The Concept of Nature Alfred North Whitehead 1337 downloads.pdf

The Project Gutenberg eBook of The Concept of Nature
This eBook is for the use of anyone anywhere in the United States and most
other parts of the world 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. If you are not located in the United States, you will
have to check the laws of the country where you are located before using
this eBook.

Title: The Concept of Nature

Author: Alfred North Whitehead

Release date: July 16, 2006 [eBook #18835]

Language: English

Other information and formats: www.gutenberg.org/ebooks/18835

Credits: Produced by Janet Kegg, Laura Wisewell and the Online
Distributed Proofreading Team at http://www.pgdp.net

*** START OF THE PROJECT GUTENBERG EBOOK THE CONCEPT
OF NATURE ***

Transcriber’s Note

Special characters This file uses the following special characters:
→ … ′ ″ α β γ δ ε η θ ι λ μ ν ο π ρ ς σ τ υ à é ê ï ô “ ” ‘ ’—

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.

Printer errors Two printer errors have been corrected: On page 51 the word “sight” has
been changed to “touch” as suggested by the sense; and on page 180 the word
“universely” has been changed to “inversely”. These are marked in the text by mouse-
hovers.

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 touch 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 en extends over all the succeeding
members such as en+1, en+2 and so on. Then corresponding to the series
e1, e2, e3, …, en, en+1, …,
there is the series
q(e1), q(e2), q(e3), …, q(en), q(en+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, …, Qn, Qn+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(en) 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, …, en, en+1, … → nothing,
and
q(e1), q(e2), q(e3), …, q(en), q(en+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 J11, J12 (=J21), J22, J23(=J32), 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 B C D E F G H I J K L M
N O P Q R S T U V W X Y Z

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 THE PROJECT GUTENBERG EBOOK THE CONCEPT OF
NATURE ***

Updated editions will replace the previous one—the old editions will be
renamed.

Creating the works from print editions not protected by U.S. copyright law
means that no one owns a United States copyright in these works, so the
Foundation (and you!) can copy and distribute it in the United States
without permission and without paying copyright royalties. Special rules,
set forth in the General Terms of Use part of this license, apply to copying
and distributing Project Gutenberg™ electronic works to protect the
PROJECT GUTENBERG™ concept and trademark. Project Gutenberg is a
registered trademark, and may not be used if you charge for an eBook,
except by following the terms of the trademark license, including paying
royalties for use of the Project Gutenberg trademark. If you do not charge
anything for copies of this eBook, complying with the trademark license is
very easy. You may use this eBook for nearly any purpose such as creation
of derivative works, reports, performances and research. Project Gutenberg
eBooks may be modified and printed and given away—you may do
practically ANYTHING in the United States with eBooks not protected by
U.S. copyright law. Redistribution is subject to the trademark license,
especially commercial redistribution.

START: FULL LICENSE

THE FULL PROJECT GUTENBERG™ LICENSE
PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK

To protect the Project Gutenberg™ mission of promoting the free
distribution of electronic works, by using or distributing this work (or any
other work associated in any way with the phrase “Project Gutenberg”), you
agree to comply with all the terms of the Full Project Gutenberg License
available with this file or online at www.gutenberg.org/license.

Section 1. General Terms of Use and Redistributing
Project Gutenberg electronic works

1.A. By reading or using any part of this Project Gutenberg electronic work,
you indicate that you have read, understand, agree to and accept all the
terms of this license and intellectual property (trademark/copyright)
agreement. If you do not agree to abide by all the terms of this agreement,
you must cease using and return or destroy all copies of Project Gutenberg
electronic works in your possession. If you paid a fee for obtaining a copy
of or access to a Project Gutenberg electronic work and you do not agree to
be bound by the terms of this agreement, you may obtain a refund from the
person or entity to whom you paid the fee as set forth in paragraph 1.E.8.

1.B. “Project Gutenberg” is a registered trademark. It may only be used on
or associated in any way with an electronic work by people who agree to be
bound by the terms of this agreement. There are a few things that you can
do with most Project Gutenberg electronic works even without complying
with the full terms of this agreement. See paragraph 1.C below. There are a
lot of things you can do with Project Gutenberg electronic works if you
follow the terms of this agreement and help preserve free future access to
Project Gutenberg electronic works. See paragraph 1.E below.

