon with these two considerations
+which are buttresses of the absolute theory. But I will not now continue
+their discussion.
+
+The absolute theory of space is analogous to the corresponding theory of
+time, but the reasons for its maintenance are weaker. Space, on this
+theory, is a system of extensionless points which are the relata in
+space-ordering relations which can technically be combined into one
+relation. This relation does not arrange the points in one linear series
+analogously to the simple method of the time-ordering relation for
+instants. The essential logical characteristics of this relation from
+which all the properties of space spring are expressed by mathematicians
+in the axioms of geometry. From these axioms[3] as framed by modern
+mathematicians the whole science of geometry can be deduced by the
+strictest logical reasoning. The details of these axioms do not now
+concern us. The points and the relations are jointly known to us in our
+apprehension of space, each implying the other. What happens in space,
+occupies space. This relation of occupation is not usually stated for
+events but for objects. For example, Pompey's statue would be said to
+occupy space, but not the event which was the assassination of Julius
+Caesar. In this I think that ordinary usage is unfortunate, and I hold
+that the relations of events to space and to time are in all respects
+analogous. But here I am intruding my own opinions which are to be
+discussed in subsequent lectures. Thus the theory of absolute space
+requires that we are aware of two fundamental relations, the
+space-ordering relation, which holds between points, and the
+space-occupation relation between points of space and material objects.
+
+[3] Cf. (for example) _Projective Geometry_ by Veblen and Young, vol. i.
+1910, vol. ii. 1917, Ginn and Company, Boston, U.S.A.
+
+This theory lacks the two main supports of the corresponding theory of
+absolute time. In the first place space does not extend beyond nature in
+the sense that time seems to do. Our thoughts do not seem to occupy
+space in quite the same intimate way in which they occupy time. For
+example, I have been thinking in a room, and to that extent my thoughts
+are in space. But it seems nonsense to ask how much volume of the room
+they occupied, whether it was a cubic foot or a cubic inch; whereas the
+same thoughts occupy a determinate duration of time, say, from eleven to
+twelve on a certain date.
+
+Thus whereas the relations of a relative theory of time are required to
+relate thoughts, it does not seem so obvious that the relations of a
+relative theory of space are required to relate them. The connexion of
+thought with space seems to have a certain character of indirectness
+which appears to be lacking in the connexion of thought with time.
+
+Again the irrevocableness of time does not seem to have any parallel for
+space. Space, on the relative theory, is the outcome of certain
+relations between objects commonly said to be in space; and whenever
+there are the objects, so related, there is the space. No difficulty
+seems to arise like that of the inconvenient instants of time which
+might conceivably turn up again when we thought that we had done with
+them.
+
+The absolute theory of space is not now generally popular. The knowledge
+of bare space, as a system of entities known to us in itself and for
+itself independently of our knowledge of the events in nature, does not
+seem to correspond to anything in our experience. Space, like time,
+would appear to be an abstraction from events. According to my own
+theory it only differentiates itself from time at a somewhat developed
+stage of the abstractive process. The more usual way of expressing the
+relational theory of space would be to consider space as an abstraction
+from the relations between material objects.
+
+Suppose now we assume absolute time and absolute space. What bearing
+has this assumption on the concept of nature as bifurcated into causal
+nature and apparent nature? Undoubtedly the separation between the two
+natures is now greatly mitigated. We can provide them with two systems
+of relations in common; for both natures can be presumed to occupy the
+same space and the same time. The theory now is this: Causal events
+occupy certain periods of the absolute time and occupy certain positions
+of the absolute space. These events influence a mind which thereupon
+perceives certain apparent events which occupy certain periods in the
+absolute time and occupy certain positions of the absolute space; and
+the periods and positions occupied by the apparent events bear a
+determinate relation to the periods and positions occupied by the causal
+events.
+
+Furthermore definite causal events produce for the mind definite
+apparent events. Delusions are apparent events which appear in temporal
+periods and spatial positions without the intervention of these causal
+events which are proper for influencing of the mind to their perception.
+
+The whole theory is perfectly logical. In these discussions we cannot
+hope to drive an unsound theory to a logical contradiction. A reasoner,
+apart from mere slips, only involves himself in a contradiction when he
+is shying at a _reductio ad absurdum_. The substantial reason for
+rejecting a philosophical theory is the 'absurdum' to which it reduces
+us. In the case of the philosophy of natural science the 'absurdum' can
+only be that our perceptual knowledge has not the character assigned to
+it by the theory. If our opponent affirms that his knowledge has that
+character, we can only--after making doubly sure that we understand
+each other--agree to differ. Accordingly the first duty of an expositor
+in stating a theory in which he disbelieves is to exhibit it as logical.
+It is not there where his trouble lies.
+
+Let me summarise the previously stated objections to this theory of
+nature. In the first place it seeks for the cause of the knowledge of
+the thing known instead of seeking for the character of the thing known:
+secondly it assumes a knowledge of time in itself apart from events
+related in time: thirdly it assumes a knowledge of space in itself apart
+from events related in space. There are in addition to these objections
+other flaws in the theory.
+
+Some light is thrown on the artificial status of causal nature in this
+theory by asking, why causal nature is presumed to occupy time and
+space. This really raises the fundamental question as to what
+characteristics causal nature should have in common with apparent
+nature. Why--on this theory--should the cause which influences the mind
+to perception have any characteristics in common with the effluent
+apparent nature? In particular, why should it be in space? Why should it
+be in time? And more generally, What do we know about mind which would
+allow us to infer any particular characteristics of a cause which should
+influence mind to particular effects?
+
+The transcendence of time beyond nature gives some slight reason for
+presuming that causal nature should occupy time. For if the mind
+occupies periods of time, there would seem to be some vague reason for
+assuming that influencing causes occupy the same periods of time, or at
+least, occupy periods which are strictly related to the mental periods.
+But if the mind does not occupy volumes of space, there seems to be no
+reason why causal nature should occupy any volumes of space. Thus space
+would seem to be merely apparent in the same sense as apparent nature is
+merely apparent. Accordingly if science is really investigating causes
+which operate on the mind, it would seem to be entirely on the wrong
+tack in presuming that the causes which it is seeking for have spatial
+relations. Furthermore there is nothing else in our knowledge analogous
+to these causes which influence the mind to perception. Accordingly,
+beyond the rashly presumed fact that they occupy time, there is really
+no ground by which we can determine any point of their character. They
+must remain for ever unknown.
+
+Now I assume as an axiom that science is not a fairy tale. It is not
+engaged in decking out unknowable entities with arbitrary and fantastic
+properties. What then is it that science is doing, granting that it is
+effecting something of importance? My answer is that it is determining
+the character of things known, namely the character of apparent nature.
+But we may drop the term 'apparent'; for there is but one nature, namely
+the nature which is before us in perceptual knowledge. The characters
+which science discerns in nature are subtle characters, not obvious at
+first sight. They are relations of relations and characters of
+characters. But for all their subtlety they are stamped with a certain
+simplicity which makes their consideration essential in unravelling the
+complex relations between characters of more perceptive insistence.
+
+The fact that the bifurcation of nature into causal and apparent
+components does not express what we mean by our knowledge is brought
+before us when we realise our thoughts in any discussion of the causes
+of our perceptions. For example, the fire is burning and we see a red
+coal. This is explained in science by radiant energy from the coal
+entering our eyes. But in seeking for such an explanation we are not
+asking what are the sort of occurrences which are fitted to cause a mind
+to see red. The chain of causation is entirely different. The mind is
+cut out altogether. The real question is, When red is found in nature,
+what else is found there also? Namely we are asking for an analysis of
+the accompaniments in nature of the discovery of red in nature. In a
+subsequent lecture I shall expand this line of thought. I simply draw
+attention to it here in order to point out that the wave-theory of light
+has not been adopted because waves are just the sort of things which
+ought to make a mind perceive colours. This is no part of the evidence
+which has ever been adduced for the wave-theory, yet on the causal
+theory of perception, it is really the only relevant part. In other
+words, science is not discussing the causes of knowledge, but the
+coherence of knowledge. The understanding which is sought by science is
+an understanding of relations within nature.
+
+So far I have discussed the bifurcation of nature in connexion with the
+theories of absolute time and of absolute space. My reason has been that
+the introduction of the relational theories only weakens the case for
+bifurcation, and I wished to discuss this case on its strongest grounds.
+
+For instance, suppose we adopt the relational theory of space. Then the
+space in which apparent nature is set is the expression of certain
+relations between the apparent objects. It is a set of apparent
+relations between apparent relata. Apparent nature is the dream, and
+the apparent relations of space are dream relations, and the space is
+the dream space. Similarly the space in which causal nature is set is
+the expression of certain relations between the causal objects. It is
+the expression of certain facts about the causal activity which is going
+on behind the scenes. Accordingly causal space belongs to a different
+order of reality to apparent space. Hence there is no pointwise
+connexion between the two and it is meaningless to say that the
+molecules of the grass are in any place which has a determinate spatial
+relation to the place occupied by the grass which we see. This
+conclusion is very paradoxical and makes nonsense of all scientific
+phraseology. The case is even worse if we admit the relativity of time.
+For the same arguments apply, and break up time into the dream time and
+causal time which belong to different orders of reality.
+
+I have however been discussing an extreme form of the bifurcation
+theory. It is, as I think, the most defensible form. But its very
+definiteness makes it the more evidently obnoxious to criticism. The
+intermediate form allows that the nature we are discussing is always the
+nature directly known, and so far it rejects the bifurcation theory. But
+it holds that there are psychic additions to nature as thus known, and
+that these additions are in no proper sense part of nature. For example,
+we perceive the red billiard ball at its proper time, in its proper
+place, with its proper motion, with its proper hardness, and with its
+proper inertia. But its redness and its warmth, and the sound of the
+click as a cannon is made off it are psychic additions, namely,
+secondary qualities which are only the mind's way of perceiving nature.
+This is not only the vaguely prevalent theory, but is, I believe, the
+historical form of the bifurcation theory in so far as it is derived
+from philosophy. I shall call it the theory of psychic additions.
+
+This theory of psychic additions is a sound common-sense theory which
+lays immense stress on the obvious reality of time, space, solidity and
+inertia, but distrusts the minor artistic additions of colour, warmth
+and sound.
+
+The theory is the outcome of common-sense in retreat. It arose in an
+epoch when the transmission theories of science were being elaborated.
+For example, colour is the result of a transmission from the material
+object to the perceiver's eye; and what is thus transmitted is not
+colour. Thus colour is not part of the reality of the material object.
+Similarly for the same reason sounds evaporate from nature. Also warmth
+is due to the transfer of something which is not temperature. Thus we
+are left with spatio-temporal positions, and what I may term the
+'pushiness' of the body. This lands us to eighteenth and nineteenth
+century materialism, namely, the belief that what is real in nature is
+matter, in time and in space and with inertia.
+
+Evidently a distinction in quality has been presupposed separating off
+some perceptions due to touch from other perceptions. These
+touch-perceptions are perceptions of the real inertia, whereas the other
+perceptions are psychic additions which must be explained on the causal
+theory. This distinction is the product of an epoch in which physical
+science has got ahead of medical pathology and of physiology.
+Perceptions of push are just as much the outcome of transmission as are
+perceptions of colour. When colour is perceived the nerves of the body
+are excited in one way and transmit their message towards the brain, and
+when push is perceived other nerves of the body are excited in another
+way and transmit their message towards the brain. The message of the one
+set is not the conveyance of colour, and the message of the other set is
+not the conveyance of push. But in one case colour is perceived and in
+the other case the push due to the object. If you snip certain nerves,
+there is an end to the perception of colour; and if you snip certain
+other nerves, there is an end to the perception of push. It would appear
+therefore that any reasons which should remove colour from the reality
+of nature should also operate to remove inertia.
+
+Thus the attempted bifurcation of apparent nature into two parts of
+which one part is both causal for its own appearance and for the
+appearance of the other part, which is purely apparent, fails owing to
+the failure to establish any fundamental distinction between our ways of
+knowing about the two parts of nature as thus partitioned. I am not
+denying that the feeling of muscular effort historically led to the
+formulation of the concept of force. But this historical fact does not
+warrant us in assigning a superior reality in nature to material inertia
+over colour or sound. So far as reality is concerned all our
+sense-perceptions are in the same boat, and must be treated on the same
+principle. The evenness of treatment is exactly what this compromise
+theory fails to achieve.
+
+The bifurcation theory however dies hard. The reason is that there
+really is a difficulty to be faced in relating within the same system of
+entities the redness of the fire with the agitation of the molecules. In
+another lecture I will give my own explanation of the origin of the
+difficulty and of its solution.
+
+Another favourite solution, the most attenuated form which the
+bifurcation theory assumes, is to maintain that the molecules and ether
+of science are purely conceptual. Thus there is but one nature, namely
+apparent nature, and atoms and ether are merely names for logical terms
+in conceptual formulae of calculation.
+
+But what is a formula of calculation? It is presumably a statement that
+something or other is true for natural occurrences. Take the simplest of
+all formulae, Two and two make four. This--so far as it applies to
+nature--asserts that if you take two natural entities, and then again
+two other natural entities, the combined class contains four natural
+entities. Such formulae which are true for any entities cannot result in
+the production of the concepts of atoms. Then again there are formulae
+which assert that there are entities in nature with such and such
+special properties, say, for example, with the properties of the atoms
+of hydrogen. Now if there are no such entities, I fail to see how any
+statements about them can apply to nature. For example, the assertion
+that there is green cheese in the moon cannot be a premiss in any
+deduction of scientific importance, unless indeed the presence of green
+cheese in the moon has been verified by experiment. The current answer
+to these objections is that, though atoms are merely conceptual, yet
+they are an interesting and picturesque way of saying something else
+which is true of nature. But surely if it is something else that you
+mean, for heaven's sake say it. Do away with this elaborate machinery of
+a conceptual nature which consists of assertions about things which
+don't exist in order to convey truths about things which do exist. I am
+maintaining the obvious position that scientific laws, if they are true,
+are statements about entities which we obtain knowledge of as being in
+nature; and that, if the entities to which the statements refer are not
+to be found in nature, the statements about them have no relevance to
+any purely natural occurrence. Thus the molecules and electrons of
+scientific theory are, so far as science has correctly formulated its
+laws, each of them factors to be found in nature. The electrons are only
+hypothetical in so far as we are not quite certain that the electron
+theory is true. But their hypothetical character does not arise from the
+essential nature of the theory in itself after its truth has been
+granted.
+
+Thus at the end of this somewhat complex discussion, we return to the
+position which was affirmed at its beginning. The primary task of a
+philosophy of natural science is to elucidate the concept of nature,
+considered as one complex fact for knowledge, to exhibit the fundamental
+entities and the fundamental relations between entities in terms of
+which all laws of nature have to be stated, and to secure that the
+entities and relations thus exhibited are adequate for the expression of
+all the relations between entities which occur in nature.
+
+The third requisite, namely that of adequacy, is the one over which all
+the difficulty occurs. The ultimate data of science are commonly assumed
+to be time, space, material, qualities of material, and relations
+between material objects. But data as they occur in the scientific laws
+do not relate all the entities which present themselves in our
+perception of nature. For example, the wave-theory of light is an
+excellent well-established theory; but unfortunately it leaves out
+colour as perceived. Thus the perceived redness--or, other colour--has
+to be cut out of nature and made into the reaction of the mind under the
+impulse of the actual events of nature. In other words this concept of
+the fundamental relations within nature is inadequate. Thus we have to
+bend our energies to the enunciation of adequate concepts.
+
+But in so doing, are we not in fact endeavouring to solve a metaphysical
+problem? I do not think so. We are merely endeavouring to exhibit the
+type of relations which hold between the entities which we in fact
+perceive as in nature. We are not called on to make any pronouncement as
+to the psychological relation of subjects to objects or as to the status
+of either in the realm of reality. It is true that the issue of our
+endeavour may provide material which is relevant evidence for a
+discussion on that question. It can hardly fail to do so. But it is only
+evidence, and is not itself the metaphysical discussion. In order to
+make clear the character of this further discussion which is out of our
+ken, I will set before you two quotations. One is from Schelling and I
+extract the quotation from the work of the Russian philosopher Lossky
+which has recently been so excellently translated into English[4]--'In
+the "Philosophy of Nature" I considered the subject-object called nature
+in its activity of self-constructing. In order to understand it, we must
+rise to an intellectual intuition of nature. The empiricist does not
+rise thereto, and for this reason in all his explanations it is always
+_he himself_ that proves to be constructing nature. It is no wonder,
+then, that his construction and that which was to be constructed so
+seldom coincide. A _Natur-philosoph_ raises nature to independence, and
+makes it construct itself, and he never feels, therefore, the necessity
+of opposing nature as constructed (_i.e._ as experience) to real
+nature, or of correcting the one by means of the other.'
+
+[4] _The Intuitive Basis of Knowledge_, by N. O. Lossky, transl. by Mrs
+Duddington, Macmillan and Co., 1919.
+
+The other quotation is from a paper read by the Dean of St Paul's before
+the Aristotelian Society in May of 1919. Dr Inge's paper is entitled
+'Platonism and Human Immortality,' and in it there occurs the following
+statement: 'To sum up. The Platonic doctrine of immortality rests on the
+_independence_ of the spiritual world. The spiritual world is not a
+world of unrealised ideals, over against a real world of unspiritual
+fact. It is, on the contrary, the real world, of which we have a true
+though very incomplete knowledge, over against a world of common
+experience which, as a complete whole, is not real, since it is
+compacted out of miscellaneous data, not all on the same level, by the
+help of the imagination. There is no world corresponding to the world of
+our common experience. Nature makes abstractions for us, deciding what
+range of vibrations we are to see and hear, what things we are to notice
+and remember.'
+
+I have cited these statements because both of them deal with topics
+which, though they lie outside the range of our discussion, are always
+being confused with it. The reason is that they lie proximate to our
+field of thought, and are topics which are of burning interest to the
+metaphysically minded. It is difficult for a philosopher to realise that
+anyone really is confining his discussion within the limits that I have
+set before you. The boundary is set up just where he is beginning to get
+excited. But I submit to you that among the necessary prolegomena for
+philosophy and for natural science is a thorough understanding of the
+types of entities, and types of relations among those entities, which
+are disclosed to us in our perceptions of nature.
+
+
+
+
+CHAPTER III
+
+TIME
+
+
+The two previous lectures of this course have been mainly critical. In
+the present lecture I propose to enter upon a survey of the kinds of
+entities which are posited for knowledge in sense-awareness. My purpose
+is to investigate the sorts of relations which these entities of various
+kinds can bear to each other. A classification of natural entities is
+the beginning of natural philosophy. To-day we commence with the
+consideration of Time.
+
+In the first place there is posited for us a general fact: namely,
+something is going on; there is an occurrence for definition.
+
+This general fact at once yields for our apprehension two factors, which
+I will name, the 'discerned' and the 'discernible.' The discerned is
+comprised of those elements of the general fact which are discriminated
+with their own individual peculiarities. It is the field directly
+perceived. But the entities of this field have relations to other
+entities which are not particularly discriminated in this individual
+way. These other entities are known merely as the relata in relation to
+the entities of the discerned field. Such an entity is merely a
+'something' which has such-and-such definite relations to some definite
+entity or entities in the discerned field. As being thus related, they
+are--owing to the particular character of these relations--known as
+elements of the general fact which is going on. But we are not aware of
+them except as entities fulfilling the functions of relata in these
+relations.
+
+Thus the complete general fact, posited as occurring, comprises both
+sets of entities, namely the entities perceived in their own
+individuality and other entities merely apprehended as relata without
+further definition. This complete general fact is the discernible and it
+comprises the discerned. The discernible is all nature as disclosed in
+that sense-awareness, and extends beyond and comprises all of nature as
+actually discriminated or discerned in that sense-awareness. The
+discerning or discrimination of nature is a peculiar awareness of
+special factors in nature in respect to their peculiar characters. But
+the factors in nature of which we have this peculiar sense-awareness are
+known as not comprising all the factors which together form the whole
+complex of related entities within the general fact there for
+discernment. This peculiarity of knowledge is what I call its
+unexhaustive character. This character may be metaphorically described
+by the statement that nature as perceived always has a ragged edge. For
+example, there is a world beyond the room to which our sight is confined
+known to us as completing the space-relations of the entities discerned
+within the room. The junction of the interior world of the room with the
+exterior world beyond is never sharp. Sounds and subtler factors
+disclosed in sense-awareness float in from the outside. Every type of
+sense has its own set of discriminated entities which are known to be
+relata in relation with entities not discriminated by that sense. For
+example we see something which we do not touch and we touch something
+which we do not see, and we have a general sense of the space-relations
+between the entity disclosed in sight and the entity disclosed in touch.
+Thus in the first place each of these two entities is known as a relatum
+in a general system of space-relations and in the second place the
+particular mutual relation of these two entities as related to each
+other in this general system is determined. But the general system of
+space-relations relating the entity discriminated by sight with that
+discriminated by sight is not dependent on the peculiar character of the
+other entity as reported by the alternative sense. For example, the
+space-relations of the thing seen would have necessitated an entity as a
+relatum in the place of the thing touched even although certain elements
+of its character had not been disclosed by touch. Thus apart from the
+touch an entity with a certain specific relation to the thing seen would
+have been disclosed by sense-awareness but not otherwise discriminated
+in respect to its individual character. An entity merely known as
+spatially related to some discerned entity is what we mean by the bare
+idea of 'place.' The concept of place marks the disclosure in
+sense-awareness of entities in nature known merely by their spatial
+relations to discerned entities. It is the disclosure of the discernible
+by means of its relations to the discerned.
+
+This disclosure of an entity as a relatum without further specific
+discrimination of quality is the basis of our concept of significance.
+In the above example the thing seen was significant, in that it
+disclosed its spatial relations to other entities not necessarily
+otherwise entering into consciousness. Thus significance is relatedness,
+but it is relatedness with the emphasis on one end only of the relation.
+
+For the sake of simplicity I have confined the argument to spatial
+relations; but the same considerations apply to temporal relations. The
+concept of 'period of time' marks the disclosure in sense-awareness of
+entities in nature known merely by their temporal relations to
+discerned entities. Still further, this separation of the ideas of space
+and time has merely been adopted for the sake of gaining simplicity of
+exposition by conformity to current language. What we discern is the
+specific character of a place through a period of time. This is what I
+mean by an 'event.' We discern some specific character of an event. But
+in discerning an event we are also aware of its significance as a
+relatum in the structure of events. This structure of events is the
+complex of events as related by the two relations of extension and
+cogredience. The most simple expression of the properties of this
+structure are to be found in our spatial and temporal relations. A
+discerned event is known as related in this structure to other events
+whose specific characters are otherwise not disclosed in that immediate
+awareness except so far as that they are relata within the structure.
+
+The disclosure in sense-awareness of the structure of events classifies
+events into those which are discerned in respect to some further
+individual character and those which are not otherwise disclosed except
+as elements of the structure. These signified events must include events
+in the remote past as well as events in the future. We are aware of
+these as the far off periods of unbounded time. But there is another
+classification of events which is also inherent in sense-awareness.
+These are the events which share the immediacy of the immediately
+present discerned events. These are the events whose characters together
+with those of the discerned events comprise all nature present for
+discernment. They form the complete general fact which is all nature now
+present as disclosed in that sense-awareness. It is in this second
+classification of events that the differentiation of space from time
+takes its origin. The germ of space is to be found in the mutual
+relations of events within the immediate general fact which is all
+nature now discernible, namely within the one event which is the
+totality of present nature. The relations of other events to this
+totality of nature form the texture of time.
+
+The unity of this general present fact is expressed by the concept of
+simultaneity. The general fact is the whole simultaneous occurrence of
+nature which is now for sense-awareness. This general fact is what I
+have called the discernible. But in future I will call it a 'duration,'
+meaning thereby a certain whole of nature which is limited only by the
+property of being a simultaneity. Further in obedience to the principle
+of comprising within nature the whole terminus of sense-awareness,
+simultaneity must not be conceived as an irrelevant mental concept
+imposed upon nature. Our sense-awareness posits for immediate
+discernment a certain whole, here called a 'duration'; thus a duration
+is a definite natural entity. A duration is discriminated as a complex
+of partial events, and the natural entities which are components of this
+complex are thereby said to be 'simultaneous with this duration.' Also
+in a derivative sense they are simultaneous with each other in respect
+to this duration. Thus simultaneity is a definite natural relation. The
+word 'duration' is perhaps unfortunate in so far as it suggests a mere
+abstract stretch of time. This is not what I mean. A duration is a
+concrete slab of nature limited by simultaneity which is an essential
+factor disclosed in sense-awareness.
+
+Nature is a process. As in the case of everything directly exhibited in
+sense-awareness, there can be no explanation of this characteristic of
+nature. All that can be done is to use language which may speculatively
+demonstrate it, and also to express the relation of this factor in
+nature to other factors.
+
+It is an exhibition of the process of nature that each duration happens
+and passes. The process of nature can also be termed the passage of
+nature. I definitely refrain at this stage from using the word 'time,'
+since the measurable time of science and of civilised life generally
+merely exhibits some aspects of the more fundamental fact of the passage
+of nature. I believe that in this doctrine I am in full accord with
+Bergson, though he uses 'time' for the fundamental fact which I call the
+'passage of nature.' Also the passage of nature is exhibited equally in
+spatial transition as well as in temporal transition. It is in virtue of
+its passage that nature is always moving on. It is involved in the
+meaning of this property of 'moving on' that not only is any act of
+sense-awareness just that act and no other, but the terminus of each act
+is also unique and is the terminus of no other act. Sense-awareness
+seizes its only chance and presents for knowledge something which is for
+it alone.
+
+There are two senses in which the terminus of sense-awareness is unique.
+It is unique for the sense-awareness of an individual mind and it is
+unique for the sense-awareness of all minds which are operating under
+natural conditions. There is an important distinction between the two
+cases. (i) For one mind not only is the discerned component of the
+general fact exhibited in any act of sense-awareness distinct from the
+discerned component of the general fact exhibited in any other act of
+sense-awareness of that mind, but the two corresponding durations which
+are respectively related by simultaneity to the two discerned components
+are necessarily distinct. This is an exhibition of the temporal passage
+of nature; namely, one duration has passed into the other. Thus not only
+is the passage of nature an essential character of nature in its _role_
+of the terminus of sense-awareness, but it is also essential for
+sense-awareness in itself. It is this truth which makes time appear to
+extend beyond nature. But what extends beyond nature to mind is not the
+serial and measurable time, which exhibits merely the character of
+passage in nature, but the quality of passage itself which is in no way
+measurable except so far as it obtains in nature. That is to say,
+'passage' is not measurable except as it occurs in nature in connexion
+with extension. In passage we reach a connexion of nature with the
+ultimate metaphysical reality. The quality of passage in durations is a
+particular exhibition in nature of a quality which extends beyond
+nature. For example passage is a quality not only of nature, which is
+the thing known, but also of sense-awareness which is the procedure of
+knowing. Durations have all the reality that nature has, though what
+that may be we need not now determine. The measurableness of time is
+derivative from the properties of durations. So also is the serial
+character of time. We shall find that there are in nature competing
+serial time-systems derived from different families of durations. These
+are a peculiarity of the character of passage as it is found in nature.
+This character has the reality of nature, but we must not necessarily
+transfer natural time to extra-natural entities. (ii) For two minds, the
+discerned components of the general facts exhibited in their respective
+acts of sense-awareness must be different. For each mind, in its
+awareness of nature is aware of a certain complex of related natural
+entities in their relations to the living body as a focus. But the
+associated durations may be identical. Here we are touching on that
+character of the passage nature which issues in the spatial relations of
+simultaneous bodies. This possible identity of the durations in the case
+of the sense-awareness of distinct minds is what binds into one nature
+the private experiences of sentient beings. We are here considering the
+spatial side of the passage of nature. Passage in this aspect of it also
+seems to extend beyond nature to mind.
+
+It is important to distinguish simultaneity from instantaneousness. I
+lay no stress on the mere current usage of the two terms. There are two
+concepts which I want to distinguish, and one I call simultaneity and
+the other instantaneousness. I hope that the words are judiciously
+chosen; but it really does not matter so long as I succeed in explaining
+my meaning. Simultaneity is the property of a group of natural elements
+which in some sense are components of a duration. A duration can be all
+nature present as the immediate fact posited by sense-awareness. A
+duration retains within itself the passage of nature. There are within
+it antecedents and consequents which are also durations which may be the
+complete specious presents of quicker consciousnesses. In other words a
+duration retains temporal thickness. Any concept of all nature as
+immediately known is always a concept of some duration though it may be
+enlarged in its temporal thickness beyond the possible specious present
+of any being known to us as existing within nature. Thus simultaneity is
+an ultimate factor in nature, immediate for sense-awareness.
+
+Instantaneousness is a complex logical concept of a procedure in thought
+by which constructed logical entities are produced for the sake of the
+simple expression in thought of properties of nature. Instantaneousness
+is the concept of all nature at an instant, where an instant is
+conceived as deprived of all temporal extension. For example we conceive
+of the distribution of matter in space at an instant. This is a very
+useful concept in science especially in applied mathematics; but it is a
+very complex idea so far as concerns its connexions with the immediate
+facts of sense-awareness. There is no such thing as nature at an instant
+posited by sense-awareness. What sense-awareness delivers over for
+knowledge is nature through a period. Accordingly nature at an instant,
+since it is not itself a natural entity, must be defined in terms of
+genuine natural entities. Unless we do so, our science, which employs
+the concept of instantaneous nature, must abandon all claim to be
+founded upon observation.
