----------------------------------------
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,transcriber's ,note3 ,in the parts     
containing mathematical                 
notation1 superscript characters have   
been used where possible4      ,the     
remaining few are denoted using         
underscores and curly                   
brackets1 for example en#a4 ,italicised 
words are marked using     underscores  
like this1 but the letters used in the  
mathematics     7which were all in      
italic font7 have not been marked1 to   
aid         legibility and to avoid     
confusion with the subscripts4          
,the special characters used in this    
file are3                               
,if you can only display the first few  
on the #bnd line1 you may       prefer  
the ,,iso-#hhei-a version of this ebook2
 if you can see all      apart from the 
last six1 then either the ,,iso-#hhei-a 
text or the      ,,html versions should 
be suitable4 ,if you can see none of the
         special characters1 use the    

,,ascii version4                        
,two printer errors have been corrected4
 ,these are3                            
444relating the entity discriminated by 
sight with that                         
discriminated by sight444 sight has been
 changed to touch as      suggested by  
the sense4                              
444universely proportional to444        
universely has been changed     to      
inversely4                              
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--------------------------              
,the ,concept of                        
,,nature                                
,,the ,,tarner ,,lectures               
,,delivered ,,in ,,trinity ,,college    
,,november #aiai                        
,alfred ,north ,whitehead     ,,preface 
,the contents of this book were         
originally delivered at ,trinity        
,college in the autumn of #aiai as the  
inaugural course of ,tarner lectures4   
,the ,tarner lectureship is an          
occasional office founded by the        

liberality of ,mr ,edward ,tarner4 ,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   
,knowledge4' ,the present book embodies 
the endeavour of the first lecturer of  
the series to fulfil his task4  ,the    
chapters retain their original lecture  
form and remain as delivered with the   
exception of minor changes designed to  
remove obscurities of expression4 ,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 way4 ,in the presentation of a 
novel outlook with wide ramifications a 
single line of communications from      
premises to conclusions is not          
sufficient for intelligibility4 ,your   
audience will construe whatever you say 
into conformity with their pre-existing 
outlook4 ,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 exposition4 ,their  
function is to prevent the reader from  
bolting up side tracks in pursuit of    
misunderstandings4 ,the same reason     
dictates my avoidance of the existing   
technical terminology of philosophy4    
,the modern natural philosophy is shot  
through and through with the fallacy of 
bifurcation which is discussed in the   
second chapter of this work4            
,accordingly all its technical terms in 
some subtle way presuppose a            
misunderstanding of my thesis4 ,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            
intelligible4  ,the last two chapters do
 not properly belong to the special     
course4 ,chapter ,,viii is a lecture    
delivered in the spring of #aibj before 
the ,chemical ,society of the students  

of the ,imperial ,college of ,science   
and ,technology4 ,it has been appended  
here as conveniently summing up and     
applying the doctrine of the book for an
 audience with one definite type of     
outlook4  ,this volume on 'the ,concept 
of ,nature' forms a companion book to my
 previous work ,an ,enquiry concerning  
the ,principles of ,natural ,knowledge4 
,either book can be read independently1 
but they supplement each other4 ,in part
 the present book supplies points of    
view which were omitted from its        
predecessor2 in part it traverses the   
same ground with an alternative         
exposition4 ,for one thing1 mathematical
 notation has been carefully avoided1   
and the results of mathematical         
deductions are assumed4 ,some of the    
explanations have been improved and     
others have been set in a new light4 ,on
 the other hand important points of the 
previous work have been omitted where ,i
 have had nothing fresh to say about    
them4 ,on the whole1 whereas the former 

work based itself chiefly on ideas      
directly drawn from mathematical        
physics1 the present book keeps closer  
to certain fields of philosophy and     
physics to the exclusion of mathematics4
 ,the two works meet in their           
discussions of some details of space and
 time4  ,i am not conscious that ,i have
 in any way altered my views4 ,some     
developments have been made4 ,those that
 are capable of a non-mathematical      
exposition have been incorporated in the
 text4 ,the mathematical developments   
are alluded to in the last two chapters4
 ,they concern the adaptation of the    
principles of mathematical physics to   
the form of the relativity principle    
which is here maintained4 ,einstein's   
method of using the theory of tensors is
 adopted1 but the application is worked 
out on different lines and from         
different assumptions4 ,those of his    
results which have been verified by     
experience are obtained also by my      
methods4 ,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-signals4 
,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           
relativity4 ,but in my judgment he has  
cramped the development of his brilliant
 mathematical method in the narrow      
bounds of a very doubtful philosophy4   
,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 physics4 ,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 relativists1 while on

 the side of philosophers it was1 ,i    
believe1 one theme of ,prof4            
,alexander's ,gifford lectures delivered
 some few years ago but not yet         
published4 ,he also summarised his      
conclusions on this question in a       
lecture to the ,aristotelian ,society in
 the ,july of #aiah4 ,since the         
publication of ,an ,enquiry concerning  
the ,principles of ,natural ,knowledge  
,i have had the advantage of reading ,mr
 ,c4 ,d4 ,broad's ,perception1 ,physics1
 and ,reality ,camb4 ,univ4 ,press1     
#aiad4 ,this valuable book has assisted 
me in my discussion in ,chapter ,,ii1   
though ,i am unaware as to how far ,mr  
,broad would assent to any of my        
arguments as there stated4  ,it remains 
for me to thank the staff of the        
,university ,press1 its compositors1 its
 proof-readers1 its clerks1 and its     
managing officials1 not only for the    
technical excellence of their work1 but 
for the way they have co-operated so as 
to secure my convenience4  ,a4 ,n4 ,w4  

,,imperial ,,college ,,of ,,science     
,,and ,,technology4             ,april1 
#aibj4     ,,contents      ,,chap4      
,,page         ,i ,,nature ,,and        
,,thought                               
#a        ,,ii ,,theories ,,of ,,the    
,,bifurcation ,,of ,,nature             
#bf       ,,iii ,,time                  
#di        ,,iv ,,the ,,method ,,of     
,,extensive ,,abstraction               
#gd         ,v ,,space ,,and ,,motion   
#ii        ,,vi ,,congruence            
#abj       ,,vii ,,objects              
#adc      ,,viii ,,summary              
#afd        ,,ix ,,the ,,ultimate       
,,physical ,,concepts                   
#ahe           ,,note3 ,,on ,,the       
,,greek ,,concept ,,of ,a ,,point       
#aig           ,,note3 ,,on             
,,significance ,,and ,,infinite ,,events
         #aig           ,,index         
#aii     ,,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   
,knowledge4' ,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          
definition2 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 devoted4  ,we   
are justified1 ,i think1 in taking the  
second clause of the definition as in   
part explanatory of the earlier clause4 
,what is the philosophy of the sciences8
 ,it is not a bad answer to say that it 
is the study of the relations between   
the different departments of knowledge4 
,then with admirable solicitude for the 
freedom of learning there is inserted in
 the definition after the word          
'relations' the phrase 'or want of      
relations4' ,a disproof of relations    
between sciences would in itself        
constitute a philosophy of the sciences4

 ,but we could not dispense either with 
the earlier or the later clause4 ,it is 
not every relation between sciences     
which enters into their philosophy4 ,for
 example biology and physics are        
connected by the use of the microscope4 
,still1 ,i may safely assert that a     
technical description of the uses of the
 microscope in biology is not part of   
the philosophy of the sciences4 ,again1 
you cannot abandon the later clause of  
the definition2 namely that referring to
 the relations between the sciences1    
without abandoning the explicit         
reference to an ideal in the absence of 
which philosophy must languish from lack
 of intrinsic interest4 ,that ideal is  
the attainment of some unifying concept 
which will set in assigned relationships
 within itself all that there is for    
knowledge1 for feeling1 and for emotion4
 ,that far off ideal is the motive power
 of philosophic research2 and claims    
allegiance even as you expel it4 ,the   
philosophic pluralist is a strict       

logician2 the ,hegelian thrives on      
contradictions by the help of his       
absolute2 the ,mohammedan divine bows   
before the creative will of ,allah2 and 
the pragmatist will swallow anything so 
long as it 'works4'  ,the mention of    
these vast systems and of the age-long  
controversies from which they spring1   
warns us to concentrate4 ,our task is   
the simpler one of the philosophy of the
 sciences4 ,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   
science4 ,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 science4 ,the philosophy
 of the sciences--conceived as one      
subject--is the endeavour to exhibit all
 sciences as one science1 or--in case of
 defeat--the disproof of such a         
possibility4  ,again ,i will make a     
further simplification1 and confine     

attention to the natural sciences1 that 
is1 to the sciences whose subject-matter
 is nature4 ,by postulating a common    
subject-matter for this group of        
sciences a unifying philosophy of       
natural science has been thereby        
presupposed4  ,what do we mean by       
nature8 ,we have to discuss the         
philosophy of natural science4 ,natural 
science is the science of nature4       
,but--,what is nature8  ,nature is that 
which we observe in perception through  
the senses4 ,in this sense-perception we
 are aware of something which is not    
thought and which is self-contained for 
thought4 ,this property of being        
self-contained for thought lies at the  
base of natural science4 ,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 about4  ,thus in a     
sense nature is independent of thought4 
,by this statement no metaphysical      
pronouncement is intended4 ,what ,i mean

 is that we can think about nature      
without thinking about thought4 ,i shall
 say that then we are thinking          
'homogeneously' about nature4  ,of      
course it is possible to think of nature
 in conjunction with thought about the  
fact that nature is thought about4 ,in  
such a case ,i shall say that we are    
thinking 'heterogeneously' about nature4
 ,in fact during the last few minutes we
 have been thinking heterogeneously     
about nature4 ,natural science is       
exclusively concerned with homogeneous  
thoughts about nature4  ,but            
sense-perception has in it an element   
which is not thought4 ,it is a difficult
 psychological question whether         
sense-perception involves thought2 and  
if it does involve thought1 what is the 
kind of thought which it necessarily    
involves4 ,note that it has been stated 
above that sense-perception is an       
awareness of something which is not     
thought4 ,namely1 nature is not thought4
 ,but this is a different question1     

namely that the fact of sense-perception
 has a factor which is not thought4 ,i  
call this factor 'sense-awareness4'     
,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-awareness4         
,however1 ,i do assert this further     
statement2 namely1 that though natural  
science is concerned with nature which  
is the terminus of sense-perception1 it 
is not concerned with the               
sense-awareness itself4  ,i repeat the  
main line of this argument1 and expand  
it in certain directions4  ,thought     
about nature is different from the      
sense-perception of nature4 ,hence the  
fact of sense-perception has an         
ingredient or factor which is not       
thought4 ,i call this ingredient        
sense-awareness4 ,it is indifferent to  
my argument whether sense-perception has
 or has not thought as another          

ingredient4 ,if sense-perception does   
not involve thought1 then               
sense-awareness and sense-perception are
 identical4 ,but the something perceived
 is perceived as an entity which is the 
terminus of the sense-awareness1        
something which for thought is beyond   
the fact of that sense-awareness4 ,also 
the something perceived certainly does  
not contain other sense-awarenesses     
which are different from the            
sense-awareness which is an ingredient  
in that perception4 ,accordingly nature 
as disclosed in sense-perception is     
self-contained as against               
sense-awareness1 in addition to being   
self-contained as against thought4 ,i   
will also express this                  
self-containedness of nature by saying  
that nature is closed to mind4  ,this   
closure of nature does not carry with it
 any metaphysical doctrine of the       
disjunction of nature and mind4 ,it     
means that in sense-perception nature is
 disclosed as a complex of entities     

whose mutual relations are expressible  
in thought without reference to mind1   
that is1 without reference either to    
sense-awareness or to thought4          
,furthermore1 ,i do not wish to be      
understood as implying that             
sense-awareness and thought are the only
 activities which are to be ascribed to 
mind4 ,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     
minds4 ,accordingly ,i will extend the  
meaning of the terms 'homogeneous       
thoughts' and 'heterogeneous thoughts'  
which have already been introduced4 ,we 
are thinking 'homogeneously' about      
nature when we are thinking about it    
without thinking about thought or about 
sense-awareness1 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 both4  ,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 activity4 ,the values of 
nature are perhaps the key to the       
metaphysical synthesis of existence4    
,but such a synthesis is exactly what ,i
 am not attempting4 ,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-awareness4  ,i have said that     
nature is disclosed in sense-perception 
as a complex of entities4 ,it is worth  
considering what we mean by an entity in
 this connexion4 ',entity' is simply the
 ,latin equivalent for 'thing' unless   
some arbitrary distinction is drawn     
between the words for technical         
purposes4 ,all thought has to be about  
things4 ,we can gain some idea of this  
necessity of things for thought by      
examination of the structure of a       
proposition4  ,let us suppose that a    

proposition is being communicated by an 
expositor to a recipient4 ,such a       
proposition is composed of phrases2 some
 of these phrases may be demonstrative  
and others may be descriptive4  ,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 phrase4    
,you will understand that ,i am here    
using 'demonstration' in the non-logical
 sense1 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 students4 ,i will call such     
demonstration 'speculative'             
demonstration1 remembering ,hamlet's use
 of the word 'speculation' when he says1
      ,there is no speculation in those 
eyes4  ,thus a demonstrative phrase     
demonstrates an entity speculatively4   
,it may happen that the expositor has   
meant some other entity--namely1 the    
phrase demonstrates to him an entity    

which is diverse from the entity which  
it demonstrates to the recipient4 ,in   
that case there is confusion2 for there 
are two diverse propositions1 namely the
 proposition for the expositor and the  
proposition for the recipient4 ,i put   
this possibility aside as irrelevant for
 our discussion1 though in practice it  
may be difficult for two persons to     
concur in the consideration of exactly  
the same proposition1 or even for one   
person to have determined exactly the   
proposition which he is considering4    
,again the demonstrative phrase may fail
 to demonstrate any entity4 ,in that    
case there is no proposition for the    
recipient4 ,i think that we may assume  
7perhaps rashly7 that the expositor     
knows what he means4  ,a demonstrative  
phrase is a gesture4 ,it is not itself a
 constituent of the proposition1 but the
 entity which it demonstrates is such a 
constituent4 ,you may quarrel with a    
demonstrative phrase as in some way     
obnoxious to you2 but if it demonstrates

 the right entity1 the proposition is   
unaffected though your taste may be     
offended4 ,this suggestiveness of the   
phraseology is part of the literary     
quality of the sentence which conveys   
the proposition4 ,this is because a     
sentence directly conveys one           
proposition1 while in its phraseology it
 suggests a penumbra of other           
propositions charged with emotional     
value4 ,we are now talking of the one   
proposition directly conveyed in any    
phraseology4  ,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 convey4 ,in such a case we will call
 the phraseology of the proposition     
elliptical4 ,in ordinary intercourse the
 phraseology of nearly all propositions 
is elliptical4  ,let us take some       
examples4 ,suppose that the expositor is
 in ,london1 say in ,regent's ,park and 
in ,bedford ,college1 the great women's 

college which is situated in that park4 
,he is speaking in the college hall and 
he says1      ',this college building is
 commodious4'  ,the phrase 'this college
 building' is a demonstrative phrase4   
,now suppose the recipient answers1     
',this is not a college building1 it is 
the lion-house in the ,zoo4'  ,then1    
provided that the expositor's original  
proposition has not been couched in     
elliptical phraseology1 the expositor   
sticks to his original proposition when 
he replies1      ',anyhow1 it is        
commodious4'  ,note that the recipient's
 answer accepts the speculative         
demonstration of the phrase ',this      
college building4' ,he does not say1    
',what do you mean8' ,he accepts the    
phrase as demonstrating an entity1 but  
declares that same entity to be the     
lion-house in the ,zoo4 ,in his reply1  
the expositor in his turn recognises the
 success of his original gesture as a   
speculative demonstration1 and waives   
the question of the suitability of its  

mode of suggestiveness with an 'anyhow4'
 ,but he is now in a position to repeat 
the original proposition with the aid of
 a demonstrative gesture robbed of any  
suggestiveness1 suitable or unsuitable1 
by saying1      ',it is commodious4'    
,the 'it' of this final statement       
presupposes that thought has seized on  
the entity as a bare objective for      
consideration4  ,we confine ourselves to
 entities disclosed in sense-awareness4 
,the entity is so disclosed as a relatum
 in the complex which is nature4 ,it    
dawns on an observer because of its     
relations2 but it is an objective for   
thought in its own bare individuality4  
,thought cannot proceed otherwise2      
namely1 it cannot proceed without the   
ideal bare 'it' which is speculatively  
demonstrated4 ,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-perception4 ,the 'it' for      
thought is essentially a relatum for    

sense-awareness4  ,the chances are that 
the dialogue as to the college building 
takes another form4 ,whatever the       
expositor originally meant1 he almost   
certainly now takes his former statement
 as couched in elliptical phraseology1  
and assumes that he was meaning1        
',this is a college building and is     
commodious4'  ,here the demonstrative   
phrase or the gesture1 which            
demonstrates the 'it' which is          
commodious1 has now been reduced to     
'this'2 and the attenuated phrase1 under
 the circumstances in which it is       
uttered1 is sufficient for the purpose  
of correct demonstration4 ,this brings  
out the point that the verbal form is   
never the whole phraseology of the      
proposition2 this phraseology also      
includes the general circumstances of   
its production4 ,thus the aim of a      
demonstrative phrase is to exhibit a    
definite 'it' as a bare objective for   
thought2 but the modus operandi of a    
demonstrative phrase is to produce an   

awareness of the entity as a particular 
relatum in an auxiliary complex1 chosen 
merely for the sake of the speculative  
demonstration and irrelevant to the     
proposition4 ,for example1 in the above 
dialogue1 colleges and buildings1 as    
related to the 'it' speculatively       
demonstrated by the phrase 'this college
 building1' set that 'it' in an         
auxiliary complex which is irrelevant to
 the proposition      ',it is           
commodious4'  ,of course in language    
every phrase is invariably highly       
elliptical4 ,accordingly the sentence   
',this college building is commodious'  
means probably      ',this college      
building is commodious as a college     
building4'  ,but it will be found that  
in the above discussion we can replace  
'commodious' by 'commodious as a college
 building' without altering our         
conclusion2 though we can guess that the
 recipient1 who thought he was in the   
lion-house of the ,zoo1 would be less   
likely to assent to4      ',anyhow1 it  

is commodious as a college building4'   
,a more obvious instance of elliptical  
phraseology arises if the expositor     
should address the recipient with the   
remark1      ',that criminal is your    
friend4'  ,the recipient might answer1  
',he is my friend and you are           
insulting4'  ,here the recipient assumes
 that the phrase ',that criminal' is    
elliptical and not merely demonstrative4
 ,in fact1 pure demonstration is        
impossible though it is the ideal of    
thought4 ,this practical impossibility  
of pure demonstration is a difficulty   
which arises in the communication of    
thought and in the retention of thought4
 ,namely1 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 it4  ,i now pass to       
descriptive phrases4 ,the expositor     
says1      ',a college in ,regent's     
,park is commodious4'  ,the recipient   

knows ,regent's ,park well4 ,the phrase 
',a college in ,regent's ,park' is      
descriptive for him4 ,if its phraseology
 is not elliptical1 which in ordinary   
life it certainly will be in some way or
 other1 this proposition simply means1  
',there is an entity which is a college 
building in ,regent's ,park     and is  
commodious4'  ,if the recipient rejoins1
      ',the lion-house in the ,zoo is   
the only commodious building in         
,regent's ,park1'  he now contradicts   
the expositor1 on the assumption that a 
lion-house in a ,zoo is not a college   
building4  ,thus whereas in the first   
dialogue the recipient merely quarrelled
 with the expositor without             
contradicting him1 in this dialogue he  
contradicts him4 ,thus a descriptive    
phrase is part of the proposition which 
it helps to express1 whereas a          
demonstrative phrase is not part of the 
proposition which it helps to express4  
,again the expositor might be standing  
in ,green ,park--where there are no     

college buildings--and say1      ',this 
college building is commodious4'        
,probably no proposition will be        
received by the recipient because the   
demonstrative phrase1      ',this       
college building'  has failed to        
demonstrate owing to the absence of the 
background of sense-awareness which it  
presupposes4  ,but if the expositor had 
said1      ',a college building in      
,green ,park is commodious1'  the       
recipient would have received a         
proposition1 but a false one4  ,language
 is usually ambiguous and it is rash to 
make general assertions as to its       
meanings4 ,but phrases which commence   
with 'this' or 'that' are usually       
demonstrative1 whereas phrases which    
commence with 'the' or 'a' are often    
descriptive4 ,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 hand4 ,the sentence       

',the college building in ,regent's     
,park is commodious'  means1 according  
to the analysis first made by ,bertrand 
,russell1 the proposition1     ',there  
is an entity which 7i7 is a college     
building in ,regent's    ,park and 7ii7 
is commodious and 7iii7 is such that any
 college    building in ,regent's ,park 
is identical with it4'  ,the descriptive
 character of the phrase ',the college  
building in ,regent's ,park' is thus    
evident4 ,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        
clauses4 ,if we had substituted ',green 
,park' for ',regent's ,park' a false    
proposition would have resulted4 ,also  
the erection of a second college in     
,regent's ,park would make the          
proposition false1 though in ordinary   
life common sense would politely treat  
it as merely ambiguous4  ',the ,iliad'  
for a classical scholar is usually a    
demonstrative phrase2 for it            

demonstrates to him a well-known poem4  
,but for the majority of mankind the    
phrase is descriptive1 namely1 it is    
synonymous with ',the poem named the    
,iliad4'  ,names may be either          
demonstrative or descriptive phrases4   
,for example ',homer' is for us a       
descriptive phrase1 namely1 the word    
with some slight difference in          
suggestiveness means ',the man who wrote
 the ,iliad4'  ,this discussion         
illustrates that thought places before  
itself bare objectives1 entities as we  
call them1 which the thinking clothes by
 expressing their mutual relations4     
,sense-awareness discloses fact with    
factors which are the entities for      
thought4 ,the separate distinction of an
 entity in thought is not a metaphysical
 assertion1 but a method of procedure   
necessary for the finite expression of  
individual propositions4 ,apart from    
entities there could be no finite       
truths2 they are the means by which the 
infinitude of irrelevance is kept out of

 thought4  ,to sum up3 the termini for  
thought are entities1 primarily with    
bare individuality1 secondarily with    
properties and relations ascribed to    
them in the procedure of thought2 the   
termini for sense-awareness are factors 
in the fact of nature1 primarily relata 
and only secondarily discriminated as   
distinct individualities4  ,no          
characteristic of nature which is       
immediately posited for knowledge by    
sense-awareness can be explained4 ,it is
 impenetrable by thought1 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 entity4 ,thus for thought 'red' is 
merely a definite entity1 though for    
awareness 'red' has the content of its  
individuality4 ,the transition from the 
'red' of awareness to the 'red' of      
thought is accompanied by a definite    
loss of content1 namely by the          
transition from the factor 'red' to the 

entity 'red4' ,this loss in the         
transition to thought is compensated by 
the fact that thought is communicable   
whereas sense-awareness is              
incommunicable4  ,thus there are three  
components in our knowledge of nature1  
namely1 fact1 factors1 and entities4    
,fact is the undifferentiated terminus  
of sense-awareness2 factors are termini 
of sense-awareness1 differentiated as   
elements of fact2 entities are factors  
in their function as the termini of     
thought4 ,the entities thus spoken of   
are natural entities4 ,thought is wider 
than nature1 so that there are entities 
for thought which are not natural       
entities4  ,when we speak of nature as a
 complex of related entities1 the       
'complex' is fact as an entity for      
thought1 to whose bare individuality is 
ascribed the property of embracing in   
its complexity the natural entities4 ,it
 is our business to analyse this        
conception and in the course of the     
analysis space and time should appear4  