1.C. The Project Gutenberg Literary Archive Foundation (“the Foundation”
or PGLAF), owns a compilation copyright in the collection of Project
Gutenberg electronic works. Nearly all the individual works in the
collection are in the public domain in the United States. If an individual
work is unprotected by copyright law in the United States and you are

located in the United States, we do not claim a right to prevent you from
copying, distributing, performing, displaying or creating derivative works
based on the work as long as all references to Project Gutenberg are
removed. Of course, we hope that you will support the Project Gutenberg
mission of promoting free access to electronic works by freely sharing
Project Gutenberg works in compliance with the terms of this agreement for
keeping the Project Gutenberg name associated with the work. You can
easily comply with the terms of this agreement by keeping this work in the
same format with its attached full Project Gutenberg License when you
share it without charge with others.

1.D. The copyright laws of the place where you are located also govern
what you can do with this work. Copyright laws in most countries are in a
constant state of change. If you are outside the United States, check the
laws of your country in addition to the terms of this agreement before
downloading, copying, displaying, performing, distributing or creating
derivative works based on this work or any other Project Gutenberg work.
The Foundation makes no representations concerning the copyright status
of any work in any country other than the United States.

1.E. Unless you have removed all references to Project Gutenberg:

1.E.1. The following sentence, with active links to, or other immediate
access to, the full Project Gutenberg License must appear prominently
whenever any copy of a Project Gutenberg work (any work on which the
phrase “Project Gutenberg” appears, or with which the phrase “Project
Gutenberg” is associated) is accessed, displayed, performed, viewed, copied
or distributed:

This eBook is for the use of anyone
anywhere in the United States and most
other parts of the world 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. If you are not located
in the United States, you will have to check

the laws of the country where you are
located before using this eBook.

1.E.2. If an individual Project Gutenberg electronic work is derived from
texts not protected by U.S. copyright law (does not contain a notice
indicating that it is posted with permission of the copyright holder), the
work can be copied and distributed to anyone in the United States without
paying any fees or charges. If you are redistributing or providing access to a
work with the phrase “Project Gutenberg” associated with or appearing on
the work, you must comply either with the requirements of paragraphs
1.E.1 through 1.E.7 or obtain permission for the use of the work and the
Project Gutenberg trademark as set forth in paragraphs 1.E.8 or 1.E.9.

1.E.3. If an individual Project Gutenberg electronic work is posted with the
permission of the copyright holder, your use and distribution must comply
with both paragraphs 1.E.1 through 1.E.7 and any additional terms imposed
by the copyright holder. Additional terms will be linked to the Project
Gutenberg License for all works posted with the permission of the
copyright holder found at the beginning of this work.

1.E.4. Do not unlink or detach or remove the full Project Gutenberg License
terms from this work, or any files containing a part of this work or any
other work associated with Project Gutenberg.

1.E.5. Do not copy, display, perform, distribute or redistribute this
electronic work, or any part of this electronic work, without prominently
displaying the sentence set forth in paragraph 1.E.1 with active links or
immediate access to the full terms of the Project Gutenberg License.

1.E.6. You may convert to and distribute this work in any binary,
compressed, marked up, nonproprietary or proprietary form, including any
word processing or hypertext form. However, if you provide access to or
distribute copies of a Project Gutenberg work in a format other than “Plain
Vanilla ASCII” or other format used in the official version posted on the
official Project Gutenberg website (www.gutenberg.org), you must, at no
additional cost, fee or expense to the user, provide a copy, a means of
exporting a copy, or a means of obtaining a copy upon request, of the work
in its original “Plain Vanilla ASCII” or other form. Any alternate format

must include the full Project Gutenberg License as specified in paragraph
1.E.1.

1.E.7. Do not charge a fee for access to, viewing, displaying, performing,
copying or distributing any Project Gutenberg works unless you comply
with paragraph 1.E.8 or 1.E.9.