+
+I will use the term 'moment' to mean 'all nature at an instant.' A
+moment, in the sense in which the term is here used, has no temporal
+extension, and is in this respect to be contrasted with a duration which
+has such extension. What is directly yielded to our knowledge by
+sense-awareness is a duration. Accordingly we have now to explain how
+moments are derived from durations, and also to explain the purpose
+served by their introduction.
+
+A moment is a limit to which we approach as we confine attention to
+durations of minimum extension. Natural relations among the ingredients
+of a duration gain in complexity as we consider durations of increasing
+temporal extension. Accordingly there is an approach to ideal simplicity
+as we approach an ideal diminution of extension.
+
+The word 'limit' has a precise signification in the logic of number and
+even in the logic of non-numerical one-dimensional series. As used here
+it is so far a mere metaphor, and it is necessary to explain directly
+the concept which it is meant to indicate.
+
+Durations can have the two-termed relational property of extending one
+over the other. Thus the duration which is all nature during a certain
+minute extends over the duration which is all nature during the
+30th second of that minute. This relation of 'extending
+over'--'extension' as I shall call it--is a fundamental natural relation
+whose field comprises more than durations. It is a relation which two
+limited events can have to each other. Furthermore as holding between
+durations the relation appears to refer to the purely temporal
+extension. I shall however maintain that the same relation of extension
+lies at the base both of temporal and spatial extension. This discussion
+can be postponed; and for the present we are simply concerned with the
+relation of extension as it occurs in its temporal aspect for the
+limited field of durations.
+
+The concept of extension exhibits in thought one side of the ultimate
+passage of nature. This relation holds because of the special character
+which passage assumes in nature; it is the relation which in the case of
+durations expresses the properties of 'passing over.' Thus the duration
+which was one definite minute passed over the duration which was its
+30th second. The duration of the 30th second was part of the duration of
+the minute. I shall use the terms 'whole' and 'part' exclusively in this
+sense, that the 'part' is an event which is extended over by the other
+event which is the 'whole.' Thus in my nomenclature 'whole' and 'part'
+refer exclusively to this fundamental relation of extension; and
+accordingly in this technical usage only events can be either wholes or
+parts.
+
+The continuity of nature arises from extension. Every event extends over
+other events, and every event is extended over by other events. Thus in
+the special case of durations which are now the only events directly
+under consideration, every duration is part of other durations; and
+every duration has other durations which are parts of it. Accordingly
+there are no maximum durations and no minimum durations. Thus there is
+no atomic structure of durations, and the perfect definition of a
+duration, so as to mark out its individuality and distinguish it from
+highly analogous durations over which it is passing, or which are
+passing over it, is an arbitrary postulate of thought. Sense-awareness
+posits durations as factors in nature but does not clearly enable
+thought to use it as distinguishing the separate individualities of the
+entities of an allied group of slightly differing durations. This is one
+instance of the indeterminateness of sense-awareness. Exactness is an
+ideal of thought, and is only realised in experience by the selection of
+a route of approximation.
+
+The absence of maximum and minimum durations does not exhaust the
+properties of nature which make up its continuity. The passage of nature
+involves the existence of a family of durations. When two durations
+belong to the same family either one contains the other, or they overlap
+each other in a subordinate duration without either containing the
+other; or they are completely separate. The excluded case is that of
+durations overlapping in finite events but not containing a third
+duration as a common part.
+
+It is evident that the relation of extension is transitive; namely as
+applied to durations, if duration A is part of duration B, and
+duration B is part of duration C, then A is part of C. Thus the
+first two cases may be combined into one and we can say that two
+durations which belong to the same family _either_ are such that there
+are durations which are parts of both _or_ are completely separate.
+
+Furthermore the converse of this proposition holds; namely, if two
+durations have other durations which are parts of both _or_ if the two
+durations are completely separate, then they belong to the same family.
+
+The further characteristics of the continuity of nature--so far as
+durations are concerned--which has not yet been formulated arises in
+connexion with a family of durations. It can be stated in this way:
+There are durations which contain as parts any two durations of the same
+family. For example a week contains as parts any two of its days. It is
+evident that a containing duration satisfies the conditions for
+belonging to the same family as the two contained durations.
+
+We are now prepared to proceed to the definition of a moment of time.
+Consider a set of durations all taken from the same family. Let it have
+the following properties: (i) of any two members of the set one contains
+the other as a part, and (ii) there is no duration which is a common
+part of every member of the set.
+
+Now the relation of whole and part is asymmetrical; and by this I mean
+that if A is part of B, then B is not part of A. Also we have
+already noted that the relation is transitive. Accordingly we can easily
+see that the durations of any set with the properties just enumerated
+must be arranged in a one-dimensional serial order in which as we
+descend the series we progressively reach durations of smaller and
+smaller temporal extension. The series may start with any arbitrarily
+assumed duration of any temporal extension, but in descending the
+series the temporal extension progressively contracts and the successive
+durations are packed one within the other like the nest of boxes of a
+Chinese toy. But the set differs from the toy in this particular: the
+toy has a smallest box which forms the end box of its series; but the
+set of durations can have no smallest duration nor can it converge
+towards a duration as its limit. For the parts either of the end
+duration or of the limit would be parts of all the durations of the set
+and thus the second condition for the set would be violated.
+
+I will call such a set of durations an 'abstractive set' of durations.
+It is evident that an abstractive set as we pass along it converges to
+the ideal of all nature with no temporal extension, namely, to the ideal
+of all nature at an instant. But this ideal is in fact the ideal of a
+nonentity. What the abstractive set is in fact doing is to guide thought
+to the consideration of the progressive simplicity of natural relations
+as we progressively diminish the temporal extension of the duration
+considered. Now the whole point of the procedure is that the
+quantitative expressions of these natural properties do converge to
+limits though the abstractive set does not converge to any limiting
+duration. The laws relating these quantitative limits are the laws of
+nature 'at an instant,' although in truth there is no nature at an
+instant and there is only the abstractive set. Thus an abstractive set
+is effectively the entity meant when we consider an instant of time
+without temporal extension. It subserves all the necessary purposes of
+giving a definite meaning to the concept of the properties of nature at
+an instant. I fully agree that this concept is fundamental in the
+expression of physical science. The difficulty is to express our
+meaning in terms of the immediate deliverances of sense-awareness, and I
+offer the above explanation as a complete solution of the problem.
+
+In this explanation a moment is the set of natural properties reached by
+a route of approximation. An abstractive series is a route of
+approximation. There are different routes of approximation to the same
+limiting set of the properties of nature. In other words there are
+different abstractive sets which are to be regarded as routes of
+approximation to the same moment. Accordingly there is a certain amount
+of technical detail necessary in explaining the relations of such
+abstractive sets with the same convergence and in guarding against
+possible exceptional cases. Such details are not suitable for exposition
+in these lectures, and I have dealt with them fully elsewhere[5].
+
+[5] Cf. _An Enquiry concerning the Principles of Natural Knowledge_,
+Cambridge University Press, 1919.
+
+It is more convenient for technical purposes to look on a moment as
+being the class of all abstractive sets of durations with the same
+convergence. With this definition (provided that we can successfully
+explain what we mean by the 'same convergence' apart from a detailed
+knowledge of the set of natural properties arrived at by approximation)
+a moment is merely a class of sets of durations whose relations of
+extension in respect to each other have certain definite peculiarities.
+We may term these connexions of the component durations the 'extrinsic'
+properties of a moment; the 'intrinsic' properties of the moment are the
+properties of nature arrived at as a limit as we proceed along any one
+of its abstractive sets. These are the properties of nature 'at that
+moment,' or 'at that instant.'
+
+The durations which enter into the composition of a moment all belong to
+one family. Thus there is one family of moments corresponding to one
+family of durations. Also if we take two moments of the same family,
+among the durations which enter into the composition of one moment the
+smaller durations are completely separated from the smaller durations
+which enter into the composition of the other moment. Thus the two
+moments in their intrinsic properties must exhibit the limits of
+completely different states of nature. In this sense the two moments are
+completely separated. I will call two moments of the same family
+'parallel.'
+
+Corresponding to each duration there are two moments of the associated
+family of moments which are the boundary moments of that duration. A
+'boundary moment' of a duration can be defined in this way. There are
+durations of the same family as the given duration which overlap it but
+are not contained in it. Consider an abstractive set of such durations.
+Such a set defines a moment which is just as much without the duration
+as within it. Such a moment is a boundary moment of the duration. Also
+we call upon our sense-awareness of the passage of nature to inform us
+that there are two such boundary moments, namely the earlier one and the
+later one. We will call them the initial and the final boundaries.
+
+There are also moments of the same family such that the shorter
+durations in their composition are entirely separated from the given
+duration. Such moments will be said to lie 'outside' the given duration.
+Again other moments of the family are such that the shorter durations in
+their composition are parts of the given duration. Such moments are said
+to lie 'within' the given duration or to 'inhere' in it. The whole
+family of parallel moments is accounted for in this way by reference to
+any given duration of the associated family of durations. Namely, there
+are moments of the family which lie without the given duration, there
+are the two moments which are the boundary moments of the given
+duration, and the moments which lie within the given duration.
+Furthermore any two moments of the same family are the boundary moments
+of some one duration of the associated family of durations.
+
+It is now possible to define the serial relation of temporal order among
+the moments of a family. For let A and C be any two moments of the
+family, these moments are the boundary moments of one duration d of
+the associated family, and any moment B which lies within the duration
+d will be said to lie between the moments A and C. Thus the
+three-termed relation of 'lying-between' as relating three moments A,
+B, and C is completely defined. Also our knowledge of the passage of
+nature assures us that this relation distributes the moments of the
+family into a serial order. I abstain from enumerating the definite
+properties which secure this result, I have enumerated them in my
+recently published book[6] to which I have already referred. Furthermore
+the passage of nature enables us to know that one direction along the
+series corresponds to passage into the future and the other direction
+corresponds to retrogression towards the past.
+
+[6] Cf. _Enquiry_.
+
+Such an ordered series of moments is what we mean by time defined as a
+series. Each element of the series exhibits an instantaneous state of
+nature. Evidently this serial time is the result of an intellectual
+process of abstraction. What I have done is to give precise definitions
+of the procedure by which the abstraction is effected. This procedure is
+merely a particular case of the general method which in my book I name
+the 'method of extensive abstraction.' This serial time is evidently not
+the very passage of nature itself. It exhibits some of the natural
+properties which flow from it. The state of nature 'at a moment' has
+evidently lost this ultimate quality of passage. Also the temporal
+series of moments only retains it as an extrinsic relation of entities
+and not as the outcome of the essential being of the terms of the
+series.
+
+Nothing has yet been said as to the measurement of time. Such
+measurement does not follow from the mere serial property of time; it
+requires a theory of congruence which will be considered in a later
+lecture.
+
+In estimating the adequacy of this definition of the temporal series as
+a formulation of experience it is necessary to discriminate between the
+crude deliverance of sense-awareness and our intellectual theories. The
+lapse of time is a measurable serial quantity. The whole of scientific
+theory depends on this assumption and any theory of time which fails to
+provide such a measurable series stands self-condemned as unable to
+account for the most salient fact in experience. Our difficulties only
+begin when we ask what it is that is measured. It is evidently something
+so fundamental in experience that we can hardly stand back from it and
+hold it apart so as to view it in its own proportions.
+
+We have first to make up our minds whether time is to be found in nature
+or nature is to be found in time. The difficulty of the latter
+alternative--namely of making time prior to nature--is that time then
+becomes a metaphysical enigma. What sort of entities are its instants
+or its periods? The dissociation of time from events discloses to our
+immediate inspection that the attempt to set up time as an independent
+terminus for knowledge is like the effort to find substance in a shadow.
+There is time because there are happenings, and apart from happenings
+there is nothing.
+
+It is necessary however to make a distinction. In some sense time
+extends beyond nature. It is not true that a timeless sense-awareness
+and a timeless thought combine to contemplate a timeful nature.
+Sense-awareness and thought are themselves processes as well as their
+termini in nature. In other words there is a passage of sense-awareness
+and a passage of thought. Thus the reign of the quality of passage
+extends beyond nature. But now the distinction arises between passage
+which is fundamental and the temporal series which is a logical
+abstraction representing some of the properties of nature. A temporal
+series, as we have defined it, represents merely certain properties of a
+family of durations--properties indeed which durations only possess
+because of their partaking of the character of passage, but on the other
+hand properties which only durations do possess. Accordingly time in the
+sense of a measurable temporal series is a character of nature only, and
+does not extend to the processes of thought and of sense-awareness
+except by a correlation of these processes with the temporal series
+implicated in their procedures.
+
+So far the passage of nature has been considered in connexion with the
+passage of durations; and in this connexion it is peculiarly associated
+with temporal series. We must remember however that the character of
+passage is peculiarly associated with the extension of events, and that
+from this extension spatial transition arises just as much as temporal
+transition. The discussion of this point is reserved for a later lecture
+but it is necessary to remember it now that we are proceeding to discuss
+the application of the concept of passage beyond nature, otherwise we
+shall have too narrow an idea of the essence of passage.
+
+It is necessary to dwell on the subject of sense-awareness in this
+connexion as an example of the way in which time concerns mind, although
+measurable time is a mere abstract from nature and nature is closed to
+mind.
+
+Consider sense-awareness--not its terminus which is nature, but
+sense-awareness in itself as a procedure of mind. Sense-awareness is a
+relation of mind to nature. Accordingly we are now considering mind as a
+relatum in sense-awareness. For mind there is the immediate
+sense-awareness and there is memory. The distinction between memory and
+the present immediacy has a double bearing. On the one hand it discloses
+that mind is not impartially aware of all those natural durations to
+which it is related by awareness. Its awareness shares in the passage of
+nature. We can imagine a being whose awareness, conceived as his private
+possession, suffers no transition, although the terminus of his
+awareness is our own transient nature. There is no essential reason why
+memory should not be raised to the vividness of the present fact; and
+then from the side of mind, What is the difference between the present
+and the past? Yet with this hypothesis we can also suppose that the
+vivid remembrance and the present fact are posited in awareness as in
+their temporal serial order. Accordingly we must admit that though we
+can imagine that mind in the operation of sense-awareness might be free
+from any character of passage, yet in point of fact our experience of
+sense-awareness exhibits our minds as partaking in this character.
+
+On the other hand the mere fact of memory is an escape from transience.
+In memory the past is present. It is not present as overleaping the
+temporal succession of nature, but it is present as an immediate fact
+for the mind. Accordingly memory is a disengagement of the mind from the
+mere passage of nature; for what has passed for nature has not passed
+for mind.
+
+Furthermore the distinction between memory and the immediate present is
+not so clear as it is conventional to suppose. There is an intellectual
+theory of time as a moving knife-edge, exhibiting a present fact without
+temporal extension. This theory arises from the concept of an ideal
+exactitude of observation. Astronomical observations are successively
+refined to be exact to tenths, to hundredths, and to thousandths of
+seconds. But the final refinements are arrived at by a system of
+averaging, and even then present us with a stretch of time as a margin
+of error. Here error is merely a conventional term to express the fact
+that the character of experience does not accord with the ideal of
+thought. I have already explained how the concept of a moment
+conciliates the observed fact with this ideal; namely, there is a
+limiting simplicity in the quantitative expression of the properties of
+durations, which is arrived at by considering any one of the abstractive
+sets included in the moment. In other words the extrinsic character of
+the moment as an aggregate of durations has associated with it the
+intrinsic character of the moment which is the limiting expression of
+natural properties.
+
+Thus the character of a moment and the ideal of exactness which it
+enshrines do not in any way weaken the position that the ultimate
+terminus of awareness is a duration with temporal thickness. This
+immediate duration is not clearly marked out for our apprehension. Its
+earlier boundary is blurred by a fading into memory, and its later
+boundary is blurred by an emergence from anticipation. There is no sharp
+distinction either between memory and the present immediacy or between
+the present immediacy and anticipation. The present is a wavering
+breadth of boundary between the two extremes. Thus our own
+sense-awareness with its extended present has some of the character of
+the sense-awareness of the imaginary being whose mind was free from
+passage and who contemplated all nature as an immediate fact. Our own
+present has its antecedents and its consequents, and for the imaginary
+being all nature has its antecedent and its consequent durations. Thus
+the only difference in this respect between us and the imaginary being
+is that for him all nature shares in the immediacy of our present
+duration.
+
+The conclusion of this discussion is that so far as sense-awareness is
+concerned there is a passage of mind which is distinguishable from the
+passage of nature though closely allied with it. We may speculate, if we
+like, that this alliance of the passage of mind with the passage of
+nature arises from their both sharing in some ultimate character of
+passage which dominates all being. But this is a speculation in which we
+have no concern. The immediate deduction which is sufficient for us is
+that--so far as sense-awareness is concerned--mind is not in time or in
+space in the same sense in which the events of nature are in time, but
+that it is derivatively in time and in space by reason of the peculiar
+alliance of its passage with the passage of nature. Thus mind is in time
+and in space in a sense peculiar to itself. This has been a long
+discussion to arrive at a very simple and obvious conclusion. We all
+feel that in some sense our minds are here in this room and at this
+time. But it is not quite in the same sense as that in which the events
+of nature which are the existences of our brains have their spatial and
+temporal positions. The fundamental distinction to remember is that
+immediacy for sense-awareness is not the same as instantaneousness for
+nature. This last conclusion bears on the next discussion with which I
+will terminate this lecture. This question can be formulated thus, Can
+alternative temporal series be found in nature?
+
+A few years ago such a suggestion would have been put aside as being
+fantastically impossible. It would have had no bearing on the science
+then current, and was akin to no ideas which had ever entered into the
+dreams of philosophy. The eighteenth and nineteenth centuries accepted
+as their natural philosophy a certain circle of concepts which were as
+rigid and definite as those of the philosophy of the middle ages, and
+were accepted with as little critical research. I will call this natural
+philosophy 'materialism.' Not only were men of science materialists, but
+also adherents of all schools of philosophy. The idealists only differed
+from the philosophic materialists on question of the alignment of nature
+in reference to mind. But no one had any doubt that the philosophy of
+nature considered in itself was of the type which I have called
+materialism. It is the philosophy which I have already examined in my
+two lectures of this course preceding the present one. It can be
+summarised as the belief that nature is an aggregate of material and
+that this material exists in some sense _at_ each successive member of a
+one-dimensional series of extensionless instants of time. Furthermore
+the mutual relations of the material entities at each instant formed
+these entities into a spatial configuration in an unbounded space. It
+would seem that space--on this theory--would be as instantaneous as the
+instants, and that some explanation is required of the relations between
+the successive instantaneous spaces. The materialistic theory is however
+silent on this point; and the succession of instantaneous spaces is
+tacitly combined into one persistent space. This theory is a purely
+intellectual rendering of experience which has had the luck to get
+itself formulated at the dawn of scientific thought. It has dominated
+the language and the imagination of science since science flourished in
+Alexandria, with the result that it is now hardly possible to speak
+without appearing to assume its immediate obviousness.
+
+But when it is distinctly formulated in the abstract terms in which I
+have just stated it, the theory is very far from obvious. The passing
+complex of factors which compose the fact which is the terminus of
+sense-awareness places before us nothing corresponding to the trinity of
+this natural materialism. This trinity is composed (i) of the temporal
+series of extensionless instants, (ii) of the aggregate of material
+entities, and (iii) of space which is the outcome of relations of
+matter.
+
+There is a wide gap between these presuppositions of the intellectual
+theory of materialism and the immediate deliverances of sense-awareness.
+I do not question that this materialistic trinity embodies important
+characters of nature. But it is necessary to express these characters in
+terms of the facts of experience. This is exactly what in this lecture I
+have been endeavouring to do so far as time is concerned; and we have
+now come up against the question, Is there only one temporal series? The
+uniqueness of the temporal series is presupposed in the materialist
+philosophy of nature. But that philosophy is merely a theory, like the
+Aristotelian scientific theories so firmly believed in the middle ages.
+If in this lecture I have in any way succeeded in getting behind the
+theory to the immediate facts, the answer is not nearly so certain. The
+question can be transformed into this alternative form, Is there only
+one family of durations? In this question the meaning of a 'family of
+durations' has been defined earlier in this lecture. The answer is now
+not at all obvious. On the materialistic theory the instantaneous
+present is the only field for the creative activity of nature. The past
+is gone and the future is not yet. Thus (on this theory) the immediacy
+of perception is of an instantaneous present, and this unique present is
+the outcome of the past and the promise of the future. But we deny this
+immediately given instantaneous present. There is no such thing to be
+found in nature. As an ultimate fact it is a nonentity. What is
+immediate for sense-awareness is a duration. Now a duration has within
+itself a past and a future; and the temporal breadths of the immediate
+durations of sense-awareness are very indeterminate and dependent on the
+individual percipient. Accordingly there is no unique factor in nature
+which for every percipient is pre-eminently and necessarily the present.
+The passage of nature leaves nothing between the past and the future.
+What we perceive as present is the vivid fringe of memory tinged with
+anticipation. This vividness lights up the discriminated field within a
+duration. But no assurance can thereby be given that the happenings of
+nature cannot be assorted into other durations of alternative families.
+We cannot even know that the series of immediate durations posited by
+the sense-awareness of one individual mind all necessarily belong to the
+same family of durations. There is not the slightest reason to believe
+that this is so. Indeed if my theory of nature be correct, it will not
+be the case.
+
+The materialistic theory has all the completeness of the thought of the
+middle ages, which had a complete answer to everything, be it in heaven
+or in hell or in nature. There is a trimness about it, with its
+instantaneous present, its vanished past, its non-existent future, and
+its inert matter. This trimness is very medieval and ill accords with
+brute fact.
+
+The theory which I am urging admits a greater ultimate mystery and a
+deeper ignorance. The past and the future meet and mingle in the
+ill-defined present. The passage of nature which is only another name
+for the creative force of existence has no narrow ledge of definite
+instantaneous present within which to operate. Its operative presence
+which is now urging nature forward must be sought for throughout the
+whole, in the remotest past as well as in the narrowest breadth of any
+present duration. Perhaps also in the unrealised future. Perhaps also in
+the future which might be as well as the actual future which will be. It
+is impossible to meditate on time and the mystery of the creative
+passage of nature without an overwhelming emotion at the limitations of
+human intelligence.
+
+
+
+
+CHAPTER IV
+
+THE METHOD OF EXTENSIVE ABSTRACTION
+
+
+To-day's lecture must commence with the consideration of limited events.
+We shall then be in a position to enter upon an investigation of the
+factors in nature which are represented by our conception of space.
+
+The duration which is the immediate disclosure of our sense-awareness is
+discriminated into parts. There is the part which is the life of all
+nature within a room, and there is the part which is the life of all
+nature within a table in the room. These parts are limited events. They
+have the endurance of the present duration, and they are parts of it.
+But whereas a duration is an unlimited whole and in a certain limited
+sense is all that there is, a limited event possesses a completely
+defined limitation of extent which is expressed for us in
+spatio-temporal terms.
+
+We are accustomed to associate an event with a certain melodramatic
+quality. If a man is run over, that is an event comprised within certain
+spatio-temporal limits. We are not accustomed to consider the endurance
+of the Great Pyramid throughout any definite day as an event. But the
+natural fact which is the Great Pyramid throughout a day, meaning
+thereby all nature within it, is an event of the same character as the
+man's accident, meaning thereby all nature with spatio-temporal
+limitations so as to include the man and the motor during the period
+when they were in contact.
+
+We are accustomed to analyse these events into three factors, time,
+space, and material. In fact, we at once apply to them the concepts of
+the materialistic theory of nature. I do not deny the utility of this
+analysis for the purpose of expressing important laws of nature. What I
+am denying is that anyone of these factors is posited for us in
+sense-awareness in concrete independence. We perceive one unit factor in
+nature; and this factor is that something is going on then--there. For
+example, we perceive the going-on of the Great Pyramid in its relations
+to the goings-on of the surrounding Egyptian events. We are so trained,
+both by language and by formal teaching and by the resulting
+convenience, to express our thoughts in terms of this materialistic
+analysis that intellectually we tend to ignore the true unity of the
+factor really exhibited in sense-awareness. It is this unit factor,
+retaining in itself the passage of nature, which is the primary concrete
+element discriminated in nature. These primary factors are what I mean
+by events.
+
+Events are the field of a two-termed relation, namely the relation of
+extension which was considered in the last lecture. Events are the
+things related by the relation of extension. If an event A extends
+over an event B, then B is 'part of' A, and A is a 'whole' of
+which B is a part. Whole and part are invariably used in these
+lectures in this definite sense. It follows that in reference to this
+relation any two events A and B may have any one of four relations
+to each other, namely (i) A may extend over B, or (ii) B may
+extend over A, or (iii) A and B may both extend over some third
+event C, but neither over the other, or (iv) A and B may be
+entirely separate. These alternatives can obviously be illustrated by
+Euler's diagrams as they appear in logical textbooks.
+
+The continuity of nature is the continuity of events. This continuity is
+merely the name for the aggregate of a variety of properties of events
+in connexion with the relation of extension.
+
+In the first place, this relation is transitive; secondly, every event
+contains other events as parts of itself; thirdly every event is a part
+of other events; fourthly given any two finite events there are events
+each of which contains both of them as parts; and fifthly there is a
+special relation between events which I term 'junction.'
+
+Two events have junction when there is a third event of which both
+events are parts, and which is such that no part of it is separated from
+both of the two given events. Thus two events with junction make up
+exactly one event which is in a sense their sum.
+
+Only certain pairs of events have this property. In general any event
+containing two events also contains parts which are separated from both
+events.
+
+There is an alternative definition of the junction of two events which I
+have adopted in my recent book[7]. Two events have junction when there
+is a third event such that (i) it overlaps both events and (ii) it has
+no part which is separated from both the given events. If either of
+these alternative definitions is adopted as the definition of junction,
+the other definition appears as an axiom respecting the character of
+junction as we know it in nature. But we are not thinking of logical
+definition so much as the formulation of the results of direct
+observation. There is a certain continuity inherent in the observed
+unity of an event, and these two definitions of junction are really
+axioms based on observation respecting the character of this continuity.
+
+[7] Cf. _Enquiry_.
+
+The relations of whole and part and of overlapping are particular cases
+of the junction of events. But it is possible for events to have
+junction when they are separate from each other; for example, the upper
+and the lower part of the Great Pyramid are divided by some imaginary
+horizontal plane.
+
+The continuity which nature derives from events has been obscured by the
+illustrations which I have been obliged to give. For example I have
+taken the existence of the Great Pyramid as a fairly well-known fact to
+which I could safely appeal as an illustration. This is a type of event
+which exhibits itself to us as the situation of a recognisable object;
+and in the example chosen the object is so widely recognised that it has
+received a name. An object is an entity of a different type from an
+event. For example, the event which is the life of nature within the
+Great Pyramid yesterday and to-day is divisible into two parts, namely
+the Great Pyramid yesterday and the Great Pyramid to-day. But the
+recognisable object which is also called the Great Pyramid is the same
+object to-day as it was yesterday. I shall have to consider the theory
+of objects in another lecture.
+
+The whole subject is invested with an unmerited air of subtlety by the
+fact that when the event is the situation of a well-marked object, we
+have no language to distinguish the event from the object. In the case
+of the Great Pyramid, the object is the perceived unit entity which as
+perceived remains self-identical throughout the ages; while the whole
+dance of molecules and the shifting play of the electromagnetic field
+are ingredients of the event. An object is in a sense out of time. It is
+only derivatively in time by reason of its having the relation to events
+which I term 'situation.' This relation of situation will require
+discussion in a subsequent lecture.
+
+The point which I want to make now is that being the situation of a
+well-marked object is not an inherent necessity for an event. Wherever
+and whenever something is going on, there is an event. Furthermore
+'wherever and whenever' in themselves presuppose an event, for space and
+time in themselves are abstractions from events. It is therefore a
+consequence of this doctrine that something is always going on
+everywhere, even in so-called empty space. This conclusion is in accord
+with modern physical science which presupposes the play of an
+electromagnetic field throughout space and time. This doctrine of
+science has been thrown into the materialistic form of an all-pervading
+ether. But the ether is evidently a mere idle concept--in the
+phraseology which Bacon applied to the doctrine of final causes, it is a
+barren virgin. Nothing is deduced from it; and the ether merely
+subserves the purpose of satisfying the demands of the materialistic
+theory. The important concept is that of the shifting facts of the
+fields of force. This is the concept of an ether of events which should
+be substituted for that of a material ether.
+
+It requires no illustration to assure you that an event is a complex
+fact, and the relations between two events form an almost impenetrable
+maze. The clue discovered by the common sense of mankind and
+systematically utilised in science is what I have elsewhere[8] called
+the law of convergence to simplicity by diminution of extent.
+
+[8] Cf. _Organisation of Thought_, pp. 146 et seq. Williams and Norgate,
+1917.
+
+If A and B are two events, and A' is part of A and B' is part
+of B, then in many respects the relations between the parts A' and
+B' will be simpler than the relations between A and B. This is the
+principle which presides over all attempts at exact observation.