,evidently the relations holding between
 natural entities are themselves natural
 entities1 namely they are also factors 
of fact1 there for sense-awareness4     
,accordingly the structure of the       
natural complex can never be completed  
in thought1 just as the factors of fact 
can never be exhausted in               
sense-awareness4 ,unexhaustiveness is an
 essential character of our knowledge of
 nature4 ,also nature does not exhaust  
the matter for thought1 namely there are
 thoughts which would not occur in any  
homogeneous thinking about nature4  ,the
 question as to whether sense-perception
 involves thought is largely verbal4 ,if
 sense-perception involves a cognition  
of individuality abstracted from the    
actual position of the entity as a      
factor in fact1 then it undoubtedly does
 involve thought4 ,but if it is         
conceived as sense-awareness of a factor
 in fact competent to evoke emotion and 
purposeful action without further       
cognition1 then it does not involve     

thought4 ,in such a case the terminus of
 the sense-awareness is something for   
mind1 but nothing for thought4 ,the     
sense-perception of some lower forms of 
life may be conjectured to approximate  
to this character habitually4 ,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 limit4  ,the   
process of discrimination in            
sense-awareness has two distinct sides4 
,there is the discrimination of fact    
into parts1 and the discrimination of   
any part of fact as exhibiting relations
 to entities which are not parts of fact
 though they are ingredients in it4     
,namely the immediate fact for awareness
 is the whole occurrence of nature4 ,it 
is nature as an event present for       
sense-awareness1 and essentially        
passing4 ,there is no holding nature    
still and looking at it4 ,we cannot     
redouble our efforts to improve our     
knowledge of the terminus of our present

 sense-awareness2 it is our subsequent  
opportunity in subsequent               
sense-awareness which gains the benefit 
of our good resolution4 ,thus the       
ultimate fact for sense-awareness is an 
event4 ,this whole event is             
discriminated by us into partial events4
 ,we are aware of an event which is our 
bodily life1 of an event which is the   
course of nature within this room1 and  
of a vaguely perceived aggregate of     
other partial events4 ,this is the      
discrimination in sense-awareness of    
fact into parts4  ,i shall use the term 
'part' in the arbitrarily limited sense 
of an event which is part of the whole  
fact disclosed in awareness4            
,sense-awareness also yields to us other
 factors in nature which are not events4
 ,for example1 sky-blue is seen as      
situated in a certain event4 ,this      
relation of situation requires further  
discussion which is postponed to a later
 lecture4 ,my present point is that     
sky-blue is found in nature with a      

definite implication in events1 but is  
not an event itself4 ,accordingly in    
addition to events1 there are other     
factors in nature directly disclosed to 
us in sense-awareness4 ,the conception  
in thought of all the factors in nature 
as distinct entities with definite      
natural relations is what ,i have in    
another place#a called the              
'diversification of nature4'  #a ,cf4   
,enquiry4  ,there is one general        
conclusion to be drawn from the         
foregoing discussion4 ,it is that the   
first task of a philosophy of science   
should be some general classification of
 the entities disclosed to us in        
sense-perception4  ,among the examples  
of entities in addition to 'events'     
which we have used for the purpose of   
illustration are the buildings of       
,bedford ,college1 ,homer1 and sky-blue4
 ,evidently these are very different    
sorts of things2 and it is likely that  
statements which are made about one kind
 of entity will not be true about other 

kinds4 ,if human thought proceeded with 
the orderly method which abstract logic 
would suggest to it1 we might go further
 and say that a classification of       
natural entities should be the first    
step in science itself4 ,perhaps you    
will be inclined to reply that this     
classification has already been         
effected1 and that science is concerned 
with the adventures of material entities
 in space and time4  ,the history of the
 doctrine of matter has yet to be       
written4 ,it is the history of the      
influence of ,greek philosophy on       
science4 ,that influence has issued in  
one long misconception of the           
metaphysical status of natural entities4
 ,the entity has been separated from the
 factor which is the terminus of        
sense-awareness4 ,it has become the     
substratum for that factor1 and the     
factor has been degraded into an        
attribute of the entity4 ,in this way a 
distinction has been imported into      
nature which is in truth no distinction 

at all4 ,a natural entity is merely a   
factor of fact1 considered in itself4   
,its disconnexion from the complex of   
fact is a mere abstraction4 ,it is not  
the substratum of the factor1 but the   
very factor itself as bared in thought4 
,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 nature4 ,in this way matter has      
emerged as being the metaphysical       
substratum of its properties1 and the   
course of nature is interpreted as the  
history of matter4  ,plato and          
,aristotle found ,greek thought         
preoccupied with the quest for the      
simple substances in terms of which the 
course of events could be expressed4 ,we
 may formulate this state of mind in the
 question1 ,what is nature made of8 ,the
 answers which their genius gave to this
 question1 and more particularly the    
concepts which underlay the terms in    
which they framed their answers1 have   

determined the unquestioned             
presuppositions as to time1 space and   
matter which have reigned in science4   
,in ,plato the forms of thought are more
 fluid than in ,aristotle1 and          
therefore1 as ,i venture to think1 the  
more valuable4 ,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     
philosophy4 ,for example in the ,timaeus
 there is a presupposition1 somewhat    
vaguely expressed1 of a distinction     
between the general becoming of nature  
and the measurable time of nature4 ,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
 passage4 ,i will not go so far as to   
claim ,plato in direct support of this  
doctrine1 but ,i do think that the      
sections of the ,timaeus which deal with
 time become clearer if my distinction  

is admitted4  ,this is however a        
digression4 ,i am now concerned with the
 origin of the scientific doctrine of   
matter in ,greek thought4 ,in the       
,timaeus ,plato asserts that nature is  
made of fire and earth with air and     
water as intermediate between them1 so  
that 'as fire is to air so is air to    
water1 and as air is to water so is     
water to earth4' ,he also suggests a    
molecular hypothesis for these four     
elements4 ,in this hypothesis everything
 depends on the shape of the atoms2 for 
earth it is cubical and for fire it is  
pyramidal4 ,to-day physicists are again 
discussing the structure of the atom1   
and its shape is no slight factor in    
that structure4 ,plato's guesses read   
much more fantastically than does       
,aristotle's systematic analysis2 but in
 some ways they are more valuable4 ,the 
main outline of his ideas is comparable 
with that of modern science4 ,it        
embodies concepts which any theory of   
natural philosophy must retain and in   

some sense must explain4 ,aristotle     
asked the fundamental question1 ,what do
 we mean by 'substance'8 ,here the      
reaction between his philosophy and his 
logic worked very unfortunately4 ,in his
 logic1 the fundamental type of         
affirmative proposition is the          
attribution of a predicate to a subject4
 ,accordingly1 amid the many current    
uses of the term 'substance' which he   
analyses1 he emphasises its meaning as  
'the ultimate substratum which is no    
longer predicated of anything else4'    
,the unquestioned acceptance of the     
,aristotelian logic has led to an       
ingrained tendency to postulate a       
substratum for whatever is disclosed in 
sense-awareness1 namely1 to look below  
what we are aware of for the substance  
in the sense of the 'concrete thing4'   
,this is the origin of the modern       
scientific concept of matter and of     
ether1 namely they are the outcome of   
this insistent habit of postulation4    
,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 matter4 ,personally1 ,i think
 that predication is a muddled notion   
confusing many different relations under
 a convenient common form of speech4    
,for example1 ,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 period1 and is
 different from the relation of the     
blade to that event4 ,in a sense ,i call
 the event the situation of the green1  
and in another sense it is the situation
 of the blade4 ,thus in one sense the   
blade is a character or property which  
can be predicated of the situation1 and 
in another sense the green is a         
character or property of the same event 
which is also its situation4 ,in this   
way the predication of properties veils 
radically different relations between   
entities4  ,accordingly 'substance1'    

which is a correlative term to          
'predication1' shares in the ambiguity4 
,if we are to look for substance        
anywhere1 ,i should find it in events   
which are in some sense the ultimate    
substance of nature4  ,matter1 in its   
modern scientific sense1 is a return to 
the ,ionian effort to find in space and 
time some stuff which composes nature4  
,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 substance4  ,earth1 water1 air1 fire1
 and matter1 and finally ether are      
related in direct succession so far as  
concerns their postulated characters of 
ultimate substrata of nature4 ,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-awareness4 ,this search is the    
origin of science4  ,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       
abstractions4 ,earth1 fire1 and water in
 the ,ionic philosophy and the shaped   
elements in the ,timaeus are comparable 
to the matter and ether of modern       
scientific doctrine4 ,but substance     
represents the final philosophic concept
 of the substratum which underlies any  
attribute4 ,matter 7in the scientific   
sense7 is already in space and time4    
,thus matter represents the refusal to  
think away spatial and temporal         
characteristics and to arrive at the    
bare concept of an individual entity4   
,it is this refusal which has caused the
 muddle of importing the mere procedure 
of thought into the fact of nature4 ,the
 entity1 bared of all characteristics   

except those of space and time1 has     
acquired a physical status as the       
ultimate texture of nature2 so that the 
course of nature is conceived as being  
merely the fortunes of matter in its    
adventure through space4  ,thus the     
origin of the doctrine of matter is the 
outcome of uncritical acceptance of     
space and time as external conditions   
for natural existence4 ,by this ,i do   
not mean that any doubt should be thrown
 on facts of space and time as          
ingredients in nature4 ,what ,i do mean 
is 'the unconscious presupposition of   
space and time as being that within     
which nature is set4' ,this is exactly  
the sort of presupposition which tinges 
thought in any reaction against the     
subtlety of philosophical criticism4 ,my
 theory of the formation of the         
scientific doctrine of matter is that   
first philosophy illegitimately         
transformed the bare entity1 which is   
simply an abstraction necessary for the 
method of thought1 into the metaphysical

 substratum of these factors in nature  
which in various senses are assigned to 
entities as their attributes2 and that1 
as a second step1 scientists 7including 
philosophers who were scientists7 in    
conscious or unconscious ignoration of  
philosophy presupposed this substratum1 
qua substratum for attributes1 as       
nevertheless in time and space4  ,this  
is surely a muddle4 ,the whole being of 
substance is as a substratum for        
attributes4 ,thus time and space should 
be attributes of the substance4 ,this   
they palpably are not1 if the matter be 
the substance of nature1 since it is    
impossible to express spatio-temporal   
truths without having recourse to       
relations involving relata other than   
bits of matter4 ,i waive this point     
however1 and come to another4 ,it is not
 the substance which is in space1 but   
the attributes4 ,what we find in space  
are the red of the rose and the smell of
 the jasmine and the noise of cannon4   
,we have all told our dentists where our

 toothache is4 ,thus space is not a     
relation between substances1 but between
 attributes4  ,thus even if you admit   
that the adherents of substance can be  
allowed to conceive substance as matter1
 it is a fraud to slip substance into   
space on the plea that space expresses  
relations between substances4 ,on the   
face of it space has nothing to do with 
substances1 but only with their         
attributes4 ,what ,i mean is1 that if   
you choose--as ,i think wrongly--to     
construe our experience of nature as an 
awareness of the attributes of          
substances1 we are by this theory       
precluded from finding any analogous    
direct relations between substances as  
disclosed in our experience4 ,what we do
 find are relations between the         
attributes of substances4 ,thus if      
matter is looked on as substance in     
space1 the space in which it finds      
itself has very little to do with the   
space of our experience4  ,the above    
argument has been expressed in terms of 

the relational theory of space4 ,but if 
space be absolute--namely1 if it have a 
being independent of things in it--the  
course of the argument is hardly        
changed4 ,for things in space must have 
a certain fundamental relation to space 
which we will call occupation4 ,thus the
 objection that it is the attributes    
which are observed as related to space1 
still holds4  ,the scientific doctrine  
of matter is held in conjunction with an
 absolute theory of time4 ,the same     
arguments apply to the relations between
 matter and time as apply to the        
relations between space and matter4     
,there is however 7in the current       
philosophy7 a difference in the         
connexions of space with matter from    
those of time with matter1 which ,i will
 proceed to explain4  ,space is not     
merely an ordering of material entities 
so that any one entity bears certain    
relations to other material entities4   
,the occupation of space impresses a    
certain character on each material      

entity in itself4 ,by reason of its     
occupation of space matter has          
extension4 ,by reason of its extension  
each bit of matter is divisible into    
parts1 and each part is a numerically   
distinct entity from every other such   
part4 ,accordingly it would seem that   
every material entity is not really one 
entity4 ,it is an essential multiplicity
 of entities4 ,there seems to be no     
stopping this dissociation of matter    
into multiplicities short of finding    
each ultimate entity occupying one      
individual point4 ,this essential       
multiplicity of material entities is    
certainly not what is meant by science1 
nor does it correspond to anything      
disclosed in sense-awareness4 ,it is    
absolutely necessary that at a certain  
stage in this dissociation of matter a  
halt should be called1 and that the     
material entities thus obtained should  
be treated as units4 ,the stage of      
arrest may be arbitrary or may be set by
 the characteristics of nature2 but all 

reasoning in science ultimately drops   
its space-analysis and poses to itself  
the problem1 ',here is one material     
entity1 what is happening to it as a    
unit entity8' ,yet this material entity 
is still retaining its extension1 and as
 thus extended is a mere multiplicity4  
,thus there is an essential atomic      
property in nature which is independent 
of the dissociation of extension4 ,there
 is something which in itself is one1   
and which is more than the logical      
aggregate of entities occupying points  
within the volume which the unit        
occupies4 ,indeed we may well be        
sceptical as to these ultimate entities 
at points1 and doubt whether there are  
any such entities at all4 ,they have the
 suspicious character that we are driven
 to accept them by abstract logic and   
not by observed fact4  ,time 7in the    
current philosophy7 does not exert the  
same disintegrating effect on matter    
which occupies it4 ,if matter occupies a
 duration of time1 the whole matter     

occupies every part of that duration4   
,thus the connexion between matter and  
time differs from the connexion between 
matter and space as expressed in current
 scientific philosophy4 ,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 space4 ,at an instant     
distinct volumes of space are occupied  
by distinct bits of matter4 ,accordingly
 there is so far no intrinsic difficulty
 in conceiving that space is merely the 
resultant of relations between the bits 
of matter4 ,but in the one-dimensional  
time the same bit of matter occupies    
different portions of time4 ,accordingly
 time would have to be expressible in   
terms of the relations of a bit of      
matter with itself4 ,my own view is a   
belief in the relational theory both of 
space and of time1 and of disbelief in  
the current form of the relational      
theory of space which exhibits bits of  

matter as the relata for spatial        
relations4 ,the true relata are events4 
,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-formation4 
,the philosophy of nature took a wrong  
turn during its development by ,greek   
thought4 ,this erroneous presupposition 
is vague and fluid in ,plato's ,timaeus4
 ,the general groundwork of the thought 
is still uncommitted and can be         
construed as merely lacking due         
explanation and the guarding emphasis4  
,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-awareness4 ,in this  
phrase the term 'matter' is not used in 
its scientific sense4  ,i will conclude 

by guarding myself against a            
misapprehension4 ,it is evident that the
 current doctrine of matter enshrines   
some fundamental law of nature4 ,any    
simple illustration will exemplify what 
,i mean4 ,for example1 in a museum some 
specimen is locked securely in a glass  
case4 ,it stays there for years3 it     
loses its colour1 and perhaps falls to  
pieces4 ,but it is the same specimen2   
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 beginning4 ,again   
the engineer and the astronomer deal    
with the motions of real permanences in 
nature4 ,any theory of nature which for 
one moment loses sight of these great   
basic facts of experience is simply     
silly4 ,but it is permissible to point  
out that the scientific expression of   
these facts has become entangled in a   
maze of doubtful metaphysics2 and that1 
when we remove the metaphysics and start
 afresh on an unprejudiced survey of    

nature1 a new light is thrown on many   
fundamental concepts which dominate     
science and guide the progress of       
research4     ,,chapter ,,ii  ,,theories
 ,,of ,,the ,,bifurcation ,,of ,,nature 
,in my previous lecture ,i criticised   
the concept of matter as the substance  
whose attributes we perceive4 ,this way 
of thinking of matter is1 ,i think1 the 
historical reason for its introduction  
into science1 and is still the vague    
view of it at the background of our     
thoughts which makes the current        
scientific doctrine appear so obvious4  
,namely we conceive ourselves as        
perceiving attributes of things1 and    
bits of matter are the things whose     
attributes we perceive4  ,in the        
seventeenth century the sweet simplicity
 of this aspect of matter received a    
rude shock4 ,the transmission doctrines 
of science were then in process of      
elaboration and by the end of the       
century were unquestioned1 though their 
particular forms have since been        

modified4 ,the establishment of these   
transmission theories marks a turning   
point in the relation between science   
and philosophy4 ,the doctrines to which 
,i am especially alluding are the       
theories of light and sound4 ,i have no 
doubt that the theories had been vaguely
 floating about before as obvious       
suggestions of common sense2 for nothing
 in thought is ever completely new4 ,but
 at that epoch they were systematised   
and made exact1 and their complete      
consequences were ruthlessly deduced4   
,it is the establishment of this        
procedure of taking the consequences    
seriously which marks the real discovery
 of a theory4 ,systematic doctrines of  
light and sound as being something      
proceeding from the emitting bodies were
 definitely established1 and in         
particular the connexion of light with  
colour was laid bare by ,newton4  ,the  
result completely destroyed the         
simplicity of the 'substance and        
attribute' theory of perception4 ,what  

we see depends on the light entering the
 eye4 ,furthermore we do not even       
perceive what enters the eye4 ,the      
things transmitted are waves or--as     
,newton thought--minute particles1 and  
the things seen are colours4 ,locke met 
this difficulty by a theory of primary  
and secondary qualities4 ,namely1 there 
are some attributes of the matter which 
we do perceive4 ,these are the primary  
qualities1 and there are other things   
which we perceive1 such as colours1     
which are not attributes of matter1 but 
are perceived by us as if they were such
 attributes4 ,these are the secondary   
qualities of matter4  ,why should we    
perceive secondary qualities8 ,it seems 
an extremely unfortunate arrangement    
that we should perceive a lot of things 
that are not there4 ,yet this is what   
the theory of secondary qualities in    
fact comes to4 ,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-awareness1 without dragging in its
 relations to mind4 ,the modern account 
of nature is not1 as it should be1      
merely an account of what the mind knows
 of nature2 but it is also confused with
 an account of what nature does to the  
mind4 ,the result has been disastrous   
both to science and to philosophy1 but  
chiefly to philosophy4 ,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 mind4        
,berkeley's polemic against matter was  
based on this confusion introduced by   
the transmission theory of light4 ,he   
advocated1 rightly as ,i think1 the     
abandonment of the doctrine of matter in
 its present form4 ,he had however      
nothing to put in its place except a    
theory of the relation of finite minds  
to the divine mind4  ,but we are        
endeavouring in these lectures to limit 
ourselves to nature itself and not to   

travel beyond entities which are        
disclosed in sense-awareness4           
,percipience in itself is taken for     
granted4 ,we consider indeed conditions 
for percipience1 but only so far as     
those conditions are among the          
disclosures of perception4 ,we leave to 
metaphysics the synthesis of the knower 
and the known4 ,some further explanation
 and defence of this position is        
necessary1 if the line of argument of   
these lectures is to be comprehensible4 
,the immediate thesis for discussion is 
that any metaphysical interpretation is 
an illegitimate importation into the    
philosophy of natural science4 ,by a    
metaphysical interpretation ,i mean any 
discussion of the how 7beyond nature7   
and of the why 7beyond nature7 of       
thought and sense-awareness4 ,in the    
philosophy of science we seek the       
general notions which apply to nature1  
namely1 to what we are aware of in      
perception4 ,it is the philosophy of the
 thing perceived1 and it should not be  

confused with the metaphysics of reality
 of which the scope embraces both       
perceiver and perceived4 ,no perplexity 
concerning the object of knowledge can  
be solved by saying that there is a mind
 knowing it#b4  #b ,cf4 ,enquiry1       
preface4  ,in other words1 the ground   
taken is this3 sense-awareness is an    
awareness of something4 ,what then is   
the general character of that something 
of which we are aware8 ,we do not ask   
about the percipient or about the       
process1 but about the perceived4 ,i    
emphasise this point because discussions
 on the philosophy of science are       
usually extremely metaphysical--in my   
opinion1 to the great detriment of the  
subject4  ,the recourse to metaphysics  
is like throwing a match into the powder
 magazine4 ,it blows up the whole arena4
 ,this is exactly what scientific       
philosophers do when they are driven    
into a corner and convicted of          
incoherence4 ,they at once drag in the  
mind and talk of entities in the mind or

 out of the mind as the case may be4    
,for natural philosophy everything      
perceived is in nature4 ,we may not pick
 and choose4 ,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 phenomenon4 ,it is for natural      
philosophy to analyse how these various 
elements of nature are connected4  ,in  
making this demand ,i conceive myself as
 adopting our immediate instinctive     
attitude towards perceptual knowledge   
which is only abandoned under the       
influence of theory4 ,we are            
instinctively willing to believe that by
 due attention1 more can be found in    
nature than that which is observed at   
first sight4 ,but we will not be content
 with less4 ,what we ask from the       
philosophy of science is some account of
 the coherence of things perceptively   
known4  ,this means a refusal to        
countenance any theory of psychic       
additions to the object known in        

perception4 ,for example1 what is given 
in perception is the green grass4 ,this 
is an object which we know as an        
ingredient in nature4 ,the theory of    
psychic additions would treat the       
greenness as a psychic addition         
furnished by the perceiving mind1 and   
would leave to nature merely the        
molecules and the radiant energy which  
influence the mind towards that         
perception4 ,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 philosophy4 ,that problem is
 to discuss the relations inter se of   
things known1 abstracted from the bare  
fact that they are known4 ,natural      
philosophy should never ask1 what is in 
the mind and what is in nature4 ,to do  
so is a confession that it has failed to
 express relations between things       
perceptively known1 namely to express   
those natural relations whose expression

 is natural philosophy4 ,it may be that 
the task is too hard for us1 that the   
relations are too complex and too       
various for our apprehension1 or are too
 trivial to be worth the trouble of     
exposition4 ,it is indeed true that we  
have gone but a very small way in the   
adequate formulation of such relations4 
,but at least do not let us endeavour to
 conceal failure under a theory of the  
byplay of the perceiving mind4  ,what ,i
 am essentially protesting against is   
the bifurcation of nature into two      
systems of reality1 which1 in so far as 
they are real1 are real in different    
senses4 ,one reality would be the       
entities such as electrons which are the
 study of speculative physics4 ,this    
would be the reality which is there for 
knowledge2 although on this theory it is
 never known4 ,for what is known is the 
other sort of reality1 which is the     
byplay of the mind4 ,thus there would be
 two natures1 one is the conjecture and 
the other is the dream4  ,another way of

 phrasing this theory which ,i am       
arguing against is to bifurcate nature  
into two divisions1 namely into the     
nature apprehended in awareness and the 
nature which is the cause of awareness4 
,the nature which is the fact           
apprehended in awareness holds within it
 the greenness of the trees1 the song of
 the birds1 the warmth of the sun1 the  
hardness of the chairs1 and the feel of 
the velvet4 ,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 nature4 ,the      
meeting point of these two natures is   
the mind1 the causal nature being       
influent and the apparent nature being  
effluent4  ,there are four questions    
which at once suggest themselves for    
discussion in connexion with this       
bifurcation theory of nature4 ,they     
concern 7i7 causality1 7ii7 time1 7iii7 
space1 and 7iv7 delusions4 ,these       
questions are not really separable4     