1.E.8. You may charge a reasonable fee for copies of or providing access to
or distributing Project Gutenberg electronic works provided that:

• You pay a royalty fee of 20% of the gross profits you derive from the
use of Project Gutenberg works calculated using the method you
already use to calculate your applicable taxes. The fee is owed to the
owner of the Project Gutenberg trademark, but he has agreed to donate
royalties under this paragraph to the Project Gutenberg Literary
Archive Foundation. Royalty payments must be paid within 60 days
following each date on which you prepare (or are legally required to
prepare) your periodic tax returns. Royalty payments should be clearly
marked as such and sent to the Project Gutenberg Literary Archive
Foundation at the address specified in Section 4, “Information about
donations to the Project Gutenberg Literary Archive Foundation.”

• You provide a full refund of any money paid by a user who notifies
you in writing (or by e-mail) within 30 days of receipt that s/he does
not agree to the terms of the full Project Gutenberg™ License. You
must require such a user to return or destroy all copies of the works
possessed in a physical medium and discontinue all use of and all
access to other copies of Project Gutenberg™ works.

• You provide, in accordance with paragraph 1.F.3, a full refund of any
money paid for a work or a replacement copy, if a defect in the
electronic work is discovered and reported to you within 90 days of
receipt of the work.

• You comply with all other terms of this agreement for free distribution
of Project Gutenberg™ works.

1.E.9. If you wish to charge a fee or distribute a Project Gutenberg™
electronic work or group of works on different terms than are set forth in
this agreement, you must obtain permission in writing from the Project
Gutenberg Literary Archive Foundation, the manager of the Project
Gutenberg™ trademark. Contact the Foundation as set forth in Section 3
below.

1.F.

1.F.1. Project Gutenberg volunteers and employees expend considerable
effort to identify, do copyright research on, transcribe and proofread works
not protected by U.S. copyright law in creating the Project Gutenberg™
collection. Despite these efforts, Project Gutenberg™ electronic works, and
the medium on which they may be stored, may contain “Defects,” such as,
but not limited to, incomplete, inaccurate or corrupt data, transcription
errors, a copyright or other intellectual property infringement, a defective or
damaged disk or other medium, a computer virus, or computer codes that
damage or cannot be read by your equipment.

1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except
for the “Right of Replacement or Refund” described in paragraph 1.F.3, the
Project Gutenberg Literary Archive Foundation, the owner of the Project
Gutenberg™ trademark, and any other party distributing a Project
Gutenberg™ electronic work under this agreement, disclaim all liability to
you for damages, costs and expenses, including legal fees. YOU AGREE
THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT
EXCEPT THOSE PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE
THAT THE FOUNDATION, THE TRADEMARK OWNER, AND ANY
DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE LIABLE
TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL,
PUNITIVE OR INCIDENTAL DAMAGES EVEN IF YOU GIVE
NOTICE OF THE POSSIBILITY OF SUCH DAMAGE.

1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you
discover a defect in this electronic work within 90 days of receiving it, you
can receive a refund of the money (if any) you paid for it by sending a
written explanation to the person you received the work from. If you

received the work on a physical medium, you must return the medium with
your written explanation. The person or entity that provided you with the
defective work may elect to provide a replacement copy in lieu of a refund.
If you received the work electronically, the person or entity providing it to
you may choose to give you a second opportunity to receive the work
electronically in lieu of a refund. If the second copy is also defective, you
may demand a refund in writing without further opportunities to fix the
problem.

1.F.4. Except for the limited right of replacement or refund set forth in
paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO OTHER
WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR
FITNESS FOR ANY PURPOSE.

1.F.5. Some states do not allow disclaimers of certain implied warranties or
the exclusion or limitation of certain types of damages. If any disclaimer or
limitation set forth in this agreement violates the law of the state applicable
to this agreement, the agreement shall be interpreted to make the maximum
disclaimer or limitation permitted by the applicable state law. The invalidity
or unenforceability of any provision of this agreement shall not void the
remaining provisions.