+
+The first outcome of the systematic use of this law has been the
+formulation of the abstract concepts of Time and Space. In the previous
+lecture I sketched how the principle was applied to obtain the
+time-series. I now proceed to consider how the spatial entities are
+obtained by the same method. The systematic procedure is identical in
+principle in both cases, and I have called the general type of procedure
+the 'method of extensive abstraction.'
+
+You will remember that in my last lecture I defined the concept of an
+abstractive set of durations. This definition can be extended so as to
+apply to any events, limited events as well as durations. The only
+change that is required is the substitution of the word 'event' for the
+word 'duration.' Accordingly an abstractive set of events is any set of
+events which possesses the two properties, (i) of any two members of the
+set one contains the other as a part, and (ii) there is no event which
+is a common part of every member of the set. Such a set, as you will
+remember, has the properties of the Chinese toy which is a nest of
+boxes, one within the other, with the difference that the toy has a
+smallest box, while the abstractive class has neither a smallest event
+nor does it converge to a limiting event which is not a member of the
+set.
+
+Thus, so far as the abstractive sets of events are concerned, an
+abstractive set converges to nothing. There is the set with its members
+growing indefinitely smaller and smaller as we proceed in thought
+towards the smaller end of the series; but there is no absolute minimum
+of any sort which is finally reached. In fact the set is just itself and
+indicates nothing else in the way of events, except itself. But each
+event has an intrinsic character in the way of being a situation of
+objects and of having parts which are situations of objects and--to
+state the matter more generally--in the way of being a field of the life
+of nature. This character can be defined by quantitative expressions
+expressing relations between various quantities intrinsic to the event
+or between such quantities and other quantities intrinsic to other
+events. In the case of events of considerable spatio-temporal extension
+this set of quantitative expressions is of bewildering complexity. If
+e be an event, let us denote by q(e) the set of quantitative expressions
+defining its character including its connexions with the rest of nature.
+Let e_1, e_2, e_3, etc. be an abstractive set, the members being so
+arranged that each member such as e_{n} extends over all the succeeding
+members such as e_{n+1}, e_{n+2} and so on. Then corresponding to the
+series
+
+    e_1, e_2, e_3, ..., e_{n}, e_{n+1}, ...,
+
+there is the series
+
+    q(e_1), q(e_2), q(e_3), ..., q(e_{n}), q(e_{n+1}), ....
+
+Call the series of events s and the series of quantitative expressions
+q(s). The series s has no last term and no events which are contained
+in every member of the series. Accordingly the series of events
+converges to nothing. It is just itself. Also the series q(s) has no
+last term. But the sets of homologous quantities running through the
+various terms of the series do converge to definite limits. For example
+if Q_1 be a quantitative measurement found in q(e_1), and Q_2 the homologue
+to Q_1 to be found in q(e_2), and Q_3 the homologue to Q_1 and Q_2 to be
+found in q(e_3), and so on, then the series
+
+    Q_1, Q_2, Q_3, ..., Q_{n}, Q_{n+1}, ...,
+
+though it has no last term, does in general converge to a definite
+limit. Accordingly there is a class of limits l(s) which is the
+class of the limits of those members of q(e_{n}) which have
+homologues throughout the series q(s) as n indefinitely increases.
+We can represent this statement diagrammatically by using an arrow (-->)
+to mean 'converges to.' Then
+
+    e_1, e_2, e_3, ..., e_{n}, e_{n+1}, ... --> nothing,
+
+and
+
+    q(e_1), q(e_2), q(e_3), ..., q(e_{n}), q(e_{n+1}), ... --> l(s).
+
+The mutual relations between the limits in the set l(s), and also
+between these limits and the limits in other sets l(s'), l(s"), ...,
+which arise from other abstractive sets s', s", etc., have a peculiar
+simplicity.
+
+Thus the set s does indicate an ideal simplicity of natural relations,
+though this simplicity is not the character of any actual event in s.
+We can make an approximation to such a simplicity which, as estimated
+numerically, is as close as we like by considering an event which is far
+enough down the series towards the small end. It will be noted that it
+is the infinite series, as it stretches away in unending succession
+towards the small end, which is of importance. The arbitrarily large
+event with which the series starts has no importance at all. We can
+arbitrarily exclude any set of events at the big end of an abstractive
+set without the loss of any important property to the set as thus
+modified.
+
+I call the limiting character of natural relations which is indicated by
+an abstractive set, the 'intrinsic character' of the set; also the
+properties, connected with the relation of whole and part as concerning
+its members, by which an abstractive set is defined together form what I
+call its 'extrinsic character.' The fact that the extrinsic character of
+an abstractive set determines a definite intrinsic character is the
+reason of the importance of the precise concepts of space and time. This
+emergence of a definite intrinsic character from an abstractive set is
+the precise meaning of the law of convergence.
+
+For example, we see a train approaching during a minute. The event which
+is the life of nature within that train during the minute is of great
+complexity and the expression of its relations and of the ingredients of
+its character baffles us. If we take one second of that minute, the more
+limited event which is thus obtained is simpler in respect to its
+ingredients, and shorter and shorter times such as a tenth of that
+second, or a hundredth, or a thousandth--so long as we have a definite
+rule giving a definite succession of diminishing events--give events
+whose ingredient characters converge to the ideal simplicity of the
+character of the train at a definite instant. Furthermore there are
+different types of such convergence to simplicity. For example, we can
+converge as above to the limiting character expressing nature at an
+instant within the whole volume of the train at that instant, or to
+nature at an instant within some portion of that volume--for example
+within the boiler of the engine--or to nature at an instant on some area
+of surface, or to nature at an instant on some line within the train, or
+to nature at an instant at some point of the train. In the last case the
+simple limiting characters arrived at will be expressed as densities,
+specific gravities, and types of material. Furthermore we need not
+necessarily converge to an abstraction which involves nature at an
+instant. We may converge to the physical ingredients of a certain point
+track throughout the whole minute. Accordingly there are different types
+of extrinsic character of convergence which lead to the approximation to
+different types of intrinsic characters as limits.
+
+We now pass to the investigation of possible connexions between
+abstractive sets. One set may 'cover' another. I define 'covering' as
+follows: An abstractive set p covers an abstractive set q when every
+member of p contains as its parts some members of q. It is evident
+that if any event e contains as a part any member of the set q, then
+owing to the transitive property of extension every succeeding member of
+the small end of q is part of e. In such a case I will say that the
+abstractive set q 'inheres in' the event e. Thus when an abstractive
+set p covers an abstractive set q, the abstractive set q inheres
+in every member of p.
+
+Two abstractive sets may each cover the other. When this is the case I
+shall call the two sets 'equal in abstractive force.' When there is no
+danger of misunderstanding I shall shorten this phrase by simply saying
+that the two abstractive sets are 'equal.' The possibility of this
+equality of abstractive sets arises from the fact that both sets, p
+and q, are infinite series towards their small ends. Thus the equality
+means, that given any event x belonging to p, we can always by
+proceeding far enough towards the small end of q find an event y
+which is part of x, and that then by proceeding far enough towards the
+small end of p we can find an event z which is part of y, and so
+on indefinitely.
+
+The importance of the equality of abstractive sets arises from the
+assumption that the intrinsic characters of the two sets are identical.
+If this were not the case exact observation would be at an end.
+
+It is evident that any two abstractive sets which are equal to a third
+abstractive set are equal to each other. An 'abstractive element' is the
+whole group of abstractive sets which are equal to any one of
+themselves. Thus all abstractive sets belonging to the same element are
+equal and converge to the same intrinsic character. Thus an abstractive
+element is the group of routes of approximation to a definite intrinsic
+character of ideal simplicity to be found as a limit among natural
+facts.
+
+If an abstractive set p covers an abstractive set q, then any
+abstractive set belonging to the abstractive element of which p is a
+member will cover any abstractive set belonging to the element of which
+q is a member. Accordingly it is useful to stretch the meaning of the
+term 'covering,' and to speak of one abstractive element 'covering'
+another abstractive element. If we attempt in like manner to stretch the
+term 'equal' in the sense of 'equal in abstractive force,' it is obvious
+that an abstractive element can only be equal to itself. Thus an
+abstractive element has a unique abstractive force and is the construct
+from events which represents one definite intrinsic character which is
+arrived at as a limit by the use of the principle of convergence to
+simplicity by diminution of extent.
+
+When an abstractive element A covers an abstractive element B, the
+intrinsic character of A in a sense includes the intrinsic character
+of B. It results that statements about the intrinsic character of B
+are in a sense statements about the intrinsic character of A; but the
+intrinsic character of A is more complex than that of B.
+
+The abstractive elements form the fundamental elements of space and
+time, and we now turn to the consideration of the properties involved in
+the formation of special classes of such elements. In my last lecture I
+have already investigated one class of abstractive elements, namely
+moments. Each moment is a group of abstractive sets, and the events
+which are members of these sets are all members of one family of
+durations. The moments of one family form a temporal series; and,
+allowing the existence of different families of moments, there will be
+alternative temporal series in nature. Thus the method of extensive
+abstraction explains the origin of temporal series in terms of the
+immediate facts of experience and at the same time allows for the
+existence of the alternative temporal series which are demanded by the
+modern theory of electromagnetic relativity.
+
+We now turn to space. The first thing to do is to get hold of the class
+of abstractive elements which are in some sense the points of space.
+Such an abstractive element must in some sense exhibit a convergence to
+an absolute minimum of intrinsic character. Euclid has expressed for all
+time the general idea of a point, as being without parts and without
+magnitude. It is this character of being an absolute minimum which we
+want to get at and to express in terms of the extrinsic characters of
+the abstractive sets which make up a point. Furthermore, points which
+are thus arrived at represent the ideal of events without any extension,
+though there are in fact no such entities as these ideal events. These
+points will not be the points of an external timeless space but of
+instantaneous spaces. We ultimately want to arrive at the timeless space
+of physical science, and also of common thought which is now tinged with
+the concepts of science. It will be convenient to reserve the term
+'point' for these spaces when we get to them. I will therefore use the
+name 'event-particles' for the ideal minimum limits to events. Thus an
+event-particle is an abstractive element and as such is a group of
+abstractive sets; and a point--namely a point of timeless space--will be
+a class of event-particles.
+
+Furthermore there is a separate timeless space corresponding to each
+separate temporal series, that is to each separate family of durations.
+We will come back to points in timeless spaces later. I merely mention
+them now that we may understand the stages of our investigation. The
+totality of event-particles will form a four-dimensional manifold, the
+extra dimension arising from time--in other words--arising from the
+points of a timeless space being each a class of event-particles.
+
+The required character of the abstractive sets which form
+event-particles would be secured if we could define them as having the
+property of being covered by any abstractive set which they cover. For
+then any other abstractive set which an abstractive set of an
+event-particle covered, would be equal to it, and would therefore be a
+member of the same event-particle. Accordingly an event-particle could
+cover no other abstractive element. This is the definition which I
+originally proposed at a congress in Paris in 1914[9]. There is however
+a difficulty involved in this definition if adopted without some further
+addition, and I am now not satisfied with the way in which I attempted
+to get over that difficulty in the paper referred to.
+
+[9] Cf. 'La Theorie Relationniste de l'Espace,' _Rev. de Metaphysique et
+de Morale_, vol. XXIII, 1916.
+
+The difficulty is this: When event-particles have once been defined it
+is easy to define the aggregate of event-particles forming the boundary
+of an event; and thence to define the point-contact at their boundaries
+possible for a pair of events of which one is part of the other. We can
+then conceive all the intricacies of tangency. In particular we can
+conceive an abstractive set of which all the members have point-contact
+at the same event-particle. It is then easy to prove that there will be
+no abstractive set with the property of being covered by every
+abstractive set which it covers. I state this difficulty at some length
+because its existence guides the development of our line of argument. We
+have got to annex some condition to the root property of being covered
+by any abstractive set which it covers. When we look into this question
+of suitable conditions we find that in addition to event-particles all
+the other relevant spatial and spatio-temporal abstractive elements can
+be defined in the same way by suitably varying the conditions.
+Accordingly we proceed in a general way suitable for employment beyond
+event-particles.
+
+Let {sigma} be the name of any condition which some abstractive sets
+fulfil. I say that an abstractive set is '{sigma}-prime' when it has the
+two properties, (i) that it satisfies the condition {sigma} and (ii)
+that it is covered by every abstractive set which both is covered by it
+and satisfies the condition {sigma}.
+
+In other words you cannot get any abstractive set satisfying the
+condition {sigma} which exhibits intrinsic character more simple than
+that of a {sigma}-prime.
+
+There are also the correlative abstractive sets which I call the sets of
+{sigma}-antiprimes. An abstractive set is a {sigma}-antiprime when it
+has the two properties, (i) that it satisfies the condition {sigma} and
+(ii) that it covers every abstractive set which both covers it and
+satisfies the condition {sigma}. In other words you cannot get any
+abstractive set satisfying the condition {sigma} which exhibits an
+intrinsic character more complex than that of a {sigma}-antiprime.
+
+The intrinsic character of a {sigma}-prime has a certain minimum of
+fullness among those abstractive sets which are subject to the condition
+of satisfying {sigma}; whereas the intrinsic character of a
+{sigma}-antiprime has a corresponding maximum of fullness, and includes
+all it can in the circumstances.
+
+Let us first consider what help the notion of antiprimes could give us
+in the definition of moments which we gave in the last lecture. Let the
+condition {sigma} be the property of being a class whose members are all
+durations. An abstractive set which satisfies this condition is thus an
+abstractive set composed wholly of durations. It is convenient then to
+define a moment as the group of abstractive sets which are equal to some
+{sigma}-antiprime, where the condition {sigma} has this special meaning.
+It will be found on consideration (i) that each abstractive set forming
+a moment is a {sigma}-antiprime, where {sigma} has this special meaning,
+and (ii) that we have excluded from membership of moments abstractive
+sets of durations which all have one common boundary, either the initial
+boundary or the final boundary. We thus exclude special cases which are
+apt to confuse general reasoning. The new definition of a moment, which
+supersedes our previous definition, is (by the aid of the notion of
+antiprimes) the more precisely drawn of the two, and the more useful.
+
+The particular condition which '{sigma}' stood for in the definition of
+moments included something additional to anything which can be derived
+from the bare notion of extension. A duration exhibits for thought a
+totality. The notion of totality is something beyond that of extension,
+though the two are interwoven in the notion of a duration.
+
+In the same way the particular condition '{sigma}' required for the
+definition of an event-particle must be looked for beyond the mere
+notion of extension. The same remark is also true of the particular
+conditions requisite for the other spatial elements. This additional
+notion is obtained by distinguishing between the notion of 'position'
+and the notion of convergence to an ideal zero of extension as exhibited
+by an abstractive set of events.
+
+In order to understand this distinction consider a point of the
+instantaneous space which we conceive as apparent to us in an almost
+instantaneous glance. This point is an event-particle. It has two
+aspects. In one aspect it is there, where it is. This is its position in
+the space. In another aspect it is got at by ignoring the circumambient
+space, and by concentrating attention on the smaller and smaller set of
+events which approximate to it. This is its extrinsic character. Thus a
+point has three characters, namely, its position in the whole
+instantaneous space, its extrinsic character, and its intrinsic
+character. The same is true of any other spatial element. For example an
+instantaneous volume in instantaneous space has three characters,
+namely, its position, its extrinsic character as a group of abstractive
+sets, and its intrinsic character which is the limit of natural
+properties which is indicated by any one of these abstractive sets.
+
+Before we can talk about position in instantaneous space, we must
+evidently be quite clear as to what we mean by instantaneous space in
+itself. Instantaneous space must be looked for as a character of a
+moment. For a moment is all nature at an instant. It cannot be the
+intrinsic character of the moment. For the intrinsic character tells us
+the limiting character of nature in space at that instant. Instantaneous
+space must be an assemblage of abstractive elements considered in their
+mutual relations. Thus an instantaneous space is the assemblage of
+abstractive elements covered by some one moment, and it is the
+instantaneous space of that moment.
+
+We have now to ask what character we have found in nature which is
+capable of according to the elements of an instantaneous space different
+qualities of position. This question at once brings us to the
+intersection of moments, which is a topic not as yet considered in these
+lectures.
+
+The locus of intersection of two moments is the assemblage of
+abstractive elements covered by both of them. Now two moments of the
+same temporal series cannot intersect. Two moments respectively of
+different families necessarily intersect. Accordingly in the
+instantaneous space of a moment we should expect the fundamental
+properties to be marked by the intersections with moments of other
+families. If M be a given moment, the intersection of M with another
+moment A is an instantaneous plane in the instantaneous space of M; and
+if B be a third moment intersecting both M and A, the intersection of M
+and B is another plane in the space M. Also the common intersection of
+A, B, and M is the intersection of the two planes in the space M, namely
+it is a straight line in the space M. An exceptional case arises if B
+and M intersect in the same plane as A and M. Furthermore if C be a
+fourth moment, then apart from special cases which we need not consider,
+it intersects M in a plane which the straight line (A, B, M) meets. Thus
+there is in general a common intersection of four moments of different
+families. This common intersection is an assemblage of abstractive
+elements which are each covered (or 'lie in') all four moments. The
+three-dimensional property of instantaneous space comes to this, that
+(apart from special relations between the four moments) any fifth moment
+either contains the whole of their common intersection or none of it. No
+further subdivision of the common intersection is possible by means of
+moments. The 'all or none' principle holds. This is not an _a priori_
+truth but an empirical fact of nature.
+
+It will be convenient to reserve the ordinary spatial terms 'plane,'
+'straight line,' 'point' for the elements of the timeless space of a
+time-system. Accordingly an instantaneous plane in the instantaneous
+space of a moment will be called a 'level,' an instantaneous straight
+line will be called a 'rect,' and an instantaneous point will be called
+a 'punct.' Thus a punct is the assemblage of abstractive elements which
+lie in each of four moments whose families have no special relations to
+each other. Also if P be any moment, either every abstractive element
+belonging to a given punct lies in P, or no abstractive element of
+that punct lies in P.
+
+Position is the quality which an abstractive element possesses in virtue
+of the moments in which it lies. The abstractive elements which lie in
+the instantaneous space of a given moment M are differentiated from
+each other by the various other moments which intersect M so as to
+contain various selections of these abstractive elements. It is this
+differentiation of the elements which constitutes their differentiation
+of position. An abstractive element which belongs to a punct has the
+simplest type of position in M, an abstractive element which belongs
+to a rect but not to a punct has a more complex quality of position, an
+abstractive element which belongs to a level and not to a rect has a
+still more complex quality of position, and finally the most complex
+quality of position belongs to an abstractive element which belongs to a
+volume and not to a level. A volume however has not yet been defined.
+This definition will be given in the next lecture.
+
+Evidently levels, rects, and puncts in their capacity as infinite
+aggregates cannot be the termini of sense-awareness, nor can they be
+limits which are approximated to in sense-awareness. Any one member of a
+level has a certain quality arising from its character as also belonging
+to a certain set of moments, but the level as a whole is a mere logical
+notion without any route of approximation along entities posited in
+sense-awareness.
+
+On the other hand an event-particle is defined so as to exhibit this
+character of being a route of approximation marked out by entities
+posited in sense-awareness. A definite event-particle is defined in
+reference to a definite punct in the following manner: Let the condition
+{sigma} mean the property of covering all the abstractive elements which
+are members of that punct; so that an abstractive set which satisfies
+the condition {sigma} is an abstractive set which covers every
+abstractive element belonging to the punct. Then the definition of the
+event-particle associated with the punct is that it is the group of all
+the {sigma}-primes, where {sigma} has this particular meaning.
+
+It is evident that--with this meaning of {sigma}--every abstractive set
+equal to a {sigma}-prime is itself a {sigma}-prime. Accordingly an
+event-particle as thus defined is an abstractive element, namely it is
+the group of those abstractive sets which are each equal to some given
+abstractive set. If we write out the definition of the event-particle
+associated with some given punct, which we will call {pi}, it is as
+follows: The event-particle associated with {pi} is the group of
+abstractive classes each of which has the two properties (i) that it
+covers every abstractive set in {pi} and (ii) that all the abstractive
+sets which also satisfy the former condition as to {pi} and which it
+covers, also cover it.
+
+An event-particle has position by reason of its association with a
+punct, and conversely the punct gains its derived character as a route
+of approximation from its association with the event-particle. These two
+characters of a point are always recurring in any treatment of the
+derivation of a point from the observed facts of nature, but in general
+there is no clear recognition of their distinction.
+
+The peculiar simplicity of an instantaneous point has a twofold origin,
+one connected with position, that is to say with its character as a
+punct, and the other connected with its character as an event-particle.
+The simplicity of the punct arises from its indivisibility by a moment.
+
+The simplicity of an event-particle arises from the indivisibility of
+its intrinsic character. The intrinsic character of an event-particle is
+indivisible in the sense that every abstractive set covered by it
+exhibits the same intrinsic character. It follows that, though there are
+diverse abstractive elements covered by event-particles, there is no
+advantage to be gained by considering them since we gain no additional
+simplicity in the expression of natural properties.
+
+These two characters of simplicity enjoyed respectively by
+event-particles and puncts define a meaning for Euclid's phrase,
+'without parts and without magnitude.'
+
+It is obviously convenient to sweep away out of our thoughts all these
+stray abstractive sets which are covered by event-particles without
+themselves being members of them. They give us nothing new in the way of
+intrinsic character. Accordingly we can think of rects and levels as
+merely loci of event-particles. In so doing we are also cutting out
+those abstractive elements which cover sets of event-particles, without
+these elements being event-particles themselves. There are classes of
+these abstractive elements which are of great importance. I will
+consider them later on in this and in other lectures. Meanwhile we will
+ignore them. Also I will always speak of 'event-particles' in preference
+to 'puncts,' the latter being an artificial word for which I have no
+great affection.
+
+Parallelism among rects and levels is now explicable.
+
+Consider the instantaneous space belonging to a moment A, and let A
+belong to the temporal series of moments which I will call {alpha}.
+Consider any other temporal series of moments which I will call {beta}.
+The moments of {beta} do not intersect each other and they intersect the
+moment A in a family of levels. None of these levels can intersect, and
+they form a family of parallel instantaneous planes in the instantaneous
+space of moment A. Thus the parallelism of moments in a temporal series
+begets the parallelism of levels in an instantaneous space, and
+thence--as it is easy to see--the parallelism of rects. Accordingly the
+Euclidean property of space arises from the parabolic property of time.
+It may be that there is reason to adopt a hyperbolic theory of time and
+a corresponding hyperbolic theory of space. Such a theory has not been
+worked out, so it is not possible to judge as to the character of the
+evidence which could be brought forward in its favour.
+
+The theory of order in an instantaneous space is immediately derived
+from time-order. For consider the space of a moment M. Let {alpha} be
+the name of a time-system to which M does not belong. Let A_1, A_2, A_3
+etc. be moments of {alpha} in the order of their occurrences. Then A_1,
+A_2, A_3, etc. intersect M in parallel levels l_1, l_2, l_3, etc. Then
+the relative order of the parallel levels in the space of M is the same
+as the relative order of the corresponding moments in the time-system
+{alpha}. Any rect in M which intersects all these levels in its set of
+puncts, thereby receives for its puncts an order of position on it. So
+spatial order is derivative from temporal order. Furthermore there are
+alternative time-systems, but there is only one definite spatial order
+in each instantaneous space. Accordingly the various modes of deriving
+spatial order from diverse time-systems must harmonise with one spatial
+order in each instantaneous space. In this way also diverse time-orders
+are comparable.
+
+We have two great questions still on hand to be settled before our
+theory of space is fully adjusted. One of these is the question of the
+determination of the methods of measurement within the space, in other
+words, the congruence-theory of the space. The measurement of space will
+be found to be closely connected with the measurement of time, with
+respect to which no principles have as yet been determined. Thus our
+congruence-theory will be a theory both for space and for time. Secondly
+there is the determination of the timeless space which corresponds to
+any particular time-system with its infinite set of instantaneous spaces
+in its successive moments. This is the space--or rather, these are the
+spaces--of physical science. It is very usual to dismiss this space by
+saying that this is conceptual. I do not understand the virtue of these
+phrases. I suppose that it is meant that the space is the conception of
+something in nature. Accordingly if the space of physical science is to
+be called conceptual, I ask, What in nature is it the conception of? For
+example, when we speak of a point in the timeless space of physical
+science, I suppose that we are speaking of something in nature. If we
+are not so speaking, our scientists are exercising their wits in the
+realms of pure fantasy, and this is palpably not the case. This demand
+for a definite Habeas Corpus Act for the production of the relevant
+entities in nature applies whether space be relative or absolute. On the
+theory of relative space, it may perhaps be argued that there is no
+timeless space for physical science, and that there is only the
+momentary series of instantaneous spaces.
+
+An explanation must then be asked for the meaning of the very common
+statement that such and such a man walked four miles in some definite
+hour. How can you measure distance from one space into another space? I
+understand walking out of the sheet of an ordnance map. But the meaning
+of saying that Cambridge at 10 o'clock this morning in the appropriate
+instantaneous space for that instant is 52 miles from London at
+11 o'clock this morning in the appropriate instantaneous space for that
+instant beats me entirely. I think that, by the time a meaning has been
+produced for this statement, you will find that you have constructed
+what is in fact a timeless space. What I cannot understand is how to
+produce an explanation of meaning without in effect making some such
+construction. Also I may add that I do not know how the instantaneous
+spaces are thus correlated into one space by any method which is
+available on the current theories of space.
+
+You will have noticed that by the aid of the assumption of alternative
+time-systems, we are arriving at an explanation of the character of
+space. In natural science 'to explain' means merely to discover
+'interconnexions.' For example, in one sense there is no explanation of
+the red which you see. It is red, and there is nothing else to be said
+about it. Either it is posited before you in sense-awareness or you are
+ignorant of the entity red. But science has explained red. Namely it has
+discovered interconnexions between red as a factor in nature and other
+factors in nature, for example waves of light which are waves of
+electromagnetic disturbances. There are also various pathological
+states of the body which lead to the seeing of red without the
+occurrence of light waves. Thus connexions have been discovered between
+red as posited in sense-awareness and various other factors in nature.
+The discovery of these connexions constitutes the scientific explanation
+of our vision of colour. In like manner the dependence of the character
+of space on the character of time constitutes an explanation in the
+sense in which science seeks to explain. The systematising intellect
+abhors bare facts. The character of space has hitherto been presented as
+a collection of bare facts, ultimate and disconnected. The theory which
+I am expounding sweeps away this disconnexion of the facts of space.
+
+
+
+
+CHAPTER V
+
+SPACE AND MOTION
+
+
+The topic for this lecture is the continuation of the task of explaining
+the construction of spaces as abstracts from the facts of nature. It was
+noted at the close of the previous lecture that the question of
+congruence had not been considered, nor had the construction of a
+timeless space which should correlate the successive momentary spaces of
+a given time-system. Furthermore it was also noted that there were many
+spatial abstractive elements which we had not yet defined. We will first
+consider the definition of some of these abstractive elements, namely
+the definitions of solids, of areas, and of routes. By a 'route' I mean
+a linear segment, whether straight or curved. The exposition of these
+definitions and the preliminary explanations necessary will, I hope,
+serve as a general explanation of the function of event-particles in the
+analysis of nature.
+
+We note that event-particles have 'position' in respect to each other.
+In the last lecture I explained that 'position' was quality gained by a
+spatial element in virtue of the intersecting moments which covered it.
+Thus each event-particle has position in this sense. The simplest mode
+of expressing the position in nature of an event-particle is by first
+fixing on any definite time-system. Call it {alpha}. There will be one
+moment of the temporal series of {alpha} which covers the given
+event-particle. Thus the position of the event-particle in the temporal
+series {alpha} is defined by this moment, which we will call M. The
+position of the particle in the space of M is then fixed in the ordinary
+way by three levels which intersect in it and in it only. This procedure
+of fixing the position of an event-particle shows that the aggregate of
+event-particles forms a four-dimensional manifold. A finite event
+occupies a limited chunk of this manifold in a sense which I now proceed
+to explain.
+
+Let e be any given event. The manifold of event-particles falls into
+three sets in reference to e. Each event-particle is a group of equal
+abstractive sets and each abstractive set towards its small-end is
+composed of smaller and smaller finite events. When we select from these
+finite events which enter into the make-up of a given event-particle
+those which are small enough, one of three cases must occur. Either (i)
+all of these small events are entirely separate from the given event
+e, or (ii) all of these small events are parts of the event e, or
+(iii) all of these small events overlap the event e but are not parts
+of it. In the first case the event-particle will be said to 'lie
+outside' the event e, in the second case the event-particle will be
+said to 'lie inside' the event e, and in the third case the
+event-particle will be said to be a 'boundary-particle' of the event
+e. Thus there are three sets of particles, namely the set of those
+which lie outside the event e, the set of those which lie inside the
+event e, and the boundary of the event e which is the set of
+boundary-particles of e. Since an event is four-dimensional, the
+boundary of an event is a three-dimensional manifold. For a finite event
+there is a continuity of boundary; for a duration the boundary consists
+of those event-particles which are covered by either of the two bounding
+moments. Thus the boundary of a duration consists of two momentary
+three-dimensional spaces. An event will be said to 'occupy' the
+aggregate of event-particles which lie within it.