,they merely constitute four distinct   
starting points from which to enter upon
 the discussion of the theory4  ,causal 
nature is the influence on the mind     
which is the cause of the effluence of  
apparent nature from the mind4 ,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 part4 ,for example1 the     
burning of the fire and the passage of  
heat from it through intervening space  
is the cause of the body1 its nerves and
 its brain1 functioning in certain ways4
 ,but this is not an action of nature on
 the mind4 ,it is an interaction within 
nature4 ,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 warmth4  ,the bifurcation  
theory is an attempt to exhibit natural 
science as an investigation of the cause
 of the fact of knowledge4 ,namely1 it  

is an attempt to exhibit apparent nature
 as an effluent from the mind because of
 causal nature4 ,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 itself1 though it     
requires an exterior reason both as     
originating and as determining the      
character of its activity4 ,but in      
considering knowledge we should wipe out
 all these spatial metaphors1 such as   
'within the mind' and 'without the      
mind4' ,knowledge is ultimate4 ,there   
can be no explanation of the 'why' of   
knowledge2 we can only describe the     
'what' of knowledge4 ,namely we can     
analyse the content and its internal    
relations1 but we cannot explain why    
there is knowledge4 ,thus causal nature 
is a metaphysical chimera2 though there 
is need of a metaphysics whose scope    
transcends the limitation to nature4    
,the object of such a metaphysical      
science is not to explain knowledge1 but

 exhibit in its utmost completeness our 
concept of reality4  ,however1 we must  
admit that the causality theory of      
nature has its strong suit4 ,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    
oxygen1 with the radiant energy from    
them1 and with the various functionings 
of the material body4 ,unless we produce
 the all-embracing relations1 we are    
faced with a bifurcated nature2 namely1 
warmth and redness on one side1 and     
molecules1 electrons and ether on the   
other side4 ,then the two factors are   
explained as being respectively the     
cause and the mind's reaction to the    
cause4  ,time and space would appear to 
provide these all-embracing relations   
which the advocates of the philosophy of
 the unity of nature require4 ,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 body4  ,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 space4 ,in succeeding  
lectures ,i shall explain my own view of
 time and space4 ,i shall endeavour to  
show that they are abstractions from    
more concrete elements of nature1       
namely1 from events4 ,the discussion of 
the details of the process of           
abstraction will exhibit time and space 
as interconnected1 and will finally lead
 us to the sort of connexions between   
their measurements which occur in the   
modern theory of electromagnetic        
relativity4 ,but this is anticipating   
our subsequent line of development4 ,at 
present ,i wish to consider how the     
ordinary views of time and space help1  
or fail to help1 in unifying our        

conception of nature4  ,first1 consider 
the absolute theories of time and space4
 ,we are to consider each1 namely both  
time and space1 to be a separate and    
independent system of entities1 each    
system known to us in itself and for    
itself concurrently with our knowledge  
of the events of nature4 ,time is the   
ordered succession of durationless      
instants2 and these instants are known  
to us merely as the relata in the serial
 relation which is the time-ordering    
relation1 and the time-ordering relation
 is merely known to us as relating the  
instants4 ,namely1 the relation and the 
instants are jointly known to us in our 
apprehension of time1 each implying the 
other4  ,this is the absolute theory of 
time4 ,frankly1 ,i confess that it seems
 to me to be very unplausible4 ,i cannot
 in my own knowledge find anything      
corresponding to the bare time of the   
absolute theory4 ,time is known to me as
 an abstraction from the passage of     
events4 ,the fundamental fact which     

renders this abstraction possible is the
 passing of nature1 its development1 its
 creative advance1 and combined with    
this fact is another characteristic of  
nature1 namely the extensive relation   
between events4 ,these two facts1 namely
 the passage of events and the extension
 of events over each other1 are in my   
opinion the qualities from which time   
and space originate as abstractions4    
,but this is anticipating my own later  
speculations4  ,meanwhile1 returning to 
the absolute theory1 we are to suppose  
that time is known to us independently  
of any events in time4 ,what happens in 
time occupies time4 ,this relation of   
events to the time occupied1 namely this
 relation of occupation1 is a           
fundamental relation of nature to time4 
,thus the theory requires that we are   
aware of two fundamental relations1 the 
time-ordering relation between instants1
 and the time-occupation relation       
between instants of time and states of  
nature which happen at those instants4  

,there are two considerations which lend
 powerful support to the reigning theory
 of absolute time4 ,in the first place  
time extends beyond nature4 ,our        
thoughts are in time4 ,accordingly it   
seems impossible to derive time merely  
from relations between elements of      
nature4 ,for in that case temporal      
relations could not relate thoughts4    
,thus1 to use a metaphor1 time would    
apparently have deeper roots in reality 
than has nature4 ,for we can imagine    
thoughts related in time without any    
perception of nature4 ,for example we   
can imagine one of ,milton's angels with
 thoughts succeeding each other in time1
 who does not happen to have noticed    
that the ,almighty has created space and
 set therein a material universe4 ,as a 
matter of fact ,i think that ,milton set
 space on the same absolute level as    
time4 ,but that need not disturb the    
illustration4 ,in the second place it is
 difficult to derive the true serial    
character of time from the relative     

theory4 ,each instant is irrevocable4   
,it can never recur by the very         
character of time4 ,but if on the       
relative theory an instant of time is   
simply the state of nature at that time1
 and the time-ordering relation is      
simply the relation between such states1
 then the irrevocableness of time would 
seem to mean that an actual state of all
 nature can never return4 ,i admit it   
seems unlikely that there should ever be
 such a recurrence down to the smallest 
particular4 ,but extreme unlikeliness is
 not the point4 ,our ignorance is so    
abysmal that our judgments of likeliness
 and unlikeliness of future events      
hardly count4 ,the real point is that   
the exact recurrence of a state of      
nature seems merely unlikely1 while the 
recurrence of an instant of time        
violates our whole concept of           
time-order4 ,the instants of time which 
have passed1 are passed1 and can never  
be again4  ,any alternative theory of   
time must reckon with these two         

considerations which are buttresses of  
the absolute theory4 ,but ,i will not   
now continue their discussion4  ,the    
absolute theory of space is analogous to
 the corresponding theory of time1 but  
the reasons for its maintenance are     
weaker4 ,space1 on this theory1 is a    
system of extensionless points which are
 the relata in space-ordering relations 
which can technically be combined into  
one relation4 ,this relation does not   
arrange the points in one linear series 
analogously to the simple method of the 
time-ordering relation for instants4    
,the essential logical characteristics  
of this relation from which all the     
properties of space spring are expressed
 by mathematicians in the axioms of     
geometry4 ,from these axioms#c as framed
 by modern mathematicians the whole     
science of geometry can be deduced by   
the strictest logical reasoning4 ,the   
details of these axioms do not now      
concern us4 ,the points and the         
relations are jointly known to us in our

 apprehension of space1 each implying   
the other4 ,what happens in space1      
occupies space4 ,this relation of       
occupation is not usually stated for    
events but for objects4 ,for example1   
,pompey's statue would be said to occupy
 space1 but not the event which was the 
assassination of ,julius ,caesar4 ,in   
this ,i think that ordinary usage is    
unfortunate1 and ,i hold that the       
relations of events to space and to time
 are in all respects analogous4 ,but    
here ,i am intruding my own opinions    
which are to be discussed in subsequent 
lectures4 ,thus the theory of absolute  
space requires that we are aware of two 
fundamental relations1 the              
space-ordering relation1 which holds    
between points1 and the space-occupation
 relation between points of space and   
material objects4  #c ,cf4 7for example7
 ,projective ,geometry by ,veblen and   
,young1 vol4 i4 #aiaj1 vol4 ii4 #aiag1  
,ginn and ,company1 ,boston1 ,u4,s4,a4  
,this theory lacks the two main supports

 of the corresponding theory of absolute
 time4 ,in the first place space does   
not extend beyond nature in the sense   
that time seems to do4 ,our thoughts do 
not seem to occupy space in quite the   
same intimate way in which they occupy  
time4 ,for example1 ,i have been        
thinking in a room1 and to that extent  
my thoughts are in space4 ,but it seems 
nonsense to ask how much volume of the  
room they occupied1 whether it was a    
cubic foot or a cubic inch2 whereas the 
same thoughts occupy a determinate      
duration of time1 say1 from eleven to   
twelve on a certain date4  ,thus whereas
 the relations of a relative theory of  
time are required to relate thoughts1 it
 does not seem so obvious that the      
relations of a relative theory of space 
are required to relate them4 ,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 time4 
,again the irrevocableness of time does 

not seem to have any parallel for space4
 ,space1 on the relative theory1 is the 
outcome of certain relations between    
objects commonly said to be in space2   
and whenever there are the objects1 so  
related1 there is the space4 ,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 them4     
,the absolute theory of space is not now
 generally popular4 ,the knowledge of   
bare space1 as a system of entities     
known to us in itself and for itself    
independently of our knowledge of the   
events in nature1 does not seem to      
correspond to anything in our           
experience4 ,space1 like time1 would    
appear to be an abstraction from events4
 ,according to my own theory it only    
differentiates itself from time at a    
somewhat developed stage of the         
abstractive process4 ,the more usual way
 of expressing the relational theory of 
space would be to consider space as an  

abstraction from the relations between  
material objects4  ,suppose now we      
assume absolute time and absolute space4
 ,what bearing has this assumption on   
the concept of nature as bifurcated into
 causal nature and apparent nature8     
,undoubtedly the separation between the 
two natures is now greatly mitigated4   
,we can provide them with two systems of
 relations in common2 for both natures  
can be presumed to occupy the same space
 and the same time4 ,the theory now is  
this3 ,causal events occupy certain     
periods of the absolute time and occupy 
certain positions of the absolute space4
 ,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 space2 and the
 periods and positions occupied by the  
apparent events bear a determinate      
relation to the periods and positions   
occupied by the causal events4          
,furthermore definite causal events     

produce for the mind definite apparent  
events4 ,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 perception4  ,the whole   
theory is perfectly logical4 ,in these  
discussions we cannot hope to drive an  
unsound theory to a logical             
contradiction4 ,a reasoner1 apart from  
mere slips1 only involves himself in a  
contradiction when he is shying at a    
reductio ad absurdum4 ,the substantial  
reason for rejecting a philosophical    
theory is the 'absurdum' to which it    
reduces us4 ,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 theory4 
,if our opponent affirms that his       
knowledge has that character1 we can    
only--after making doubly sure that we  
understand each other--agree to differ4 

,accordingly the first duty of an       
expositor in stating a theory in which  
he disbelieves is to exhibit it as      
logical4 ,it is not there where his     
trouble lies4  ,let me summarise the    
previously stated objections to this    
theory of nature4 ,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 known3       
secondly it assumes a knowledge of time 
in itself apart from events related in  
time3 thirdly it assumes a knowledge of 
space in itself apart from events       
related in space4 ,there are in addition
 to these objections other flaws in the 
theory4  ,some light is thrown on the   
artificial status of causal nature in   
this theory by asking1 why causal nature
 is presumed to occupy time and space4  
,this really raises the fundamental     
question as to what characteristics     
causal nature should have in common with
 apparent nature4 ,why--on this         
theory--should the cause which          

influences the mind to perception have  
any characteristics in common with the  
effluent apparent nature8 ,in           
particular1 why should it be in space8  
,why should it be in time8 ,and more    
generally1 ,what do we know about mind  
which would allow us to infer any       
particular characteristics of a cause   
which should influence mind to          
particular effects8  ,the transcendence 
of time beyond nature gives some slight 
reason for presuming that causal nature 
should occupy time4 ,for if the mind    
occupies periods of time1 there would   
seem to be some vague reason for        
assuming that influencing causes occupy 
the same periods of time1 or at least1  
occupy periods which are strictly       
related to the mental periods4 ,but if  
the mind does not occupy volumes of     
space1 there seems to be no reason why  
causal nature should occupy any volumes 
of space4 ,thus space would seem to be  
merely apparent in the same sense as    
apparent nature is merely apparent4     

,accordingly if science is really       
investigating causes which operate on   
the mind1 it would seem to be entirely  
on the wrong tack in presuming that the 
causes which it is seeking for have     
spatial relations4 ,furthermore there is
 nothing else in our knowledge analogous
 to these causes which influence the    
mind to perception4 ,accordingly1 beyond
 the rashly presumed fact that they     
occupy time1 there is really no ground  
by which we can determine any point of  
their character4 ,they must remain for  
ever unknown4  ,now ,i assume as an     
axiom that science is not a fairy tale4 
,it is not engaged in decking out       
unknowable entities with arbitrary and  
fantastic properties4 ,what then is it  
that science is doing1 granting that it 
is effecting something of importance8   
,my answer is that it is determining the
 character of things known1 namely the  
character of apparent nature4 ,but we   
may drop the term 'apparent'2 for there 
is but one nature1 namely the nature    

which is before us in perceptual        
knowledge4 ,the characters which science
 discerns in nature are subtle          
characters1 not obvious at first sight4 
,they are relations of relations and    
characters of characters4 ,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 insistence4  ,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 perceptions4 ,for example1
 the fire is burning and we see a red   
coal4 ,this is explained in science by  
radiant energy from the coal entering   
our eyes4 ,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 red4 ,the chain 
of causation is entirely different4 ,the

 mind is cut out altogether4 ,the real  
question is1 ,when red is found in      
nature1 what else is found there also8  
,namely we are asking for an analysis of
 the accompaniments in nature of the    
discovery of red in nature4 ,in a       
subsequent lecture ,i shall expand this 
line of thought4 ,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 colours4 ,this is no part
 of the evidence which has ever been    
adduced for the wave-theory1 yet on the 
causal theory of perception1 it is      
really the only relevant part4 ,in other
 words1 science is not discussing the   
causes of knowledge1 but the coherence  
of knowledge4 ,the understanding which  
is sought by science is an understanding
 of relations within nature4  ,so far ,i
 have discussed the bifurcation of      
nature in connexion with the theories of
 absolute time and of absolute space4   

,my reason has been that the            
introduction of the relational theories 
only weakens the case for bifurcation1  
and ,i wished to discuss this case on   
its strongest grounds4  ,for instance1  
suppose we adopt the relational theory  
of space4 ,then the space in which      
apparent nature is set is the expression
 of certain relations between the       
apparent objects4 ,it is a set of       
apparent relations between apparent     
relata4 ,apparent nature is the dream1  
and the apparent relations of space are 
dream relations1 and the space is the   
dream space4 ,similarly the space in    
which causal nature is set is the       
expression of certain relations between 
the causal objects4 ,it is the          
expression of certain facts about the   
causal activity which is going on behind
 the scenes4 ,accordingly causal space  
belongs to a different order of reality 
to apparent space4 ,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 see4 ,this conclusion is very  
paradoxical and makes nonsense of all   
scientific phraseology4 ,the case is    
even worse if we admit the relativity of
 time4 ,for the same arguments apply1   
and break up time into the dream time   
and causal time which belong to         
different orders of reality4  ,i have   
however been discussing an extreme form 
of the bifurcation theory4 ,it is1 as ,i
 think1 the most defensible form4 ,but  
its very definiteness makes it the more 
evidently obnoxious to criticism4 ,the  
intermediate form allows that the nature
 we are discussing is always the nature 
directly known1 and so far it rejects   
the bifurcation theory4 ,but it holds   
that there are psychic additions to     
nature as thus known1 and that these    
additions are in no proper sense part of
 nature4 ,for example1 we perceive the  
red billiard ball at its proper time1 in

 its proper place1 with its proper      
motion1 with its proper hardness1 and   
with its proper inertia4 ,but its       
redness and its warmth1 and the sound of
 the click as a cannon is made off it   
are psychic additions1 namely1 secondary
 qualities which are only the mind's way
 of perceiving nature4 ,this is not only
 the vaguely prevalent theory1 but is1  
,i believe1 the historical form of the  
bifurcation theory in so far as it is   
derived from philosophy4 ,i shall call  
it the theory of psychic additions4     
,this theory of psychic additions is a  
sound common-sense theory which lays    
immense stress on the obvious reality of
 time1 space1 solidity and inertia1 but 
distrusts the minor artistic additions  
of colour1 warmth and sound4  ,the      
theory is the outcome of common-sense in
 retreat4 ,it arose in an epoch when the
 transmission theories of science were  
being elaborated4 ,for example1 colour  
is the result of a transmission from the
 material object to the perceiver's eye2

 and what is thus transmitted is not    
colour4 ,thus colour is not part of the 
reality of the material object4         
,similarly for the same reason sounds   
evaporate from nature4 ,also warmth is  
due to the transfer of something which  
is not temperature4 ,thus we are left   
with spatio-temporal positions1 and what
 ,i may term the 'pushiness' of the     
body4 ,this lands us to eighteenth and  
nineteenth century materialism1 namely1 
the belief that what is real in nature  
is matter1 in time and in space and with
 inertia4  ,evidently a distinction in  
quality has been presupposed separating 
off some perceptions due to touch from  
other perceptions4 ,these               
touch-perceptions are perceptions of the
 real inertia1 whereas the other        
perceptions are psychic additions which 
must be explained on the causal theory4 
,this distinction is the product of an  
epoch in which physical science has got 
ahead of medical pathology and of       
physiology4 ,perceptions of push are    

just as much the outcome of transmission
 as are perceptions of colour4 ,when    
colour is perceived the nerves of the   
body are excited in one way and transmit
 their message towards the brain1 and   
when push is perceived other nerves of  
the body are excited in another way and 
transmit their message towards the      
brain4 ,the message of the one set is   
not the conveyance of colour1 and the   
message of the other set is not the     
conveyance of push4 ,but in one case    
colour is perceived and in the other    
case the push due to the object4 ,if you
 snip certain nerves1 there is an end to
 the perception of colour2 and if you   
snip certain other nerves1 there is an  
end to the perception of push4 ,it would
 appear therefore that any reasons which
 should remove colour from the reality  
of nature should also operate to remove 
inertia4  ,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 part1 which is  
purely apparent1 fails owing to the     
failure to establish any fundamental    
distinction between our ways of knowing 
about the two parts of nature as thus   
partitioned4 ,i am not denying that the 
feeling of muscular effort historically 
led to the formulation of the concept of
 force4 ,but this historical fact does  
not warrant us in assigning a superior  
reality in nature to material inertia   
over colour or sound4 ,so far as reality
 is concerned all our sense-perceptions 
are in the same boat1 and must be       
treated on the same principle4 ,the     
evenness of treatment is exactly what   
this compromise theory fails to achieve4
  ,the bifurcation theory however dies  
hard4 ,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 molecules4 ,in another lecture ,i
 will give my own explanation of the    
origin of the difficulty and of its     

solution4  ,another favourite solution1 
the most attenuated form which the      
bifurcation theory assumes1 is to       
maintain that the molecules and ether of
 science are purely conceptual4 ,thus   
there is but one nature1 namely apparent
 nature1 and atoms and ether are merely 
names for logical terms in conceptual   
formulae of calculation4  ,but what is a
 formula of calculation8 ,it is         
presumably a statement that something or
 other is true for natural occurrences4 
,take the simplest of all formulae1 ,two
 and two make four4 ,this--so far as it 
applies to nature--asserts that if you  
take two natural entities1 and then     
again two other natural entities1 the   
combined class contains four natural    
entities4 ,such formulae which are true 
for any entities cannot result in the   
production of the concepts of atoms4    
,then again there are formulae which    
assert that there are entities in nature
 with such and such special properties1 
say1 for example1 with the properties of

 the atoms of hydrogen4 ,now if there   
are no such entities1 ,i fail to see how
 any statements about them can apply to 
nature4 ,for example1 the assertion that
 there is green cheese in the moon      
cannot be a premiss in any deduction of 
scientific importance1 unless indeed the
 presence of green cheese in the moon   
has been verified by experiment4 ,the   
current answer to these objections is   
that1 though atoms are merely           
conceptual1 yet they are an interesting 
and picturesque way of saying something 
else which is true of nature4 ,but      
surely if it is something else that you 
mean1 for heaven's sake say it4 ,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 exist4 ,i am maintaining
 the obvious position that scientific   
laws1 if they are true1 are statements  
about entities which we obtain knowledge
 of as being in nature2 and that1 if the

 entities to which the statements refer 
are not to be found in nature1 the      
statements about them have no relevance 
to any purely natural occurrence4 ,thus 
the molecules and electrons of          
scientific theory are1 so far as science
 has correctly formulated its laws1 each
 of them factors to be found in nature4 
,the electrons are only hypothetical in 
so far as we are not quite certain that 
the electron theory is true4 ,but their 
hypothetical character does not arise   
from the essential nature of the theory 
in itself after its truth has been      
granted4  ,thus at the end of this      
somewhat complex discussion1 we return  
to the position which was affirmed at   
its beginning4 ,the primary task of a   
philosophy of natural science is to     
elucidate the concept of nature1        
considered as one complex fact for      
knowledge1 to exhibit the fundamental   
entities and the fundamental relations  
between entities in terms of which all  
laws of nature have to be stated1 and to

 secure that the entities and relations 
thus exhibited are adequate for the     
expression of all the relations between 
entities which occur in nature4  ,the   
third requisite1 namely that of         
adequacy1 is the one over which all the 
difficulty occurs4 ,the ultimate data of
 science are commonly assumed to be     
time1 space1 material1 qualities of     
material1 and relations between material
 objects4 ,but data as they occur in the
 scientific laws do not relate all the  
entities which present themselves in our
 perception of nature4 ,for example1 the
 wave-theory of light is an excellent   
well-established theory2 but            
unfortunately it leaves out colour as   
perceived4 ,thus the perceived          
redness--or1 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 nature4 ,in     
other words this concept of the         
fundamental relations within nature is  
inadequate4 ,thus we have to bend our   

energies to the enunciation of adequate 
concepts4  ,but in so doing1 are we not 
in fact endeavouring to solve a         
metaphysical problem8 ,i do not think   
so4 ,we are merely endeavouring to      
exhibit the type of relations which hold
 between the entities which we in fact  
perceive as in nature4 ,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 reality4 ,it  
is true that the issue of our endeavour 
may provide material which is relevant  
evidence for a discussion on that       
question4 ,it can hardly fail to do so4 
,but it is only evidence1 and is not    
itself the metaphysical discussion4 ,in 
order to make clear the character of    
this further discussion which is out of 
our ken1 ,i will set before you two     
quotations4 ,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#d--';,in the   
,philosophy of ,nature ,i considered the
 subject-object called nature in its    
activity of self-constructing4 ,in order
 to understand it1 we must rise to an   
intellectual intuition of nature4 ,the  
empiricist does not rise thereto1 and   
for this reason in all his explanations 
it is always he himself that proves to  
be constructing nature4 ,it is no       
wonder1 then1 that his construction and 
that which was to be constructed so     
seldom coincide4 ,a ,natur-philosoph    
raises nature to independence1 and makes
 it construct itself1 and he never      
feels1 therefore1 the necessity of      
opposing nature as constructed 7i4e4 as 
experience7 to real nature1 or of       
correcting the one by means of the      
other4'  #d ,the ,intuitive ,basis of   
,knowledge1 by ,n4 ,o4 ,lossky1 transl4 
by ,mrs ,duddington1 ,macmillan and     
,co41 #aiai4  ,the other quotation is   
from a paper read by the ,dean of ,st   
,paul's before the ,aristotelian        