1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
trademark owner, any agent or employee of the Foundation, anyone
providing copies of Project Gutenberg™ electronic works in accordance
with this agreement, and any volunteers associated with the production,
promotion and distribution of Project Gutenberg™ electronic works,
harmless from all liability, costs and expenses, including legal fees, that
arise directly or indirectly from any of the following which you do or cause
to occur: (a) distribution of this or any Project Gutenberg work, (b)
alteration, modification, or additions or deletions to any Project Gutenberg
work, and (c) any Defect you cause.

Section 2. Information about the Mission of Project
Gutenberg

Project Gutenberg is synonymous with the free distribution of electronic
works in formats readable by the widest variety of computers including
obsolete, old, middle-aged and new computers. It exists because of the
efforts of hundreds of volunteers and donations from people in all walks of
life.

Volunteers and financial support to provide volunteers with the assistance
they need are critical to reaching Project Gutenberg’s goals and ensuring
that the Project Gutenberg collection will remain freely available for
generations to come. In 2001, the Project Gutenberg Literary Archive
Foundation was created to provide a secure and permanent future for
Project Gutenberg and future generations. To learn more about the Project
Gutenberg Literary Archive Foundation and how your efforts and donations
can help, see Sections 3 and 4 and the Foundation information page at
www.gutenberg.org.

Section 3. Information about the Project Gutenberg
Literary Archive Foundation

The Project Gutenberg Literary Archive Foundation is a non-profit 501(c)
(3) educational corporation organized under the laws of the state of
Mississippi and granted tax exempt status by the Internal Revenue Service.
The Foundation’s EIN or federal tax identification number is 64-6221541.
Contributions to the Project Gutenberg Literary Archive Foundation are tax
deductible to the full extent permitted by U.S. federal laws and your state’s
laws.

The Foundation’s business office is located at 41 Watchung Plaza #516,
Montclair NJ 07042, USA, +1 (862) 621-9288. Email contact links and up
to date contact information can be found at the Foundation’s website and
official page at www.gutenberg.org/contact

Section 4. Information about Donations to the Project
Gutenberg Literary Archive Foundation

Project Gutenberg™ depends upon and cannot survive without widespread
public support and donations to carry out its mission of increasing the

number of public domain and licensed works that can be freely distributed
in machine-readable form accessible by the widest array of equipment
including outdated equipment. Many small donations ($1 to $5,000) are
particularly important to maintaining tax exempt status with the IRS.

The Foundation is committed to complying with the laws regulating
charities and charitable donations in all 50 states of the United States.
Compliance requirements are not uniform and it takes a considerable effort,
much paperwork and many fees to meet and keep up with these
requirements. We do not solicit donations in locations where we have not
received written confirmation of compliance. To SEND DONATIONS or
determine the status of compliance for any particular state visit
www.gutenberg.org/donate.

While we cannot and do not solicit contributions from states where we have
not met the solicitation requirements, we know of no prohibition against
accepting unsolicited donations from donors in such states who approach us
with offers to donate.

International donations are gratefully accepted, but we cannot make any
statements concerning tax treatment of donations received from outside the
United States. U.S. laws alone swamp our small staff.

Please check the Project Gutenberg web pages for current donation methods
and addresses. Donations are accepted in a number of other ways including
checks, online payments and credit card donations. To donate, please visit:
www.gutenberg.org/donate.

Section 5. General Information About Project Gutenberg
electronic works

Professor Michael S. Hart was the originator of the Project Gutenberg
concept of a library of electronic works that could be freely shared with
anyone. For forty years, he produced and distributed Project Gutenberg
eBooks with only a loose network of volunteer support.

Project Gutenberg eBooks are often created from several printed editions,
all of which are confirmed as not protected by copyright in the U.S. unless a
copyright notice is included. Thus, we do not necessarily keep eBooks in
compliance with any particular paper edition.

Most people start at our website which has the main PG search facility:
www.gutenberg.org.

This website includes information about Project Gutenberg, including how
to make donations to the Project Gutenberg Literary Archive Foundation,
how to help produce our new eBooks, and how to subscribe to our email
newsletter to hear about new eBooks.