+
+Two events which have 'junction' in the sense in which junction was
+described in my last lecture, and yet are separated so that neither
+event either overlaps or is part of the other event, are said to be
+'adjoined.'
+
+This relation of adjunction issues in a peculiar relation between the
+boundaries of the two events. The two boundaries must have a common
+portion which is in fact a continuous three-dimensional locus of
+event-particles in the four-dimensional manifold.
+
+A three-dimensional locus of event-particles which is the common portion
+of the boundary of two adjoined events will be called a 'solid.' A solid
+may or may not lie completely in one moment. A solid which does not lie
+in one moment will be called 'vagrant.' A solid which does lie in one
+moment will be called a volume. A volume may be defined as the locus of
+the event-particles in which a moment intersects an event, provided that
+the two do intersect. The intersection of a moment and an event will
+evidently consist of those event-particles which are covered by the
+moment and lie in the event. The identity of the two definitions of a
+volume is evident when we remember that an intersecting moment divides
+the event into two adjoined events.
+
+A solid as thus defined, whether it be vagrant or be a volume, is a mere
+aggregate of event-particles illustrating a certain quality of position.
+We can also define a solid as an abstractive element. In order to do so
+we recur to the theory of primes explained in the preceding lecture. Let
+the condition named {sigma} stand for the fact that each of the events
+of any abstractive set satisfying it has all the event-particles of some
+particular solid lying in it. Then the group of all the {sigma}-primes
+is the abstractive element which is associated with the given solid. I
+will call this abstractive element the solid as an abstractive element,
+and I will call the aggregate of event-particles the solid as a locus.
+The instantaneous volumes in instantaneous space which are the ideals of
+our sense-perception are volumes as abstractive elements. What we really
+perceive with all our efforts after exactness are small events far
+enough down some abstractive set belonging to the volume as an
+abstractive element.
+
+It is difficult to know how far we approximate to any perception of
+vagrant solids. We certainly do not think that we make any such
+approximation. But then our thoughts--in the case of people who do think
+about such topics--are so much under the control of the materialistic
+theory of nature that they hardly count for evidence. If Einstein's
+theory of gravitation has any truth in it, vagrant solids are of great
+importance in science. The whole boundary of a finite event may be
+looked on as a particular example of a vagrant solid as a locus. Its
+particular property of being closed prevents it from being definable as
+an abstractive element.
+
+When a moment intersects an event, it also intersects the boundary of
+that event. This locus, which is the portion of the boundary contained
+in the moment, is the bounding surface of the corresponding volume of
+that event contained in the moment. It is a two-dimensional locus.
+
+The fact that every volume has a bounding surface is the origin of the
+Dedekindian continuity of space.
+
+Another event may be cut by the same moment in another volume and this
+volume will also have its boundary. These two volumes in the
+instantaneous space of one moment may mutually overlap in the familiar
+way which I need not describe in detail and thus cut off portions from
+each other's surfaces. These portions of surfaces are 'momental areas.'
+
+It is unnecessary at this stage to enter into the complexity of a
+definition of vagrant areas. Their definition is simple enough when the
+four-dimensional manifold of event-particles has been more fully
+explored as to its properties.
+
+Momental areas can evidently be defined as abstractive elements by
+exactly the same method as applied to solids. We have merely to
+substitute 'area' for a 'solid' in the words of the definition already
+given. Also, exactly as in the analogous case of a solid, what we
+perceive as an approximation to our ideal of an area is a small event
+far enough down towards the small end of one of the equal abstractive
+sets which belongs to the area as an abstractive element.
+
+Two momental areas lying in the same moment can cut each other in a
+momental segment which is not necessarily rectilinear. Such a segment
+can also be defined as an abstractive element. It is then called a
+'momental route.' We will not delay over any general consideration of
+these momental routes, nor is it important for us to proceed to the
+still wider investigation of vagrant routes in general. There are
+however two simple sets of routes which are of vital importance. One is
+a set of momental routes and the other of vagrant routes. Both sets can
+be classed together as straight routes. We proceed to define them
+without any reference to the definitions of volumes and surfaces.
+
+The two types of straight routes will be called rectilinear routes and
+stations. Rectilinear routes are momental routes and stations are
+vagrant routes. Rectilinear routes are routes which in a sense lie in
+rects. Any two event-particles on a rect define the set of
+event-particles which lie between them on that rect. Let the
+satisfaction of the condition {sigma} by an abstractive set mean that
+the two given event-particles and the event-particles lying between them
+on the rect all lie in every event belonging to the abstractive set. The
+group of {sigma}-primes, where {sigma} has this meaning, form an
+abstractive element. Such abstractive elements are rectilinear routes.
+They are the segments of instantaneous straight lines which are the
+ideals of exact perception. Our actual perception, however exact, will
+be the perception of a small event sufficiently far down one of the
+abstractive sets of the abstractive element.
+
+A station is a vagrant route and no moment can intersect any station in
+more than one event-particle. Thus a station carries with it a
+comparison of the positions in their respective moments of the
+event-particles covered by it. Rects arise from the intersection of
+moments. But as yet no properties of events have been mentioned by which
+any analogous vagrant loci can be found out.
+
+The general problem for our investigation is to determine a method of
+comparison of position in one instantaneous space with positions in
+other instantaneous spaces. We may limit ourselves to the spaces of the
+parallel moments of one time-system. How are positions in these various
+spaces to be compared? In other words, What do we mean by motion? It is
+the fundamental question to be asked of any theory of relative space,
+and like many other fundamental questions it is apt to be left
+unanswered. It is not an answer to reply, that we all know what we mean
+by motion. Of course we do, so far as sense-awareness is concerned. I am
+asking that your theory of space should provide nature with something to
+be observed. You have not settled the question by bringing forward a
+theory according to which there is nothing to be observed, and by then
+reiterating that nevertheless we do observe this non-existent fact.
+Unless motion is something as a fact in nature, kinetic energy and
+momentum and all that depends on these physical concepts evaporate from
+our list of physical realities. Even in this revolutionary age my
+conservatism resolutely opposes the identification of momentum and
+moonshine.
+
+Accordingly I assume it as an axiom, that motion is a physical fact. It
+is something that we perceive as in nature. Motion presupposes rest.
+Until theory arose to vitiate immediate intuition, that is to say to
+vitiate the uncriticised judgments which immediately arise from
+sense-awareness, no one doubted that in motion you leave behind that
+which is at rest. Abraham in his wanderings left his birthplace where it
+had ever been. A theory of motion and a theory of rest are the same
+thing viewed from different aspects with altered emphasis.
+
+Now you cannot have a theory of rest without in some sense admitting a
+theory of absolute position. It is usually assumed that relative space
+implies that there is no absolute position. This is, according to my
+creed, a mistake. The assumption arises from the failure to make another
+distinction; namely, that there may be alternative definitions of
+absolute position. This possibility enters with the admission of
+alternative time-systems. Thus the series of spaces in the parallel
+moments of one temporal series may have their own definition of absolute
+position correlating sets of event-particles in these successive spaces,
+so that each set consists of event-particles, one from each space, all
+with the property of possessing the same absolute position in that
+series of spaces. Such a set of event-particles will form a point in the
+timeless space of that time-system. Thus a point is really an absolute
+position in the timeless space of a given time-system.
+
+But there are alternative time-systems, and each time-system has its own
+peculiar group of points--that is to say, its own peculiar definition of
+absolute position. This is exactly the theory which I will elaborate.
+
+In looking to nature for evidence of absolute position it is of no use
+to recur to the four-dimensional manifold of event-particles. This
+manifold has been obtained by the extension of thought beyond the
+immediacy of observation. We shall find nothing in it except what we
+have put there to represent the ideas in thought which arise from our
+direct sense-awareness of nature. To find evidence of the properties
+which are to be found in the manifold of event-particles we must always
+recur to the observation of relations between events. Our problem is to
+determine those relations between events which issue in the property of
+absolute position in a timeless space. This is in fact the problem of
+the determination of the very meaning of the timeless spaces of physical
+science.
+
+In reviewing the factors of nature as immediately disclosed in
+sense-awareness, we should note the fundamental character of the percept
+of 'being here.' We discern an event merely as a factor in a determinate
+complex in which each factor has its own peculiar share.
+
+There are two factors which are always ingredient in this complex, one
+is the duration which is represented in thought by the concept of all
+nature that is present now, and the other is the peculiar _locus standi_
+for mind involved in the sense-awareness. This _locus standi_ in nature
+is what is represented in thought by the concept of 'here,' namely of an
+'event here.'
+
+This is the concept of a definite factor in nature. This factor is an
+event in nature which is the focus in nature for that act of awareness,
+and the other events are perceived as referred to it. This event is part
+of the associated duration. I call it the 'percipient event.' This event
+is not the mind, that is to say, not the percipient. It is that in
+nature from which the mind perceives. The complete foothold of the mind
+in nature is represented by the pair of events, namely, the present
+duration which marks the 'when' of awareness and the percipient event
+which marks the 'where' of awareness and the 'how' of awareness. This
+percipient event is roughly speaking the bodily life of the incarnate
+mind. But this identification is only a rough one. For the functions of
+the body shade off into those of other events in nature; so that for
+some purposes the percipient event is to be reckoned as merely part of
+the bodily life and for other purposes it may even be reckoned as more
+than the bodily life. In many respects the demarcation is purely
+arbitrary, depending upon where in a sliding scale you choose to draw
+the line.
+
+I have already in my previous lecture on Time discussed the association
+of mind with nature. The difficulty of the discussion lies in the
+liability of constant factors to be overlooked. We never note them by
+contrast with their absences. The purpose of a discussion of such
+factors may be described as being to make obvious things look odd. We
+cannot envisage them unless we manage to invest them with some of the
+freshness which is due to strangeness.
+
+It is because of this habit of letting constant factors slip from
+consciousness that we constantly fall into the error of thinking of the
+sense-awareness of a particular factor in nature as being a two-termed
+relation between the mind and the factor. For example, I perceive a
+green leaf. Language in this statement suppresses all reference to any
+factors other than the percipient mind and the green leaf and the
+relation of sense-awareness. It discards the obvious inevitable factors
+which are essential elements in the perception. I am here, the leaf is
+there; and the event here and the event which is the life of the leaf
+there are both embedded in a totality of nature which is now, and within
+this totality there are other discriminated factors which it is
+irrelevant to mention. Thus language habitually sets before the mind a
+misleading abstract of the indefinite complexity of the fact of
+sense-awareness.
+
+What I now want to discuss is the special relation of the percipient
+event which is 'here' to the duration which is 'now.' This relation is a
+fact in nature, namely the mind is aware of nature as being with these
+two factors in this relation.
+
+Within the short present duration the 'here' of the percipient event has
+a definite meaning of some sort. This meaning of 'here' is the content
+of the special relation of the percipient event to its associated
+duration. I will call this relation 'cogredience.' Accordingly I ask for
+a description of the character of the relation of cogredience. The
+present snaps into a past and a present when the 'here' of cogredience
+loses its single determinate meaning. There has been a passage of nature
+from the 'here' of perception within the past duration to the different
+'here' of perception within the present duration. But the two 'heres' of
+sense-awareness within neighbouring durations may be indistinguishable.
+In this case there has been a passage from the past to the present, but
+a more retentive perceptive force might have retained the passing nature
+as one complete present instead of letting the earlier duration slip
+into the past. Namely, the sense of rest helps the integration of
+durations into a prolonged present, and the sense of motion
+differentiates nature into a succession of shortened durations. As we
+look out of a railway carriage in an express train, the present is past
+before reflexion can seize it. We live in snippits too quick for
+thought. On the other hand the immediate present is prolonged according
+as nature presents itself to us in an aspect of unbroken rest. Any
+change in nature provides ground for a differentiation among durations
+so as to shorten the present. But there is a great distinction between
+self-change in nature and change in external nature. Self-change in
+nature is change in the quality of the standpoint of the percipient
+event. It is the break up of the 'here' which necessitates the break up
+of the present duration. Change in external nature is compatible with a
+prolongation of the present of contemplation rooted in a given
+standpoint. What I want to bring out is that the preservation of a
+peculiar relation to a duration is a necessary condition for the
+function of that duration as a present duration for sense-awareness.
+This peculiar relation is the relation of cogredience between the
+percipient event and the duration. Cogredience is the preservation of
+unbroken quality of standpoint within the duration. It is the
+continuance of identity of station within the whole of nature which is
+the terminus of sense-awareness. The duration may comprise change within
+itself, but cannot--so far as it is one present duration--comprise
+change in the quality of its peculiar relation to the contained
+percipient event.
+
+In other words, perception is always 'here,' and a duration can only be
+posited as present for sense-awareness on condition that it affords one
+unbroken meaning of 'here' in its relation to the percipient event. It
+is only in the past that you can have been 'there' with a standpoint
+distinct from your present 'here.'
+
+Events there and events here are facts of nature, and the qualities of
+being 'there' and 'here' are not merely qualities of awareness as a
+relation between nature and mind. The quality of determinate station in
+the duration which belongs to an event which is 'here' in one
+determinate sense of 'here' is the same kind of quality of station which
+belongs to an event which is 'there' in one determinate sense of
+'there.' Thus cogredience has nothing to do with any biological
+character of the event which is related by it to the associated
+duration. This biological character is apparently a further condition
+for the peculiar connexion of a percipient event with the percipience of
+mind; but it has nothing to do with the relation of the percipient event
+to the duration which is the present whole of nature posited as the
+disclosure of the percipience.
+
+Given the requisite biological character, the event in its character of
+a percipient event selects that duration with which the operative past
+of the event is practically cogredient within the limits of the
+exactitude of observation. Namely, amid the alternative time-systems
+which nature offers there will be one with a duration giving the best
+average of cogredience for all the subordinate parts of the percipient
+event. This duration will be the whole of nature which is the terminus
+posited by sense-awareness. Thus the character of the percipient event
+determines the time-system immediately evident in nature. As the
+character of the percipient event changes with the passage of
+nature--or, in other words, as the percipient mind in its passage
+correlates itself with the passage of the percipient event into another
+percipient event--the time-system correlated with the percipience of
+that mind may change. When the bulk of the events perceived are
+cogredient in a duration other than that of the percipient event, the
+percipience may include a double consciousness of cogredience, namely
+the consciousness of the whole within which the observer in the train is
+'here,' and the consciousness of the whole within which the trees and
+bridges and telegraph posts are definitely 'there.' Thus in perceptions
+under certain circumstances the events discriminated assert their own
+relations of cogredience. This assertion of cogredience is peculiarly
+evident when the duration to which the perceived event is cogredient is
+the same as the duration which is the present whole of nature--in other
+words, when the event and the percipient event are both cogredient to
+the same duration.
+
+We are now prepared to consider the meaning of stations in a duration,
+where stations are a peculiar kind of routes, which define absolute
+position in the associated timeless space.
+
+There are however some preliminary explanations. A finite event will be
+said to extend throughout a duration when it is part of the duration
+and is intersected by any moment which lies in the duration. Such an
+event begins with the duration and ends with it. Furthermore every event
+which begins with the duration and ends with it, extends throughout the
+duration. This is an axiom based on the continuity of events. By
+beginning with a duration and ending with it, I mean (i) that the event
+is part of the duration, and (ii) that both the initial and final
+boundary moments of the duration cover some event-particles on the
+boundary of the event.
+
+Every event which is cogredient with a duration extends throughout that
+duration.
+
+It is not true that all the parts of an event cogredient with a duration
+are also cogredient with the duration. The relation of cogredience may
+fail in either of two ways. One reason for failure may be that the part
+does not extend throughout the duration. In this case the part may be
+cogredient with another duration which is part of the given duration,
+though it is not cogredient with the given duration itself. Such a part
+would be cogredient if its existence were sufficiently prolonged in that
+time-system. The other reason for failure arises from the
+four-dimensional extension of events so that there is no determinate
+route of transition of events in linear series. For example, the tunnel
+of a tube railway is an event at rest in a certain time-system, that is
+to say, it is cogredient with a certain duration. A train travelling in
+it is part of that tunnel, but is not itself at rest.
+
+If an event e be cogredient with a duration d, and d' be any
+duration which is part of d. Then d' belongs to the same time-system
+as d. Also d' intersects e in an event e' which is part of e
+and is cogredient with d'.
+
+Let P be any event-particle lying in a given duration d. Consider
+the aggregate of events in which P lies and which are also cogredient
+with d. Each of these events occupies its own aggregate of
+event-particles. These aggregates will have a common portion, namely the
+class of event-particle lying in all of them. This class of
+event-particles is what I call the 'station' of the event-particle P
+in the duration d. This is the station in the character of a locus. A
+station can also be defined in the character of an abstractive element.
+Let the property {sigma} be the name of the property which an
+abstractive set possesses when (i) each of its events is cogredient with
+the duration d and (ii) the event-particle P lies in each of its events.
+Then the group of {sigma}-primes, where {sigma} has this meaning, is an
+abstractive element and is the station of P in d as an abstractive
+element. The locus of event-particles covered by the station of P in d
+as an abstractive element is the station of P in d as a locus. A station
+has accordingly the usual three characters, namely, its character of
+position, its extrinsic character as an abstractive element, and its
+intrinsic character.
+
+It follows from the peculiar properties of rest that two stations
+belonging to the same duration cannot intersect. Accordingly every
+event-particle on a station of a duration has that station as its
+station in the duration. Also every duration which is part of a given
+duration intersects the stations of the given duration in loci which are
+its own stations. By means of these properties we can utilise the
+overlappings of the durations of one family--that is, of one
+time-system--to prolong stations indefinitely backwards and forwards.
+Such a prolonged station will be called a point-track. A point-track is
+a locus of event-particles. It is defined by reference to one particular
+time-system, {alpha} say. Corresponding to any other time-system these
+will be a different group of point-tracks. Every event-particle will lie
+on one and only one point-track of the group belonging to any one
+time-system. The group of point-tracks of the time-system {alpha} is the
+group of points of the timeless space of {alpha}. Each such point
+indicates a certain quality of absolute position in reference to the
+durations of the family associated with {alpha}, and thence in reference
+to the successive instantaneous spaces lying in the successive moments
+of {alpha}. Each moment of {alpha} will intersect a point-track in one
+and only one event-particle.
+
+This property of the unique intersection of a moment and a point-track
+is not confined to the case when the moment and the point-track belong
+to the same time-system. Any two event-particles on a point-track are
+sequential, so that they cannot lie in the same moment. Accordingly no
+moment can intersect a point-track more than once, and every moment
+intersects a point-track in one event-particle.
+
+Anyone who at the successive moments of {alpha} should be at the
+event-particles where those moments intersect a given point of {alpha}
+will be at rest in the timeless space of time-system {alpha}. But in any
+other timeless space belonging to another time-system he will be at a
+different point at each succeeding moment of that time-system. In other
+words he will be moving. He will be moving in a straight line with
+uniform velocity. We might take this as the definition of a straight
+line. Namely, a straight line in the space of time-system {beta} is the
+locus of those points of {beta} which all intersect some one point-track
+which is a point in the space of some other time-system. Thus each point
+in the space of a time-system {alpha} is associated with one and only
+one straight line of the space of any other time-system {beta}.
+Furthermore the set of straight lines in space {beta} which are thus
+associated with points in space {alpha} form a complete family of
+parallel straight lines in space {beta}. Thus there is a one-to-one
+correlation of points in space {alpha} with the straight lines of a
+certain definite family of parallel straight lines in space {beta}.
+Conversely there is an analogous one-to-one correlation of the points in
+space {beta} with the straight lines of a certain family of parallel
+straight lines in space {alpha}. These families will be called
+respectively the family of parallels in {beta} associated with {alpha},
+and the family of parallels in {alpha} associated with {beta}. The
+direction in the space of {beta} indicated by the family of parallels in
+{beta} will be called the direction of {alpha} in space {beta}, and the
+family of parallels in {alpha} is the direction of {beta} in space
+{alpha}. Thus a being at rest at a point of space {alpha} will be moving
+uniformly along a line in space {beta} which is in the direction of
+{alpha} in space {beta}, and a being at rest at a point of space {beta}
+will be moving uniformly along a line in space {alpha} which is in the
+direction of {beta} in space {alpha}.
+
+I have been speaking of the timeless spaces which are associated with
+time-systems. These are the spaces of physical science and of any
+concept of space as eternal and unchanging. But what we actually
+perceive is an approximation to the instantaneous space indicated by
+event-particles which lie within some moment of the time-system
+associated with our awareness. The points of such an instantaneous space
+are event-particles and the straight lines are rects. Let the
+time-system be named {alpha}, and let the moment of time-system {alpha}
+to which our quick perception of nature approximates be called M. Any
+straight line r in space {alpha} is a locus of points and each point is
+a point-track which is a locus of event-particles. Thus in the
+four-dimensional geometry of all event-particles there is a
+two-dimensional locus which is the locus of all event-particles on
+points lying on the straight line r. I will call this locus of
+event-particles the matrix of the straight line r. A matrix intersects
+any moment in a rect. Thus the matrix of r intersects the moment M in a
+rect {rho}. Thus {rho} is the instantaneous rect in M which occupies at
+the moment M the straight line r in the space of {alpha}. Accordingly
+when one sees instantaneously a moving being and its path ahead of it,
+what one really sees is the being at some event-particle A lying in the
+rect {rho} which is the apparent path on the assumption of uniform
+motion. But the actual rect {rho} which is a locus of event-particles is
+never traversed by the being. These event-particles are the
+instantaneous facts which pass with the instantaneous moment. What is
+really traversed are other event-particles which at succeeding instants
+occupy the same points of space {alpha} as those occupied by the
+event-particles of the rect {rho}. For example, we see a stretch of road
+and a lorry moving along it. The instantaneously seen road is a portion
+of the rect {rho}--of course only an approximation to it. The lorry is
+the moving object. But the road as seen is never traversed. It is
+thought of as being traversed because the intrinsic characters of the
+later events are in general so similar to those of the instantaneous
+road that we do not trouble to discriminate. But suppose a land mine
+under the road has been exploded before the lorry gets there. Then it is
+fairly obvious that the lorry does not traverse what we saw at first.
+Suppose the lorry is at rest in space {beta}. Then the straight line r
+of space {alpha} is in the direction of {beta} in space {alpha}, and the
+rect {rho} is the representative in the moment M of the line r of space
+{alpha}. The direction of {rho} in the instantaneous space of the moment
+M is the direction of {beta} in M, where M is a moment of time-system
+{alpha}. Again the matrix of the line r of space {alpha} will also be
+the matrix of some line s of space {beta} which will be in the direction
+of {alpha} in space {beta}. Thus if the lorry halts at some point P of
+space {alpha} which lies on the line r, it is now moving along the line
+s of space {beta}. This is the theory of relative motion; the common
+matrix is the bond which connects the motion of {beta} in space {alpha}
+with the motions of {alpha} in space {beta}.
+
+Motion is essentially a relation between some object of nature and the
+one timeless space of a time-system. An instantaneous space is static,
+being related to the static nature at an instant. In perception when we
+see things moving in an approximation to an instantaneous space, the
+future lines of motion as immediately perceived are rects which are
+never traversed. These approximate rects are composed of small events,
+namely approximate routes and event-particles, which are passed away
+before the moving objects reach them. Assuming that our forecasts of
+rectilinear motion are correct, these rects occupy the straight lines in
+timeless space which are traversed. Thus the rects are symbols in
+immediate sense-awareness of a future which can only be expressed in
+terms of timeless space.
+
+We are now in a position to explore the fundamental character of
+perpendicularity. Consider the two time-systems {alpha} and {beta}, each
+with its own timeless space and its own family of instantaneous moments
+with their instantaneous spaces. Let M and N be respectively a moment of
+{alpha} and a moment of {beta}. In M there is the direction of {beta}
+and in N there is the direction of {alpha}. But M and N, being moments
+of different time-systems, intersect in a level. Call this level
+{lambda}. Then {lambda} is an instantaneous plane in the instantaneous
+space of M and also in the instantaneous space of N. It is the locus of
+all the event-particles which lie both in M and in N.
+
+In the instantaneous space of M the level {lambda} is perpendicular to
+the direction of {beta} in M, and in the instantaneous space of N the
+level {lambda} is perpendicular to the direction of {alpha} in N. This
+is the fundamental property which forms the definition of
+perpendicularity. The symmetry of perpendicularity is a particular
+instance of the symmetry of the mutual relations between two
+time-systems. We shall find in the next lecture that it is from this
+symmetry that the theory of congruence is deduced.
+
+The theory of perpendicularity in the timeless space of any time-system
+{alpha} follows immediately from this theory of perpendicularity in each
+of its instantaneous spaces. Let {rho} be any rect in the moment M of
+{alpha} and let {lambda} be a level in M which is perpendicular to
+{rho}. The locus of those points of the space of {alpha} which intersect
+M in event-particles on {rho} is the straight line r of space {alpha},
+and the locus of those points of the space of {alpha} which intersect M
+in event-particles on {lambda} is the plane l of space {alpha}. Then the
+plane l is perpendicular to the line r.
+
+In this way we have pointed out unique and definite properties in nature
+which correspond to perpendicularity. We shall find that this discovery
+of definite unique properties defining perpendicularity is of critical
+importance in the theory of congruence which is the topic for the next
+lecture.
+
+I regret that it has been necessary for me in this lecture to administer
+such a large dose of four-dimensional geometry. I do not apologise,
+because I am really not responsible for the fact that nature in its most
+fundamental aspect is four-dimensional. Things are what they are; and it
+is useless to disguise the fact that 'what things are' is often very
+difficult for our intellects to follow. It is a mere evasion of the
+ultimate problems to shirk such obstacles.
+
+
+
+
+CHAPTER VI
+
+CONGRUENCE
+
+
+The aim of this lecture is to establish a theory of congruence. You must
+understand at once that congruence is a controversial question. It is
+the theory of measurement in space and in time. The question seems
+simple. In fact it is simple enough for a standard procedure to have
+been settled by act of parliament; and devotion to metaphysical
+subtleties is almost the only crime which has never been imputed to any
+English parliament. But the procedure is one thing and its meaning is
+another.
+
+First let us fix attention on the purely mathematical question. When the
+segment between two points A and B is congruent to that between the
+two points C and D, the quantitative measurements of the two
+segments are equal. The equality of the numerical measures and the
+congruence of the two segments are not always clearly discriminated, and
+are lumped together under the term equality. But the procedure of
+measurement presupposes congruence. For example, a yard measure is
+applied successively to measure two distances between two pairs of
+points on the floor of a room. It is of the essence of the procedure of
+measurement that the yard measure remains unaltered as it is transferred
+from one position to another. Some objects can palpably alter as they
+move--for example, an elastic thread; but a yard measure does not alter
+if made of the proper material. What is this but a judgment of
+congruence applied to the train of successive positions of the yard
+measure? We know that it does not alter because we judge it to be
+congruent to itself in various positions. In the case of the thread we
+can observe the loss of self-congruence. Thus immediate judgments of
+congruence are presupposed in measurement, and the process of
+measurement is merely a procedure to extend the recognition of
+congruence to cases where these immediate judgments are not available.
+Thus we cannot define congruence by measurement.
+
+In modern expositions of the axioms of geometry certain conditions are
+laid down which the relation of congruence between segments is to
+satisfy. It is supposed that we have a complete theory of points,
+straight lines, planes, and the order of points on planes--in fact, a
+complete theory of non-metrical geometry. We then enquire about
+congruence and lay down the set of conditions--or axioms as they are
+called--which this relation satisfies. It has then been proved that
+there are alternative relations which satisfy these conditions equally
+well and that there is nothing intrinsic in the theory of space to lead
+us to adopt any one of these relations in preference to any other as the
+relation of congruence which we adopt. In other words there are
+alternative metrical geometries which all exist by an equal right so far
+as the intrinsic theory of space is concerned.
+
+Poincare, the great French mathematician, held that our actual choice
+among these geometries is guided purely by convention, and that the
+effect of a change of choice would be simply to alter our expression of
+the physical laws of nature. By 'convention' I understand Poincare to
+mean that there is nothing inherent in nature itself giving any peculiar
+_role_ to one of these congruence relations, and that the choice of one
+particular relation is guided by the volitions of the mind at the other
+end of the sense-awareness. The principle of guidance is intellectual
+convenience and not natural fact.
+
+This position has been misunderstood by many of Poincare's expositors.
+They have muddled it up with another question, namely that owing to the
+inexactitude of observation it is impossible to make an exact statement
+in the comparison of measures. It follows that a certain subset of
+closely allied congruence relations can be assigned of which each member
+equally well agrees with that statement of observed congruence when the
+statement is properly qualified with its limits of error.
+
+This is an entirely different question and it presupposes a rejection of
+Poincare's position. The absolute indetermination of nature in respect
+of all the relations of congruence is replaced by the indetermination of
+observation with respect to a small subgroup of these relations.
+
+Poincare's position is a strong one. He in effect challenges anyone to
+point out any factor in nature which gives a preeminent status to the
+congruence relation which mankind has actually adopted. But undeniably
+the position is very paradoxical. Bertrand Russell had a controversy
+with him on this question, and pointed out that on Poincare's principles
+there was nothing in nature to determine whether the earth is larger or
+smaller than some assigned billiard ball. Poincare replied that the
+attempt to find reasons in nature for the selection of a definite
+congruence relation in space is like trying to determine the position of
+a ship in the ocean by counting the crew and observing the colour of
+the captain's eyes.