,society in ,may of #aiai4 ,dr ,inge's  
paper is entitled ',platonism and ,human
 ,immortality1' and in it there occurs  
the following statement3 ',to sum up4   
,the ,platonic doctrine of immortality  
rests on the independence of the        
spiritual world4 ,the spiritual world is
 not a world of unrealised ideals1 over 
against a real world of unspiritual     
fact4 ,it is1 on the contrary1 the real 
world1 of which we have a true though   
very incomplete knowledge1 over against 
a world of common experience which1 as a
 complete whole1 is not real1 since it  
is compacted out of miscellaneous data1 
not all on the same level1 by the help  
of the imagination4 ,there is no world  
corresponding to the world of our common
 experience4 ,nature makes abstractions 
for us1 deciding what range of          
vibrations we are to see and hear1 what 
things we are to notice and remember4'  
,i have cited these statements because  
both of them deal with topics which1    
though they lie outside the range of our

 discussion1 are always being confused  
with it4 ,the reason is that they lie   
proximate to our field of thought1 and  
are topics which are of burning interest
 to the metaphysically minded4 ,it is   
difficult for a philosopher to realise  
that anyone really is confining his     
discussion within the limits that ,i    
have set before you4 ,the boundary is   
set up just where he is beginning to get
 excited4 ,but ,i submit to you that    
among the necessary prolegomena for     
philosophy and for natural science is a 
thorough understanding of the types of  
entities1 and types of relations among  
those entities1 which are disclosed to  
us in our perceptions of nature4        
,,chapter ,,iii  ,,time   ,the two      
previous lectures of this course have   
been mainly critical4 ,in the present   
lecture ,i propose to enter upon a      
survey of the kinds of entities which   
are posited for knowledge in            
sense-awareness4 ,my purpose is to      
investigate the sorts of relations which

 these entities of various kinds can    
bear to each other4 ,a classification of
 natural entities is the beginning of   
natural philosophy4 ,to-day we commence 
with the consideration of ,time4  ,in   
the first place there is posited for us 
a general fact3 namely1 something is    
going on2 there is an occurrence for    
definition4  ,this general fact at once 
yields for our apprehension two factors1
 which ,i will name1 the 'discerned' and
 the 'discernible4' ,the discerned is   
comprised of those elements of the      
general fact which are discriminated    
with their own individual peculiarities4
 ,it is the field directly perceived4   
,but the entities of this field have    
relations to other entities which are   
not particularly discriminated in this  
individual way4 ,these other entities   
are known merely as the relata in       
relation to the entities of the         
discerned field4 ,such an entity is     
merely a 'something' which has          
such-and-such definite relations to some

 definite entity or entities in the     
discerned field4 ,as being thus related1
 they are--owing to the particular      
character of these relations--known as  
elements of the general fact which is   
going on4 ,but we are not aware of them 
except as entities fulfilling the       
functions of relata in these relations4 
,thus the complete general fact1 posited
 as occurring1 comprises both sets of   
entities1 namely the entities perceived 
in their own individuality and other    
entities merely apprehended as relata   
without further definition4 ,this       
complete general fact is the discernible
 and it comprises the discerned4 ,the   
discernible is all nature as disclosed  
in that sense-awareness1 and extends    
beyond and comprises all of nature as   
actually discriminated or discerned in  
that sense-awareness4 ,the discerning or
 discrimination of nature is a peculiar 
awareness of special factors in nature  
in respect to their peculiar characters4
 ,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 discernment4 ,this       
peculiarity of knowledge is what ,i call
 its unexhaustive character4 ,this      
character may be metaphorically         
described by the statement that nature  
as perceived always has a ragged edge4  
,for example1 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 room4 ,the junction
 of the interior world of the room with 
the exterior world beyond is never      
sharp4 ,sounds and subtler factors      
disclosed in sense-awareness float in   
from the outside4 ,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 sense4 ,for       
example we see something which we do not

 touch and we touch something which we  
do not see1 and we have a general sense 
of the space-relations between the      
entity disclosed in sight and the entity
 disclosed in touch4 ,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         
determined4 ,but the general system of  
space-relations relating the entity     
discriminated by sight with that        
discriminated by sight is not dependent 
on the peculiar character of the other  
entity as reported by the alternative   
sense4 ,for example1 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     
touch4 ,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 character4 ,an entity    
merely known as spatially related to    
some discerned entity is what we mean by
 the bare idea of 'place4' ,the concept 
of place marks the disclosure in        
sense-awareness of entities in nature   
known merely by their spatial relations 
to discerned entities4 ,it is the       
disclosure of the discernible by means  
of its relations to the discerned4      
,this disclosure of an entity as a      
relatum without further specific        
discrimination of quality is the basis  
of our concept of significance4 ,in the 
above example the thing seen was        
significant1 in that it disclosed its   
spatial relations to other entities not 
necessarily otherwise entering into     
consciousness4 ,thus significance is    
relatedness1 but it is relatedness with 
the emphasis on one end only of the     
relation4  ,for the sake of simplicity  

,i have confined the argument to spatial
 relations2 but the same considerations 
apply to temporal relations4 ,the       
concept of 'period of time' marks the   
disclosure in sense-awareness of        
entities in nature known merely by their
 temporal relations to discerned        
entities4 ,still further1 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 language4     
,what we discern is the specific        
character of a place through a period of
 time4 ,this is what ,i mean by an      
'event4' ,we discern some specific      
character of an event4 ,but in          
discerning an event we are also aware of
 its significance as a relatum in the   
structure of events4 ,this structure of 
events is the complex of events as      
related by the two relations of         
extension and cogredience4 ,the most    
simple expression of the properties of  
this structure are to be found in our   

spatial and temporal relations4 ,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 structure4  ,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 structure4 ,these   
signified events must include events in 
the remote past as well as events in the
 future4 ,we are aware of these as the  
far off periods of unbounded time4 ,but 
there is another classification of      
events which is also inherent in        
sense-awareness4 ,these are the events  
which share the immediacy of the        
immediately present discerned events4   
,these are the events whose characters  
together with those of the discerned    
events comprise all nature present for  

discernment4 ,they form the complete    
general fact which is all nature now    
present as disclosed in that            
sense-awareness4 ,it is in this second  
classification of events that the       
differentiation of space from time takes
 its origin4 ,the germ of space is to be
 found in the mutual relations of events
 within the immediate general fact which
 is all nature now discernible1 namely  
within the one event which is the       
totality of present nature4 ,the        
relations of other events to this       
totality of nature form the texture of  
time4  ,the unity of this general       
present fact is expressed by the concept
 of simultaneity4 ,the general fact is  
the whole simultaneous occurrence of    
nature which is now for sense-awareness4
 ,this general fact is what ,i have     
called the discernible4 ,but in future  
,i will call it a 'duration1' meaning   
thereby a certain whole of nature which 
is limited only by the property of being
 a simultaneity4 ,further in obedience  

to the principle of comprising within   
nature the whole terminus of            
sense-awareness1 simultaneity must not  
be conceived as an irrelevant mental    
concept imposed upon nature4 ,our       
sense-awareness posits for immediate    
discernment a certain whole1 here called
 a 'duration'2 thus a duration is a     
definite natural entity4 ,a duration is 
discriminated as a complex of partial   
events1 and the natural entities which  
are components of this complex are      
thereby said to be 'simultaneous with   
this duration4' ,also in a derivative   
sense they are simultaneous with each   
other in respect to this duration4 ,thus
 simultaneity is a definite natural     
relation4 ,the word 'duration' is       
perhaps unfortunate in so far as it     
suggests a mere abstract stretch of     
time4 ,this is not what ,i mean4 ,a     
duration is a concrete slab of nature   
limited by simultaneity which is an     
essential factor disclosed in           
sense-awareness4  ,nature is a process4 

,as in the case of everything directly  
exhibited in sense-awareness1 there can 
be no explanation of this characteristic
 of nature4 ,all that can be done is to 
use language which may speculatively    
demonstrate it1 and also to express the 
relation of this factor in nature to    
other factors4  ,it is an exhibition of 
the process of nature that each duration
 happens and passes4 ,the process of    
nature can also be termed the passage of
 nature4 ,i definitely refrain at this  
stage from using the word 'time1' since 
the measurable time of science and of   
civilised life generally merely exhibits
 some aspects of the more fundamental   
fact of the passage of nature4 ,i       
believe that in this doctrine ,i am in  
full accord with ,bergson1 though he    
uses 'time' for the fundamental fact    
which ,i call the 'passage of nature4'  
,also the passage of nature is exhibited
 equally in spatial transition as well  
as in temporal transition4 ,it is in    
virtue of its passage that nature is    

always moving on4 ,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    
other1 but the terminus of each act is  
also unique and is the terminus of no   
other act4 ,sense-awareness seizes its  
only chance and presents for knowledge  
something which is for it alone4  ,there
 are two senses in which the terminus of
 sense-awareness is unique4 ,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 conditions4     
,there is an important distinction      
between the two cases4 7i7 ,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 mind1 but the   
two corresponding durations which are   
respectively related by simultaneity to 

the two discerned components are        
necessarily distinct4 ,this is an       
exhibition of the temporal passage of   
nature2 namely1 one duration has passed 
into the other4 ,thus not only is the   
passage of nature an essential character
 of nature in its rle of the terminus of
 sense-awareness1 but it is also        
essential for sense-awareness in itself4
 ,it is this truth which makes time     
appear to extend beyond nature4 ,but    
what extends beyond nature to mind is   
not the serial and measurable time1     
which exhibits merely the character of  
passage in nature1 but the quality of   
passage itself which is in no way       
measurable except so far as it obtains  
in nature4 ,that is to say1 'passage' is
 not measurable except as it occurs in  
nature in connexion with extension4 ,in 
passage we reach a connexion of nature  
with the ultimate metaphysical reality4 
,the quality of passage in durations is 
a particular exhibition in nature of a  
quality which extends beyond nature4    

,for example passage is a quality not   
only of nature1 which is the thing      
known1 but also of sense-awareness which
 is the procedure of knowing4 ,durations
 have all the reality that nature has1  
though what that may be we need not now 
determine4 ,the measurableness of time  
is derivative from the properties of    
durations4 ,so also is the serial       
character of time4 ,we shall find that  
there are in nature competing serial    
time-systems derived from different     
families of durations4 ,these are a     
peculiarity of the character of passage 
as it is found in nature4 ,this         
character has the reality of nature1 but
 we must not necessarily transfer       
natural time to extra-natural entities4 
7ii7 ,for two minds1 the discerned      
components of the general facts         
exhibited in their respective acts of   
sense-awareness must be different4 ,for 
each mind1 in its awareness of nature is
 aware of a certain complex of related  
natural entities in their relations to  

the living body as a focus4 ,but the    
associated durations may be identical4  
,here we are touching on that character 
of the passage nature which issues in   
the spatial relations of simultaneous   
bodies4 ,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 beings4 ,we are 
here considering the spatial side of the
 passage of nature4 ,passage in this    
aspect of it also seems to extend beyond
 nature to mind4  ,it is important to   
distinguish simultaneity from           
instantaneousness4 ,i lay no stress on  
the mere current usage of the two terms4
 ,there are two concepts which ,i want  
to distinguish1 and one ,i call         
simultaneity and the other              
instantaneousness4 ,i hope that the     
words are judiciously chosen2 but it    
really does not matter so long as ,i    
succeed in explaining my meaning4       
,simultaneity is the property of a group

 of natural elements which in some sense
 are components of a duration4 ,a       
duration can be all nature present as   
the immediate fact posited by           
sense-awareness4 ,a duration retains    
within itself the passage of nature4    
,there are within it antecedents and    
consequents which are also durations    
which may be the complete specious      
presents of quicker consciousnesses4 ,in
 other words a duration retains temporal
 thickness4 ,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
 nature4 ,thus simultaneity is an       
ultimate factor in nature1 immediate for
 sense-awareness4  ,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  

nature4 ,instantaneousness is the       
concept of all nature at an instant1    
where an instant is conceived as        
deprived of all temporal extension4 ,for
 example we conceive of the distribution
 of matter in space at an instant4 ,this
 is a very useful concept in science    
especially in applied mathematics2 but  
it is a very complex idea so far as     
concerns its connexions with the        
immediate facts of sense-awareness4     
,there is no such thing as nature at an 
instant posited by sense-awareness4     
,what sense-awareness delivers over for 
knowledge is nature through a period4   
,accordingly nature at an instant1 since
 it is not itself a natural entity1 must
 be defined in terms of genuine natural 
entities4 ,unless we do so1 our science1
 which employs the concept of           
instantaneous nature1 must abandon all  
claim to be founded upon observation4   
,i will use the term 'moment' to mean   
'all nature at an instant4' ,a moment1  
in the sense in which the term is here  

used1 has no temporal extension1 and is 
in this respect to be contrasted with a 
duration which has such extension4 ,what
 is directly yielded to our knowledge by
 sense-awareness is a duration4         
,accordingly we have now to explain how 
moments are derived from durations1 and 
also to explain the purpose served by   
their introduction4  ,a moment is a     
limit to which we approach as we confine
 attention to durations of minimum      
extension4 ,natural relations among the 
ingredients of a duration gain in       
complexity as we consider durations of  
increasing temporal extension4          
,accordingly there is an approach to    
ideal simplicity as we approach an ideal
 diminution of extension4  ,the word    
'limit' has a precise signification in  
the logic of number and even in the     
logic of non-numerical one-dimensional  
series4 ,as used here it is so far a    
mere metaphor1 and it is necessary to   
explain directly the concept which it is
 meant to indicate4  ,durations can have

 the two-termed relational property of  
extending one over the other4 ,thus the 
duration which is all nature during a   
certain minute extends over the duration
 which is all nature during the #cjth   
second of that minute4 ,this relation of
 'extending over'--'extension' as ,i    
shall call it--is a fundamental natural 
relation whose field comprises more than
 durations4 ,it is a relation which two 
limited events can have to each other4  
,furthermore as holding between         
durations the relation appears to refer 
to the purely temporal extension4 ,i    
shall however maintain that the same    
relation of extension lies at the base  
both of temporal and spatial extension4 
,this discussion can be postponed2 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 durations4  ,the       
concept of extension exhibits in thought
 one side of the ultimate passage of    
nature4 ,this relation holds because of 

the special character which passage     
assumes in nature2 it is the relation   
which in the case of durations expresses
 the properties of 'passing over4' ,thus
 the duration which was one definite    
minute passed over the duration which   
was its #cjth second4 ,the duration of  
the #cjth second was part of the        
duration of the minute4 ,i shall use the
 terms 'whole' and 'part' exclusively in
 this sense1 that the 'part' is an event
 which is extended over by the other    
event which is the 'whole4' ,thus in my 
nomenclature 'whole' and 'part' refer   
exclusively to this fundamental relation
 of extension2 and accordingly in this  
technical usage only events can be      
either wholes or parts4  ,the continuity
 of nature arises from extension4 ,every
 event extends over other events1 and   
every event is extended over by other   
events4 ,thus in the special case of    
durations which are now the only events 
directly under consideration1 every     
duration is part of other durations2 and

 every duration has other durations     
which are parts of it4 ,accordingly     
there are no maximum durations and no   
minimum durations4 ,thus there is no    
atomic structure of durations1 and the  
perfect definition of a duration1 so as 
to mark out its individuality and       
distinguish it from highly analogous    
durations over which it is passing1 or  
which are passing over it1 is an        
arbitrary postulate of thought4         
,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      
durations4 ,this is one instance of the 
indeterminateness of sense-awareness4   
,exactness is an ideal of thought1 and  
is only realised in experience by the   
selection of a route of approximation4  
,the absence of maximum and minimum     
durations does not exhaust the          
properties of nature which make up its  

continuity4 ,the passage of nature      
involves the existence of a family of   
durations4 ,when two durations belong to
 the same family either one contains the
 other1 or they overlap each other in a 
subordinate duration without either     
containing the other2 or they are       
completely separate4 ,the excluded case 
is that of durations overlapping in     
finite events but not containing a third
 duration as a common part4  ,it is     
evident that the relation of extension  
is transitive2 namely as applied to     
durations1 if duration ,a is part of    
duration ,b1 and duration ,b is part of 
duration ,c1 then ,a is part of ,c4     
,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 separate4  ,furthermore the 
converse of this proposition holds2     
namely1 if two durations have other     
durations which are parts of both or if 

the two durations are completely        
separate1 then they belong to the same  
family4  ,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 durations4 ,it can be  
stated in this way3 ,there are durations
 which contain as parts any two         
durations of the same family4 ,for      
example a week contains as parts any two
 of its days4 ,it is evident that a     
containing duration satisfies the       
conditions for belonging to the same    
family as the two contained durations4  
,we are now prepared to proceed to the  
definition of a moment of time4         
,consider a set of durations all taken  
from the same family4 ,let it have the  
following properties3 7i7 of any two    
members of the set one contains the     
other as a part1 and 7ii7 there is no   
duration which is a common part of every
 member of the set4  ,now the relation  
of whole and part is asymmetrical2 and  

by this ,i mean that if ,a is part of   
,b1 then ,b is not part of ,a4 ,also we 
have already noted that the relation is 
transitive4 ,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 extension4 
,the series may start with any          
arbitrarily assumed duration of any     
temporal extension1 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 toy4 ,but the set differs 
from the toy in this particular3 the toy
 has a smallest box which forms the end 
box of its series2 but the set of       
durations can have no smallest duration 
nor can it converge towards a duration  
as its limit4 ,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 violated4  ,i will call    
such a set of durations an 'abstractive 
set' of durations4 ,it is evident that  
an abstractive set as we pass along it  
converges to the ideal of all nature    
with no temporal extension1 namely1 to  
the ideal of all nature at an instant4  
,but this ideal is in fact the ideal of 
a nonentity4 ,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 considered4   
,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 duration4  
,the laws relating these quantitative   
limits are the laws of nature 'at an    
instant1' although in truth there is no 
nature at an instant and there is only  

the abstractive set4 ,thus an           
abstractive set is effectively the      
entity meant when we consider an instant
 of time without temporal extension4 ,it
 subserves all the necessary purposes of
 giving a definite meaning to the       
concept of the properties of nature at  
an instant4 ,i fully agree that this    
concept is fundamental in the expression
 of physical science4 ,the difficulty is
 to express our meaning in terms of the 
immediate deliverances of               
sense-awareness1 and ,i offer the above 
explanation as a complete solution of   
the problem4  ,in this explanation a    
moment is the set of natural properties 
reached by a route of approximation4 ,an
 abstractive series is a route of       
approximation4 ,there are different     
routes of approximation to the same     
limiting set of the properties of       
nature4 ,in other words there are       
different abstractive sets which are to 
be regarded as routes of approximation  
to the same moment4 ,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 cases4 ,such       
details are not suitable for exposition 
in these lectures1 and ,i have dealt    
with them fully elsewhere#e4  #e ,cf4   
,an ,enquiry concerning the ,principles 
of ,natural ,knowledge1 ,cambridge      
,university ,press1 #aiai4  ,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 convergence4 ,with this        
definition 7provided 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 approximation7
 a moment is merely a class of sets of  
durations whose relations of extension  
in respect to each other have certain   
definite peculiarities4 ,we may term    
these connexions of the component       

durations the 'extrinsic' properties of 
a moment2 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 sets4  
,these are the properties of nature 'at 
that moment1' or 'at that instant4'     
,the durations which enter into the     
composition of a moment all belong to   
one family4 ,thus there is one family of
 moments corresponding to one family of 
durations4 ,also if we take two moments 
of the same family1 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 moment4 ,thus  
the two moments in their intrinsic      
properties must exhibit the limits of   
completely different states of nature4  
,in this sense the two moments are      
completely separated4 ,i will call two  
moments of the same family 'parallel4'  
,corresponding to each duration there   

are two moments of the associated family
 of moments which are the boundary      
moments of that duration4 ,a 'boundary  
moment' of a duration can be defined in 
this way4 ,there are durations of the   
same family as the given duration which 
overlap it but are not contained in it4 
,consider an abstractive set of such    
durations4 ,such a set defines a moment 
which is just as much without the       
duration as within it4 ,such a moment is
 a boundary moment of the duration4     
,also we call upon our sense-awareness  
of the passage of nature to inform us   
that there are two such boundary        
moments1 namely the earlier one and the 
later one4 ,we will call them the       
initial and the final boundaries4       
,there are also moments of the same     
family such that the shorter durations  
in their composition are entirely       
separated from the given duration4 ,such
 moments will be said to lie 'outside'  
the given duration4 ,again other moments
 of the family are such that the shorter

 durations in their composition are     
parts of the given duration4 ,such      
moments are said to lie 'within' the    
given duration or to 'inhere' in it4    
,the whole family of parallel moments is
 accounted for in this way by reference 
to any given duration of the associated 
family of durations4 ,namely1 there are 
moments of the family which lie without 
the given duration1 there are the two   
moments which are the boundary moments  
of the given duration1 and the moments  
which lie within the given duration4    
,furthermore any two moments of the same
 family are the boundary moments of some
 one duration of the associated family  
of durations4  ,it is now possible to   
define the serial relation of temporal  
order among the moments of a family4    
,for let ,a and ,c be any two moments of
 the family1 these moments are the      
boundary moments of one duration d of   
the associated family1 and any moment ,b
 which lies within the duration d will  
be said to lie between the moments ,a   

and ,c4 ,thus the three-termed relation 
of 'lying-between' as relating three    
moments ,a1 ,b1 and ,c is completely    
defined4 ,also our knowledge of the     
passage of nature assures us that this  
relation distributes the moments of the 
family into a serial order4 ,i abstain  
from enumerating the definite properties
 which secure this result1 ,i have      
enumerated them in my recently published
 book#f to which ,i have already        
referred4 ,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 past4  #f ,cf4 ,enquiry4    
,such an ordered series of moments is   
what we mean by time defined as a       
series4 ,each element of the series     
exhibits an instantaneous state of      
nature4 ,evidently this serial time is  
the result of an intellectual process of
 abstraction4 ,what ,i have done is to  
give precise definitions of the         

procedure by which the abstraction is   
effected4 ,this procedure is merely a   
particular case of the general method   
which in my book ,i name the 'method of 
extensive abstraction4' ,this serial    
time is evidently not the very passage  
of nature itself4 ,it exhibits some of  
the natural properties which flow from  
it4 ,the state of nature 'at a moment'  
has evidently lost this ultimate quality
 of passage4 ,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 series4  ,nothing has 
yet been said as to the measurement of  
time4 ,such measurement does not follow 
from the mere serial property of time2  
it requires a theory of congruence which
 will be considered in a later lecture4 
,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 theories4 ,the lapse  
of time is a measurable serial quantity4
 ,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 experience4 ,our        
difficulties only begin when we ask what
 it is that is measured4 ,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 proportions4  ,we have   
first to make up our minds whether time 
is to be found in nature or nature is to
 be found in time4 ,the difficulty of   
the latter alternative--namely of making
 time prior to nature--is that time then
 becomes a metaphysical enigma4 ,what   
sort of entities are its instants or its
 periods8 ,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 shadow4 ,there is time   
because there are happenings1 and apart 
from happenings there is nothing4  ,it  
is necessary however to make a          
distinction4 ,in some sense time extends
 beyond nature4 ,it is not true that a  
timeless sense-awareness and a timeless 
thought combine to contemplate a timeful
 nature4 ,sense-awareness and thought   
are themselves processes as well as     
their termini in nature4 ,in other words
 there is a passage of sense-awareness  
and a passage of thought4 ,thus the     
reign of the quality of passage extends 
beyond nature4 ,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  
nature4 ,a temporal series1 as we have  
defined it1 represents merely certain   
properties of a family of               
durations--properties indeed which      
durations only possess because of their 

partaking of the character of passage1  
but on the other hand properties which  
only durations do possess4 ,accordingly 
time in the sense of a measurable       
temporal series is a character of nature
 only1 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 procedures4  
,so far the passage of nature has been  
considered in connexion with the passage
 of durations2 and in this connexion it 
is peculiarly associated with temporal  
series4 ,we must remember however that  
the character of passage is peculiarly  
associated with the extension of events1
 and that from this extension spatial   
transition arises just as much as       
temporal transition4 ,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 nature1 otherwise we     

shall have too narrow an idea of the    
essence of passage4  ,it is necessary to
 dwell on the subject of sense-awareness
 in this connexion as an example of the 
way in which time concerns mind1        
although measurable time is a mere      
abstract from nature and nature is      
closed to mind4  ,consider              
sense-awareness--not its terminus which 
is nature1 but sense-awareness in itself
 as a procedure of mind4                
,sense-awareness is a relation of mind  
to nature4 ,accordingly we are now      
considering mind as a relatum in        
sense-awareness4 ,for mind there is the 
immediate sense-awareness and there is  
memory4 ,the distinction between memory 
and the present immediacy has a double  
bearing4 ,on the one hand it discloses  
that mind is not impartially aware of   
all those natural durations to which it 
is related by awareness4 ,its awareness 
shares in the passage of nature4 ,we can
 imagine a being whose awareness1       
conceived as his private possession1    

suffers no transition1 although the     
terminus of his awareness is our own    
transient nature4 ,there is no essential
 reason why memory should not be raised 
to the vividness of the present fact2   
and then from the side of mind1 ,what is
 the difference between the present and 
the past8 ,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 order4 ,accordingly we  
must admit that though we can imagine   
that mind in the operation of           
sense-awareness might be free from any  
character of passage1 yet in point of   
fact our experience of sense-awareness  
exhibits our minds as partaking in this 
character4  ,on the other hand the mere 
fact of memory is an escape from        
transience4 ,in memory the past is      
present4 ,it is not present as          
overleaping the temporal succession of  
nature1 but it is present as an         
immediate fact for the mind4            