+
+In my opinion both disputants were right, assuming the grounds on which
+the discussion was based. Russell in effect pointed out that apart from
+minor inexactitudes a determinate congruence relation is among the
+factors in nature which our sense-awareness posits for us. Poincare asks
+for information as to the factor in nature which might lead any
+particular congruence relation to play a preeminent _role_ among the
+factors posited in sense-awareness. I cannot see the answer to either of
+these contentions provided that you admit the materialistic theory of
+nature. With this theory nature at an instant in space is an independent
+fact. Thus we have to look for our preeminent congruence relation amid
+nature in instantaneous space; and Poincare is undoubtedly right in
+saying that nature on this hypothesis gives us no help in finding it.
+
+On the other hand Russell is in an equally strong position when he
+asserts that, as a fact of observation, we do find it, and what is more
+agree in finding the same congruence relation. On this basis it is one
+of the most extraordinary facts of human experience that all mankind
+without any assignable reason should agree in fixing attention on just
+one congruence relation amid the indefinite number of indistinguishable
+competitors for notice. One would have expected disagreement on this
+fundamental choice to have divided nations and to have rent families.
+But the difficulty was not even discovered till the close of the
+nineteenth century by a few mathematical philosophers and philosophic
+mathematicians. The case is not like that of our agreement on some
+fundamental fact of nature such as the three dimensions of space. If
+space has only three dimensions we should expect all mankind to be aware
+of the fact, as they are aware of it. But in the case of congruence,
+mankind agree in an arbitrary interpretation of sense-awareness when
+there is nothing in nature to guide it.
+
+I look on it as no slight recommendation of the theory of nature which I
+am expounding to you that it gives a solution of this difficulty by
+pointing out the factor in nature which issues in the preeminence of one
+congruence relation over the indefinite herd of other such relations.
+
+The reason for this result is that nature is no longer confined within
+space at an instant. Space and time are now interconnected; and this
+peculiar factor of time which is so immediately distinguished among the
+deliverances of our sense-awareness, relates itself to one particular
+congruence relation in space.
+
+Congruence is a particular example of the fundamental fact of
+recognition. In perception we recognise. This recognition does not
+merely concern the comparison of a factor of nature posited by memory
+with a factor posited by immediate sense-awareness. Recognition takes
+place within the present without any intervention of pure memory. For
+the present fact is a duration with its antecedent and consequent
+durations which are parts of itself. The discrimination in
+sense-awareness of a finite event with its quality of passage is also
+accompanied by the discrimination of other factors of nature which do
+not share in the passage of events. Whatever passes is an event. But we
+find entities in nature which do not pass; namely we recognise
+samenesses in nature. Recognition is not primarily an intellectual act
+of comparison; it is in its essence merely sense-awareness in its
+capacity of positing before us factors in nature which do not pass. For
+example, green is perceived as situated in a certain finite event within
+the present duration. This green preserves its self-identity throughout,
+whereas the event passes and thereby obtains the property of breaking
+into parts. The green patch has parts. But in talking of the green patch
+we are speaking of the event in its sole capacity of being for us the
+situation of green. The green itself is numerically one self-identical
+entity, without parts because it is without passage.
+
+Factors in nature which are without passage will be called objects.
+There are radically different kinds of objects which will be considered
+in the succeeding lecture.
+
+Recognition is reflected into the intellect as comparison. The
+recognised objects of one event are compared with the recognised objects
+of another event. The comparison may be between two events in the
+present, or it may be between two events of which one is posited by
+memory-awareness and the other by immediate sense-awareness. But it is
+not the events which are compared. For each event is essentially unique
+and incomparable. What are compared are the objects and relations of
+objects situated in events. The event considered as a relation between
+objects has lost its passage and in this aspect is itself an object.
+This object is not the event but only an intellectual abstraction. The
+same object can be situated in many events; and in this sense even the
+whole event, viewed as an object, can recur, though not the very event
+itself with its passage and its relations to other events.
+
+Objects which are not posited by sense-awareness may be known to the
+intellect. For example, relations between objects and relations between
+relations may be factors in nature not disclosed in sense-awareness but
+known by logical inference as necessarily in being. Thus objects for our
+knowledge may be merely logical abstractions. For example, a complete
+event is never disclosed in sense-awareness, and thus the object which
+is the sum total of objects situated in an event as thus inter-related
+is a mere abstract concept. Again a right-angle is a perceived object
+which can be situated in many events; but, though rectangularity is
+posited by sense-awareness, the majority of geometrical relations are
+not so posited. Also rectangularity is in fact often not perceived when
+it can be proved to have been there for perception. Thus an object is
+often known merely as an abstract relation not directly posited in
+sense-awareness although it is there in nature.
+
+The identity of quality between congruent segments is generally of this
+character. In certain special cases this identity of quality can be
+directly perceived. But in general it is inferred by a process of
+measurement depending on our direct sense-awareness of selected cases
+and a logical inference from the transitive character of congruence.
+
+Congruence depends on motion, and thereby is generated the connexion
+between spatial congruence and temporal congruence. Motion along a
+straight line has a symmetry round that line. This symmetry is expressed
+by the symmetrical geometrical relations of the line to the family of
+planes normal to it.
+
+Also another symmetry in the theory of motion arises from the fact that
+rest in the points of {beta} corresponds to uniform motion along a
+definite family of parallel straight lines in the space of {alpha}. We
+must note the three characteristics, (i) of the uniformity of the motion
+corresponding to any point of {beta} along its correlated straight line
+in {alpha}, and (ii) of the equality in magnitude of the velocities
+along the various lines of {alpha} correlated to rest in the various
+points of {beta}, and (iii) of the parallelism of the lines of this
+family.
+
+We are now in possession of a theory of parallels and a theory of
+perpendiculars and a theory of motion, and from these theories the
+theory of congruence can be constructed. It will be remembered that a
+family of parallel levels in any moment is the family of levels in which
+that moment is intersected by the family of moments of some other
+time-system. Also a family of parallel moments is the family of moments
+of some one time-system. Thus we can enlarge our concept of a family of
+parallel levels so as to include levels in different moments of one
+time-system. With this enlarged concept we say that a complete family of
+parallel levels in a time-system {alpha} is the complete family of
+levels in which the moments of {alpha} intersect the moments of {beta}.
+This complete family of parallel levels is also evidently a family lying
+in the moments of the time-system {beta}. By introducing a third
+time-system {gamma}, parallel rects are obtained. Also all the points of
+any one time-system form a family of parallel point-tracks. Thus there
+are three types of parallelograms in the four-dimensional manifold of
+event-particles.
+
+In parallelograms of the first type the two pairs of parallel sides are
+both of them pairs of rects. In parallelograms of the second type one
+pair of parallel sides is a pair of rects and the other pair is a pair
+of point-tracks. In parallelograms of the third type the two pairs of
+parallel sides are both of them pairs of point-tracks.
+
+The first axiom of congruence is that the opposite sides of any
+parallelogram are congruent. This axiom enables us to compare the
+lengths of any two segments either respectively on parallel rects or on
+the same rect. Also it enables us to compare the lengths of any two
+segments either respectively on parallel point-tracks or on the same
+point-track. It follows from this axiom that two objects at rest in any
+two points of a time-system {beta} are moving with equal velocities in any
+other time-system {alpha} along parallel lines. Thus we can speak of the
+velocity in {alpha} due to the time-system {beta} without specifying any
+particular point in {beta}. The axiom also enables us to measure time in
+any time-system; but does not enable us to compare times in different
+time-systems.
+
+The second axiom of congruence concerns parallelograms on congruent
+bases and between the same parallels, which have also their other pairs
+of sides parallel. The axiom asserts that the rect joining the two
+event-particles of intersection of the diagonals is parallel to the rect
+on which the bases lie. By the aid of this axiom it easily follows that
+the diagonals of a parallelogram bisect each other.
+
+Congruence is extended in any space beyond parallel rects to all rects
+by two axioms depending on perpendicularity. The first of these axioms,
+which is the third axiom of congruence, is that if ABC is a triangle
+of rects in any moment and D is the middle event-particle of the base
+BC, then the level through D perpendicular to BC contains A when
+and only when AB is congruent to AC. This axiom evidently expresses
+the symmetry of perpendicularity, and is the essence of the famous pons
+asinorum expressed as an axiom.
+
+The second axiom depending on perpendicularity, and the fourth axiom of
+congruence, is that if r and A be a rect and an event-particle in the
+same moment and AB and AC be a pair of rectangular rects intersecting r
+in B and C, and AD and AE be another pair of rectangular rects
+intersecting r in D and E, then either D or E lies in the segment BC and
+the other one of the two does not lie in this segment. Also as a
+particular case of this axiom, if AB be perpendicular to r and in
+consequence AC be parallel to r, then D and E lie on opposite sides of B
+respectively. By the aid of these two axioms the theory of congruence
+can be extended so as to compare lengths of segments on any two rects.
+Accordingly Euclidean metrical geometry in space is completely
+established and lengths in the spaces of different time-systems are
+comparable as the result of definite properties of nature which indicate
+just that particular method of comparison.
+
+The comparison of time-measurements in diverse time-systems requires two
+other axioms. The first of these axioms, forming the fifth axiom of
+congruence, will be called the axiom of 'kinetic symmetry.' It expresses
+the symmetry of the quantitative relations between two time-systems when
+the times and lengths in the two systems are measured in congruent
+units.
+
+The axiom can be explained as follows: Let {alpha} and {beta} be the names
+of two time-systems. The directions of motion in the space of {alpha} due
+to rest in a point of {beta} is called the '{beta}-direction in {alpha}'
+and the direction of motion in the space of {beta} due to rest in a
+point of {alpha} is called the '{alpha}-direction in {beta}.' Consider a
+motion in the space of {alpha} consisting of a certain velocity in the
+{beta}-direction of {alpha} and a certain velocity at right-angles to
+it. This motion represents rest in the space of another time-system--call
+it {pi}. Rest in {pi} will also be represented in the space of {beta} by
+a certain velocity in the {alpha}-direction in {beta} and a certain
+velocity at right-angles to this {alpha}-direction. Thus a certain
+motion in the space of {alpha} is correlated to a certain motion in the
+space of {beta}, as both representing the same fact which can also be
+represented by rest in {pi}. Now another time-system, which I will name
+{sigma}, can be found which is such that rest in its space is
+represented by the same magnitudes of velocities along and perpendicular
+to the {alpha}-direction in {beta} as those velocities in {alpha}, along
+and perpendicular to the {beta}-direction, which represent rest in {pi}.
+The required axiom of kinetic symmetry is that rest in {sigma} will be
+represented in {alpha} by the same velocities along and perpendicular to
+the {beta}-direction in {alpha} as those velocities in {beta} along and
+perpendicular to the {alpha}-direction which represent rest in {pi}.
+
+A particular case of this axiom is that relative velocities are equal
+and opposite. Namely rest in {alpha} is represented in {beta} by a
+velocity along the {alpha}-direction which is equal to the velocity
+along the {beta}-direction in {alpha} which represents rest in {beta}.
+
+Finally the sixth axiom of congruence is that the relation of congruence
+is transitive. So far as this axiom applies to space, it is superfluous.
+For the property follows from our previous axioms. It is however
+necessary for time as a supplement to the axiom of kinetic symmetry. The
+meaning of the axiom is that if the time-unit of system {alpha} is
+congruent to the time-unit of system {beta}, and the time-unit of system
+{beta} is congruent to the time-unit of system {gamma}, then the
+time-units of {alpha} and {gamma} are also congruent.
+
+By means of these axioms formulae for the transformation of
+measurements made in one time-system to measurements of the same facts
+of nature made in another time-system can be deduced. These formulae
+will be found to involve one arbitrary constant which I will call k.
+
+It is of the dimensions of the square of a velocity. Accordingly four
+cases arise. In the first case k is zero. This case produces
+nonsensical results in opposition to the elementary deliverances of
+experience. We put this case aside.
+
+In the second case k is infinite. This case yields the ordinary
+formulae for transformation in relative motion, namely those formulae
+which are to be found in every elementary book on dynamics.
+
+In the third case, k is negative. Let us call it -c squared, where c
+will be of the dimensions of a velocity. This case yields the formulae
+of transformation which Larmor discovered for the transformation of
+Maxwell's equations of the electromagnetic field. These formulae were
+extended by H. A. Lorentz, and used by Einstein and Minkowski as the
+basis of their novel theory of relativity. I am not now speaking of
+Einstein's more recent theory of general relativity by which he deduces
+his modification of the law of gravitation. If this be the case which
+applies to nature, then c must be a close approximation to the
+velocity of light _in vacuo_. Perhaps it is this actual velocity. In
+this connexion '_in vacuo_' must not mean an absence of events, namely
+the absence of the all-pervading ether of events. It must mean the
+absence of certain types of objects.
+
+In the fourth case, k is positive. Let us call it h squared, where h
+will be of the dimensions of a velocity. This gives a perfectly possible
+type of transformation formulae, but not one which explains any facts
+of experience. It has also another disadvantage. With the assumption of
+this fourth case the distinction between space and time becomes unduly
+blurred. The whole object of these lectures has been to enforce the
+doctrine that space and time spring from a common root, and that the
+ultimate fact of experience is a space-time fact. But after all mankind
+does distinguish very sharply between space and time, and it is owing to
+this sharpness of distinction that the doctrine of these lectures is
+somewhat of a paradox. Now in the third assumption this sharpness of
+distinction is adequately preserved. There is a fundamental distinction
+between the metrical properties of point-tracks and rects. But in the
+fourth assumption this fundamental distinction vanishes.
+
+Neither the third nor the fourth assumption can agree with experience
+unless we assume that the velocity c of the third assumption, and the
+velocity h of the fourth assumption, are extremely large compared to
+the velocities of ordinary experience. If this be the case the formulae
+of both assumptions will obviously reduce to a close approximation to
+the formulae of the second assumption which are the ordinary formulae of
+dynamical textbooks. For the sake of a name, I will call these textbook
+formulae the 'orthodox' formulae.
+
+There can be no question as to the general approximate correctness of
+the orthodox formulae. It would be merely silly to raise doubts on this
+point. But the determination of the status of these formulae is by no
+means settled by this admission. The independence of time and space is
+an unquestioned presupposition of the orthodox thought which has
+produced the orthodox formulae. With this presupposition and given the
+absolute points of one absolute space, the orthodox formulae are
+immediate deductions. Accordingly, these formulae are presented to our
+imaginations as facts which cannot be otherwise, time and space being
+what they are. The orthodox formulae have therefore attained to the
+status of necessities which cannot be questioned in science. Any attempt
+to replace these formulae by others was to abandon the _role_ of
+physical explanation and to have recourse to mere mathematical formulae.
+
+But even in physical science difficulties have accumulated round the
+orthodox formulae. In the first place Maxwell's equations of the
+electromagnetic field are not invariant for the transformations of the
+orthodox formulae; whereas they are invariant for the transformations of
+the formulae arising from the third of the four cases mentioned above,
+provided that the velocity c is identified with a famous
+electromagnetic constant quantity.
+
+Again the null results of the delicate experiments to detect the earth's
+variations of motion through the ether in its orbital path are explained
+immediately by the formulae of the third case. But if we assume the
+orthodox formulae we have to make a special and arbitrary assumption as
+to the contraction of matter during motion. I mean the Fitzgerald-Lorentz
+assumption.
+
+Lastly Fresnel's coefficient of drag which represents the variation of
+the velocity of light in a moving medium is explained by the formulae of
+the third case, and requires another arbitrary assumption if we use the
+orthodox formulae.
+
+It appears therefore that on the mere basis of physical explanation
+there are advantages in the formulae of the third case as compared with
+the orthodox formulae. But the way is blocked by the ingrained belief
+that these latter formulae possess a character of necessity. It is
+therefore an urgent requisite for physical science and for philosophy to
+examine critically the grounds for this supposed necessity. The only
+satisfactory method of scrutiny is to recur to the first principles of
+our knowledge of nature. This is exactly what I am endeavouring to do in
+these lectures. I ask what it is that we are aware of in our
+sense-perception of nature. I then proceed to examine those factors in
+nature which lead us to conceive nature as occupying space and
+persisting through time. This procedure has led us to an investigation
+of the characters of space and time. It results from these
+investigations that the formulae of the third case and the orthodox
+formulae are on a level as possible formulae resulting from the basic
+character of our knowledge of nature. The orthodox formulae have thus
+lost any advantage as to necessity which they enjoyed over the serial
+group. The way is thus open to adopt whichever of the two groups best
+accords with observation.
+
+I take this opportunity of pausing for a moment from the course of my
+argument, and of reflecting on the general character which my doctrine
+ascribes to some familiar concepts of science. I have no doubt that some
+of you have felt that in certain aspects this character is very
+paradoxical.
+
+This vein of paradox is partly due to the fact that educated language
+has been made to conform to the prevalent orthodox theory. We are thus,
+in expounding an alternative doctrine, driven to the use of either
+strange terms or of familiar words with unusual meanings. This victory
+of the orthodox theory over language is very natural. Events are named
+after the prominent objects situated in them, and thus both in language
+and in thought the event sinks behind the object, and becomes the mere
+play of its relations. The theory of space is then converted into a
+theory of the relations of objects instead of a theory of the relations
+of events. But objects have not the passage of events. Accordingly space
+as a relation between objects is devoid of any connexion with time. It
+is space at an instant without any determinate relations between the
+spaces at successive instants. It cannot be one timeless space because
+the relations between objects change.
+
+A few minutes ago in speaking of the deduction of the orthodox formulae
+for relative motion I said that they followed as an immediate deduction
+from the assumption of absolute points in absolute space. This reference
+to absolute space was not an oversight. I know that the doctrine of the
+relativity of space at present holds the field both in science and
+philosophy. But I do not think that its inevitable consequences are
+understood. When we really face them the paradox of the presentation of
+the character of space which I have elaborated is greatly mitigated. If
+there is no absolute position, a point must cease to be a simple entity.
+What is a point to one man in a balloon with his eyes fixed on an
+instrument is a track of points to an observer on the earth who is
+watching the balloon through a telescope, and is another track of points
+to an observer in the sun who is watching the balloon through some
+instrument suited to such a being. Accordingly if I am reproached with
+the paradox of my theory of points as classes of event-particles, and of
+my theory of event-particles as groups of abstractive sets, I ask my
+critic to explain exactly what he means by a point. While you explain
+your meaning about anything, however simple, it is always apt to look
+subtle and fine spun. I have at least explained exactly what I do mean
+by a point, what relations it involves and what entities are the relata.
+If you admit the relativity of space, you also must admit that points
+are complex entities, logical constructs involving other entities and
+their relations. Produce your theory, not in a few vague phrases of
+indefinite meaning, but explain it step by step in definite terms
+referring to assigned relations and assigned relata. Also show that your
+theory of points issues in a theory of space. Furthermore note that the
+example of the man in the balloon, the observer on earth, and the
+observer in the sun, shows that every assumption of relative rest
+requires a timeless space with radically different points from those
+which issue from every other such assumption. The theory of the
+relativity of space is inconsistent with any doctrine of one unique set
+of points of one timeless space.
+
+The fact is that there is no paradox in my doctrine of the nature of
+space which is not in essence inherent in the theory of the relativity
+of space. But this doctrine has never really been accepted in science,
+whatever people say. What appears in our dynamical treatises is Newton's
+doctrine of relative motion based on the doctrine of differential motion
+in absolute space. When you once admit that the points are radically
+different entities for differing assumptions of rest, then the orthodox
+formulae lose all their obviousness. They were only obvious because you
+were really thinking of something else. When discussing this topic you
+can only avoid paradox by taking refuge from the flood of criticism in
+the comfortable ark of no meaning.
+
+The new theory provides a definition of the congruence of periods of
+time. The prevalent view provides no such definition. Its position is
+that if we take such time-measurements so that certain familiar
+velocities which seem to us to be uniform are uniform, then the laws of
+motion are true. Now in the first place no change could appear either as
+uniform or non-uniform without involving a definite determination of the
+congruence for time-periods. So in appealing to familiar phenomena it
+allows that there is some factor in nature which we can intellectually
+construct as a congruence theory. It does not however say anything about
+it except that the laws of motion are then true. Suppose that with some
+expositors we cut out the reference to familiar velocities such as the
+rate of rotation of the earth. We are then driven to admit that there is
+no meaning in temporal congruence except that certain assumptions make
+the laws of motion true. Such a statement is historically false. King
+Alfred the Great was ignorant of the laws of motion, but knew very well
+what he meant by the measurement of time, and achieved his purpose by
+means of burning candles. Also no one in past ages justified the use of
+sand in hour-glasses by saying that some centuries later interesting
+laws of motion would be discovered which would give a meaning to the
+statement that the sand was emptied from the bulbs in equal times.
+Uniformity in change is directly perceived, and it follows that mankind
+perceives in nature factors from which a theory of temporal congruence
+can be formed. The prevalent theory entirely fails to produce such
+factors.
+
+The mention of the laws of motion raises another point where the
+prevalent theory has nothing to say and the new theory gives a complete
+explanation. It is well known that the laws of motion are not valid for
+any axes of reference which you may choose to take fixed in any rigid
+body. You must choose a body which is not rotating and has no
+acceleration. For example they do not really apply to axes fixed in the
+earth because of the diurnal rotation of that body. The law which fails
+when you assume the wrong axes as at rest is the third law, that action
+and reaction are equal and opposite. With the wrong axes uncompensated
+centrifugal forces and uncompensated composite centrifugal forces
+appear, due to rotation. The influence of these forces can be
+demonstrated by many facts on the earth's surface, Foucault's pendulum,
+the shape of the earth, the fixed directions of the rotations of
+cyclones and anticyclones. It is difficult to take seriously the
+suggestion that these domestic phenomena on the earth are due to the
+influence of the fixed stars. I cannot persuade myself to believe that a
+little star in its twinkling turned round Foucault's pendulum in the
+Paris Exhibition of 1861. Of course anything is believable when a
+definite physical connexion has been demonstrated, for example the
+influence of sunspots. Here all demonstration is lacking in the form of
+any coherent theory. According to the theory of these lectures the axes
+to which motion is to be referred are axes at rest in the space of some
+time-system. For example, consider the space of a time-system {alpha}.
+There are sets of axes at rest in the space of {alpha}. These are
+suitable dynamical axes. Also a set of axes in this space which is
+moving with uniform velocity without rotation is another suitable set.
+All the moving points fixed in these moving axes are really tracing out
+parallel lines with one uniform velocity. In other words they are the
+reflections in the space of {alpha} of a set of fixed axes in the space
+of some other time-system {beta}. Accordingly the group of dynamical
+axes required for Newton's Laws of Motion is the outcome of the
+necessity of referring motion to a body at rest in the space of some one
+time-system in order to obtain a coherent account of physical
+properties. If we do not do so the meaning of the motion of one portion
+of our physical configuration is different from the meaning of the
+motion of another portion of the same configuration. Thus the meaning of
+motion being what it is, in order to describe the motion of any system
+of objects without changing the meaning of your terms as you proceed
+with your description, you are bound to take one of these sets of axes
+as axes of reference; though you may choose their reflections into the
+space of any time-system which you wish to adopt. A definite physical
+reason is thereby assigned for the peculiar property of the dynamical
+group of axes.
+
+On the orthodox theory the position of the equations of motion is most
+ambiguous. The space to which they refer is completely undetermined and
+so is the measurement of the lapse of time. Science is simply setting
+out on a fishing expedition to see whether it cannot find some procedure
+which it can call the measurement of space and some procedure which it
+can call the measurement of time, and something which it can call a
+system of forces, and something which it can call masses, so that these
+formulae may be satisfied. The only reason--on this theory--why anyone
+should want to satisfy these formulae is a sentimental regard for
+Galileo, Newton, Euler and Lagrange. The theory, so far from founding
+science on a sound observational basis, forces everything to conform to
+a mere mathematical preference for certain simple formulae.
+
+I do not for a moment believe that this is a true account of the real
+status of the Laws of Motion. These equations want some slight
+adjustment for the new formulae of relativity. But with these
+adjustments, imperceptible in ordinary use, the laws deal with
+fundamental physical quantities which we know very well and wish to
+correlate.
+
+The measurement of time was known to all civilised nations long before
+the laws were thought of. It is this time as thus measured that the laws
+are concerned with. Also they deal with the space of our daily life.
+When we approach to an accuracy of measurement beyond that of
+observation, adjustment is allowable. But within the limits of
+observation we know what we mean when we speak of measurements of space
+and measurements of time and uniformity of change. It is for science to
+give an intellectual account of what is so evident in sense-awareness.
+It is to me thoroughly incredible that the ultimate fact beyond which
+there is no deeper explanation is that mankind has really been swayed by
+an unconscious desire to satisfy the mathematical formulae which we call
+the Laws of Motion, formulae completely unknown till the seventeenth
+century of our epoch.
+
+The correlation of the facts of sense-experience effected by the
+alternative account of nature extends beyond the physical properties of
+motion and the properties of congruence. It gives an account of the
+meaning of the geometrical entities such as points, straight lines, and
+volumes, and connects the kindred ideas of extension in time and
+extension in space. The theory satisfies the true purpose of an
+intellectual explanation in the sphere of natural philosophy. This
+purpose is to exhibit the interconnexions of nature, and to show that
+one set of ingredients in nature requires for the exhibition of its
+character the presence of the other sets of ingredients.
+
+The false idea which we have to get rid of is that of nature as a mere
+aggregate of independent entities, each capable of isolation. According
+to this conception these entities, whose characters are capable of
+isolated definition, come together and by their accidental relations
+form the system of nature. This system is thus thoroughly accidental;
+and, even if it be subject to a mechanical fate, it is only accidentally
+so subject.
+
+With this theory space might be without time, and time might be without
+space. The theory admittedly breaks down when we come to the relations
+of matter and space. The relational theory of space is an admission that
+we cannot know space without matter or matter without space. But the
+seclusion of both from time is still jealously guarded. The relations
+between portions of matter in space are accidental facts owing to the
+absence of any coherent account of how space springs from matter or how
+matter springs from space. Also what we really observe in nature, its
+colours and its sounds and its touches are secondary qualities; in other
+words, they are not in nature at all but are accidental products of the
+relations between nature and mind.
+
+The explanation of nature which I urge as an alternative ideal to this
+accidental view of nature, is that nothing in nature could be what it is
+except as an ingredient in nature as it is. The whole which is present
+for discrimination is posited in sense-awareness as necessary for the
+discriminated parts. An isolated event is not an event, because every
+event is a factor in a larger whole and is significant of that whole.
+There can be no time apart from space; and no space apart from time; and
+no space and no time apart from the passage of the events of nature. The
+isolation of an entity in thought, when we think of it as a bare 'it,'
+has no counterpart in any corresponding isolation in nature. Such
+isolation is merely part of the procedure of intellectual knowledge.
+
+The laws of nature are the outcome of the characters of the entities
+which we find in nature. The entities being what they are, the laws must
+be what they are; and conversely the entities follow from the laws. We
+are a long way from the attainment of such an ideal; but it remains as
+the abiding goal of theoretical science.
+
+
+
+
+CHAPTER VII
+
+OBJECTS
+
+
+The ensuing lecture is concerned with the theory of objects. Objects are
+elements in nature which do not pass. The awareness of an object as some
+factor not sharing in the passage of nature is what I call
+'recognition.' It is impossible to recognise an event, because an event
+is essentially distinct from every other event. Recognition is an
+awareness of sameness. But to call recognition an awareness of sameness
+implies an intellectual act of comparison accompanied with judgment. I
+use recognition for the non-intellectual relation of sense-awareness
+which connects the mind with a factor of nature without passage. On the
+intellectual side of the mind's experience there are comparisons of
+things recognised and consequent judgments of sameness or diversity.
+Probably 'sense-recognition' would be a better term for what I mean by
+'recognition.' I have chosen the simpler term because I think that I
+shall be able to avoid the use of 'recognition' in any other meaning
+than that of 'sense-recognition.' I am quite willing to believe that
+recognition, in my sense of the term, is merely an ideal limit, and that
+there is in fact no recognition without intellectual accompaniments of
+comparison and judgment. But recognition is that relation of the mind to
+nature which provides the material for the intellectual activity.
+
+An object is an ingredient in the character of some event. In fact the
+character of an event is nothing but the objects which are ingredient in
+it and the ways in which those objects make their ingression into the
+event. Thus the theory of objects is the theory of the comparison of
+events. Events are only comparable because they body forth permanences.
+We are comparing objects in events whenever we can say, 'There it is
+again.' Objects are the elements in nature which can 'be again.'
+
+Sometimes permanences can be proved to exist which evade recognition in
+the sense in which I am using that term. The permanences which evade
+recognition appear to us as abstract properties either of events or of
+objects. All the same they are there for recognition although
+undiscriminated in our sense-awareness. The demarcation of events, the
+splitting of nature up into parts is effected by the objects which we
+recognise as their ingredients. The discrimination of nature is the
+recognition of objects amid passing events. It is a compound of the
+awareness of the passage of nature, of the consequent partition of
+nature, and of the definition of certain parts of nature by the modes of
+the ingression of objects into them.
+
+You may have noticed that I am using the term 'ingression' to denote the
+general relation of objects to events. The ingression of an object into
+an event is the way the character of the event shapes itself in virtue
+of the being of the object. Namely the event is what it is, because the
+object is what it is; and when I am thinking of this modification of the
+event by the object, I call the relation between the two 'the ingression
+of the object into the event.' It is equally true to say that objects
+are what they are because events are what they are. Nature is such that
+there can be no events and no objects without the ingression of objects
+into events. Although there are events such that the ingredient objects
+evade our recognition. These are the events in empty space. Such events
+are only analysed for us by the intellectual probing of science.
+
+Ingression is a relation which has various modes. There are obviously
+very various kinds of objects; and no one kind of object can have the
+same sort of relations to events as objects of another kind can have. We
+shall have to analyse out some of the different modes of ingression
+which different kinds of objects have into events.
+
+But even if we stick to one and the same kind of objects, an object of
+that kind has different modes of ingression into different events.
+Science and philosophy have been apt to entangle themselves in a
+simple-minded theory that an object is at one place at any definite
+time, and is in no sense anywhere else. This is in fact the attitude of
+common sense thought, though it is not the attitude of language which is
+naively expressing the facts of experience. Every other sentence in a
+work of literature which is endeavouring truly to interpret the facts of
+experience expresses differences in surrounding events due to the
+presence of some object. An object is ingredient throughout its
+neighbourhood, and its neighbourhood is indefinite. Also the
+modification of events by ingression is susceptible of quantitative
+differences. Finally therefore we are driven to admit that each object
+is in some sense ingredient throughout nature; though its ingression may
+be quantitatively irrelevant in the expression of our individual
+experiences.
+
+This admission is not new either in philosophy or science. It is
+obviously a necessary axiom for those philosophers who insist that
+reality is a system. In these lectures we are keeping off the profound
+and vexed question as to what we mean by 'reality.' I am maintaining the
+humbler thesis that nature is a system. But I suppose that in this case
+the less follows from the greater, and that I may claim the support of
+these philosophers. The same doctrine is essentially interwoven in all
+modern physical speculation. As long ago as 1847 Faraday in a paper in
+the _Philosophical Magazine_ remarked that his theory of tubes of force
+implies that in a sense an electric charge is everywhere. The
+modification of the electromagnetic field at every point of space at
+each instant owing to the past history of each electron is another way
+of stating the same fact. We can however illustrate the doctrine by the
+more familiar facts of life without recourse to the abstruse
+speculations of theoretical physics.
+
+The waves as they roll on to the Cornish coast tell of a gale in
+mid-Atlantic; and our dinner witnesses to the ingression of the cook
+into the dining room. It is evident that the ingression of objects into
+events includes the theory of causation. I prefer to neglect this aspect
+of ingression, because causation raises the memory of discussions based
+upon theories of nature which are alien to my own. Also I think that
+some new light may be thrown on the subject by viewing it in this fresh
+aspect.
+
+The examples which I have given of the ingression of objects into events
+remind us that ingression takes a peculiar form in the case of some
+events; in a sense, it is a more concentrated form. For example, the
+electron has a certain position in space and a certain shape. Perhaps it
+is an extremely small sphere in a certain test-tube. The storm is a
+gale situated in mid-Atlantic with a certain latitude and longitude, and
+the cook is in the kitchen. I will call this special form of ingression
+the 'relation of situation'; also, by a double use of the word
+'situation,' I will call the event in which an object is situated 'the
+situation of the object.' Thus a situation is an event which is a
+relatum in the relation of situation. Now our first impression is that
+at last we have come to the simple plain fact of where the object really
+is; and that the vaguer relation which I call ingression should not be
+muddled up with the relation of situation, as if including it as a
+particular case. It seems so obvious that any object is in such and such
+a position, and that it is influencing other events in a totally
+different sense. Namely, in a sense an object is the character of the
+event which is its situation, but it only influences the character of
+other events. Accordingly the relations of situation and influencing are
+not generally the same sort of relation, and should not be subsumed
+under the same term 'ingression.' I believe that this notion is a
+mistake, and that it is impossible to draw a clear distinction between
+the two relations.
+
+For example, Where was your toothache? You went to a dentist and pointed
+out the tooth to him. He pronounced it perfectly sound, and cured you by
+stopping another tooth. Which tooth was the situation of the toothache?
+Again, a man has an arm amputated, and experiences sensations in the
+hand which he has lost. The situation of the imaginary hand is in fact
+merely thin air. You look into a mirror and see a fire. The flames that
+you see are situated behind the mirror. Again at night you watch the
+sky; if some of the stars had vanished from existence hours ago, you
+would not be any the wiser. Even the situations of the planets differ
+from those which science would assign to them.
+
+Anyhow you are tempted to exclaim, the cook is in the kitchen. If you
+mean her mind, I will not agree with you on the point; for I am only
+talking of nature. Let us think only of her bodily presence. What do you
+mean by this notion? We confine ourselves to typical manifestations of
+it. You can see her, touch her, and hear her. But the examples which I
+have given you show that the notions of the situations of what you see,
+what you touch, and what you hear are not so sharply separated out as to
+defy further questioning. You cannot cling to the idea that we have two
+sets of experiences of nature, one of primary qualities which belong to
+the objects perceived, and one of secondary qualities which are the
+products of our mental excitements. All we know of nature is in the same
+boat, to sink or swim together. The constructions of science are merely
+expositions of the characters of things perceived. Accordingly to affirm
+that the cook is a certain dance of molecules and electrons is merely to
+affirm that the things about her which are perceivable have certain
+characters. The situations of the perceived manifestations of her bodily
+presence have only a very general relation to the situations of the
+molecules, to be determined by discussion of the circumstances of
+perception.
+
+In discussing the relations of situation in particular and of ingression
+in general, the first requisite is to note that objects are of radically
+different types. For each type 'situation' and 'ingression' have their
+own special meanings which are different from their meanings for other
+types, though connexions can be pointed out. It is necessary therefore
+in discussing them to determine what type of objects are under
+consideration. There are, I think, an indefinite number of types of
+objects. Happily we need not think of them all. The idea of situation
+has its peculiar importance in reference to three types of objects which
+I call sense-objects, perceptual objects and scientific objects. The
+suitability of these names for the three types is of minor importance,
+so long as I can succeed in explaining what I mean by them.
+
+These three types form an ascending hierarchy, of which each member
+presupposes the type below. The base of the hierarchy is formed by the
+sense-objects. These objects do not presuppose any other type of
+objects. A sense-object is a factor of nature posited by sense-awareness
+which (i), in that it is an object, does not share in the passage of
+nature and (ii) is not a relation between other factors of nature. It
+will of course be a relatum in relations which also implicate other
+factors of nature. But it is always a relatum and never the relation
+itself. Examples of sense-objects are a particular sort of colour, say
+Cambridge blue, or a particular sort of sound, or a particular sort of
+smell, or a particular sort of feeling. I am not talking of a particular
+patch of blue as seen during a particular second of time at a definite
+date. Such a patch is an event where Cambridge blue is situated.
+Similarly I am not talking of any particular concert-room as filled with
+the note. I mean the note itself and not the patch of volume filled by
+the sound for a tenth of a second. It is natural for us to think of the
+note in itself, but in the case of colour we are apt to think of it
+merely as a property of the patch. No one thinks of the note as a
+property of the concert-room. We see the blue and we hear the note. Both
+the blue and the note are immediately posited by the discrimination of
+sense-awareness which relates the mind to nature. The blue is posited as
+in nature related to other factors in nature. In particular it is
+posited as in the relation of being situated in the event which is its
+situation.
+
+The difficulties which cluster around the relation of situation arise
+from the obstinate refusal of philosophers to take seriously the
+ultimate fact of multiple relations. By a multiple relation I mean a
+relation which in any concrete instance of its occurrence necessarily
+involves more than two relata. For example, when John likes Thomas there
+are only two relata, John and Thomas. But when John gives that book to
+Thomas there are three relata, John, that book, and Thomas.
+
+Some schools of philosophy, under the influence of the Aristotelian
+logic and the Aristotelian philosophy, endeavour to get on without
+admitting any relations at all except that of substance and attribute.
+Namely all apparent relations are to be resolvable into the concurrent
+existence of substances with contrasted attributes. It is fairly obvious
+that the Leibnizian monadology is the necessary outcome of any such
+philosophy. If you dislike pluralism, there will be only one monad.
+
+Other schools of philosophy admit relations but obstinately refuse to
+contemplate relations with more than two relata. I do not think that
+this limitation is based on any set purpose or theory. It merely arises
+from the fact that more complicated relations are a bother to people
+without adequate mathematical training, when they are admitted into the
+reasoning.
+
+I must repeat that we have nothing to do in these lectures with the
+ultimate character of reality. It is quite possible that in the true
+philosophy of reality there are only individual substances with
+attributes, or that there are only relations with pairs of relata. I do
+not believe that such is the case; but I am not concerned to argue about
+it now. Our theme is Nature. So long as we confine ourselves to the
+factors posited in the sense-awareness of nature, it seems to me that
+there certainly are instances of multiple relations between these
+factors, and that the relation of situation for sense-objects is one
+example of such multiple relations.
+
+Consider a blue coat, a flannel coat of Cambridge blue belonging to some
+athlete. The coat itself is a perceptual object and its situation is not
+what I am talking about. We are talking of someone's definite
+sense-awareness of Cambridge blue as situated in some event of nature.
+He may be looking at the coat directly. He then sees Cambridge blue as
+situated practically in the same event as the coat at that instant. It
+is true that the blue which he sees is due to light which left the coat
+some inconceivably small fraction of a second before. This difference
+would be important if he were looking at a star whose colour was
+Cambridge blue. The star might have ceased to exist days ago, or even
+years ago. The situation of the blue will not then be very intimately
+connected with the situation (in another sense of 'situation') of any
+perceptual object. This disconnexion of the situation of the blue and
+the situation of some associated perceptual object does not require a
+star for its exemplification. Any looking glass will suffice. Look at
+the coat through a looking glass. Then blue is seen as situated behind
+the mirror. The event which is its situation depends upon the position
+of the observer.
+
+The sense-awareness of the blue as situated in a certain event which I
+call the situation, is thus exhibited as the sense-awareness of a
+relation between the blue, the percipient event of the observer, the
+situation, and intervening events. All nature is in fact required,
+though only certain intervening events require their characters to be of
+certain definite sorts. The ingression of blue into the events of nature
+is thus exhibited as systematically correlated. The awareness of the
+observer depends on the position of the percipient event in this
+systematic correlation. I will use the term 'ingression into nature' for
+this systematic correlation of the blue with nature. Thus the ingression
+of blue into any definite event is a part statement of the fact of the
+ingression of blue into nature.
+
+In respect to the ingression of blue into nature events may be roughly
+put into four classes which overlap and are not very clearly separated.
+These classes are (i) the percipient events, (ii) the situations, (iii)
+the active conditioning events, (iv) the passive conditioning events. To
+understand this classification of events in the general fact of the
+ingression of blue into nature, let us confine attention to one
+situation for one percipient event and to the consequent _roles_ of the
+conditioning events for the ingression as thus limited. The percipient
+event is the relevant bodily state of the observer. The situation is
+where he sees the blue, say, behind the mirror. The active conditioning
+events are the events whose characters are particularly relevant for the
+event (which is the situation) to be the situation for that percipient
+event, namely the coat, the mirror, and the state of the room as to
+light and atmosphere. The passive conditioning events are the events of
+the rest of nature.
+
+In general the situation is an active conditioning event; namely the
+coat itself, when there is no mirror or other such contrivance to
+produce abnormal effects. But the example of the mirror shows us that
+the situation may be one of the passive conditioning events. We are then
+apt to say that our senses have been cheated, because we demand as a
+right that the situation should be an active condition in the
+ingression.
+
+This demand is not so baseless as it may seem when presented as I have
+put it. All we know of the characters of the events of nature is based
+on the analysis of the relations of situations to percipient events. If
+situations were not in general active conditions, this analysis would
+tell us nothing. Nature would be an unfathomable enigma to us and there
+could be no science. Accordingly the incipient discontent when a
+situation is found to be a passive condition is in a sense justifiable;
+because if that sort of thing went on too often, the _role_ of the
+intellect would be ended.
+
+Furthermore the mirror is itself the situation of other sense-objects
+either for the same observer with the same percipient event, or for
+other observers with other percipient events. Thus the fact that an
+event is a situation in the ingression of one set of sense-objects into
+nature is presumptive evidence that that event is an active condition in
+the ingression of other sense-objects into nature which may have other
+situations.
+
+This is a fundamental principle of science which it has derived from
+common sense.
+
+I now turn to perceptual objects. When we look at the coat, we do not in
+general say, There is a patch of Cambridge blue; what naturally occurs
+to us is, There is a coat. Also the judgment that what we have seen is
+a garment of man's attire is a detail. What we perceive is an object
+other than a mere sense-object. It is not a mere patch of colour, but
+something more; and it is that something more which we judge to be a
+coat. I will use the word 'coat' as the name for that crude object which
+is more than a patch of colour, and without any allusion to the
+judgments as to its usefulness as an article of attire either in the
+past or the future. The coat which is perceived--in this sense of the
+word 'coat'--is what I call a perceptual object. We have to investigate
+the general character of these perceptual objects.
+
+It is a law of nature that in general the situation of a sense-object is
+not only the situation of that sense-object for one definite percipient
+event, but is the situation of a variety of sense-objects for a variety
+of percipient events. For example, for any one percipient event, the
+situation of a sense-object of sight is apt also to be the situations of
+sense-objects of sight, of touch, of smell, and of sound. Furthermore
+this concurrence in the situations of sense-objects has led to the
+body--_i.e._ the percipient event--so adapting itself that the
+perception of one sense-object in a certain situation leads to a
+subconscious sense-awareness of other sense-objects in the same
+situation. This interplay is especially the case between touch and
+sight. There is a certain correlation between the ingressions of
+sense-objects of touch and sense-objects of sight into nature, and in a
+slighter degree between the ingressions of other pairs of sense-objects.
+I call this sort of correlation the 'conveyance' of one sense-object by
+another. When you see the blue flannel coat you subconsciously feel
+yourself wearing it or otherwise touching it. If you are a smoker, you
+may also subconsciously be aware of the faint aroma of tobacco. The
+peculiar fact, posited by this sense-awareness of the concurrence of
+subconscious sense-objects along with one or more dominating
+sense-objects in the same situation, is the sense-awareness of the
+perceptual object. The perceptual object is not primarily the issue of a
+judgment. It is a factor of nature directly posited in sense-awareness.
+The element of judgment comes in when we proceed to classify the
+particular perceptual object. For example, we say, That is flannel, and
+we think of the properties of flannel and the uses of athletes' coats.
+But that all takes place after we have got hold of the perceptual
+object. Anticipatory judgments affect the perceptual object perceived by
+focussing and diverting attention.
+
+The perceptual object is the outcome of the habit of experience.
+Anything which conflicts with this habit hinders the sense-awareness of
+such an object. A sense-object is not the product of the association of
+intellectual ideas; it is the product of the association of
+sense-objects in the same situation. This outcome is not intellectual;
+it is an object of peculiar type with its own particular ingression into
+nature.
+
+There are two kinds of perceptual objects, namely, 'delusive perceptual
+objects' and 'physical objects.' The situation of a delusive perceptual
+object is a passive condition in the ingression of that object into
+nature. Also the event which is the situation will have the relation of
+situation to the object only for one particular percipient event. For
+example, an observer sees the image of the blue coat in a mirror. It is
+a blue coat that he sees and not a mere patch of colour. This shows that
+the active conditions for the conveyance of a group of subconscious
+sense-objects by a dominating sense-object are to be found in the
+percipient event. Namely we are to look for them in the investigations
+of medical psychologists. The ingression into nature of the delusive
+sense-object is conditioned by the adaptation of bodily events to the
+more normal occurrence, which is the ingression of the physical object.
+
+A perceptual object is a physical object when (i) its situation is an
+active conditioning event for the ingression of any of its component
+sense-objects, and (ii) the same event can be the situation of the
+perceptual object for an indefinite number of possible percipient
+events. Physical objects are the ordinary objects which we perceive when
+our senses are not cheated, such as chairs, tables and trees. In a way
+physical objects have more insistent perceptive power than
+sense-objects. Attention to the fact of their occurrence in nature is
+the first condition for the survival of complex living organisms. The
+result of this high perceptive power of physical objects is the
+scholastic philosophy of nature which looks on the sense-objects as mere
+attributes of the physical objects. This scholastic point of view is
+directly contradicted by the wealth of sense-objects which enter into
+our experience as situated in events without any connexion with physical
+objects. For example, stray smells, sounds, colours and more subtle
+nameless sense-objects. There is no perception of physical objects
+without perception of sense-objects. But the converse does not hold:
+namely, there is abundant perception of sense-objects unaccompanied by
+any perception of physical objects. This lack of reciprocity in the
+relations between sense-objects and physical objects is fatal to the
+scholastic natural philosophy.
+
+There is a great difference in the _roles_ of the situations of
+sense-objects and physical objects. The situations of a physical object
+are conditioned by uniqueness and continuity. The uniqueness is an ideal
+limit to which we approximate as we proceed in thought along an
+abstractive set of durations, considering smaller and smaller durations
+in the approach to the ideal limit of the moment of time. In other
+words, when the duration is small enough, the situation of the physical
+object within that duration is practically unique.
+
+The identification of the same physical object as being situated in
+distinct events in distinct durations is effected by the condition of
+continuity. This condition of continuity is the condition that a
+continuity of passage of events, each event being a situation of the
+object in its corresponding duration, can be found from the earlier to
+the later of the two given events. So far as the two events are
+practically adjacent in one specious present, this continuity of passage
+may be directly perceived. Otherwise it is a matter of judgment and
+inference.
+
+The situations of a sense-object are not conditioned by any such
+conditions either of uniqueness or of continuity. In any durations
+however small a sense-object may have any number of situations separated
+from each other. Thus two situations of a sense-object, either in the
+same duration or in different durations, are not necessarily connected
+by any continuous passage of events which are also situations of that
+sense-object.
+
+The characters of the conditioning events involved in the ingression of
+a sense-object into nature can be largely expressed in terms of the
+physical objects which are situated in those events. In one respect this
+is also a tautology. For the physical object is nothing else than the
+habitual concurrence of a certain set of sense-objects in one situation.
+Accordingly when we know all about the physical object, we thereby know
+its component sense-objects. But a physical object is a condition for
+the occurrence of sense-objects other than those which are its
+components. For example, the atmosphere causes the events which are its
+situations to be active conditioning events in the transmission of
+sound. A mirror which is itself a physical object is an active condition
+for the situation of a patch of colour behind it, due to the reflection
+of light in it.
+
+Thus the origin of scientific knowledge is the endeavour to express in
+terms of physical objects the various _roles_ of events as active
+conditions in the ingression of sense-objects into nature. It is in the
+progress of this investigation that scientific objects emerge. They
+embody those aspects of the character of the situations of the physical
+objects which are most permanent and are expressible without reference
+to a multiple relation including a percipient event. Their relations to
+each other are also characterised by a certain simplicity and
+uniformity. Finally the characters of the observed physical objects and
+sense-objects can be expressed in terms of these scientific objects. In
+fact the whole point of the search for scientific objects is the
+endeavour to obtain this simple expression of the characters of events.
+These scientific objects are not themselves merely formulae for
+calculation; because formulae must refer to things in nature, and the
+scientific objects are the things in nature to which the formulae refer.
+
+A scientific object such as a definite electron is a systematic
+correlation of the characters of all events throughout all nature. It is
+an aspect of the systematic character of nature. The electron is not
+merely where its charge is. The charge is the quantitative character of
+certain events due to the ingression of the electron into nature. The
+electron is its whole field of force. Namely the electron is the
+systematic way in which all events are modified as the expression of its
+ingression. The situation of an electron in any small duration may be
+defined as that event which has the quantitative character which is the
+charge of the electron. We may if we please term the mere charge the
+electron. But then another name is required for the scientific object
+which is the full entity which concerns science, and which I have called
+the electron.
+
+According to this conception of scientific objects, the rival theories
+of action at a distance and action by transmission through a medium are
+both incomplete expressions of the true process of nature. The stream of
+events which form the continuous series of situations of the electron is
+entirely self-determined, both as regards having the intrinsic character
+of being the series of situations of that electron and as regards the
+time-systems with which its various members are cogredient, and the flux
+of their positions in their corresponding durations. This is the
+foundation of the denial of action at a distance; namely the progress of
+the stream of the situations of a scientific object can be determined by
+an analysis of the stream itself.
+
+On the other hand the ingression of every electron into nature modifies
+to some extent the character of every event. Thus the character of the
+stream of events which we are considering bears marks of the existence
+of every other electron throughout the universe. If we like to think of
+the electrons as being merely what I call their charges, then the
+charges act at a distance. But this action consists in the modification
+of the situation of the other electron under consideration. This
+conception of a charge acting at a distance is a wholly artificial one.
+The conception which most fully expresses the character of nature is
+that of each event as modified by the ingression of each electron into
+nature. The ether is the expression of this systematic modification of
+events throughout space and throughout time. The best expression of the
+character of this modification is for physicists to find out. My theory
+has nothing to do with that and is ready to accept any outcome of
+physical research.
+
+The connexion of objects with space requires elucidation. Objects are
+situated in events. The relation of situation is a different relation
+for each type of object, and in the case of sense-objects it cannot be
+expressed as a two-termed relation. It would perhaps be better to use a
+different word for these different types of the relation of situation.
+It has not however been necessary to do so for our purposes in these
+lectures. It must be understood however that, when situation is spoken
+of, some one definite type is under discussion, and it may happen that
+the argument may not apply to situation of another type. In all cases
+however I use situation to express a relation between objects and events
+and not between objects and abstractive elements. There is a derivative
+relation between objects and spatial elements which I call the relation
+of location; and when this relation holds, I say that the object is
+located in the abstractive element. In this sense, an object may be
+located in a moment of time, in a volume of space, an area, a line, or a
+point. There will be a peculiar type of location corresponding to each
+type of situation; and location is in each case derivative from the
+corresponding relation of situation in a way which I will proceed to
+explain.
+
+Also location in the timeless space of some time-system is a relation
+derivative from location in instantaneous spaces of the same
+time-system. Accordingly location in an instantaneous space is the
+primary idea which we have to explain. Great confusion has been
+occasioned in natural philosophy by the neglect to distinguish between
+the different types of objects, the different types of situation, the
+different types of location, and the difference between location and
+situation. It is impossible to reason accurately in the vague concerning
+objects and their positions without keeping these distinctions in view.
+An object is located in an abstractive element, when an abstractive set
+belonging to that element can be found such that each event belonging to
+that set is a situation of the object. It will be remembered that an
+abstractive element is a certain group of abstractive sets, and that
+each abstractive set is a set of events. This definition defines the
+location of an element in any type of abstractive element. In this sense
+we can talk of the existence of an object at an instant, meaning thereby
+its location in some definite moment. It may also be located in some
+spatial element of the instantaneous space of that moment.
+
+A quantity can be said to be located in an abstractive element when an
+abstractive set belonging to the element can be found such that the
+quantitative expressions of the corresponding characters of its events
+converge to the measure of the given quantity as a limit when we pass
+along the abstractive set towards its converging end.
+
+By these definitions location in elements of instantaneous spaces is
+defined. These elements occupy corresponding elements of timeless
+spaces. An object located in an element of an instantaneous space will
+also be said to be located at that moment in the timeless element of the
+timeless space which is occupied by that instantaneous element.
+
+It is not every object which can be located in a moment. An object which
+can be located in every moment of some duration will be called a
+'uniform' object throughout that duration. Ordinary physical objects
+appear to us to be uniform objects, and we habitually assume that
+scientific objects such as electrons are uniform. But some sense-objects
+certainly are not uniform. A tune is an example of a non-uniform object.
+We have perceived it as a whole in a certain duration; but the tune as a
+tune is not at any moment of that duration though one of the individual
+notes may be located there.
+
+It is possible therefore that for the existence of certain sorts of
+objects, _e.g._ electrons, minimum quanta of time are requisite. Some
+such postulate is apparently indicated by the modern quantum theory and
+it is perfectly consistent with the doctrine of objects maintained in
+these lectures.
+
+Also the instance of the distinction between the electron as the mere
+quantitative electric charge of its situation and the electron as
+standing for the ingression of an object throughout nature illustrates
+the indefinite number of types of objects which exist in nature. We can
+intellectually distinguish even subtler and subtler types of objects.
+Here I reckon subtlety as meaning seclusion from the immediate
+apprehension of sense-awareness. Evolution in the complexity of life
+means an increase in the types of objects directly sensed. Delicacy of
+sense-apprehension means perceptions of objects as distinct entities
+which are mere subtle ideas to cruder sensibilities. The phrasing of
+music is a mere abstract subtlety to the unmusical; it is a direct
+sense-apprehension to the initiated. For example, if we could imagine
+some lowly type of organic being thinking and aware of our thoughts, it
+would wonder at the abstract subtleties in which we indulge as we think
+of stones and bricks and drops of water and plants. It only knows of
+vague undifferentiated feelings in nature. It would consider us as given
+over to the play of excessively abstract intellects. But then if it
+could think, it would anticipate; and if it anticipated, it would soon
+perceive for itself.
+
+In these lectures we have been scrutinising the foundations of natural
+philosophy. We are stopping at the very point where a boundless ocean of
+enquiries opens out for our questioning.
+
+I agree that the view of Nature which I have maintained in these
+lectures is not a simple one. Nature appears as a complex system whose
+factors are dimly discerned by us. But, as I ask you, Is not this the
+very truth? Should we not distrust the jaunty assurance with which every
+age prides itself that it at last has hit upon the ultimate concepts in
+which all that happens can be formulated? The aim of science is to seek
+the simplest explanations of complex facts. We are apt to fall into the
+error of thinking that the facts are simple because simplicity is the
+goal of our quest. The guiding motto in the life of every natural
+philosopher should be, Seek simplicity and distrust it.
+
+
+
+
+CHAPTER VIII
+
+SUMMARY
+
+
+There is a general agreement that Einstein's investigations have one
+fundamental merit irrespective of any criticisms which we may feel
+inclined to pass on them. They have made us think. But when we have
+admitted so far, we are most of us faced with a distressing perplexity.
+What is it that we ought to think about? The purport of my lecture this
+afternoon will be to meet this difficulty and, so far as I am able, to
+set in a clear light the changes in the background of our scientific
+thought which are necessitated by any acceptance, however qualified, of
+Einstein's main positions. I remember that I am lecturing to the members
+of a chemical society who are not for the most part versed in advanced
+mathematics. The first point that I would urge upon you is that what
+immediately concerns you is not so much the detailed deductions of the
+new theory as this general change in the background of scientific
+conceptions which will follow from its acceptance. Of course, the
+detailed deductions are important, because unless our colleagues the
+astronomers and the physicists find these predictions to be verified we
+can neglect the theory altogether. But we may now take it as granted
+that in many striking particulars these deductions have been found to be
+in agreement with observation. Accordingly the theory has to be taken
+seriously and we are anxious to know what will be the consequences of
+its final acceptance. Furthermore during the last few weeks the
+scientific journals and the lay press have been filled with articles as
+to the nature of the crucial experiments which have been made and as to
+some of the more striking expressions of the outcome of the new theory.
+'Space caught bending' appeared on the news-sheet of a well-known
+evening paper. This rendering is a terse but not inapt translation of
+Einstein's own way of interpreting his results. I should say at once
+that I am a heretic as to this explanation and that I shall expound to
+you another explanation based upon some work of my own, an explanation
+which seems to me to be more in accordance with our scientific ideas and
+with the whole body of facts which have to be explained. We have to
+remember that a new theory must take account of the old well-attested
+facts of science just as much as of the very latest experimental results
+which have led to its production.
+
+To put ourselves in the position to assimilate and to criticise any
+change in ultimate scientific conceptions we must begin at the
+beginning. So you must bear with me if I commence by making some simple
+and obvious reflections. Let us consider three statements, (i)
+'Yesterday a man was run over on the Chelsea Embankment,' (ii)
+'Cleopatra's Needle is on the Charing Cross Embankment,' and (iii)
+'There are dark lines in the Solar Spectrum.' The first statement about
+the accident to the man is about what we may term an 'occurrence,' a
+'happening,' or an 'event.' I will use the term 'event' because it is
+the shortest. In order to specify an observed event, the place, the
+time, and character of the event are necessary. In specifying the place
+and the time you are really stating the relation of the assigned event
+to the general structure of other observed events. For example, the man
+was run over between your tea and your dinner and adjacently to a
+passing barge in the river and the traffic in the Strand. The point
+which I want to make is this: Nature is known to us in our experience as
+a complex of passing events. In this complex we discern definite mutual
+relations between component events, which we may call their relative
+positions, and these positions we express partly in terms of space and
+partly in terms of time. Also in addition to its mere relative position
+to other events, each particular event has its own peculiar character.
+In other words, nature is a structure of events and each event has its
+position in this structure and its own peculiar character or quality.