,accordingly memory is a disengagement  
of the mind from the mere passage of    
nature2 for what has passed for nature  
has not passed for mind4  ,furthermore  
the distinction between memory and the  
immediate present is not so clear as it 
is conventional to suppose4 ,there is an
 intellectual theory of time as a moving
 knife-edge1 exhibiting a present fact  
without temporal extension4 ,this theory
 arises from the concept of an ideal    
exactitude of observation4 ,astronomical
 observations are successively refined  
to be exact to tenths1 to hundredths1   
and to thousandths of seconds4 ,but the 
final refinements are arrived at by a   
system of averaging1 and even then      
present us with a stretch of time as a  
margin of error4 ,here error is merely a
 conventional term to express the fact  
that the character of experience does   
not accord with the ideal of thought4 ,i
 have already explained how the concept 
of a moment conciliates the observed    
fact with this ideal2 namely1 there is a

 limiting simplicity in the quantitative
 expression of the properties of        
durations1 which is arrived at by       
considering any one of the abstractive  
sets included in the moment4 ,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          
properties4  ,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
 thickness4 ,this immediate duration is 
not clearly marked out for our          
apprehension4 ,its earlier boundary is  
blurred by a fading into memory1 and its
 later boundary is blurred by an        
emergence from anticipation4 ,there is  
no sharp distinction either between     
memory and the present immediacy or     
between the present immediacy and       
anticipation4 ,the present is a wavering

 breadth of boundary between the two    
extremes4 ,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 fact4 ,our own   
present has its antecedents and its     
consequents1 and for the imaginary being
 all nature has its antecedent and its  
consequent durations4 ,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 duration4  ,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 it4 ,we may         
speculate1 if we like1 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 being4   

,but this is a speculation in which we  
have no concern4 ,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 time1 but that  
it is derivatively in time and in space 
by reason of the peculiar alliance of   
its passage with the passage of nature4 
,thus mind is in time and in space in a 
sense peculiar to itself4 ,this has been
 a long discussion to arrive at a very  
simple and obvious conclusion4 ,we all  
feel that in some sense our minds are   
here in this room and at this time4 ,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 positions4   
,the fundamental distinction to remember
 is that immediacy for sense-awareness  
is not the same as instantaneousness for
 nature4 ,this last conclusion bears on 
the next discussion with which ,i will  

terminate this lecture4 ,this question  
can be formulated thus1 ,can alternative
 temporal series be found in nature8  ,a
 few years ago such a suggestion would  
have been put aside as being            
fantastically impossible4 ,it would have
 had no bearing on the science then     
current1 and was akin to no ideas which 
had ever entered into the dreams of     
philosophy4 ,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 ages1 and were accepted with 
as little critical research4 ,i will    
call this natural philosophy            
'materialism4' ,not only were men of    
science materialists1 but also adherents
 of all schools of philosophy4 ,the     
idealists only differed from the        
philosophic materialists on question of 
the alignment of nature in reference to 
mind4 ,but no one had any doubt that the
 philosophy of nature considered in     

itself was of the type which ,i have    
called materialism4 ,it is the          
philosophy which ,i have already        
examined in my two lectures of this     
course preceding the present one4 ,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 time4 ,furthermore the      
mutual relations of the material        
entities at each instant formed these   
entities into a spatial configuration in
 an unbounded space4 ,it would seem that
 space--on this theory--would be as     
instantaneous as the instants1 and that 
some explanation is required of the     
relations between the successive        
instantaneous spaces4 ,the materialistic
 theory is however silent on this point2
 and the succession of instantaneous    
spaces is tacitly combined into one     
persistent space4 ,this theory is a     
purely intellectual rendering of        

experience which has had the luck to get
 itself formulated at the dawn of       
scientific thought4 ,it has dominated   
the language and the imagination of     
science since science flourished in     
,alexandria1 with the result that it is 
now hardly possible to speak without    
appearing to assume its immediate       
obviousness4  ,but when it is distinctly
 formulated in the abstract terms in    
which ,i have just stated it1 the theory
 is very far from obvious4 ,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 materialism4 ,this trinity is   
composed 7i7 of the temporal series of  
extensionless instants1 7ii7 of the     
aggregate of material entities1 and     
7iii7 of space which is the outcome of  
relations of matter4  ,there is a wide  
gap between these presuppositions of the
 intellectual theory of materialism and 
the immediate deliverances of           

sense-awareness4 ,i do not question that
 this materialistic trinity embodies    
important characters of nature4 ,but it 
is necessary to express these characters
 in terms of the facts of experience4   
,this is exactly what in this lecture ,i
 have been endeavouring to do so far as 
time is concerned2 and we have now come 
up against the question1 ,is there only 
one temporal series8 ,the uniqueness of 
the temporal series is presupposed in   
the materialist philosophy of nature4   
,but that philosophy is merely a theory1
 like the ,aristotelian scientific      
theories so firmly believed in the      
middle ages4 ,if in this lecture ,i have
 in any way succeeded in getting behind 
the theory to the immediate facts1 the  
answer is not nearly so certain4 ,the   
question can be transformed into this   
alternative form1 ,is there only one    
family of durations8 ,in this question  
the meaning of a 'family of durations'  
has been defined earlier in this        
lecture4 ,the answer is now not at all  

obvious4 ,on the materialistic theory   
the instantaneous present is the only   
field for the creative activity of      
nature4 ,the past is gone and the future
 is not yet4 ,thus 7on this theory7 the 
immediacy of perception is of an        
instantaneous present1 and this unique  
present is the outcome of the past and  
the promise of the future4 ,but we deny 
this immediately given instantaneous    
present4 ,there is no such thing to be  
found in nature4 ,as an ultimate fact it
 is a nonentity4 ,what is immediate for 
sense-awareness is a duration4 ,now a   
duration has within itself a past and a 
future2 and the temporal breadths of the
 immediate durations of sense-awareness 
are very indeterminate and dependent on 
the individual percipient4 ,accordingly 
there is no unique factor in nature     
which for every percipient is           
pre-eminently and necessarily the       
present4 ,the passage of nature leaves  
nothing between the past and the future4
 ,what we perceive as present is the    

vivid fringe of memory tinged with      
anticipation4 ,this vividness lights up 
the discriminated field within a        
duration4 ,but no assurance can thereby 
be given that the happenings of nature  
cannot be assorted into other durations 
of alternative families4 ,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 durations4 
,there is not the slightest reason to   
believe that this is so4 ,indeed if my  
theory of nature be correct1 it will not
 be the case4  ,the materialistic theory
 has all the completeness of the thought
 of the middle ages1 which had a        
complete answer to everything1 be it in 
heaven or in hell or in nature4 ,there  
is a trimness about it1 with its        
instantaneous present1 its vanished     
past1 its non-existent future1 and its  
inert matter4 ,this trimness is very    
medieval and ill accords with brute     
fact4  ,the theory which ,i am urging   

admits a greater ultimate mystery and a 
deeper ignorance4 ,the past and the     
future meet and mingle in the           
ill-defined present4 ,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 operate4 ,its   
operative presence which is now urging  
nature forward must be sought for       
throughout the whole1 in the remotest   
past as well as in the narrowest breadth
 of any present duration4 ,perhaps also 
in the unrealised future4 ,perhaps also 
in the future which might be as well as 
the actual future which will be4 ,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             
intelligence4     ,,chapter ,,iv  ,,the 
,,method ,,of ,,extensive ,,abstraction 
,to-day's lecture must commence with the
 consideration of limited events4 ,we   
shall then be in a position to enter    

upon an investigation of the factors in 
nature which are represented by our     
conception of space4  ,the duration     
which is the immediate disclosure of our
 sense-awareness is discriminated into  
parts4 ,there is the part which is the  
life of all nature within a room1 and   
there is the part which is the life of  
all nature within a table in the room4  
,these parts are limited events4 ,they  
have the endurance of the present       
duration1 and they are parts of it4 ,but
 whereas a duration is an unlimited     
whole and in a certain limited sense is 
all that there is1 a limited event      
possesses a completely defined          
limitation of extent which is expressed 
for us in spatio-temporal terms4  ,we   
are accustomed to associate an event    
with a certain melodramatic quality4 ,if
 a man is run over1 that is an event    
comprised within certain spatio-temporal
 limits4 ,we are not accustomed to      
consider the endurance of the ,great    
,pyramid throughout any definite day as 

an event4 ,but the natural fact which is
 the ,great ,pyramid throughout a day1  
meaning thereby all nature within it1 is
 an event of the same character as the  
man's accident1 meaning thereby all     
nature with spatio-temporal limitations 
so as to include the man and the motor  
during the period when they were in     
contact4  ,we are accustomed to analyse 
these events into three factors1 time1  
space1 and material4 ,in fact1 we at    
once apply to them the concepts of the  
materialistic theory of nature4 ,i do   
not deny the utility of this analysis   
for the purpose of expressing important 
laws of nature4 ,what ,i am denying is  
that anyone of these factors is posited 
for us in sense-awareness in concrete   
independence4 ,we perceive one unit     
factor in nature2 and this factor is    
that something is going on then--there4 
,for example1 we perceive the going-on  
of the ,great ,pyramid in its relations 
to the goings-on of the surrounding     
,egyptian events4 ,we are so trained1   

both by language and by formal teaching 
and by the resulting convenience1 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-awareness4 ,it is    
this unit factor1 retaining in itself   
the passage of nature1 which is the     
primary concrete element discriminated  
in nature4 ,these primary factors are   
what ,i mean by events4  ,events are the
 field of a two-termed relation1 namely 
the relation of extension which was     
considered in the last lecture4 ,events 
are the things related by the relation  
of extension4 ,if an event ,a extends   
over an event ,b1 then ,b is 'part of'  
,a1 and ,a is a 'whole' of which ,b is a
 part4 ,whole and part are invariably   
used in these lectures in this definite 
sense4 ,it follows that in reference to 
this relation any two events ,a and ,b  
may have any one of four relations to   
each other1 namely 7i7 ,a may extend    

over ,b1 or 7ii7 ,b may extend over ,a1 
or 7iii7 ,a and ,b may both extend over 
some third event ,c1 but neither over   
the other1 or 7iv7 ,a and ,b may be     
entirely separate4 ,these alternatives  
can obviously be illustrated by ,euler's
 diagrams as they appear in logical     
textbooks4  ,the continuity of nature is
 the continuity of events4 ,this        
continuity is merely the name for the   
aggregate of a variety of properties of 
events in connexion with the relation of
 extension4  ,in the first place1 this  
relation is transitive2 secondly1 every 
event contains other events as parts of 
itself2 thirdly every event is a part of
 other events2 fourthly given any two   
finite events there are events each of  
which contains both of them as parts2   
and fifthly there is a special relation 
between events which ,i term 'junction4'
  ,two events have junction when there  
is a third event of which both events   
are parts1 and which is such that no    
part of it is separated from both of the

 two given events4 ,thus two events with
 junction make up exactly one event     
which is in a sense their sum4  ,only   
certain pairs of events have this       
property4 ,in general any event         
containing two events also contains     
parts which are separated from both     
events4  ,there is an alternative       
definition of the junction of two events
 which ,i have adopted in my recent     
book#g4 ,two events have junction when  
there is a third event such that 7i7 it 
overlaps both events and 7ii7 it has no 
part which is separated from both the   
given events4 ,if either of these       
alternative definitions is adopted as   
the definition of junction1 the other   
definition appears as an axiom          
respecting the character of junction as 
we know it in nature4 ,but we are not   
thinking of logical definition so much  
as the formulation of the results of    
direct observation4 ,there is a certain 
continuity inherent in the observed     
unity of an event1 and these two        

definitions of junction are really      
axioms based on observation respecting  
the character of this continuity4  #g   
,cf4 ,enquiry4  ,the relations of whole 
and part and of overlapping are         
particular cases of the junction of     
events4 ,but it is possible for events  
to have junction when they are separate 
from each other2 for example1 the upper 
and the lower part of the ,great        
,pyramid are divided by some imaginary  
horizontal plane4  ,the continuity which
 nature derives from events has been    
obscured by the illustrations which ,i  
have been obliged to give4 ,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 illustration4 ,this is a type of     
event which exhibits itself to us as the
 situation of a recognisable object2 and
 in the example chosen the object is so 
widely recognised that it has received a
 name4 ,an object is an entity of a     
different type from an event4 ,for      

example1 the event which is the life of 
nature within the ,great ,pyramid       
yesterday and to-day is divisible into  
two parts1 namely the ,great ,pyramid   
yesterday and the ,great ,pyramid       
to-day4 ,but the recognisable object    
which is also called the ,great ,pyramid
 is the same object to-day as it was    
yesterday4 ,i shall have to consider the
 theory of objects in another lecture4  
,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 object1 we have no        
language to distinguish the event from  
the object4 ,in the case of the ,great  
,pyramid1 the object is the perceived   
unit entity which as perceived remains  
self-identical throughout the ages2     
while the whole dance of molecules and  
the shifting play of the electromagnetic
 field are ingredients of the event4 ,an
 object is in a sense out of time4 ,it  
is only derivatively in time by reason  
of its having the relation to events    

which ,i term 'situation4' ,this        
relation of situation will require      
discussion in a subsequent lecture4     
,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 event4 ,wherever and   
whenever something is going on1 there is
 an event4 ,furthermore 'wherever and   
whenever' in themselves presuppose an   
event1 for space and time in themselves 
are abstractions from events4 ,it is    
therefore a consequence of this doctrine
 that something is always going on      
everywhere1 even in so-called empty     
space4 ,this conclusion is in accord    
with modern physical science which      
presupposes the play of an              
electromagnetic field throughout space  
and time4 ,this doctrine of science has 
been thrown into the materialistic form 
of an all-pervading ether4 ,but the     
ether is evidently a mere idle          
concept--in the phraseology which ,bacon
 applied to the doctrine of final       

causes1 it is a barren virgin4 ,nothing 
is deduced from it2 and the ether merely
 subserves the purpose of satisfying the
 demands of the materialistic theory4   
,the important concept is that of the   
shifting facts of the fields of force4  
,this is the concept of an ether of     
events which should be substituted for  
that of a material ether4  ,it requires 
no illustration to assure you that an   
event is a complex fact1 and the        
relations between two events form an    
almost impenetrable maze4 ,the clue     
discovered by the common sense of       
mankind and systematically utilised in  
science is what ,i have elsewhere#h     
called the law of convergence to        
simplicity by diminution of extent4  #h 
,cf4 ,organisation of ,thought1 pp4 #adf
 et seq4 ,williams and ,norgate1 #aiag4 
,if ,a and ,b are two events1 and ,a is 
part of ,a and ,b is part of ,b1 then in
 many respects the relations between the
 parts ,a and ,b will be simpler than   
the relations between ,a and ,b4 ,this  

is the principle which presides over all
 attempts at exact observation4  ,the   
first outcome of the systematic use of  
this law has been the formulation of the
 abstract concepts of ,time and ,space4 
,in the previous lecture ,i sketched how
 the principle was applied to obtain the
 time-series4 ,i now proceed to consider
 how the spatial entities are obtained  
by the same method4 ,the systematic     
procedure is identical in principle in  
both cases1 and ,i have called the      
general type of procedure the 'method of
 extensive abstraction4'  ,you will     
remember that in my last lecture ,i     
defined the concept of an abstractive   
set of durations4 ,this definition can  
be extended so as to apply to any       
events1 limited events as well as       
durations4 ,the only change that is     
required is the substitution of the word
 'event' for the word 'duration4'       
,accordingly an abstractive set of      
events is any set of events which       
possesses the two properties1 7i7 of any

 two members of the set one contains the
 other as a part1 and 7ii7 there is no  
event which is a common part of every   
member of the set4 ,such a set1 as you  
will remember1 has the properties of the
 ,chinese toy which is a nest of boxes1 
one within the other1 with the          
difference that the toy has a smallest  
box1 while the abstractive class has    
neither a smallest event nor does it    
converge to a limiting event which is   
not a member of the set4  ,thus1 so far 
as the abstractive sets of events are   
concerned1 an abstractive set converges 
to nothing4 ,there is the set with its  
members growing indefinitely smaller and
 smaller as we proceed in thought       
towards the smaller end of the series2  
but there is no absolute minimum of any 
sort which is finally reached4 ,in fact 
the set is just itself and indicates    
nothing else in the way of events1      
except itself4 ,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 nature4 ,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     
events4 ,in the case of events of       
considerable spatio-temporal extension  
this set of quantitative expressions is 
of bewildering complexity4 ,if e be an  
event1 let us denote by q7e7 the set of 
quantitative expressions defining its   
character including its connexions with 
the rest of nature4 ,let e1 e1 e1 etc4  
be an abstractive set1 the members being
 so arranged that each member such as en
 extends over all the succeeding members
 such as en#a1 en#b and so on4 ,then    
corresponding to the series      e1 e1  
e1 4441 en1 en#a1 4441  there is the    
series      q7e71 q7e71 q7e71 4441      
q7en71 q7en#a71 4444  ,call the series  

of events s and the series of           
quantitative expressions q7s74 ,the     
series s has no last term and no events 
which are contained in every member of  
the series4 ,accordingly the series of  
events converges to nothing4 ,it is just
 itself4 ,also the series q7s7 has no   
last term4 ,but the sets of homologous  
quantities running through the various  
terms of the series do converge to      
definite limits4 ,for example if ,q be a
 quantitative measurement found in q7e71
 and ,q the homologue to ,q to be found 
in q7e71 and ,q the homologue to ,q and 
,q to be found in q7e71 and so on1 then 
the series      ,q1 ,q1 ,q1 4441 ,qn1   
,qn#a1 4441  though it has no last term1
 does in general converge to a definite 
limit4 ,accordingly there is a class of 
limits l7s7 which is the class of the   
limits of those members of q7en7 which  
have homologues throughout the series   
q7s7 as n indefinitely increases4 ,we   
can represent this statement            
diagrammatically by using an arrow 77 to

 mean 'converges to4' ,then      e1 e1  
e1 4441 en1 en#a1 444  nothing1  and    
q7e71 q7e71 q7e71 4441 q7en71 q7en#a71  
444  l7s74  ,the mutual relations       
between the limits in the set l7s71 and 
also between these limits and the limits
 in other sets l7s71 l7s71 4441 which   
arise from other abstractive sets s1 s1 
etc41 have a peculiar simplicity4  ,thus
 the set s does indicate an ideal       
simplicity of natural relations1 though 
this simplicity is not the character of 
any actual event in s4 ,we can make an  
approximation to such a simplicity      
which1 as estimated numerically1 is as  
close as we like by considering an event
 which is far enough down the series    
towards the small end4 ,it will be noted
 that it is the infinite series1 as it  
stretches away in unending succession   
towards the small end1 which is of      
importance4 ,the arbitrarily large event
 with which the series starts has no    
importance at all4 ,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 modified4  ,i call the limiting    
character of natural relations which is 
indicated by an abstractive set1 the    
'intrinsic character' of the set2 also  
the properties1 connected with the      
relation of whole and part as concerning
 its members1 by which an abstractive   
set is defined together form what ,i    
call its 'extrinsic character4' ,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 time4 ,this emergence of a    
definite intrinsic character from an    
abstractive set is the precise meaning  
of the law of convergence4  ,for        
example1 we see a train approaching     
during a minute4 ,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

 us4 ,if we take one second of that     
minute1 the more limited event which is 
thus obtained is simpler in respect to  
its ingredients1 and shorter and shorter
 times such as a tenth of that second1  
or a hundredth1 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 instant4 ,furthermore    
there are different types of such       
convergence to simplicity4 ,for example1
 we can converge as above to the        
limiting character expressing nature at 
an instant within the whole volume of   
the train at that instant1 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 surface1 or to 
nature at an instant on some line within
 the train1 or to nature at an instant  
at some point of the train4 ,in the last

 case the simple limiting characters    
arrived at will be expressed as         
densities1 specific gravities1 and types
 of material4 ,furthermore we need not  
necessarily converge to an abstraction  
which involves nature at an instant4 ,we
 may converge to the physical           
ingredients of a certain point track    
throughout the whole minute4            
,accordingly there are different types  
of extrinsic character of convergence   
which lead to the approximation to      
different types of intrinsic characters 
as limits4  ,we now pass to the         
investigation of possible connexions    
between abstractive sets4 ,one set may  
'cover' another4 ,i define 'covering' as
 follows3 ,an abstractive set p covers  
an abstractive set q when every member  
of p contains as its parts some members 
of q4 ,it is evident that if any event e
 contains as a part any member of the   
set q1 then owing to the transitive     
property of extension every succeeding  
member of the small end of q is part of 

e4 ,in such a case ,i will say that the 
abstractive set q 'inheres in' the event
 e4 ,thus when an abstractive set p     
covers an abstractive set q1 the        
abstractive set q inheres in every      
member of p4  ,two abstractive sets may 
each cover the other4 ,when this is the 
case ,i shall call the two sets 'equal  
in abstractive force4' ,when there is no
 danger of misunderstanding ,i shall    
shorten this phrase by simply saying    
that the two abstractive sets are       
'equal4' ,the possibility of this       
equality of abstractive sets arises from
 the fact that both sets1 p and q1 are  
infinite series towards their small     
ends4 ,thus the equality means1 that    
given any event x belonging to p1 we can
 always by proceeding far enough towards
 the small end of q find an event y     
which is part of x1 and that then by    
proceeding far enough towards the small 
end of p we can find an event z which is
 part of y1 and so on indefinitely4     
,the importance of the equality of      

abstractive sets arises from the        
assumption that the intrinsic characters
 of the two sets are identical4 ,if this
 were not the case exact observation    
would be at an end4  ,it is evident that
 any two abstractive sets which are     
equal to a third abstractive set are    
equal to each other4 ,an 'abstractive   
element' is the whole group of          
abstractive sets which are equal to any 
one of themselves4 ,thus all abstractive
 sets belonging to the same element are 
equal and converge to the same intrinsic
 character4 ,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 facts4  ,if an abstractive
 set p covers an abstractive set q1 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
 member4 ,accordingly it is useful to   
stretch the meaning of the term         