+
+Let us now examine the other two statements in the light of this general
+principle as to the meaning of nature. Take the second statement,
+'Cleopatra's Needle is on the Charing Cross Embankment.' At first sight
+we should hardly call this an event. It seems to lack the element of
+time or transitoriness. But does it? If an angel had made the remark
+some hundreds of millions of years ago, the earth was not in existence,
+twenty millions of years ago there was no Thames, eighty years ago there
+was no Thames Embankment, and when I was a small boy Cleopatra's Needle
+was not there. And now that it is there, we none of us expect it to be
+eternal. The static timeless element in the relation of Cleopatra's
+Needle to the Embankment is a pure illusion generated by the fact that
+for purposes of daily intercourse its emphasis is needless. What it
+comes to is this: Amidst the structure of events which form the medium
+within which the daily life of Londoners is passed we know how to
+identify a certain stream of events which maintain permanence of
+character, namely the character of being the situations of Cleopatra's
+Needle. Day by day and hour by hour we can find a certain chunk in the
+transitory life of nature and of that chunk we say, 'There is
+Cleopatra's Needle.' If we define the Needle in a sufficiently abstract
+manner we can say that it never changes. But a physicist who looks on
+that part of the life of nature as a dance of electrons, will tell you
+that daily it has lost some molecules and gained others, and even the
+plain man can see that it gets dirtier and is occasionally washed. Thus
+the question of change in the Needle is a mere matter of definition. The
+more abstract your definition, the more permanent the Needle. But
+whether your Needle change or be permanent, all you mean by stating that
+it is situated on the Charing Cross Embankment, is that amid the
+structure of events you know of a certain continuous limited stream of
+events, such that any chunk of that stream, during any hour, or any day,
+or any second, has the character of being the situation of Cleopatra's
+Needle.
+
+Finally, we come to the third statement, 'There are dark lines in the
+Solar Spectrum.' This is a law of nature. But what does that mean? It
+means merely this. If any event has the character of being an exhibition
+of the solar spectrum under certain assigned circumstances, it will also
+have the character of exhibiting dark lines in that spectrum.
+
+This long discussion brings us to the final conclusion that the concrete
+facts of nature are events exhibiting a certain structure in their
+mutual relations and certain characters of their own. The aim of science
+is to express the relations between their characters in terms of the
+mutual structural relations between the events thus characterised. The
+mutual structural relations between events are both spatial and
+temporal. If you think of them as merely spatial you are omitting the
+temporal element, and if you think of them as merely temporal you are
+omitting the spatial element. Thus when you think of space alone, or of
+time alone, you are dealing in abstractions, namely, you are leaving out
+an essential element in the life of nature as known to you in the
+experience of your senses. Furthermore there are different ways of
+making these abstractions which we think of as space and as time; and
+under some circumstances we adopt one way and under other circumstances
+we adopt another way. Thus there is no paradox in holding that what we
+mean by space under one set of circumstances is not what we mean by
+space under another set of circumstances. And equally what we mean by
+time under one set of circumstances is not what we mean by time under
+another set of circumstances. By saying that space and time are
+abstractions, I do not mean that they do not express for us real facts
+about nature. What I mean is that there are no spatial facts or temporal
+facts apart from physical nature, namely that space and time are merely
+ways of expressing certain truths about the relations between events.
+Also that under different circumstances there are different sets of
+truths about the universe which are naturally presented to us as
+statements about space. In such a case what a being under the one set of
+circumstances means by space will be different from that meant by a
+being under the other set of circumstances. Accordingly when we are
+comparing two observations made under different circumstances we have to
+ask 'Do the two observers mean the same thing by space and the same
+thing by time?' The modern theory of relativity has arisen because
+certain perplexities as to the concordance of certain delicate
+observations such as the motion of the earth through the ether, the
+perihelion of mercury, and the positions of the stars in the
+neighbourhood of the sun, have been solved by reference to this purely
+relative significance of space and time.
+
+I want now to recall your attention to Cleopatra's Needle, which I have
+not yet done with. As you are walking along the Embankment you suddenly
+look up and say, 'Hullo, there's the Needle.' In other words, you
+recognise it. You cannot recognise an event; because when it is gone, it
+is gone. You may observe another event of analogous character, but the
+actual chunk of the life of nature is inseparable from its unique
+occurrence. But a character of an event can be recognised. We all know
+that if we go to the Embankment near Charing Cross we shall observe an
+event having the character which we recognise as Cleopatra's Needle.
+Things which we thus recognise I call objects. An object is situated in
+those events or in that stream of events of which it expresses the
+character. There are many sorts of objects. For example, the colour
+green is an object according to the above definition. It is the purpose
+of science to trace the laws which govern the appearance of objects in
+the various events in which they are found to be situated. For this
+purpose we can mainly concentrate on two types of objects, which I will
+call material physical objects and scientific objects. A material
+physical object is an ordinary bit of matter, Cleopatra's Needle for
+example. This is a much more complicated type of object than a mere
+colour, such as the colour of the Needle. I call these simple objects,
+such as colours or sounds, sense-objects. An artist will train himself
+to attend more particularly to sense-objects where the ordinary person
+attends normally to material objects. Thus if you were walking with an
+artist, when you said 'There's Cleopatra's Needle,' perhaps he
+simultaneously exclaimed 'There's a nice bit of colour.' Yet you were
+both expressing your recognition of different component characters of
+the same event. But in science we have found out that when we know all
+about the adventures amid events of material physical objects and of
+scientific objects we have most of the relevant information which will
+enable us to predict the conditions under which we shall perceive
+sense-objects in specific situations. For example, when we know that
+there is a blazing fire (_i.e._ material and scientific objects
+undergoing various exciting adventures amid events) and opposite to it a
+mirror (which is another material object) and the positions of a man's
+face and eyes gazing into the mirror, we know that he can perceive the
+redness of the flame situated in an event behind the mirror--thus, to a
+large extent, the appearance of sense-objects is conditioned by the
+adventures of material objects. The analysis of these adventures makes
+us aware of another character of events, namely their characters as
+fields of activity which determine the subsequent events to which they
+will pass on the objects situated in them. We express these fields of
+activity in terms of gravitational, electromagnetic, or chemical forces
+and attractions. But the exact expression of the nature of these fields
+of activity forces us intellectually to acknowledge a less obvious type
+of objects as situated in events. I mean molecules and electrons. These
+objects are not recognised in isolation. We cannot well miss Cleopatra's
+Needle, if we are in its neighbourhood; but no one has seen a single
+molecule or a single electron, yet the characters of events are only
+explicable to us by expressing them in terms of these scientific
+objects. Undoubtedly molecules and electrons are abstractions. But then
+so is Cleopatra's Needle. The concrete facts are the events
+themselves--I have already explained to you that to be an abstraction
+does not mean that an entity is nothing. It merely means that its
+existence is only one factor of a more concrete element of nature. So an
+electron is abstract because you cannot wipe out the whole structure of
+events and yet retain the electron in existence. In the same way the
+grin on the cat is abstract; and the molecule is really in the event in
+the same sense as the grin is really on the cat's face. Now the more
+ultimate sciences such as Chemistry or Physics cannot express their
+ultimate laws in terms of such vague objects as the sun, the earth,
+Cleopatra's Needle, or a human body. Such objects more properly belong
+to Astronomy, to Geology, to Engineering, to Archaeology, or to Biology.
+Chemistry and Physics only deal with them as exhibiting statistical
+complexes of the effects of their more intimate laws. In a certain
+sense, they only enter into Physics and Chemistry as technological
+applications. The reason is that they are too vague. Where does
+Cleopatra's Needle begin and where does it end? Is the soot part of it?
+Is it a different object when it sheds a molecule or when its surface
+enters into chemical combination with the acid of a London fog? The
+definiteness and permanence of the Needle is nothing to the possible
+permanent definiteness of a molecule as conceived by science, and the
+permanent definiteness of a molecule in its turn yields to that of an
+electron. Thus science in its most ultimate formulation of law seeks
+objects with the most permanent definite simplicity of character and
+expresses its final laws in terms of them.
+
+Again when we seek definitely to express the relations of events which
+arise from their spatio-temporal structure, we approximate to simplicity
+by progressively diminishing the extent (both temporal and spatial) of
+the events considered. For example, the event which is the life of the
+chunk of nature which is the Needle during one minute has to the life of
+nature within a passing barge during the same minute a very complex
+spatio-temporal relation. But suppose we progressively diminish the time
+considered to a second, to a hundredth of a second, to a thousandth of a
+second, and so on. As we pass along such a series we approximate to an
+ideal simplicity of structural relations of the pairs of events
+successively considered, which ideal we call the spatial relations of
+the Needle to the barge at some instant. Even these relations are too
+complicated for us, and we consider smaller and smaller bits of the
+Needle and of the barge. Thus we finally reach the ideal of an event so
+restricted in its extension as to be without extension in space or
+extension in time. Such an event is a mere spatial point-flash of
+instantaneous duration. I call such an ideal event an 'event-particle.'
+You must not think of the world as ultimately built up of
+event-particles. That is to put the cart before the horse. The world we
+know is a continuous stream of occurrence which we can discriminate into
+finite events forming by their overlappings and containings of each
+other and separations a spatio-temporal structure. We can express the
+properties of this structure in terms of the ideal limits to routes of
+approximation, which I have termed event-particles. Accordingly
+event-particles are abstractions in their relations to the more concrete
+events. But then by this time you will have comprehended that you cannot
+analyse concrete nature without abstracting. Also I repeat, the
+abstractions of science are entities which are truly in nature, though
+they have no meaning in isolation from nature.
+
+The character of the spatio-temporal structure of events can be fully
+expressed in terms of relations between these more abstract
+event-particles. The advantage of dealing with event-particles is that
+though they are abstract and complex in respect to the finite events
+which we directly observe, they are simpler than finite events in
+respect to their mutual relations. Accordingly they express for us the
+demands of an ideal accuracy, and of an ideal simplicity in the
+exposition of relations. These event-particles are the ultimate elements
+of the four-dimensional space-time manifold which the theory of
+relativity presupposes. You will have observed that each event-particle
+is as much an instant of time as it is a point of space. I have called
+it an instantaneous point-flash. Thus in the structure of this
+space-time manifold space is not finally discriminated from time, and
+the possibility remains open for diverse modes of discrimination
+according to the diverse circumstances of observers. It is this
+possibility which makes the fundamental distinction between the new way
+of conceiving the universe and the old way. The secret of understanding
+relativity is to understand this. It is of no use rushing in with
+picturesque paradoxes, such as 'Space caught bending,' if you have not
+mastered this fundamental conception which underlies the whole theory.
+When I say that it underlies the whole theory, I mean that in my opinion
+it ought to underlie it, though I may confess some doubts as to how far
+all expositions of the theory have really understood its implications
+and its premises.
+
+Our measurements when they are expressed in terms of an ideal accuracy
+are measurements which express properties of the space-time manifold.
+Now there are measurements of different sorts. You can measure lengths,
+or angles, or areas, or volumes, or times. There are also other sorts of
+measures such as measurements of intensity of illumination, but I will
+disregard these for the moment and will confine attention to those
+measurements which particularly interest us as being measurements of
+space or of time. It is easy to see that four such measurements of the
+proper characters are necessary to determine the position of an
+event-particle in the space-time manifold in its relation to the rest of
+the manifold. For example, in a rectangular field you start from one
+corner at a given time, you measure a definite distance along one side,
+you then strike out into the field at right angles, and then measure a
+definite distance parallel to the other pair of sides, you then rise
+vertically a definite height and take the time. At the point and at the
+time which you thus reach there is occurring a definite instantaneous
+point-flash of nature. In other words, your four measurements have
+determined a definite event-particle belonging to the four-dimension
+space-time manifold. These measurements have appeared to be very simple
+to the land-surveyor and raise in his mind no philosophic difficulties.
+But suppose there are beings on Mars sufficiently advanced in
+scientific invention to be able to watch in detail the operations of
+this survey on earth. Suppose that they construe the operations of the
+English land-surveyors in reference to the space natural to a being on
+Mars, namely a Martio-centric space in which that planet is fixed. The
+earth is moving relatively to Mars and is rotating. To the beings on
+Mars the operations, construed in this fashion, effect measurements of
+the greatest complication. Furthermore, according to the relativistic
+doctrine, the operation of time-measurement on earth will not correspond
+quite exactly to any time-measurement on Mars.
+
+I have discussed this example in order to make you realise that in
+thinking of the possibilities of measurement in the space-time manifold,
+we must not confine ourselves merely to those minor variations which
+might seem natural to human beings on the earth. Let us make therefore
+the general statement that four measurements, respectively of
+independent types (such as measurements of lengths in three directions
+and a time), can be found such that a definite event-particle is
+determined by them in its relations to other parts of the manifold.
+
+If (p_1, p_2, p_3, p_4) be a set of measurements of this system, then
+the event-particle which is thus determined will be said to have p_1,
+p_2, p_3, p_4 as its co-ordinates in this system of measurement. Suppose
+that we name it the p-system of measurement. Then in the same p-system
+by properly varying (p_1, p_2, p_3, p_4) every event-particle that has
+been, or will be, or instantaneously is now, can be indicated.
+Furthermore, according to any system of measurement that is natural to
+us, three of the co-ordinates will be measurements of space and one will
+be a measurement of time. Let us always take the last co-ordinate to
+represent the time-measurement. Then we should naturally say that (p_1,
+p_2, p_3) determined a point in space and that the event-particle
+happened at that point at the time p_4. But we must not make the mistake
+of thinking that there is a space in addition to the space-time
+manifold. That manifold is all that there is for the determination of
+the meaning of space and time. We have got to determine the meaning of a
+space-point in terms of the event-particles of the four-dimensional
+manifold. There is only one way to do this. Note that if we vary the
+time and take times with the same three space co-ordinates, then the
+event-particles, thus indicated, are all at the same point. But seeing
+that there is nothing else except the event-particles, this can only
+mean that the point (p_1, p_2, p_3) of the space in the p-system is
+merely the collection of event-particles (p_1, p_2, p_3, [p_4]), where
+p_4 is varied and (p_1, p_2, p_3) is kept fixed. It is rather
+disconcerting to find that a point in space is not a simple entity; but
+it is a conclusion which follows immediately from the relative theory of
+space.
+
+Furthermore the inhabitant of Mars determines event-particles by another
+system of measurements. Call his system the q-system. According to him
+(q_1, q_2, q_3, q_4) determines an event-particle, and (q_1, q_2, q_3)
+determines a point and q_4 a time. But the collection of event-particles
+which he thinks of as a point is entirely different from any such
+collection which the man on earth thinks of as a point. Thus the q-space
+for the man on Mars is quite different from the p-space for the
+land-surveyor on earth.
+
+So far in speaking of space we have been talking of the timeless space
+of physical science, namely, of our concept of eternal space in which
+the world adventures. But the space which we see as we look about is
+instantaneous space. Thus if our natural perceptions are adjustable to
+the p-system of measurements we see instantaneously all the
+event-particles at some definite time p_4, and observe a succession
+of such spaces as time moves on. The timeless space is achieved by
+stringing together all these instantaneous spaces. The points of an
+instantaneous space are event-particles, and the points of an eternal
+space are strings of event-particles occurring in succession. But the
+man on Mars will never perceive the same instantaneous spaces as the man
+on the earth. This system of instantaneous spaces will cut across the
+earth-man's system. For the earth-man there is one instantaneous space
+which is the instantaneous present, there are the past spaces and the
+future spaces. But the present space of the man on Mars cuts across the
+present space of the man on the earth. So that of the event-particles
+which the earth-man thinks of as happening now in the present, the man
+on Mars thinks that some are already past and are ancient history, that
+others are in the future, and others are in the immediate present. This
+break-down in the neat conception of a past, a present, and a future is
+a serious paradox. I call two event-particles which on some or other
+system of measurement are in the same instantaneous space 'co-present'
+event-particles. Then it is possible that A and B may be co-present,
+and that A and C may be co-present, but that B and C may not be
+co-present. For example, at some inconceivable distance from us there
+are events co-present with us now and also co-present with the birth of
+Queen Victoria. If A and B are co-present there will be some systems
+in which A precedes B and some in which B precedes A. Also there
+can be no velocity quick enough to carry a material particle from A to
+B or from B to A. These different measure-systems with their
+divergences of time-reckoning are puzzling, and to some extent affront
+our common sense. It is not the usual way in which we think of the
+Universe. We think of one necessary time-system and one necessary space.
+According to the new theory, there are an indefinite number of
+discordant time-series and an indefinite number of distinct spaces. Any
+correlated pair, a time-system and a space-system, will do in which to
+fit our description of the Universe. We find that under given conditions
+our measurements are necessarily made in some one pair which together
+form our natural measure-system. The difficulty as to discordant
+time-systems is partly solved by distinguishing between what I call the
+creative advance of nature, which is not properly serial at all, and any
+one time series. We habitually muddle together this creative advance,
+which we experience and know as the perpetual transition of nature into
+novelty, with the single-time series which we naturally employ for
+measurement. The various time-series each measure some aspect of the
+creative advance, and the whole bundle of them express all the
+properties of this advance which are measurable. The reason why we have
+not previously noted this difference of time-series is the very small
+difference of properties between any two such series. Any observable
+phenomena due to this cause depend on the square of the ratio of any
+velocity entering into the observation to the velocity of light. Now
+light takes about fifty minutes to get round the earth's orbit; and the
+earth takes rather more than 17,531 half-hours to do the same. Hence all
+the effects due to this motion are of the order of the ratio of one to
+the square of 10,000. Accordingly an earth-man and a sun-man have only
+neglected effects whose quantitative magnitudes all contain the factor
+1/10^8. Evidently such effects can only be noted by means of the most
+refined observations. They have been observed however. Suppose we
+compare two observations on the velocity of light made with the same
+apparatus as we turn it through a right angle. The velocity of the earth
+relatively to the sun is in one direction, the velocity of light
+relatively to the ether should be the same in all directions. Hence if
+space when we take the ether as at rest means the same thing as space
+when we take the earth as at rest, we ought to find that the velocity of
+light relatively to the earth varies according to the direction from
+which it comes.
+
+These observations on earth constitute the basic principle of the famous
+experiments designed to detect the motion of the earth through the
+ether. You all know that, quite unexpectedly, they gave a null result.
+This is completely explained by the fact that, the space-system and the
+time-system which we are using are in certain minute ways different from
+the space and the time relatively to the sun or relatively to any other
+body with respect to which it is moving.
+
+All this discussion as to the nature of time and space has lifted above
+our horizon a great difficulty which affects the formulation of all the
+ultimate laws of physics--for example, the laws of the electromagnetic
+field, and the law of gravitation. Let us take the law of gravitation
+as an example. Its formulation is as follows: Two material bodies
+attract each other with a force proportional to the product of their
+masses and inversely proportional to the square of their distances.
+In this statement the bodies are supposed to be small enough to be
+treated as material particles in relation to their distances; and we
+need not bother further about that minor point. The difficulty to which
+I want to draw your attention is this: In the formulation of the law one
+definite time and one definite space are presupposed. The two masses are
+assumed to be in simultaneous positions.
+
+But what is simultaneous in one time-system may not be simultaneous in
+another time-system. So according to our new views the law is in this
+respect not formulated so as to have any exact meaning. Furthermore an
+analogous difficulty arises over the question of distance. The distance
+between two instantaneous positions, _i.e._ between two event-particles,
+is different in different space-systems. What space is to be chosen?
+Thus again the law lacks precise formulation, if relativity is accepted.
+Our problem is to seek a fresh interpretation of the law of gravity in
+which these difficulties are evaded. In the first place we must avoid
+the abstractions of space and time in the formulation of our fundamental
+ideas and must recur to the ultimate facts of nature, namely to events.
+Also in order to find the ideal simplicity of expressions of the
+relations between events, we restrict ourselves to event-particles. Thus
+the life of a material particle is its adventure amid a track of
+event-particles strung out as a continuous series or path in the
+four-dimensional space-time manifold. These event-particles are the
+various situations of the material particle. We usually express this
+fact by adopting our natural space-time system and by talking of the
+path in space of the material particle as it exists at successive
+instants of time.
+
+We have to ask ourselves what are the laws of nature which lead the
+material particle to adopt just this path among event-particles and no
+other. Think of the path as a whole. What characteristic has that path
+got which would not be shared by any other slightly varied path? We are
+asking for more than a law of gravity. We want laws of motion and a
+general idea of the way to formulate the effects of physical forces.
+
+In order to answer our question we put the idea of the attracting masses
+in the background and concentrate attention on the field of activity of
+the events in the neighbourhood of the path. In so doing we are acting
+in conformity with the whole trend of scientific thought during the last
+hundred years, which has more and more concentrated attention on the
+field of force as the immediate agent in directing motion, to the
+exclusion of the consideration of the immediate mutual influence between
+two distant bodies. We have got to find the way of expressing the field
+of activity of events in the neighbourhood of some definite
+event-particle E of the four-dimensional manifold. I bring in a
+fundamental physical idea which I call the 'impetus' to express this
+physical field. The event-particle E is related to any neighbouring
+event-particle P by an element of impetus. The assemblage of all the
+elements of impetus relating E to the assemblage of event-particles in
+the neighbourhood of E expresses the character of the field of
+activity in the neighbourhood of E. Where I differ from Einstein is
+that he conceives this quantity which I call the impetus as merely
+expressing the characters of the space and time to be adopted and thus
+ends by talking of the gravitational field expressing a curvature in the
+space-time manifold. I cannot attach any clear conception to his
+interpretation of space and time. My formulae differ slightly from his,
+though they agree in those instances where his results have been
+verified. I need hardly say that in this particular of the formulation
+of the law of gravitation I have drawn on the general method of
+procedure which constitutes his great discovery.
+
+Einstein showed how to express the characters of the assemblage of
+elements of impetus of the field surrounding an event-particle E in
+terms of ten quantities which I will call J_{11}, J_{12}
+(=J_{21}), J_{22}, J_{23}(=J_{32}), etc. It will be noted that
+there are four spatio-temporal measurements relating E to its
+neighbour P, and that there are ten pairs of such measurements if we
+are allowed to take any one measurement twice over to make one such
+pair. The ten J's depend merely on the position of E in the
+four-dimensional manifold, and the element of impetus between E and
+P can be expressed in terms of the ten J's and the ten pairs of the
+four spatio-temporal measurements relating E and P. The numerical
+values of the J's will depend on the system of measurement adopted,
+but are so adjusted to each particular system that the same value is
+obtained for the element of impetus between E and P, whatever be the
+system of measurement adopted. This fact is expressed by saying that the
+ten J's form a 'tensor.' It is not going too far to say that the
+announcement that physicists would have in future to study the theory of
+tensors created a veritable panic among them when the verification of
+Einstein's predictions was first announced.
+
+The ten J's at any event-particle E can be expressed in terms of two
+functions which I call the potential and the 'associate-potential' at
+E. The potential is practically what is meant by the ordinary
+gravitation potential, when we express ourselves in terms of the
+Euclidean space in reference to which the attracting mass is at rest.
+The associate-potential is defined by the modification of substituting
+the direct distance for the inverse distance in the definition of the
+potential, and its calculation can easily be made to depend on that of
+the old-fashioned potential. Thus the calculation of the J's--the
+coefficients of impetus, as I will call them--does not involve anything
+very revolutionary in the mathematical knowledge of physicists. We now
+return to the path of the attracted particle. We add up all the elements
+of impetus in the whole path, and obtain thereby what I call the
+'integral impetus.' The characteristic of the actual path as compared
+with neighbouring alternative paths is that in the actual paths the
+integral impetus would neither gain nor lose, if the particle wobbled
+out of it into a small extremely near alternative path. Mathematicians
+would express this by saying, that the integral impetus is stationary
+for an infinitesimal displacement. In this statement of the law of
+motion I have neglected the existence of other forces. But that would
+lead me too far afield.
+
+The electromagnetic theory has to be modified to allow for the presence
+of a gravitational field. Thus Einstein's investigations lead to the
+first discovery of any relation between gravity and other physical
+phenomena. In the form in which I have put this modification, we deduce
+Einstein's fundamental principle, as to the motion of light along its
+rays, as a first approximation which is absolutely true for infinitely
+short waves. Einstein's principle, thus partially verified, stated in my
+language is that a ray of light always follows a path such that the
+integral impetus along it is zero. This involves that every element of
+impetus along it is zero.
+
+In conclusion, I must apologise. In the first place I have considerably
+toned down the various exciting peculiarities of the original theory and
+have reduced it to a greater conformity with the older physics. I do not
+allow that physical phenomena are due to oddities of space. Also I have
+added to the dullness of the lecture by my respect for the audience. You
+would have enjoyed a more popular lecture with illustrations of
+delightful paradoxes. But I know also that you are serious students who
+are here because you really want to know how the new theories may affect
+your scientific researches.
+
+
+
+
+CHAPTER IX
+
+THE ULTIMATE PHYSICAL CONCEPTS
+
+
+The second chapter of this book lays down the first principle to be
+guarded in framing our physical concept. We must avoid vicious
+bifurcation. Nature is nothing else than the deliverance of
+sense-awareness. We have no principles whatever to tell us what could
+stimulate mind towards sense-awareness. Our sole task is to exhibit in
+one system the characters and inter-relations of all that is observed.
+Our attitude towards nature is purely 'behaviouristic,' so far as
+concerns the formulation of physical concepts.
+
+Our knowledge of nature is an experience of activity (or passage). The
+things previously observed are active entities, the 'events.' They are
+chunks in the life of nature. These events have to each other relations
+which in our knowledge differentiate themselves into space-relations and
+time-relations. But this differentiation between space and time, though
+inherent in nature, is comparatively superficial; and space and time are
+each partial expressions of one fundamental relation between events
+which is neither spatial nor temporal. This relation I call 'extension.'
+The relation of 'extending over' is the relation of 'including,' either
+in a spatial or in a temporal sense, or in both. But the mere
+'inclusion' is more fundamental than either alternative and does not
+require any spatio-temporal differentiation. In respect to extension two
+events are mutually related so that either (i) one includes the other,
+or (ii) one overlaps the other without complete inclusion, or (iii)
+they are entirely separate. But great care is required in the
+definition of spatial and temporal elements from this basis in order to
+avoid tacit limitations really depending on undefined relations and
+properties.
+
+Such fallacies can be avoided by taking account of two elements in our
+experience, namely, (i) our observational 'present,' and (ii) our
+'percipient event.'
+
+Our observational 'present' is what I call a 'duration.' It is the whole
+of nature apprehended in our immediate observation. It has therefore the
+nature of an event, but possesses a peculiar completeness which marks
+out such durations as a special type of events inherent in nature. A
+duration is not instantaneous. It is all that there is of nature with
+certain temporal limitations. In contradistinction to other events a
+duration will be called infinite and the other events are finite[10]. In
+our knowledge of a duration we distinguish (i) certain included events
+which are particularly discriminated as to their peculiar
+individualities, and (ii) the remaining included events which are only
+known as necessarily in being by reason of their relations to the
+discriminated events and to the whole duration. The duration as a whole
+is signified[11] by that quality of relatedness (in respect to
+extension) possessed by the part which is immediately under observation;
+namely, by the fact that there is essentially a beyond to whatever is
+observed. I mean by this that every event is known as being related to
+other events which it does not include. This fact, that every event is
+known as possessing the quality of exclusion, shows that exclusion is as
+positive a relation as inclusion. There are of course no merely
+negative relations in nature, and exclusion is not the mere negative of
+inclusion, though the two relations are contraries. Both relations are
+concerned solely with events, and exclusion is capable of logical
+definition in terms of inclusion.
+
+[10] Cf. note on 'significance,' pp. 197, 198.
+
+[11] Cf. Ch. III, pp. 51 et seq.
+
+Perhaps the most obvious exhibition of significance is to be found in
+our knowledge of the geometrical character of events inside an opaque
+material object. For example we know that an opaque sphere has a centre.
+This knowledge has nothing to do with the material; the sphere may be a
+solid uniform billiard ball or a hollow lawn-tennis ball. Such knowledge
+is essentially the product of significance, since the general character
+of the external discriminated events has informed us that there are
+events within the sphere and has also informed us of their geometrical
+structure.
+
+Some criticisms on 'The Principles of Natural Knowledge' show that
+difficulty has been found in apprehending durations as real
+stratifications of nature. I think that this hesitation arises from the
+unconscious influence of the vicious principle of bifurcation, so deeply
+embedded in modern philosophical thought. We observe nature as extended
+in an immediate present which is simultaneous but not instantaneous, and
+therefore the whole which is immediately discerned or signified as an
+inter-related system forms a stratification of nature which is a
+physical fact. This conclusion immediately follows unless we admit
+bifurcation in the form of the principle of psychic additions, here
+rejected.
+
+Our 'percipient event' is that event included in our observational
+present which we distinguish as being in some peculiar way our
+standpoint for perception. It is roughly speaking that event which is
+our bodily life within the present duration. The theory of perception
+as evolved by medical psychology is based on significance. The distant
+situation of a perceived object is merely known to us as signified by
+our bodily state, _i.e._ by our percipient event. In fact perception
+requires sense-awareness of the significations of our percipient event
+together with sense-awareness of a peculiar relation (situation) between
+certain objects and the events thus signified. Our percipient event is
+saved by being the whole of nature by this fact of its significations.
+This is the meaning of calling the percipient event our standpoint for
+perception. The course of a ray of light is only derivatively connected
+with perception. What we do perceive are objects as related to events
+signified by the bodily states excited by the ray. These signified
+events (as is the case of images seen behind a mirror) may have very
+little to do with the actual course of the ray. In the course of
+evolution those animals have survived whose sense-awareness is
+concentrated on those significations of their bodily states which are on
+the average important for their welfare. The whole world of events is
+signified, but there are some which exact the death penalty for
+inattention.