'covering1' and to speak of one         
abstractive element 'covering' another  
abstractive element4 ,if we attempt in  
like manner to stretch the term 'equal' 
in the sense of 'equal in abstractive   
force1' it is obvious that an           
abstractive element can only be equal to
 itself4 ,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 extent4  ,when an abstractive element
 ,a covers an abstractive element ,b1   
the intrinsic character of ,a in a sense
 includes the intrinsic character of ,b4
 ,it results that statements about the  
intrinsic character of ,b are in a sense
 statements about the intrinsic         
character of ,a2 but the intrinsic      
character of ,a is more complex than    
that of ,b4  ,the abstractive elements  
form the fundamental elements of space  

and time1 and we now turn to the        
consideration of the properties involved
 in the formation of special classes of 
such elements4 ,in my last lecture ,i   
have already investigated one class of  
abstractive elements1 namely moments4   
,each moment is a group of abstractive  
sets1 and the events which are members  
of these sets are all members of one    
family of durations4 ,the moments of one
 family form a temporal series2 and1    
allowing the existence of different     
families of moments1 there will be      
alternative temporal series in nature4  
,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 relativity4  ,we now    
turn to space4 ,the first thing to do is
 to get hold of the class of abstractive
 elements which are in some sense the   

points of space4 ,such an abstractive   
element must in some sense exhibit a    
convergence to an absolute minimum of   
intrinsic character4 ,euclid has        
expressed for all time the general idea 
of a point1 as being without parts and  
without magnitude4 ,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 point4 
,furthermore1 points which are thus     
arrived at represent the ideal of events
 without any extension1 though there are
 in fact no such entities as these ideal
 events4 ,these points will not be the  
points of an external timeless space but
 of instantaneous spaces4 ,we ultimately
 want to arrive at the timeless space of
 physical science1 and also of common   
thought which is now tinged with the    
concepts of science4 ,it will be        
convenient to reserve the term 'point'  
for these spaces when we get to them4 ,i
 will therefore use the name            

'event-particles' for the ideal minimum 
limits to events4 ,thus an              
event-particle is an abstractive element
 and as such is a group of abstractive  
sets2 and a point--namely a point of    
timeless space--will be a class of      
event-particles4  ,furthermore there is 
a separate timeless space corresponding 
to each separate temporal series1 that  
is to each separate family of durations4
 ,we will come back to points in        
timeless spaces later4 ,i merely mention
 them now that we may understand the    
stages of our investigation4 ,the       
totality of event-particles will form a 
four-dimensional manifold1 the extra    
dimension arising from time--in other   
words--arising from the points of a     
timeless space being each a class of    
event-particles4  ,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 cover4 ,for  

then any other abstractive set which an 
abstractive set of an event-particle    
covered1 would be equal to it1 and would
 therefore be a member of the same      
event-particle4 ,accordingly an         
event-particle could cover no other     
abstractive element4 ,this is the       
definition which ,i originally proposed 
at a congress in ,paris in #aiadi4      
,there is however a difficulty involved 
in this definition if adopted without   
some further addition1 and ,i am now not
 satisfied with the way in which ,i     
attempted to get over that difficulty in
 the paper referred to4  #i ,cf4 ',la   
,thorie ,relationniste de l',espace1'   
,rev4 de ,mtaphysique et de ,morale1    
vol4 ,,xxiii1 #aiaf4  ,the difficulty is
 this3 ,when event-particles have once  
been defined it is easy to define the   
aggregate of event-particles forming the
 boundary of an event2 and thence to    
define the point-contact at their       
boundaries possible for a pair of events
 of which one is part of the other4 ,we 

can then conceive all the intricacies of
 tangency4 ,in particular we can        
conceive an abstractive set of which all
 the members have point-contact at the  
same event-particle4 ,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       
covers4 ,i state this difficulty at some
 length because its existence guides the
 development of our line of argument4   
,we have got to annex some condition to 
the root property of being covered by   
any abstractive set which it covers4    
,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 conditions4 ,accordingly we 
proceed in a general way suitable for   
employment beyond event-particles4  ,let
  be the name of any condition which    
some abstractive sets fulfil4 ,i say    

that an abstractive set is '-prime' when
 it has the two properties1 7i7 that it 
satisfies the condition  and 7ii7 that  
it is covered by every abstractive set  
which both is covered by it and         
satisfies the condition 4  ,in other    
words you cannot get any abstractive set
 satisfying the condition  which        
exhibits intrinsic character more simple
 than that of a -prime4  ,there are also
 the correlative abstractive sets which 
,i call the sets of -antiprimes4 ,an    
abstractive set is a -antiprime when it 
has the two properties1 7i7 that it     
satisfies the condition  and 7ii7 that  
it covers every abstractive set which   
both covers it and satisfies the        
condition 4 ,in other words you cannot  
get any abstractive set satisfying the  
condition  which exhibits an intrinsic  
character more complex than that of a   
-antiprime4  ,the intrinsic character of
 a -prime has a certain minimum of      
fullness among those abstractive sets   
which are subject to the condition of   

satisfying 2 whereas the intrinsic      
character of a -antiprime has a         
corresponding maximum of fullness1 and  
includes all it can in the              
circumstances4  ,let us first consider  
what help the notion of antiprimes could
 give us in the definition of moments   
which we gave in the last lecture4 ,let 
the condition  be the property of being 
a class whose members are all durations4
 ,an abstractive set which satisfies    
this condition is thus an abstractive   
set composed wholly of durations4 ,it is
 convenient then to define a moment as  
the group of abstractive sets which are 
equal to some -antiprime1 where the     
condition  has this special meaning4 ,it
 will be found on consideration 7i7 that
 each abstractive set forming a moment  
is a -antiprime1 where  has this special
 meaning1 and 7ii7 that we have excluded
 from membership of moments abstractive 
sets of durations which all have one    
common boundary1 either the initial     
boundary or the final boundary4 ,we thus

 exclude special cases which are apt to 
confuse general reasoning4 ,the new     
definition of a moment1 which supersedes
 our previous definition1 is 7by the aid
 of the notion of antiprimes7 the more  
precisely drawn of the two1 and the more
 useful4  ,the particular condition     
which '' stood for in the definition of 
moments included something additional to
 anything which can be derived from the 
bare notion of extension4 ,a duration   
exhibits for thought a totality4 ,the   
notion of totality is something beyond  
that of extension1 though the two are   
interwoven in the notion of a duration4 
,in the same way the particular         
condition '' required for the definition
 of an event-particle must be looked for
 beyond the mere notion of extension4   
,the same remark is also true of the    
particular conditions requisite for the 
other spatial elements4 ,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 events4  ,in order to
 understand this distinction consider a 
point of the instantaneous space which  
we conceive as apparent to us in an     
almost instantaneous glance4 ,this point
 is an event-particle4 ,it has two      
aspects4 ,in one aspect it is there1    
where it is4 ,this is its position in   
the space4 ,in another aspect it is got 
at by ignoring the circumambient space1 
and by concentrating attention on the   
smaller and smaller set of events which 
approximate to it4 ,this is its         
extrinsic character4 ,thus a point has  
three characters1 namely1 its position  
in the whole instantaneous space1 its   
extrinsic character1 and its intrinsic  
character4 ,the same is true of any     
other spatial element4 ,for example an  
instantaneous volume in instantaneous   
space has three characters1 namely1 its 
position1 its extrinsic character as a  
group of abstractive sets1 and its      
intrinsic character which is the limit  

of natural properties which is indicated
 by any one of these abstractive sets4  
,before we can talk about position in   
instantaneous space1 we must evidently  
be quite clear as to what we mean by    
instantaneous space in itself4          
,instantaneous space must be looked for 
as a character of a moment4 ,for a      
moment is all nature at an instant4 ,it 
cannot be the intrinsic character of the
 moment4 ,for the intrinsic character   
tells us the limiting character of      
nature in space at that instant4        
,instantaneous space must be an         
assemblage of abstractive elements      
considered in their mutual relations4   
,thus an instantaneous space is the     
assemblage of abstractive elements      
covered by some one moment1 and it is   
the instantaneous space of that moment4 
,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 position4 ,this question at once     

brings us to the intersection of        
moments1 which is a topic not as yet    
considered in these lectures4  ,the     
locus of intersection of two moments is 
the assemblage of abstractive elements  
covered by both of them4 ,now two       
moments of the same temporal series     
cannot intersect4 ,two moments          
respectively of different families      
necessarily intersect4 ,accordingly in  
the instantaneous space of a moment we  
should expect the fundamental properties
 to be marked by the intersections with 
moments of other families4 ,if ,m be a  
given moment1 the intersection of ,m    
with another moment ,a is an            
instantaneous plane in the instantaneous
 space of ,m2 and if ,b be a third      
moment intersecting both ,m and ,a1 the 
intersection of ,m and ,b is another    
plane in the space ,m4 ,also the common 
intersection of ,a1 ,b1 and ,m is the   
intersection of the two planes in the   
space ,m1 namely it is a straight line  
in the space ,m4 ,an exceptional case   

arises if ,b and ,m intersect in the    
same plane as ,a and ,m4 ,furthermore if
 ,c be a fourth moment1 then apart from 
special cases which we need not         
consider1 it intersects ,m in a plane   
which the straight line 7,a1 ,b1 ,m7    
meets4 ,thus there is in general a      
common intersection of four moments of  
different families4 ,this common        
intersection is an assemblage of        
abstractive elements which are each     
covered 7or 'lie in'7 all four moments4 
,the three-dimensional property of      
instantaneous space comes to this1 that 
7apart from special relations between   
the four moments7 any fifth moment      
either contains the whole of their      
common intersection or none of it4 ,no  
further subdivision of the common       
intersection is possible by means of    
moments4 ,the 'all or none' principle   
holds4 ,this is not an  priori truth but
 an empirical fact of nature4  ,it will 
be convenient to reserve the ordinary   
spatial terms 'plane1' 'straight line1' 

'point' for the elements of the timeless
 space of a time-system4 ,accordingly an
 instantaneous plane in the             
instantaneous space of a moment will be 
called a 'level1' an instantaneous      
straight line will be called a 'rect1'  
and an instantaneous point will be      
called a 'punct4' ,thus a punct is the  
assemblage of abstractive elements which
 lie in each of four moments whose      
families have no special relations to   
each other4 ,also if ,p be any moment1  
either every abstractive element        
belonging to a given punct lies in ,p1  
or no abstractive element of that punct 
lies in ,p4  ,position is the quality   
which an abstractive element possesses  
in virtue of the moments in which it    
lies4 ,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 
elements4 ,it is this differentiation of

 the elements which constitutes their   
differentiation of position4 ,an        
abstractive element which belongs to a  
punct has the simplest type of position 
in ,m1 an abstractive element which     
belongs to a rect but not to a punct has
 a more complex quality of position1 an 
abstractive element which belongs to a  
level and not to a rect has a still more
 complex quality of position1 and       
finally the most complex quality of     
position belongs to an abstractive      
element which belongs to a volume and   
not to a level4 ,a volume however has   
not yet been defined4 ,this definition  
will be given in the next lecture4      
,evidently levels1 rects1 and puncts in 
their capacity as infinite aggregates   
cannot be the termini of                
sense-awareness1 nor can they be limits 
which are approximated to in            
sense-awareness4 ,any one member of a   
level has a certain quality arising from
 its character as also belonging to a   
certain set of moments1 but the level as

 a whole is a mere logical notion       
without any route of approximation along
 entities posited in sense-awareness4   
,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-awareness4 ,a definite            
event-particle is defined in reference  
to a definite punct in the following    
manner3 ,let the condition  mean the    
property of covering all the abstractive
 elements which are members of that     
punct2 so that an abstractive set which 
satisfies the condition  is an          
abstractive set which covers every      
abstractive element belonging to the    
punct4 ,then the definition of the      
event-particle associated with the punct
 is that it is the group of all the     
-primes1 where  has this particular     
meaning4  ,it is evident that--with this
 meaning of --every abstractive set     
equal to a -prime is itself a -prime4   
,accordingly an event-particle as thus  

defined is an abstractive element1      
namely it is the group of those         
abstractive sets which are each equal to
 some given abstractive set4 ,if we     
write out the definition of the         
event-particle associated with some     
given punct1 which we will call 1 it is 
as follows3 ,the event-particle         
associated with  is the group of        
abstractive classes each of which has   
the two properties 7i7 that it covers   
every abstractive set in  and 7ii7 that 
all the abstractive sets which also     
satisfy the former condition as to  and 
which it covers1 also cover it4  ,an    
event-particle has position by reason of
 its association with a punct1 and      
conversely the punct gains its derived  
character as a route of approximation   
from its association with the           
event-particle4 ,these two characters of
 a point are always recurring in any    
treatment of the derivation of a point  
from the observed facts of nature1 but  
in general there is no clear recognition

 of their distinction4  ,the peculiar   
simplicity of an instantaneous point has
 a twofold origin1 one connected with   
position1 that is to say with its       
character as a punct1 and the other     
connected with its character as an      
event-particle4 ,the simplicity of the  
punct arises from its indivisibility by 
a moment4  ,the simplicity of an        
event-particle arises from the          
indivisibility of its intrinsic         
character4 ,the intrinsic character of  
an event-particle is indivisible in the 
sense that every abstractive set covered
 by it exhibits the same intrinsic      
character4 ,it follows that1 though     
there are diverse abstractive elements  
covered by event-particles1 there is no 
advantage to be gained by considering   
them since we gain no additional        
simplicity in the expression of natural 
properties4  ,these two characters of   
simplicity enjoyed respectively by      
event-particles and puncts define a     
meaning for ,euclid's phrase1 'without  

parts and without magnitude4'  ,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 them4 ,they give us nothing 
new in the way of intrinsic character4  
,accordingly we can think of rects and  
levels as merely loci of                
event-particles4 ,in so doing we are    
also cutting out those abstractive      
elements which cover sets of            
event-particles1 without these elements 
being event-particles themselves4 ,there
 are classes of these abstractive       
elements which are of great importance4 
,i will consider them later on in this  
and in other lectures4 ,meanwhile we    
will ignore them4 ,also ,i will always  
speak of 'event-particles' in preference
 to 'puncts1' the latter being an       
artificial word for which ,i have no    
great affection4  ,parallelism among    
rects and levels is now explicable4     
,consider the instantaneous space       

belonging to a moment ,a1 and let ,a    
belong to the temporal series of moments
 which ,i will call 4 ,consider any     
other temporal series of moments which  
,i will call 4 ,the moments of  do not  
intersect each other and they intersect 
the moment ,a in a family of levels4    
,none of these levels can intersect1 and
 they form a family of parallel         
instantaneous planes in the             
instantaneous space of moment ,a4 ,thus 
the parallelism of moments in a temporal
 series begets the parallelism of levels
 in an instantaneous space1 and         
thence--as it is easy to see--the       
parallelism of rects4 ,accordingly the  
,euclidean property of space arises from
 the parabolic property of time4 ,it may
 be that there is reason to adopt a     
hyperbolic theory of time and a         
corresponding hyperbolic theory of      
space4 ,such a theory has not been      
worked out1 so it is not possible to    
judge as to the character of the        
evidence which could be brought forward 

in its favour4  ,the theory of order in 
an instantaneous space is immediately   
derived from time-order4 ,for consider  
the space of a moment ,m4 ,let  be the  
name of a time-system to which ,m does  
not belong4 ,let ,a1 ,a1 ,a etc4 be     
moments of  in the order of their       
occurrences4 ,then ,a1 ,a1 ,a1 etc4     
intersect ,m in parallel levels l1 l1 l1
 etc4 ,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
 4 ,any rect in ,m which intersects all 
these levels in its set of puncts1      
thereby receives for its puncts an order
 of position on it4 ,so spatial order is
 derivative from temporal order4        
,furthermore there are alternative      
time-systems1 but there is only one     
definite spatial order in each          
instantaneous space4 ,accordingly the   
various modes of deriving spatial order 
from diverse time-systems must harmonise
 with one spatial order in each         

instantaneous space4 ,in this way also  
diverse time-orders are comparable4  ,we
 have two great questions still on hand 
to be settled before our theory of space
 is fully adjusted4 ,one of these is the
 question of the determination of the   
methods of measurement within the space1
 in other words1 the congruence-theory  
of the space4 ,the measurement of space 
will be found to be closely connected   
with the measurement of time1 with      
respect to which no principles have as  
yet been determined4 ,thus our          
congruence-theory will be a theory both 
for space and for time4 ,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 moments4 ,this is the        
space--or rather1 these are the         
spaces--of physical science4 ,it is very
 usual to dismiss this space by saying  
that this is conceptual4 ,i do not      
understand the virtue of these phrases4 

,i suppose that it is meant that the    
space is the conception of something in 
nature4 ,accordingly if the space of    
physical science is to be called        
conceptual1 ,i ask1 ,what in nature is  
it the conception of8 ,for example1 when
 we speak of a point in the timeless    
space of physical science1 ,i suppose   
that we are speaking of something in    
nature4 ,if we are not so speaking1 our 
scientists are exercising their wits in 
the realms of pure fantasy1 and this is 
palpably not the case4 ,this demand for 
a definite ,habeas ,corpus ,act for the 
production of the relevant entities in  
nature applies whether space be relative
 or absolute4 ,on the theory of relative
 space1 it may perhaps be argued that   
there is no timeless space for physical 
science1 and that there is only the     
momentary series of instantaneous       
spaces4  ,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 hour4

 ,how can you measure distance from one 
space into another space8 ,i understand 
walking out of the sheet of an ordnance 
map4 ,but the meaning of saying that    
,cambridge at #aj o'clock this morning  
in the appropriate instantaneous space  
for that instant is #eb miles from      
,london at #aa o'clock this morning in  
the appropriate instantaneous space for 
that instant beats me entirely4 ,i think
 that1 by the time a meaning has been   
produced for this statement1 you will   
find that you have constructed what is  
in fact a timeless space4 ,what ,i      
cannot understand is how to produce an  
explanation of meaning without in effect
 making some such construction4 ,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    
space4  ,you will have noticed that by  
the aid of the assumption of alternative
 time-systems1 we are arriving at an    
explanation of the character of space4  

,in natural science 'to explain' means  
merely to discover 'interconnexions4'   
,for example1 in one sense there is no  
explanation of the red which you see4   
,it is red1 and there is nothing else to
 be said about it4 ,either it is posited
 before you in sense-awareness or you   
are ignorant of the entity red4 ,but    
science has explained red4 ,namely it   
has discovered interconnexions between  
red as a factor in nature and other     
factors in nature1 for example waves of 
light which are waves of electromagnetic
 disturbances4 ,there are also various  
pathological states of the body which   
lead to the seeing of red without the   
occurrence of light waves4 ,thus        
connexions have been discovered between 
red as posited in sense-awareness and   
various other factors in nature4 ,the   
discovery of these connexions           
constitutes the scientific explanation  
of our vision of colour4 ,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 explain4 ,the 
systematising intellect abhors bare     
facts4 ,the character of space has      
hitherto been presented as a collection 
of bare facts1 ultimate and             
disconnected4 ,the theory which ,i am   
expounding sweeps away this disconnexion
 of the facts of space4     ,,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
 nature4 ,it was noted at the close of  
the previous lecture that the question  
of congruence had not been considered1  
nor had the construction of a timeless  
space which should correlate the        
successive momentary spaces of a given  
time-system4 ,furthermore it was also   
noted that there were many spatial      
abstractive elements which we had not   
yet defined4 ,we will first consider the
 definition of some of these abstractive
 elements1 namely the definitions of    

solids1 of areas1 and of routes4 ,by a  
'route' ,i mean a linear segment1       
whether straight or curved4 ,the        
exposition of these definitions and the 
preliminary explanations necessary will1
 ,i hope1 serve as a general explanation
 of the function of event-particles in  
the analysis of nature4  ,we note that  
event-particles have 'position' in      
respect to each other4 ,in the last     
lecture ,i explained that 'position' was
 quality gained by a spatial element in 
virtue of the intersecting moments which
 covered it4 ,thus each event-particle  
has position in this sense4 ,the        
simplest mode of expressing the position
 in nature of an event-particle is by   
first fixing on any definite            
time-system4 ,call it 4 ,there will be  
one moment of the temporal series of    
which covers the given event-particle4  
,thus the position of the event-particle
 in the temporal series  is defined by  
this moment1 which we will call ,m4 ,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 only4 ,this procedure of      
fixing the position of an event-particle
 shows that the aggregate of            
event-particles forms a four-dimensional
 manifold4 ,a finite event occupies a   
limited chunk of this manifold in a     
sense which ,i now proceed to explain4  
,let e be any given event4 ,the manifold
 of event-particles falls into three    
sets in reference to e4 ,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 events4     
,when we select from these finite events
 which enter into the make-up of a given
 event-particle those which are small   
enough1 one of three cases must occur4  
,either 7i7 all of these small events   
are entirely separate from the given    
event e1 or 7ii7 all of these small     
events are parts of the event e1 or     
7iii7 all of these small events overlap 

the event e but are not parts of it4 ,in
 the first case the event-particle will 
be said to 'lie outside' the event e1 in
 the second case the event-particle will
 be said to 'lie inside' the event e1   
and in the third case the event-particle
 will be said to be a                   
'boundary-particle' of the event e4     
,thus there are three sets of particles1
 namely the set of those which lie      
outside the event e1 the set of those   
which lie inside the event e1 and the   
boundary of the event e which is the set
 of boundary-particles of e4 ,since an  
event is four-dimensional1 the boundary 
of an event is a three-dimensional      
manifold4 ,for a finite event there is a
 continuity of boundary2 for a duration 
the boundary consists of those          
event-particles which are covered by    
either of the two bounding moments4     
,thus the boundary of a duration        
consists of two momentary               
three-dimensional spaces4 ,an event will
 be said to 'occupy' the aggregate of   

event-particles which lie within it4    
,two events which have 'junction' in the
 sense in which junction was described  
in my last lecture1 and yet are         
separated so that neither event either  
overlaps or is part of the other event1 
are said to be 'adjoined4'  ,this       
relation of adjunction issues in a      
peculiar relation between the boundaries
 of the two events4 ,the two boundaries 
must have a common portion which is in  
fact a continuous three-dimensional     
locus of event-particles in the         
four-dimensional manifold4  ,a          
three-dimensional locus of              
event-particles which is the common     
portion of the boundary of two adjoined 
events will be called a 'solid4' ,a     
solid may or may not lie completely in  
one moment4 ,a solid which does not lie 
in one moment will be called 'vagrant4' 
,a solid which does lie in one moment   
will be called a volume4 ,a volume may  
be defined as the locus of the          
event-particles in which a moment       

intersects an event1 provided that the  
two do intersect4 ,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
 event4 ,the identity of the two        
definitions of a volume is evident when 
we remember that an intersecting moment 
divides the event into two adjoined     
events4  ,a solid as thus defined1      
whether it be vagrant or be a volume1 is
 a mere aggregate of event-particles    
illustrating a certain quality of       
position4 ,we can also define a solid as
 an abstractive element4 ,in order to do
 so we recur to the theory of primes    
explained in the preceding lecture4 ,let
 the condition named  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 it4 ,then the group of   
all the -primes is the abstractive      
element which is associated with the    
given solid4 ,i will call this          

abstractive element the solid as an     
abstractive element1 and ,i will call   
the aggregate of event-particles the    
solid as a locus4 ,the instantaneous    
volumes in instantaneous space which are
 the ideals of our sense-perception are 
volumes as abstractive elements4 ,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 element4  ,it is difficult  
to know how far we approximate to any   
perception of vagrant solids4 ,we       
certainly do not think that we make any 
such approximation4 ,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 evidence4 ,if ,einstein's theory of 
gravitation has any truth in it1 vagrant
 solids are of great importance in      
science4 ,the whole boundary of a finite
 event may be looked on as a particular 

example of a vagrant solid as a locus4  
,its particular property of being closed
 prevents it from being definable as an 
abstractive element4  ,when a moment    
intersects an event1 it also intersects 
the boundary of that event4 ,this locus1
 which is the portion of the boundary   
contained in the moment1 is the bounding
 surface of the corresponding volume of 
that event contained in the moment4 ,it 
is a two-dimensional locus4  ,the fact  
that every volume has a bounding surface
 is the origin of the ,dedekindian      
continuity of space4  ,another event may
 be cut by the same moment in another   
volume and this volume will also have   
its boundary4 ,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
 surfaces4 ,these portions of surfaces  
are 'momental areas4'  ,it is           
unnecessary at this stage to enter into 
the complexity of a definition of       

vagrant areas4 ,their definition is     
simple enough when the four-dimensional 
manifold of event-particles has been    
more fully explored as to its           
properties4  ,momental areas can        
evidently be defined as abstractive     
elements by exactly the same method as  
applied to solids4 ,we have merely to   
substitute 'area' for a 'solid' in the  
words of the definition already given4  
,also1 exactly as in the analogous case 
of a solid1 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 element4  ,two   
momental areas lying in the same moment 
can cut each other in a momental segment
 which is not necessarily rectilinear4  
,such a segment can also be defined as  
an abstractive element4 ,it is then     
called a 'momental route4' ,we will not 
delay over any general consideration of 
these momental routes1 nor is it        

important for us to proceed to the still
 wider investigation of vagrant routes  
in general4 ,there are however two      
simple sets of routes which are of vital
 importance4 ,one is a set of momental  
routes and the other of vagrant routes4 
,both sets can be classed together as   
straight routes4 ,we proceed to define  
them without any reference to the       
definitions of volumes and surfaces4    
,the two types of straight routes will  
be called rectilinear routes and        
stations4 ,rectilinear routes are       
momental routes and stations are vagrant
 routes4 ,rectilinear routes are routes 
which in a sense lie in rects4 ,any two 
event-particles on a rect define the set
 of event-particles which lie between   
them on that rect4 ,let the satisfaction
 of the condition  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 set4 ,the  
group of -primes1 where  has this       

meaning1 form an abstractive element4   
,such abstractive elements are          
rectilinear routes4 ,they are the       
segments of instantaneous straight lines
 which are the ideals of exact          
perception4 ,our actual perception1     
however exact1 will be the perception of
 a small event sufficiently far down one
 of the abstractive sets of the         
abstractive element4  ,a station is a   
vagrant route and no moment can         
intersect any station in more than one  
event-particle4 ,thus a station carries 
with it a comparison of the positions in
 their respective moments of the        
event-particles covered by it4 ,rects   
arise from the intersection of moments4 
,but as yet no properties of events have
 been mentioned by which any analogous  
vagrant loci can be found out4  ,the    
general problem for our investigation is
 to determine a method of comparison of 
position in one instantaneous space with
 positions in other instantaneous       
spaces4 ,we may limit ourselves to the  

spaces of the parallel moments of one   
time-system4 ,how are positions in these
 various spaces to be compared8 ,in     
other words1 ,what do we mean by motion8
 ,it is the fundamental question to be  
asked of any theory of relative space1  
and like many other fundamental         
questions it is apt to be left          
unanswered4 ,it is not an answer to     
reply1 that we all know what we mean by 
motion4 ,of course we do1 so far as     
sense-awareness is concerned4 ,i am     
asking that your theory of space should 
provide nature with something to be     
observed4 ,you have not settled the     
question by bringing forward a theory   
according to which there is nothing to  
be observed1 and by then reiterating    
that nevertheless we do observe this    
non-existent fact4 ,unless motion is    
something as a fact in nature1 kinetic  
energy and momentum and all that depends
 on these physical concepts evaporate   
from our list of physical realities4    
,even in this revolutionary age my      

conservatism resolutely opposes the     
identification of momentum and          
moonshine4  ,accordingly ,i assume it as
 an axiom1 that motion is a physical    
fact4 ,it is something that we perceive 
as in nature4 ,motion presupposes rest4 
,until theory arose to vitiate immediate
 intuition1 that is to say to vitiate   
the uncriticised judgments which        
immediately arise from sense-awareness1 
no one doubted that in motion you leave 
behind that which is at rest4 ,abraham  
in his wanderings left his birthplace   
where it had ever been4 ,a theory of    
motion and a theory of rest are the same
 thing viewed from different aspects    
with altered emphasis4  ,now you cannot 
have a theory of rest without in some   
sense admitting a theory of absolute    
position4 ,it is usually assumed that   
relative space implies that there is no 
absolute position4 ,this is1 according  
to my creed1 a mistake4 ,the assumption 
arises from the failure to make another 
distinction2 namely1 that there may be  

alternative definitions of absolute     
position4 ,this possibility enters with 
the admission of alternative            
time-systems4 ,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     
spaces1 so that each set consists of    
event-particles1 one from each space1   
all with the property of possessing the 
same absolute position in that series of
 spaces4 ,such a set of event-particles 
will form a point in the timeless space 
of that time-system4 ,thus a point is   
really an absolute position in the      
timeless space of a given time-system4  
,but there are alternative time-systems1
 and each time-system has its own       
peculiar group of points--that is to    
say1 its own peculiar definition of     
absolute position4 ,this is exactly the 
theory which ,i will elaborate4  ,in    
looking to nature for evidence of       
absolute position it is of no use to    

recur to the four-dimensional manifold  
of event-particles4 ,this manifold has  
been obtained by the extension of       
thought beyond the immediacy of         
observation4 ,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
 nature4 ,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 events4 ,our problem  
is to determine those relations between 
events which issue in the property of   
absolute position in a timeless space4  
,this is in fact the problem of the     
determination of the very meaning of the
 timeless spaces of physical science4   
,in reviewing the factors of nature as  
immediately disclosed in                
sense-awareness1 we should note the     
fundamental character of the percept of 
'being here4' ,we discern an event      
merely as a factor in a determinate     

complex in which each factor has its own
 peculiar share4  ,there are two factors
 which are always ingredient in this    
complex1 one is the duration which is   
represented in thought by the concept of
 all nature that is present now1 and the
 other is the peculiar locus standi for 
mind involved in the sense-awareness4   
,this locus standi in nature is what is 
represented in thought by the concept of
 'here1' namely of an 'event here4'     
,this is the concept of a definite      
factor in nature4 ,this factor is an    
event in nature which is the focus in   
nature for that act of awareness1 and   
the other events are perceived as       
referred to it4 ,this event is part of  
the associated duration4 ,i call it the 
'percipient event4' ,this event is not  
the mind1 that is to say1 not the       
percipient4 ,it is that in nature from  
which the mind perceives4 ,the complete 
foothold of the mind in nature is       
represented by the pair of events1      
namely1 the present duration which marks

 the 'when' of awareness and the        
percipient event which marks the 'where'
 of awareness and the 'how' of          
awareness4 ,this percipient event is    
roughly speaking the bodily life of the 
incarnate mind4 ,but this identification
 is only a rough one4 ,for the functions
 of the body shade off into those of    
other events in nature2 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     
life4 ,in many respects the demarcation 
is purely arbitrary1 depending upon     
where in a sliding scale you choose to  
draw the line4  ,i have already in my   
previous lecture on ,time discussed the 
association of mind with nature4 ,the   
difficulty of the discussion lies in the
 liability of constant factors to be    
overlooked4 ,we never note them by      
contrast with their absences4 ,the      
purpose of a discussion of such factors 
may be described as being to make       

obvious things look odd4 ,we cannot     
envisage them unless we manage to invest
 them with some of the freshness which  
is due to strangeness4  ,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 factor4 ,for example1 ,i perceive a
 green leaf4 ,language in this statement
 suppresses all reference to any factors
 other than the percipient mind and the 
green leaf and the relation of          
sense-awareness4 ,it discards the       
obvious inevitable factors which are    
essential elements in the perception4 ,i
 am here1 the leaf is there2 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 now1  
and within this totality there are other
 discriminated factors which it is      
irrelevant to mention4 ,thus language   

habitually sets before the mind a       
misleading abstract of the indefinite   
complexity of the fact of               
sense-awareness4  ,what ,i now want to  
discuss is the special relation of the  
percipient event which is 'here' to the 
duration which is 'now4' ,this relation 
is a fact in nature1 namely the mind is 
aware of nature as being with these two 
factors in this relation4  ,within the  
short present duration the 'here' of the
 percipient event has a definite meaning
 of some sort4 ,this meaning of 'here'  
is the content of the special relation  
of the percipient event to its          
associated duration4 ,i will call this  
relation 'cogredience4' ,accordingly ,i 
ask for a description of the character  
of the relation of cogredience4 ,the    
present snaps into a past and a present 
when the 'here' of cogredience loses its
 single determinate meaning4 ,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 duration4 ,but the   
two 'heres' of sense-awareness within   
neighbouring durations may be           
indistinguishable4 ,in this case there  
has been a passage from the past to the 
present1 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 past4 ,namely1 the sense of    
rest helps the integration of durations 
into a prolonged present1 and the sense 
of motion differentiates nature into a  
succession of shortened durations4 ,as  
we look out of a railway carriage in an 
express train1 the present is past      
before reflexion can seize it4 ,we live 
in snippits too quick for thought4 ,on  
the other hand the immediate present is 
prolonged according as nature presents  
itself to us in an aspect of unbroken   
rest4 ,any change in nature provides    
ground for a differentiation among      
durations so as to shorten the present4 
,but there is a great distinction       

between self-change in nature and change
 in external nature4 ,self-change in    
nature is change in the quality of the  
standpoint of the percipient event4 ,it 
is the break up of the 'here' which     
necessitates the break up of the present
 duration4 ,change in external nature is
 compatible with a prolongation of the  
present of contemplation rooted in a    
given standpoint4 ,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-awareness4 ,this peculiar relation
 is the relation of cogredience between 
the percipient event and the duration4  
,cogredience is the preservation of     
unbroken quality of standpoint within   
the duration4 ,it is the continuance of 
identity of station within the whole of 
nature which is the terminus of         
sense-awareness4 ,the duration may      
comprise change within itself1 but      
cannot--so far as it is one present     

duration--comprise change in the quality
 of its peculiar relation to the        
contained percipient event4  ,in other  
words1 perception is always 'here1' 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 event4 ,it is only in the    
past that you can have been 'there' with
 a standpoint distinct from your present
 'here4'  ,events there and events here 
are facts of nature1 and the qualities  
of being 'there' and 'here' are not     
merely qualities of awareness as a      
relation between nature and mind4 ,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  
'there4' ,thus cogredience has nothing  
to do with any biological character of  
the event which is related by it to the 

associated duration4 ,this biological   
character is apparently a further       
condition for the peculiar connexion of 
a percipient event with the percipience 
of mind2 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 percipience4  ,given the requisite  
biological character1 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 observation4 ,namely1 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 event4 ,this    
duration will be the whole of nature    
which is the terminus posited by        
sense-awareness4 ,thus the character of 
the percipient event determines the     
time-system immediately evident in      

nature4 ,as the character of the        
percipient event changes with the       
passage of nature--or1 in other words1  
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 change4 ,when the bulk of the  
events perceived are cogredient in a    
duration other than that of the         
percipient event1 the percipience may   
include a double consciousness of       
cogredience1 namely the consciousness of
 the whole within which the observer in 
the train is 'here1' and the            
consciousness of the whole within which 
the trees and bridges and telegraph     
posts are definitely 'there4' ,thus in  
perceptions under certain circumstances 
the events discriminated assert their   
own relations of cogredience4 ,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 words1
 when the event and the percipient event
 are both cogredient to the same        
duration4  ,we are now prepared to      
consider the meaning of stations in a   
duration1 where stations are a peculiar 
kind of routes1 which define absolute   
position in the associated timeless     
space4  ,there are however some         
preliminary explanations4 ,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 duration4 ,such
 an event begins with the duration and  
ends with it4 ,furthermore every event  
which begins with the duration and ends 
with it1 extends throughout the         
duration4 ,this is an axiom based on the
 continuity of events4 ,by beginning    
with a duration and ending with it1 ,i  
mean 7i7 that the event is part of the  
duration1 and 7ii7 that both the initial
 and final boundary moments of the      

duration cover some event-particles on  
the boundary of the event4  ,every event
 which is cogredient with a duration    
extends throughout that duration4  ,it  
is not true that all the parts of an    
event cogredient with a duration are    
also cogredient with the duration4 ,the 
relation of cogredience may fail in     
either of two ways4 ,one reason for     
failure may be that the part does not   
extend throughout the duration4 ,in this
 case the part may be cogredient with   
another duration which is part of the   
given duration1 though it is not        
cogredient with the given duration      
itself4 ,such a part would be cogredient
 if its existence were sufficiently     
prolonged in that time-system4 ,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 series4  
,for example1 the tunnel of a tube      
railway is an event at rest in a certain
 time-system1 that is to say1 it is     

cogredient with a certain duration4 ,a  
train travelling in it is part of that  
tunnel1 but is not itself at rest4  ,if 
an event e be cogredient with a duration
 d1 and d be any duration which is part 
of d4 ,then d belongs to the same       
time-system as d4 ,also d intersects e  
in an event e which is part of e and is 
cogredient with d4  ,let ,p be any      
event-particle lying in a given duration
 d4 ,consider the aggregate of events in
 which ,p lies and which are also       
cogredient with d4 ,each of these events
 occupies its own aggregate of          
event-particles4 ,these aggregates will 
have a common portion1 namely the class 
of event-particle lying in all of them4 
,this class of event-particles is what  
,i call the 'station' of the            
event-particle ,p in the duration d4    
,this is the station in the character of
 a locus4 ,a station can also be defined
 in the character of an abstractive     
element4 ,let the property  be the name 
of the property which an abstractive set

 possesses when 7i7 each of its events  
is cogredient with the duration d and   
7ii7 the event-particle ,p lies in each 
of its events4 ,then the group of       
-primes1 where  has this meaning1 is an 
abstractive element and is the station  
of ,p in d as an abstractive element4   
,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 locus4 ,a station has        
accordingly the usual three characters1 
namely1 its character of position1 its  
extrinsic character as an abstractive   
element1 and its intrinsic character4   
,it follows from the peculiar properties
 of rest that two stations belonging to 
the same duration cannot intersect4     
,accordingly every event-particle on a  
station of a duration has that station  
as its station in the duration4 ,also   
every duration which is part of a given 
duration intersects the stations of the 
given duration in loci which are its own
 stations4 ,by means of these properties

 we can utilise the overlappings of the 
durations of one family--that is1 of one
 time-system--to prolong stations       
indefinitely backwards and forwards4    
,such a prolonged station will be called
 a point-track4 ,a point-track is a     
locus of event-particles4 ,it is defined
 by reference to one particular         
time-system1  say4 ,corresponding to any
 other time-system these will be a      
different group of point-tracks4 ,every 
event-particle will lie on one and only 
one point-track of the group belonging  
to any one time-system4 ,the group of   
point-tracks of the time-system  is the 
group of points of the timeless space of
 4 ,each such point indicates a certain 
quality of absolute position in         
reference to the durations of the family
 associated with 1 and thence in        
reference to the successive             
instantaneous spaces lying in the       
successive moments of 4 ,each moment of 
will intersect a point-track in one and 
only one event-particle4  ,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-system4 ,any two event-particles on
 a point-track are sequential1 so that  
they cannot lie in the same moment4     
,accordingly no moment can intersect a  
point-track more than once1 and every   
moment intersects a point-track in one  
event-particle4  ,anyone who at the     
successive moments of  should be at the 
event-particles where those moments     
intersect a given point of  will be at  
rest in the timeless space of           
time-system 4 ,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-system4  
,in other words he will be moving4 ,he  
will be moving in a straight line with  
uniform velocity4 ,we might take this as
 the definition of a straight line4     
,namely1 a straight line in the space of
 time-system  is the locus of those     

points of  which all intersect some one 
point-track which is a point in the     
space of some other time-system4 ,thus  
each point in the space of a time-system
  is associated with one and only one   
straight line of the space of any other 
time-system 4 ,furthermore the set of   
straight lines in space  which are thus 
associated with points in space  form a 
complete family of parallel straight    
lines in space 4 ,thus there is a       
one-to-one correlation of points in     
space  with the straight lines of a     
certain definite family of parallel     
straight lines in space 4 ,conversely   
there is an analogous one-to-one        
correlation of the points in space  with
 the straight lines of a certain family 
of parallel straight lines in space 4   
,these families will be called          
respectively the family of parallels in 
associated with 1 and the family of     
parallels in  associated with 4 ,the    
direction in the space of  indicated by 
the family of parallels in  will be     

called the direction of  in space 1 and 
the family of parallels in  is the      
direction of  in space 4 ,thus a being  
at rest at a point of space  will be    
moving uniformly along a line in space  
which is in the direction of  in space 1
 and a being at rest at a point of space
  will be moving uniformly along a line 
in space  which is in the direction of  
in space 4  ,i have been speaking of the
 timeless spaces which are associated   
with time-systems4 ,these are the spaces
 of physical science and of any concept 
of space as eternal and unchanging4 ,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 awareness4 ,the     
points of such an instantaneous space   
are event-particles and the straight    
lines are rects4 ,let the time-system be
 named 1 and let the moment of          
time-system  to which our quick         
perception of nature approximates be    

called ,m4 ,any straight line r in space
  is a locus of points and each point is
 a point-track which is a locus of      
event-particles4 ,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 r4 ,i will call    
this locus of event-particles the matrix
 of the straight line r4 ,a matrix      
intersects any moment in a rect4 ,thus  
the matrix of r intersects the moment ,m
 in a rect 4 ,thus  is the instantaneous
 rect in ,m which occupies at the moment
 ,m the straight line r in the space of 
4 ,accordingly when one sees            
instantaneously a moving being and its  
path ahead of it1 what one really sees  
is the being at some event-particle ,a  
lying in the rect  which is the apparent
 path on the assumption of uniform      
motion4 ,but the actual rect  which is a
 locus of event-particles is never      
traversed by the being4 ,these          

event-particles are the instantaneous   
facts which pass with the instantaneous 
moment4 ,what is really traversed are   
other event-particles which at          
succeeding instants occupy the same     
points of space  as those occupied by   
the event-particles of the rect 4 ,for  
example1 we see a stretch of road and a 
lorry moving along it4 ,the             
instantaneously seen road is a portion  
of the rect --of course only an         
approximation to it4 ,the lorry is the  
moving object4 ,but the road as seen is 
never traversed4 ,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 discriminate4 ,but suppose a 
land mine under the road has been       
exploded before the lorry gets there4   
,then it is fairly obvious that the     
lorry does not traverse what we saw at  
first4 ,suppose the lorry is at rest in 
space 4 ,then the straight line r of    

space  is in the direction of  in space 
1 and the rect  is the representative in
 the moment ,m of the line r of space 4 
,the direction of  in the instantaneous 
space of the moment ,m is the direction 
of  in ,m1 where ,m is a moment of      
time-system 4 ,again the matrix of the  
line r of space  will also be the matrix
 of some line s of space  which will be 
in the direction of  in space 4 ,thus if
 the lorry halts at some point ,p of    
space  which lies on the line r1 it is  
now moving along the line s of space 4  
,this is the theory of relative motion2 
the common matrix is the bond which     
connects the motion of  in space  with  
the motions of  in space 4  ,motion is  
essentially a relation between some     
object of nature and the one timeless   
space of a time-system4 ,an             
instantaneous space is static1 being    
related to the static nature at an      
instant4 ,in perception when we see     
things moving in an approximation to an 
instantaneous space1 the future lines of

 motion as immediately perceived are    
rects which are never traversed4 ,these 
approximate rects are composed of small 
events1 namely approximate routes and   
event-particles1 which are passed away  
before the moving objects reach them4   
,assuming that our forecasts of         
rectilinear motion are correct1 these   
rects occupy the straight lines in      
timeless space which are traversed4     
,thus the rects are symbols in immediate
 sense-awareness of a future which can  
only be expressed in terms of timeless  
space4  ,we are now in a position to    
explore the fundamental character of    
perpendicularity4 ,consider the two     
time-systems  and 1 each with its own   
timeless space and its own family of    
instantaneous moments with their        
instantaneous spaces4 ,let ,m and ,n be 
respectively a moment of  and a moment  
of 4 ,in ,m there is the direction of   
and in ,n there is the direction of 4   
,but ,m and ,n1 being moments of        
different time-systems1 intersect in a  

level4 ,call this level 4 ,then  is an  
instantaneous plane in the instantaneous
 space of ,m and also in the            
instantaneous space of ,n4 ,it is the   
locus of all the event-particles which  
lie both in ,m and in ,n4  ,in the      
instantaneous space of ,m the level  is 
perpendicular to the direction of  in   
,m1 and in the instantaneous space of ,n
 the level  is perpendicular to the     
direction of  in ,n4 ,this is the       
fundamental property which forms the    
definition of perpendicularity4 ,the    
symmetry of perpendicularity is a       
particular instance of the symmetry of  
the mutual relations between two        
time-systems4 ,we shall find in the next
 lecture that it is from this symmetry  
that the theory of congruence is        
deduced4  ,the theory of                
perpendicularity in the timeless space  
of any time-system  follows immediately 
from this theory of perpendicularity in 
each of its instantaneous spaces4 ,let  
be any rect in the moment ,m of  and let