+
+The percipient event is always here and now in the associated present
+duration. It has, what may be called, an absolute position in that
+duration. Thus one definite duration is associated with a definite
+percipient event, and we are thus aware of a peculiar relation which
+finite events can bear to durations. I call this relation 'cogredience.'
+The notion of rest is derivative from that of cogredience, and the
+notion of motion is derivative from that of inclusion within a duration
+without cogredience with it. In fact motion is a relation (of varying
+character) between an observed event and an observed duration, and
+cogredience is the most simple character or subspecies of motion. To sum
+up, a duration and a percipient event are essentially involved in the
+general character of each observation of nature, and the percipient
+event is cogredient with the duration.
+
+Our knowledge of the peculiar characters of different events depends
+upon our power of comparison. I call the exercise of this factor in our
+knowledge 'recognition,' and the requisite sense-awareness of the
+comparable characters I call 'sense-recognition.' Recognition and
+abstraction essentially involve each other. Each of them exhibits an
+entity for knowledge which is less than the concrete fact, but is a real
+factor in that fact. The most concrete fact capable of separate
+discrimination is the event. We cannot abstract without recognition, and
+we cannot recognise without abstraction. Perception involves
+apprehension of the event and recognition of the factors of its
+character.
+
+The things recognised are what I call 'objects.' In this general sense
+of the term the relation of extension is itself an object. In practice
+however I restrict the term to those objects which can in some sense or
+other be said to have a situation in an event; namely, in the phrase
+'There it is again' I restrict the 'there' to be the indication of a
+special event which is the situation of the object. Even so, there are
+different types of objects, and statements which are true of objects of
+one type are not in general true of objects of other types. The objects
+with which we are here concerned in the formulation of physical laws are
+material objects, such as bits of matter, molecules and electrons. An
+object of one of these types has relations to events other than those
+belonging to the stream of its situations. The fact of its situations
+within this stream has impressed on all other events certain
+modifications of their characters. In truth the object in its
+completeness may be conceived as a specific set of correlated
+modifications of the characters of all events, with the property that
+these modifications attain to a certain focal property for those events
+which belong to the stream of its situations. The total assemblage of
+the modifications of the characters of events due to the existence of an
+object in a stream of situations is what I call the 'physical field' due
+to the object. But the object cannot really be separated from its field.
+The object is in fact nothing else than the systematically adjusted set
+of modifications of the field. The conventional limitation of the object
+to the focal stream of events in which it is said to be 'situated' is
+convenient for some purposes, but it obscures the ultimate fact of
+nature. From this point of view the antithesis between action at a
+distance and action by transmission is meaningless. The doctrine of this
+paragraph is nothing else than another way of expressing the
+unresolvable multiple relation of an object to events.
+
+A complete time-system is formed by any one family of parallel
+durations. Two durations are parallel if either (i) one includes the
+other, or (ii) they overlap so as to include a third duration common to
+both, or (iii) are entirely separate. The excluded case is that of two
+durations overlapping so as to include in common an aggregate of finite
+events but including in common no other complete duration. The
+recognition of the fact of an indefinite number of families of parallel
+durations is what differentiates the concept of nature here put forward
+from the older orthodox concept of the essentially unique time-systems.
+Its divergence from Einstein's concept of nature will be briefly
+indicated later.
+
+The instantaneous spaces of a given time-system are the ideal
+(non-existent) durations of zero temporal thickness indicated by routes
+of approximation along series formed by durations of the associated
+family. Each such instantaneous space represents the ideal of nature at
+an instant and is also a moment of time. Each time-system thus possesses
+an aggregate of moments belonging to it alone. Each event-particle lies
+in one and only one moment of a given time-system. An event-particle has
+three characters[12]: (i) its extrinsic character which is its character
+as a definite route of convergence among events, (ii) its intrinsic
+character which is the peculiar quality of nature in its neighbourhood,
+namely, the character of the physical field in the neighbourhood, and
+(iii) its position.
+
+[12] Cf. pp. 82 et seq.
+
+The position of an event-particle arises from the aggregate of moments
+(no two of the same family) in which it lies. We fix our attention on
+one of these moments which is approximated to by the short duration of
+our immediate experience, and we express position as the position in
+this moment. But the event-particle receives its position in moment M
+in virtue of the whole aggregate of other moments M{'}, M{''}, etc.,
+in which it also lies. The differentiation of M into a geometry of
+event-particles (instantaneous points) expresses the differentiation of
+M by its intersections with moments of alien time-systems. In this way
+planes and straight lines and event-particles themselves find their
+being. Also the parallelism of planes and straight lines arises from the
+parallelism of the moments of one and the same time-system intersecting
+M. Similarly the order of parallel planes and of event-particles on
+straight lines arises from the time-order of these intersecting moments.
+The explanation is not given here[13]. It is sufficient now merely to
+mention the sources from which the whole of geometry receives its
+physical explanation.
+
+[13] Cf. _Principles of Natural Knowledge_, and previous chapters of the
+present work.
+
+The correlation of the various momentary spaces of one time-system is
+achieved by the relation of cogredience. Evidently motion in an
+instantaneous space is unmeaning. Motion expresses a comparison between
+position in one instantaneous space with positions in other
+instantaneous spaces of the same time-system. Cogredience yields the
+simplest outcome of such comparison, namely, rest.
+
+Motion and rest are immediately observed facts. They are relative in the
+sense that they depend on the time-system which is fundamental for the
+observation. A string of event-particles whose successive occupation
+means rest in the given time-system forms a timeless point in the
+timeless space of that time-system. In this way each time-system
+possesses its own permanent timeless space peculiar to it alone, and
+each such space is composed of timeless points which belong to that
+time-system and to no other. The paradoxes of relativity arise from
+neglecting the fact that different assumptions as to rest involve the
+expression of the facts of physical science in terms of radically
+different spaces and times, in which points and moments have different
+meanings.
+
+The source of order has already been indicated and that of congruence is
+now found. It depends on motion. From cogredience, perpendicularity
+arises; and from perpendicularity in conjunction with the reciprocal
+symmetry between the relations of any two time-systems congruence both
+in time and space is completely defined (cf. _loc. cit._).
+
+The resulting formulae are those for the electromagnetic theory of
+relativity, or, as it is now termed, the restricted theory. But there is
+this vital difference: the critical velocity c which occurs in these
+formulae has now no connexion whatever with light or with any other fact
+of the physical field (in distinction from the extensional structure of
+events). It simply marks the fact that our congruence determination
+embraces both times and spaces in one universal system, and therefore if
+two arbitrary units are chosen, one for all spaces and one for all
+times, their ratio will be a velocity which is a fundamental property of
+nature expressing the fact that times and spaces are really comparable.
+
+The physical properties of nature are expressed in terms of material
+objects (electrons, etc.). The physical character of an event arises
+from the fact that it belongs to the field of the whole complex of such
+objects. From another point of view we can say that these objects are
+nothing else than our way of expressing the mutual correlation of the
+physical characters of events.
+
+The spatio-temporal measurableness of nature arises from (i) the
+relation of extension between events, and (ii) the stratified character
+of nature arising from each of the alternative time-systems, and (iii)
+rest and motion, as exhibited in the relations of finite events to
+time-systems. None of these sources of measurement depend on the
+physical characters of finite events as exhibited by the situated
+objects. They are completely signified for events whose physical
+characters are unknown. Thus the spatio-temporal measurements are
+independent of the objectival physical characters. Furthermore the
+character of our knowledge of a whole duration, which is essentially
+derived from the significance of the part within the immediate field of
+discrimination, constructs it for us as a uniform whole independent, so
+far as its extension is concerned, of the unobserved characters of
+remote events. Namely, there is a definite whole of nature,
+simultaneously now present, whatever may be the character of its remote
+events. This consideration reinforces the previous conclusion. This
+conclusion leads to the assertion of the essential uniformity of the
+momentary spaces of the various time-systems, and thence to the
+uniformity of the timeless spaces of which there is one to each
+time-system.
+
+The analysis of the general character of observed nature set forth above
+affords explanations of various fundamental observational facts:
+({alpha}) It explains the differentiation of the one quality of
+extension into time and space. ({beta}) It gives a meaning to the
+observed facts of geometrical and temporal position, of geometrical and
+temporal order, and of geometrical straightness and planeness. ({gamma})
+It selects one definite system of congruence embracing both space and
+time, and thus explains the concordance as to measurement which is in
+practice attained. ({delta}) It explains (consistently with the theory
+of relativity) the observed phenomena of rotation, _e.g._ Foucault's
+pendulum, the equatorial bulge of the earth, the fixed senses of
+rotation of cyclones and anticyclones, and the gyro-compass. It does
+this by its admission of definite stratifications of nature which are
+disclosed by the very character of our knowledge of it. ({epsilon}) Its
+explanations of motion are more fundamental than those expressed in
+({delta}); for it explains what is meant by motion itself. The observed
+motion of an extended object is the relation of its various situations
+to the stratification of nature expressed by the time-system fundamental
+to the observation. This motion expresses a real relation of the object
+to the rest of nature. The quantitative expression of this relation will
+vary according to the time-system selected for its expression.
+
+This theory accords no peculiar character to light beyond that accorded
+to other physical phenomena such as sound. There is no ground for such a
+differentiation. Some objects we know by sight only, and other objects
+we know by sound only, and other objects we observe neither by light nor
+by sound but by touch or smell or otherwise. The velocity of light
+varies according to its medium and so does that of sound. Light moves in
+curved paths under certain conditions and so does sound. Both light and
+sound are waves of disturbance in the physical characters of events; and
+(as has been stated above, p. 188) the actual course of the light is of
+no more importance for perception than is the actual course of the
+sound. To base the whole philosophy of nature upon light is a baseless
+assumption. The Michelson-Morley and analogous experiments show that
+within the limits of our inexactitude of observation the velocity of
+light is an approximation to the critical velocity 'c' which expresses
+the relation between our space and time units. It is provable that the
+assumption as to light by which these experiments and the influence of
+the gravitational field on the light-rays are explained is deducible _as
+an approximation_ from the equations of the electromagnetic field. This
+completely disposes of any necessity for differentiating light from
+other physical phenomena as possessing any peculiar fundamental
+character.
+
+It is to be observed that the measurement of extended nature by means of
+extended objects is meaningless apart from some observed fact of
+simultaneity inherent in nature and not merely a play of thought.
+Otherwise there is no meaning to the concept of one presentation of your
+extended measuring rod AB. Why not AB' where B' is the end B
+five minutes later? Measurement presupposes for its possibility nature
+as a simultaneity, and an observed object present then and present now.
+In other words, measurement of extended nature requires some inherent
+character in nature affording a rule of presentation of events.
+Furthermore congruence cannot be defined by the permanence of the
+measuring rod. The permanence is itself meaningless apart from some
+immediate judgment of self-congruence. Otherwise how is an elastic
+string differentiated from a rigid measuring rod? Each remains the same
+self-identical object. Why is one a possible measuring rod and the other
+not so? The meaning of congruence lies beyond the self-identity of the
+object. In other words measurement presupposes the measurable, and the
+theory of the measurable is the theory of congruence.
+
+Furthermore the admission of stratifications of nature bears on the
+formulation of the laws of nature. It has been laid down that these laws
+are to be expressed in differential equations which, as expressed in any
+general system of measurement, should bear no reference to any other
+particular measure-system. This requirement is purely arbitrary. For a
+measure-system measures something inherent in nature; otherwise it has
+no connexion with nature at all. And that something which is measured
+by a particular measure-system may have a special relation to the
+phenomenon whose law is being formulated. For example the gravitational
+field due to a material object at rest in a certain time-system may be
+expected to exhibit in its formulation particular reference to spatial
+and temporal quantities of that time-system. The field can of course be
+expressed in any measure-systems, but the particular reference will
+remain as the simple physical explanation.
+
+
+NOTE: ON THE GREEK CONCEPT OF A POINT
+
+The preceding pages had been passed for press before I had the pleasure
+of seeing Sir T. L. Heath's _Euclid in Greek_[14]. In the original
+Euclid's first definition is
+
+    semeion estin, ou meros outhen.
+
+I have quoted it on p. 86 in the expanded form taught to me in
+childhood, 'without parts and without magnitude.' I should have
+consulted Heath's English edition--a classic from the moment of its
+issue--before committing myself to a statement about Euclid. This is
+however a trivial correction not affecting sense and not worth a note. I
+wish here to draw attention to Heath's own note to this definition in
+his _Euclid in Greek_. He summarises Greek thought on the nature of a
+point, from the Pythagoreans, through Plato and Aristotle, to Euclid. My
+analysis of the requisite character of a point on pp. 89 and 90 is in
+complete agreement with the outcome of the Greek discussion.
+
+[14] Camb. Univ. Press, 1920.
+
+
+NOTE: ON SIGNIFICANCE AND INFINITE EVENTS
+
+The theory of significance has been expanded and made more definite in
+the present volume. It had already been introduced in the _Principles of
+Natural Knowledge_ (cf. subarticles 3.3 to 3.8 and 16.1, 16.2, 19.4, and
+articles 20, 21). In reading over the proofs of the present volume, I
+come to the conclusion that in the light of this development my
+limitation of infinite events to durations is untenable. This limitation
+is stated in article 33 of the _Principles_ and at the beginning of
+Chapter IV (p. 74) of this book. There is not only a significance of the
+discerned events embracing the whole present duration, but there is a
+significance of a cogredient event involving its extension through a
+whole time-system backwards and forwards. In other words the essential
+'beyond' in nature is a definite beyond in time as well as in space [cf.
+pp. 53, 194]. This follows from my whole thesis as to the assimilation
+of time and space and their origin in extension. It also has the same
+basis in the analysis of the character of our knowledge of nature. It
+follows from this admission that it is possible to define point-tracks
+[_i.e._ the points of timeless spaces] as abstractive elements. This is
+a great improvement as restoring the balance between moments and points.
+I still hold however to the statement in subarticle 35.4 of the
+_Principles_ that the intersection of a pair of non-parallel durations
+does not present itself to us as one event. This correction does not
+affect any of the subsequent reasoning in the two books.
+
+I may take this opportunity of pointing out that the 'stationary events'
+of article 57 of the _Principles_ are merely cogredient events got at
+from an abstract mathematical point of view.
+
+
+
+
+INDEX
+
+_In the case of terms of frequent occurrence, only those occurrences are
+indexed which are of peculiar importance for the elucidation of
+meaning._
+
+  A [_or_ an], 11
+
+  Abraham, 105
+
+  Absolute position, 105, 106, 114, 188
+
+  Abstraction, 33, 37, 168, 171, 173;
+    extensive, 65, 79, 85
+
+  Abstractive element, 84;
+    set, 61, 79
+
+  Action at a distance, 159, 190
+
+  Action by transmission, 159, 190
+
+  Active conditions, 158
+
+  Activity, field of, 170, 181
+
+  Adjunction, 101
+
+  Aggregate, 23
+
+  Alexander, Prof., viii
+
+  Alexandria, 71
+
+  Alfred the Great, 137
+
+  Anticipation, 69
+
+  Anti-prime, 88
+
+  Apparent nature, 31, 39
+
+  Area, 99;
+    momental, 103;
+    vagrant, 103
+
+  Aristotelian logic, 150
+
+  Aristotle, 16, 17, 18, 24, 197
+
+  Associate-potential, 183
+
+  Atom, 17
+
+  Attribute, 21, 26, 150
+
+  Awareness, 3
+
+  Axiom, 36, 121
+
+  Axioms of congruence, 128 et seqq.
+
+
+  Bacon, Francis, 78
+
+  Behaviouristic, 185
+
+  Bergson, 54
+
+  Berkeley, 28
+
+  Between, 64
+
+  Beyond, 186, 198
+
+  Bifurcation, vi, 30, 185, 187
+
+  Boundary, 100;
+    moment, 63;
+    particle, 100
+
+  Broad, C. D., viii
+
+
+  Calculation, formula of, 45, 158
+
+  Cambridge, 97
+
+  Causal nature, 31, 39
+
+  Causation, 31, 146
+
+  Centrifugal force, 138
+
+  Change, uniformity of, 140
+
+  Character, extrinsic, 82, 89, 90, 113, 191;
+    intrinsic, 80, 82, 90, 113, 191
+
+  Charge, 160
+
+  Closure of nature, 4
+
+  Coefficient of drag, 133
+
+  Coefficients of impetus, 183
+
+  Cogredience, 110, 188
+
+  Coherence, 29
+
+  Comparison, 124, 125, 143, 189
+
+  Complex, 13
+
+  Conceptual nature, 45;
+    space, 96
+
+  Concrete facts, 167, 171, 189
+
+  Conditioning events, 152
+
+  Conditions, active, 158
+
+  Congruence, 65, 96, 118, 120, 127, 196
+
+  Continuity, 157;
+    Dedekindian, 102;
+    of events, 76;
+    of nature, 59, 76
+
+  Convention, 121
+
+  Convergence, 62, 79;
+    law of, 82
+
+  Conveyance, 154, 155
+
+  Co-present, 177
+
+  Covering, 83
+
+  Creative advance, 178
+
+  Critical velocity, 193, 195
+
+  Curvature of space-time, 182
+
+  Cyclone, 194
+
+
+  Dedekindian continuity, 102
+
+  Definite, 53, 194, 198
+
+  Delusions, 31, 38
+
+  Delusive perceptual object, 153
+
+  Demarcation of events, 144
+
+  Demonstrative phrase, 6
+
+  Descriptive phrase, 6, 10
+
+  Differential equations, 196
+
+  Discrimination, 14, 50, 144
+
+  Diversification of nature, 15
+
+  Duddington, Mrs, 47
+
+  Duration, 37, 53, 55, 186
+
+  Durations, families of, 59, 73, 190
+
+  Dynamical axes, 138
+
+
+  Einstein, vii, 102, 131, 164, 165, 181, 182, 183, 184, 191
+
+  Electromagnetic field, 179
+
+  Electron, 30, 146, 158, 171
+
+  Element, 17;
+    abstractive, 84
+
+  Elliptical phraseology, 7
+
+  Empty space, 145
+
+  Entity, 5, 13
+
+  Equal in abstractive force, 83
+
+  Error, 68
+
+  Ether, 18, 78, 160;
+    material, 78;
+    of events, 78
+
+  Euclid, 85, 94, 197
+
+  Euler, 140
+
+  Event, 15, 52, 75, 165;
+    percipient, 107, 152, 186
+
+  Event-particle, 86, 93, 94, 172, 191
+
+  Events, conditioning, 152;
+    continuity of, 76;
+    demarcation of, 144;
+    ether of, 78;
+    infinite, 197, 198;
+    limited, 74;
+    passage of, 34;
+    signified, 52;
+    stationary, 198;
+    stream of, 167;
+    structure of, 52, 166
+
+  Exclusion, 186
+
+  Explanation, 97, 141
+
+  Extended nature, 196
+
+  Extension, 22, 58, 75, 185
+
+  Extensive abstraction, 65, 79, 85
+
+  Extrinsic character, 82, 89, 90, 113, 191;
+    properties, 62
+
+
+  Fact, 12, 13
+
+  Factors, 12, 13, 15
+
+  Facts, concrete, 167, 171
+
+  Family of durations, 59, 63, 73;
+    of moments, 63
+
+  Faraday, 146
+
+  Field, gravitational, 197;
+    of activity, 170, 181;
+    physical, 190
+
+  Finite truths, 12
+
+  Fitzgerald, 133
+
+  Formula of calculation, 45, 158
+
+  Foucault, 138, 194
+
+  Four-dimensional manifold, 86
+
+  Fresnel, 133
+
+  Future, the, 72, 177
+
+
+  Galileo, 139
+
+  Geometrical order, 194
+
+  Geometry, 36;
+    metrical, 129
+
+  Gravitation, 179 et seqq.
+
+  Gravitational field, 197
+
+  Greek philosophy, 16;
+    thought, 197
+
+  Gyro-compass, 194
+
+
+  Heath, Sir T. L., 197
+
+  Here, 107
+
+
+  Idealists, 70
+
+  Immediacy, 52;
+    of perception, 72
+
+  Impetus, 181, 182;
+    coefficients of, 183;
+    integral, 183
+
+  Inclusion, 186
+
+  Individuality, 13
+
+  Infinite events, 197, 198
+
+  Inge, Dr, 48
+
+  Ingredient, 14
+
+  Ingression, 144, 145, 148, 152
+
+  Inherence, 83
+
+  Inside, 106
+
+  Instant, 33, 35, 57
+
+  Instantaneous plane, 91;
+    present, 72;
+    spaces, 86, 90, 177
+
+  Instantaneousness, 56, 57
+
+  Intersection, locus of, 90
+
+  Intrinsic character, 80, 82, 90, 113, 191;
+    properties, 62
+
+  Ionian thinkers, 19
+
+  Irrelevance, infinitude of, 12
+
+  Irrevocableness, 35, 37
+
+  It, 8
+
+
+  Julius Caesar, 36
+
+  Junction, 76, 101
+
+
+  Kinetic energy, 105;
+    symmetry, 129
+
+  Knowledge, 28, 32
+
+
+  Lagrange, 140
+
+  Larmor, 131
+
+  Law of convergence, 82
+
+  Laws of motion, 137, 139;
+    of nature, 196
+
+  Leibnizian monadology, 150
+
+  Level, 91, 92
+
+  Light, 195;
+    ray of, 188;
+    velocity of, 131
+
+  Limit, 57
+
+  Limited events, 74
+
+  Location, 160, 161
+
+  Locke, 27
+
+  Locus, 102;
+    of intersection, 90
+
+  London, 97
+
+  Lorentz, H. A., 131, 133
+
+  Lossky, 47
+
+
+  Manifold, four-dimensional, 86;
+    space-time, 173
+
+  Material ether, 78;
+    object, 169
+
+  Materialism, 43, 70
+
+  Matrix, 116
+
+  Matter, 16, 17, 19, 20, 26
+
+  Maxwell, 131, 133
+
+  Measurableness, 196;
+    of nature, 193
+
+  Measurement, 96, 120, 174, 196;
+    of time, 65, 140
+
+  Measure-system, 196
+
+  Memory, 68
+
+  Metaphysics, 28, 32
+
+  Metrical geometry, 129
+
+  Michelson-Morley, 195
+
+  Milton, 35
+
+  Mind, 27, 28
+
+  Minkowski, viii, 131
+
+  Molecule, 32, 171
+
+  Moment, 57, 60, 88
+
+  Momental area, 103;
+    route, 103
+
+  Momentum, 105
+
+  Motion, 105, 114, 117, 127, 188, 192
+
+  Multiplicity, 22
+
+
+  Natural philosophy, 29, 30
+
+  Natural science, philosophy of, 46
+
+  Nature, 3;
+    apparent, 31, 39;
+    causal, 31, 39;
+    conceptual, 45;
+    continuity of, 59, 76;
+    discrimination of, 144;
+    extended, 196;
+    laws of, 196;
+    passage of, 54;
+    stratification of, 194, 196;
+    system of, 146
+
+  Newton, 27, 136, 139, 140
+
+
+  Object, 77, 125, 143, 169, 189;
+    delusive perceptual, 155;
+    material, 169;
+    perceptual, 153;
+    physical, 155, 157;
+    scientific, 158, 169;
+    uniform, 162
+
+  Occupation, 22, 34, 36, 100, 101
+
+  Order, source of, 192;
+    spatial, 95, 194;
+    temporal, 64, 95, 194
+
+  Organisation of thought, 79
+
+  Outside, 63, 100
+
+
+  Paradox, 192
+
+  Parallel, 63, 127;
+    durations, 190
+
+  Parallelism, 95, 191
+
+  Parallelogram, 127
+
+  Paris, 87, 138
+
+  Parliament, 120
+
+  Part, 14, 15, 58
+
+  Passage of events, 34;
+    of nature, 54
+
+  Past, the, 72, 177
+
+  Perception, 3
+
+  Perceptual objects, 149, 153
+
+  Percipience, 28
+
+  Percipient event, 107, 152, 186, 187
+
+  Period of time, 51
+
+  Permanence, 144
+
+  Perpendicularity, 117, 127, 193
+
+  Philosophy, 1;
+    natural, 29, 30;
+    of natural science, 46;
+    of the sciences, 2
+
+  Physical field, 190;
+    object, 155, 156, 157
+
+  Physics, speculative, 30
+
+  Place, 51
+
+  Plane, 191;
+    instantaneous, 91
+
+  Plato, 16, 17, 18, 24, 197
+
+  Poincare, 121, 122, 123
+
+  Point, 35, 89, 91, 114, 173, 176
+
+  Point-flash, 172, 173
+
+  Point of space, 85
+
+  Point, timeless, 192
+
+  Point-track, 113, 198
+
+  Pompey, 36
+
+  Position, 89, 90, 92, 93, 99, 113, 191;
+    absolute, 105, 106, 114, 188
+
+  Potential, 183;
+    associate-, 183
+
+  Predicate, 18
+
+  Predication, 18
+
+  Present, the, 69, 72, 177;
+    instantaneous, 72;
+    observational, 186
+
+  Primary qualities, 27
+
+  Prime, 88
+
+  Process, 53, 54;
+    of nature, 54
+
+  Psychic additions, 29, 187
+
+  Punct, 92, 93, 94
+
+  Pythagoreans, 197
+
+
+  Quality, 27
+
+  Quantum of time, 162
+
+  Quantum theory, 162
+
+
+  Ray of light, 188
+
+  Reality, 30;
+    of durations, 55, 187
+
+  Recognition, 124, 143, 189
+
+  Rect, 91, 92
+
+  Recurrence, 35
+
+  Relative motion, 117;
+    velocity, 130
+
+  Relativity, 169;
+    restricted theory of, 193
+
+  Rest, 105, 114, 188, 192
+
+  Rotation, 138, 194
+
+  Route, 99;
+    momental, 103;
+    straight, 103
+
+  Russell, Bertrand, 11, 122, 123
+
+
+  Schelling, 47
+
+  Science, 2;
+    metaphysical, 32
+
+  Scientific objects, 149, 158, 169
+
+  Secondary qualities, 27
+
+  Self-congruence, 196
+
+  Self-containedness of nature, 4
+
+  Sense-awareness, 3, 67
+
+  Sense-object, 149, 170
+
+  Sense-perception, 3, 14
+
+  Sense-recognition, 143, 189
+
+  Series, temporal, 66, 70, 85, 178
+
+  Set, abstractive, 61, 79
+
+  Significance, 51, 186, 187, 188, 194, 197, 198
+
+  Signified events, 52
+
+  Simplicity, 163, 173
+
+  Simultaneity, 53, 56, 196
+
+  Situation, 15, 78, 147, 148, 152, 160, 189
+
+  Solid, 99, 101, 102;
+    vagrant, 101
+
+  Sound, 195
+
+  Space, 16, 17, 31, 33, 79;
+    empty, 145;
+    timeless, 86, 106, 114;
+    uniformity of, 194
+
+  Spaces, instantaneous, 86, 90
+
+  Space-system, 179
+
+  Space-time manifold, 173
+
+  Spatial-order, 95
+
+  Spatio-temporal structure, 173
+
+  Speculative demonstration, 6
+
+  Speculative physics, 30
+
+  Standpoint for perception, 107, 188
+
+  Station, 103, 104, 113
+
+  Stationary events, 198
+
+  Straight line, 91, 114, 191;
+    route, 103
+
+  Stratification of nature, 187, 194, 196
+
+  Stream of events, 167
+
+  Structure of events, 52, 166
+
+  Structure, spatio-temporal, 173
+
+  Subject, 18
+
+  Substance, 16, 18, 19, 150
+
+  Substratum, 16, 18, 21
+
+  Symmetry, 118, 126;
+    kinetic, 129
+
+  System of nature, 146
+
+  System, time-, 192
+
+
+  Tarner, Edward, v, 1
+
+  Temporal order, 64, 95, 194
+
+  Temporal series, 66, 70, 85
+
+  Tensor, 182
+
+  Terminus, 4
+
+  The, 11
+
+  Theory, quantum, 162
+
+  There, 110, 189
+
+  This, 11
+
+  Thought, 3, 14
+
+  Timaeus, the, 17, 20, 24
+
+  Time, 16, 17, 31, 33, 49, 79;
+    measurement of, 140;
+    quantum of, 162;
+    transcendence of, 39
+
+  Time-series, 178, also cf. Temporal series
+
+  Time-system, see Time-series, also 91, 97, 104, 179, 192
+
+  Timeless point, 192;
+    space, 86, 106, 114, 177
+
+  Totality, 89
+
+  Transcendence of time, 39
+
+  Transmission, 26, 28;
+    action by, 159, 190
+
+  Tubes of force, 146
+
+
+  Unexhaustiveness, 50
+
+  Uniform object, 162
+
+  Uniformity of change, 140;
+    of space, 194
+
+
+  Vagrant area, 103;
+    solid, 101
+
+  Veblen and Young, 36
+
+  Velocity, critical, 193, 195;
+    of light, 131, 195;
+    relative, 130
+
+  Volume, 92, 101
+
+
+  When, 107
+
+  Where, 107
+
+  Whole, 58
+
+  Within, 63
+
+
+  Young, Veblen and, 36
+
+
+
+
+
+End of Project Gutenberg's The Concept of Nature, by Alfred North Whitehead
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