  be a level in ,m which is             
perpendicular to 4 ,the locus of those  
points of the space of  which intersect 
,m in event-particles on  is the        
straight line r of space 1 and the locus
 of those points of the space of  which 
intersect ,m in event-particles on  is  
the plane l of space 4 ,then the plane l
 is perpendicular to the line r4  ,in   
this way we have pointed out unique and 
definite properties in nature which     
correspond to perpendicularity4 ,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 lecture4
  ,i regret that it has been necessary  
for me in this lecture to administer    
such a large dose of four-dimensional   
geometry4 ,i do not apologise1 because  
,i am really not responsible for the    
fact that nature in its most fundamental
 aspect is four-dimensional4 ,things are
 what they are2 and it is useless to    

disguise the fact that 'what things are'
 is often very difficult for our        
intellects to follow4 ,it is a mere     
evasion of the ultimate problems to     
shirk such obstacles4     ,,chapter ,,vi
  ,,congruence   ,the aim of this       
lecture is to establish a theory of     
congruence4 ,you must understand at once
 that congruence is a controversial     
question4 ,it is the theory of          
measurement in space and in time4 ,the  
question seems simple4 ,in fact it is   
simple enough for a standard procedure  
to have been settled by act of          
parliament2 and devotion to metaphysical
 subtleties is almost the only crime    
which has never been imputed to any     
,english parliament4 ,but the procedure 
is one thing and its meaning is another4
  ,first let us fix attention on the    
purely mathematical question4 ,when the 
segment between two points ,a and ,b is 
congruent to that between the two points
 ,c and ,d1 the quantitative            
measurements of the two segments are    

equal4 ,the equality of the numerical   
measures and the congruence of the two  
segments are not always clearly         
discriminated1 and are lumped together  
under the term equality4 ,but the       
procedure of measurement presupposes    
congruence4 ,for example1 a yard measure
 is applied successively to measure two 
distances between two pairs of points on
 the floor of a room4 ,it is of the     
essence of the procedure of measurement 
that the yard measure remains unaltered 
as it is transferred from one position  
to another4 ,some objects can palpably  
alter as they move--for example1 an     
elastic thread2 but a yard measure does 
not alter if made of the proper         
material4 ,what is this but a judgment  
of congruence applied to the train of   
successive positions of the yard        
measure8 ,we know that it does not alter
 because we judge it to be congruent to 
itself in various positions4 ,in the    
case of the thread we can observe the   
loss of self-congruence4 ,thus immediate

 judgments of congruence are presupposed
 in measurement1 and the process of     
measurement is merely a procedure to    
extend the recognition of congruence to 
cases where these immediate judgments   
are not available4 ,thus we cannot      
define congruence by measurement4  ,in  
modern expositions of the axioms of     
geometry certain conditions are laid    
down which the relation of congruence   
between segments is to satisfy4 ,it is  
supposed that we have a complete theory 
of points1 straight lines1 planes1 and  
the order of points on planes--in fact1 
a complete theory of non-metrical       
geometry4 ,we then enquire about        
congruence and lay down the set of      
conditions--or axioms as they are       
called--which this relation satisfies4  
,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 adopt4 ,in other words there   
are alternative metrical geometries     
which all exist by an equal right so far
 as the intrinsic theory of space is    
concerned4  ,poincar1 the great ,french 
mathematician1 held that our actual     
choice among these geometries is guided 
purely by convention1 and that the      
effect of a change of choice would be   
simply to alter our expression of the   
physical laws of nature4 ,by            
'convention' ,i understand ,poincar to  
mean that there is nothing inherent in  
nature itself giving any peculiar rle to
 one of these congruence relations1 and 
that the choice of one particular       
relation is guided by the volitions of  
the mind at the other end of the        
sense-awareness4 ,the principle of      
guidance is intellectual convenience and
 not natural fact4  ,this position has  
been misunderstood by many of ,poincar's
 expositors4 ,they have muddled it up   
with another question1 namely that owing

 to the inexactitude of observation it  
is impossible to make an exact statement
 in the comparison of measures4 ,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
 error4  ,this is an entirely different 
question and it presupposes a rejection 
of ,poincar's position4 ,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 relations4  ,poincar's
 position is a strong one4 ,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     
adopted4 ,but undeniably the position is
 very paradoxical4 ,bertrand ,russell   
had a controversy with him on this      

question1 and pointed out that on       
,poincar's principles there was nothing 
in nature to determine whether the earth
 is larger or smaller than some assigned
 billiard ball4 ,poincar replied that   
the attempt to find reasons in nature   
for the selection of a definite         
congruence relation in space is like    
trying to determine the position of a   
ship in the ocean by counting the crew  
and observing the colour of the         
captain's eyes4  ,in my opinion both    
disputants were right1 assuming the     
grounds on which the discussion was     
based4 ,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 us4 ,poincar 
asks for information as to the factor in
 nature which might lead any particular 
congruence relation to play a preeminent
 rle among the factors posited in       
sense-awareness4 ,i cannot see the      
answer to either of these contentions   

provided that you admit the             
materialistic theory of nature4 ,with   
this theory nature at an instant in     
space is an independent fact4 ,thus we  
have to look for our preeminent         
congruence relation amid nature in      
instantaneous space2 and ,poincar is    
undoubtedly right in saying that nature 
on this hypothesis gives us no help in  
finding it4  ,on the other hand ,russell
 is in an equally strong position when  
he asserts that1 as a fact of           
observation1 we do find it1 and what is 
more agree in finding the same          
congruence relation4 ,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 notice4 ,one would have expected    
disagreement on this fundamental choice 
to have divided nations and to have rent
 families4 ,but the difficulty was not  

even discovered till the close of the   
nineteenth century by a few mathematical
 philosophers and philosophic           
mathematicians4 ,the case is not like   
that of our agreement on some           
fundamental fact of nature such as the  
three dimensions of space4 ,if space has
 only three dimensions we should expect 
all mankind to be aware of the fact1 as 
they are aware of it4 ,but in the case  
of congruence1 mankind agree in an      
arbitrary interpretation of             
sense-awareness when there is nothing in
 nature to guide it4  ,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 relations4
  ,the reason for this result is that   
nature is no longer confined within     
space at an instant4 ,space and time are
 now interconnected2 and this peculiar  

factor of time which is so immediately  
distinguished among the deliverances of 
our sense-awareness1 relates itself to  
one particular congruence relation in   
space4  ,congruence is a particular     
example of the fundamental fact of      
recognition4 ,in perception we          
recognise4 ,this recognition does not   
merely concern the comparison of a      
factor of nature posited by memory with 
a factor posited by immediate           
sense-awareness4 ,recognition takes     
place within the present without any    
intervention of pure memory4 ,for the   
present fact is a duration with its     
antecedent and consequent durations     
which are parts of itself4 ,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 events4 ,whatever passes is an      
event4 ,but we find entities in nature  
which do not pass2 namely we recognise  

samenesses in nature4 ,recognition is   
not primarily an intellectual act of    
comparison2 it is in its essence merely 
sense-awareness in its capacity of      
positing before us factors in nature    
which do not pass4 ,for example1 green  
is perceived as situated in a certain   
finite event within the present         
duration4 ,this green preserves its     
self-identity throughout1 whereas the   
event passes and thereby obtains the    
property of breaking into parts4 ,the   
green patch has parts4 ,but in talking  
of the green patch we are speaking of   
the event in its sole capacity of being 
for us the situation of green4 ,the     
green itself is numerically one         
self-identical entity1 without parts    
because it is without passage4  ,factors
 in nature which are without passage    
will be called objects4 ,there are      
radically different kinds of objects    
which will be considered in the         
succeeding lecture4  ,recognition is    
reflected into the intellect as         

comparison4 ,the recognised objects of  
one event are compared with the         
recognised objects of another event4    
,the comparison may be between two      
events in the present1 or it may be     
between two events of which one is      
posited by memory-awareness and the     
other by immediate sense-awareness4 ,but
 it is not the events which are         
compared4 ,for each event is essentially
 unique and incomparable4 ,what are     
compared are the objects and relations  
of objects situated in events4 ,the     
event considered as a relation between  
objects has lost its passage and in this
 aspect is itself an object4 ,this      
object is not the event but only an     
intellectual abstraction4 ,the same     
object can be situated in many events2  
and in this sense even the whole event1 
viewed as an object1 can recur1 though  
not the very event itself with its      
passage and its relations to other      
events4  ,objects which are not posited 
by sense-awareness may be known to the  

intellect4 ,for example1 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  
being4 ,thus objects for our knowledge  
may be merely logical abstractions4 ,for
 example1 a complete event is never     
disclosed in sense-awareness1 and thus  
the object which is the sum total of    
objects situated in an event as thus    
inter-related is a mere abstract        
concept4 ,again a right-angle is a      
perceived object which can be situated  
in many events2 but1 though             
rectangularity is posited by            
sense-awareness1 the majority of        
geometrical relations are not so        
posited4 ,also rectangularity is in fact
 often not perceived when it can be     
proved to have been there for           
perception4 ,thus an object is often    
known merely as an abstract relation not
 directly posited in sense-awareness    
although it is there in nature4  ,the   

identity of quality between congruent   
segments is generally of this character4
 ,in certain special cases this identity
 of quality can be directly perceived4  
,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 congruence4     
,congruence depends on motion1 and      
thereby is generated the connexion      
between spatial congruence and temporal 
congruence4 ,motion along a straight    
line has a symmetry round that line4    
,this symmetry is expressed by the      
symmetrical geometrical relations of the
 line to the family of planes normal to 
it4  ,also another symmetry in the      
theory of motion arises from the fact   
that rest in the points of  corresponds 
to uniform motion along a definite      
family of parallel straight lines in the
 space of 4 ,we must note the three     
characteristics1 7i7 of the uniformity  
of the motion corresponding to any point

 of  along its correlated straight line 
in 1 and 7ii7 of the equality in        
magnitude of the velocities along the   
various lines of  correlated to rest in 
the various points of 1 and 7iii7 of the
 parallelism of the lines of this       
family4  ,we are now in possession of a 
theory of parallels and a theory of     
perpendiculars and a theory of motion1  
and from these theories the theory of   
congruence can be constructed4 ,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-system4 ,also a family  
of parallel moments is the family of    
moments of some one time-system4 ,thus  
we can enlarge our concept of a family  
of parallel levels so as to include     
levels in different moments of one      
time-system4 ,with this enlarged concept
 we say that a complete family of       
parallel levels in a time-system  is the
 complete family of levels in which the 

moments of  intersect the moments of 4  
,this complete family of parallel levels
 is also evidently a family lying in the
 moments of the time-system 4 ,by       
introducing a third time-system 1       
parallel rects are obtained4 ,also all  
the points of any one time-system form a
 family of parallel point-tracks4 ,thus 
there are three types of parallelograms 
in the four-dimensional manifold of     
event-particles4  ,in parallelograms of 
the first type the two pairs of parallel
 sides are both of them pairs of rects4 
,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-tracks4 ,in parallelograms of the 
third type the two pairs of parallel    
sides are both of them pairs of         
point-tracks4  ,the first axiom of      
congruence is that the opposite sides of
 any parallelogram are congruent4 ,this 
axiom enables us to compare the lengths 
of any two segments either respectively 
on parallel rects or on the same rect4  

,also it enables us to compare the      
lengths of any two segments either      
respectively on parallel point-tracks or
 on the same point-track4 ,it follows   
from this axiom that two objects at rest
 in any two points of a time-system  are
 moving with equal velocities in any    
other time-system  along parallel lines4
 ,thus we can speak of the velocity in  
due to the time-system  without         
specifying any particular point in 4    
,the axiom also enables us to measure   
time in any time-system2 but does not   
enable us to compare times in different 
time-systems4  ,the second axiom of     
congruence concerns parallelograms on   
congruent bases and between the same    
parallels1 which have also their other  
pairs of sides parallel4 ,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 lie4 ,by the aid of this
 axiom it easily follows that the       
diagonals of a parallelogram bisect each

 other4  ,congruence is extended in any 
space beyond parallel rects to all rects
 by two axioms depending on             
perpendicularity4 ,the first of these   
axioms1 which is the third axiom of     
congruence1 is that if ,,abc is a       
triangle of rects in any moment and ,d  
is the middle event-particle of the base
 ,,bc1 then the level through ,d        
perpendicular to ,,bc contains ,a when  
and only when ,,ab is congruent to ,,ac4
 ,this axiom evidently expresses the    
symmetry of perpendicularity1 and is the
 essence of the famous pons asinorum    
expressed as an axiom4  ,the second     
axiom depending on perpendicularity1 and
 the fourth axiom of congruence1 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 ,c1 and  
,,ad and ,,ae be another pair of        
rectangular rects intersecting r in ,d  
and ,e1 then either ,d or ,e lies in the
 segment ,,bc and the other one of the  

two does not lie in this segment4 ,also 
as a particular case of this axiom1 if  
,,ab be perpendicular to r and in       
consequence ,,ac be parallel to r1 then 
,d and ,e lie on opposite sides of ,b   
respectively4 ,by the aid of these two  
axioms the theory of congruence can be  
extended so as to compare lengths of    
segments on any two rects4 ,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 comparison4  
,the comparison of time-measurements in 
diverse time-systems requires two other 
axioms4 ,the first of these axioms1     
forming the fifth axiom of congruence1  
will be called the axiom of 'kinetic    
symmetry4' ,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 units4  ,the axiom can be     

explained as follows3 ,let  and  be the 
names of two time-systems4 ,the         
directions of motion in the space of    
due to rest in a point of  is called the
 '-direction in ' and the direction of  
motion in the space of  due to rest in a
 point of  is called the '-direction in 
4' ,consider a motion in the space of   
consisting of a certain velocity in the 
-direction of  and a certain velocity at
 right-angles to it4 ,this motion       
represents rest in the space of another 
time-system--call it 4 ,rest in  will   
also be represented in the space of  by 
a certain velocity in the -direction in 
and a certain velocity at right-angles  
to this -direction4 ,thus a certain     
motion in the space of  is correlated to
 a certain motion in the space of 1 as  
both representing the same fact which   
can also be represented by rest in 4    
,now another time-system1 which ,i will 
name 1 can be found which is such that  
rest in its space is represented by the 
same magnitudes of velocities along and 

perpendicular to the -direction in  as  
those velocities in 1 along and         
perpendicular to the -direction1 which  
represent rest in 4 ,the required axiom 
of kinetic symmetry is that rest in     
will be represented in  by the same     
velocities along and perpendicular to   
the -direction in  as those velocities  
in  along and perpendicular to the      
-direction which represent rest in 4  ,a
 particular case of this axiom is that  
relative velocities are equal and       
opposite4 ,namely rest in  is           
represented in  by a velocity along the 
-direction which is equal to the        
velocity along the -direction in  which 
represents rest in 4  ,finally the sixth
 axiom of congruence is that the        
relation of congruence is transitive4   
,so far as this axiom applies to space1 
it is superfluous4 ,for the property    
follows from our previous axioms4 ,it is
 however necessary for time as a        
supplement to the axiom of kinetic      
symmetry4 ,the meaning of the axiom is  

that if the time-unit of system  is     
congruent to the time-unit of system 1  
and the time-unit of system  is         
congruent to the time-unit of system 1  
then the time-units of  and  are also   
congruent4  ,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     
deduced4 ,these formulae will be found  
to involve one arbitrary constant which 
,i will call k4  ,it is of the          
dimensions of the square of a velocity4 
,accordingly four cases arise4 ,in the  
first case k is zero4 ,this case        
produces nonsensical results in         
opposition to the elementary            
deliverances of experience4 ,we put this
 case aside4  ,in the second case k is  
infinite4 ,this case yields the ordinary
 formulae for transformation in relative
 motion1 namely those formulae which are
 to be found in every elementary book on
 dynamics4  ,in the third case1 k is    

negative4 ,let us call it -c1 where c   
will be of the dimensions of a velocity4
 ,this case yields the formulae of      
transformation which ,larmor discovered 
for the transformation of ,maxwell's    
equations of the electromagnetic field4 
,these formulae were extended by ,h4 ,a4
 ,lorentz1 and used by ,einstein and    
,minkowski as the basis of their novel  
theory of relativity4 ,i am not now     
speaking of ,einstein's more recent     
theory of general relativity by which he
 deduces his modification of the law of 
gravitation4 ,if this be the case which 
applies to nature1 then c must be a     
close approximation to the velocity of  
light in vacuo4 ,perhaps it is this     
actual velocity4 ,in this connexion 'in 
vacuo' must not mean an absence of      
events1 namely the absence of the       
all-pervading ether of events4 ,it must 
mean the absence of certain types of    
objects4  ,in the fourth case1 k is     
positive4 ,let us call it h1 where h    
will be of the dimensions of a velocity4

 ,this gives a perfectly possible type  
of transformation formulae1 but not one 
which explains any facts of experience4 
,it has also another disadvantage4 ,with
 the assumption of this fourth case the 
distinction between space and time      
becomes unduly blurred4 ,the whole      
object of these lectures has been to    
enforce the doctrine that space and time
 spring from a common root1 and that the
 ultimate fact of experience is a       
space-time fact4 ,but after all mankind 
does distinguish very sharply between   
space and time1 and it is owing to this 
sharpness of distinction that the       
doctrine of these lectures is somewhat  
of a paradox4 ,now in the third         
assumption this sharpness of distinction
 is adequately preserved4 ,there is a   
fundamental distinction between the     
metrical properties of point-tracks and 
rects4 ,but in the fourth assumption    
this fundamental distinction vanishes4  
,neither the third nor the fourth       
assumption can agree with experience    

unless we assume that the velocity c of 
the third assumption1 and the velocity h
 of the fourth assumption1 are extremely
 large compared to the velocities of    
ordinary experience4 ,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 textbooks4 ,for  
the sake of a name1 ,i will call these  
textbook formulae the 'orthodox'        
formulae4  ,there can be no question as 
to the general approximate correctness  
of the orthodox formulae4 ,it would be  
merely silly to raise doubts on this    
point4 ,but the determination of the    
status of these formulae is by no means 
settled by this admission4 ,the         
independence of time and space is an    
unquestioned presupposition of the      
orthodox thought which has produced the 
orthodox formulae4 ,with this           
presupposition and given the absolute   
points of one absolute space1 the       

orthodox formulae are immediate         
deductions4 ,accordingly1 these formulae
 are presented to our imaginations as   
facts which cannot be otherwise1 time   
and space being what they are4 ,the     
orthodox formulae have therefore        
attained to the status of necessities   
which cannot be questioned in science4  
,any attempt to replace these formulae  
by others was to abandon the rle of     
physical explanation and to have        
recourse to mere mathematical formulae4 
,but even in physical science           
difficulties have accumulated round the 
orthodox formulae4 ,in the first place  
,maxwell's equations of the             
electromagnetic field are not invariant 
for the transformations of the orthodox 
formulae2 whereas they are invariant for
 the transformations of the formulae    
arising from the third of the four cases
 mentioned above1 provided that the     
velocity c is identified with a famous  
electromagnetic constant quantity4      
,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
 case4 ,but if we assume the orthodox   
formulae we have to make a special and  
arbitrary assumption as to the          
contraction of matter during motion4 ,i 
mean the ,fitzgerald-,lorentz           
assumption4  ,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 case1 and requires
 another arbitrary assumption if we use 
the orthodox formulae4  ,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      
formulae4 ,but the way is blocked by the
 ingrained belief that these latter     
formulae possess a character of         
necessity4 ,it is therefore an urgent   
requisite for physical science and for  

philosophy to examine critically the    
grounds for this supposed necessity4    
,the only satisfactory method of        
scrutiny is to recur to the first       
principles of our knowledge of nature4  
,this is exactly what ,i am endeavouring
 to do in these lectures4 ,i ask what it
 is that we are aware of in our         
sense-perception of nature4 ,i then     
proceed to examine those factors in     
nature which lead us to conceive nature 
as occupying space and persisting       
through time4 ,this procedure has led us
 to an investigation of the characters  
of space and time4 ,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 nature4   
,the orthodox formulae have thus lost   
any advantage as to necessity which they
 enjoyed over the serial group4 ,the way
 is thus open to adopt whichever of the 
two groups best accords with            

observation4  ,i take this opportunity  
of pausing for a moment from the course 
of my argument1 and of reflecting on the
 general character which my doctrine    
ascribes to some familiar concepts of   
science4 ,i have no doubt that some of  
you have felt that in certain aspects   
this character is very paradoxical4     
,this vein of paradox is partly due to  
the fact that educated language has been
 made to conform to the prevalent       
orthodox theory4 ,we are thus1 in       
expounding an alternative doctrine1     
driven to the use of either strange     
terms or of familiar words with unusual 
meanings4 ,this victory of the orthodox 
theory over language is very natural4   
,events are named after the prominent   
objects situated in them1 and thus both 
in language and in thought the event    
sinks behind the object1 and becomes the
 mere play of its relations4 ,the theory
 of space is then converted into a      
theory of the relations of objects      
instead of a theory of the relations of 

events4 ,but objects have not the       
passage of events4 ,accordingly space as
 a relation between objects is devoid of
 any connexion with time4 ,it is space  
at an instant without any determinate   
relations between the spaces at         
successive instants4 ,it cannot be one  
timeless space because the relations    
between objects change4  ,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 space4 ,this
 reference to absolute space was not an 
oversight4 ,i know that the doctrine of 
the relativity of space at present holds
 the field both in science and          
philosophy4 ,but ,i do not think that   
its inevitable consequences are         
understood4 ,when we really face them   
the paradox of the presentation of the  
character of space which ,i have        
elaborated is greatly mitigated4 ,if    
there is no absolute position1 a point  

must cease to be a simple entity4 ,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 telescope1 and is another     
track of points to an observer in the   
sun who is watching the balloon through 
some instrument suited to such a being4 
,accordingly if ,i am reproached with   
the paradox of my theory of points as   
classes of event-particles1 and of my   
theory of event-particles as groups of  
abstractive sets1 ,i ask my critic to   
explain exactly what he means by a      
point4 ,while you explain your meaning  
about anything1 however simple1 it is   
always apt to look subtle and fine spun4
 ,i have at least explained exactly what
 ,i do mean by a point1 what relations  
it involves and what entities are the   
relata4 ,if you admit the relativity of 
space1 you also must admit that points  
are complex entities1 logical constructs
 involving other entities and their     

relations4 ,produce your theory1 not in 
a few vague phrases of indefinite       
meaning1 but explain it step by step in 
definite terms referring to assigned    
relations and assigned relata4 ,also    
show that your theory of points issues  
in a theory of space4 ,furthermore note 
that the example of the man in the      
balloon1 the observer on earth1 and the 
observer in the sun1 shows that every   
assumption of relative rest requires a  
timeless space with radically different 
points from those which issue from every
 other such assumption4 ,the theory of  
the relativity of space is inconsistent 
with any doctrine of one unique set of  
points of one timeless space4  ,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 space4 ,but this   
doctrine has never really been accepted 
in science1 whatever people say4 ,what  
appears in our dynamical treatises is   
,newton's doctrine of relative motion   

based on the doctrine of differential   
motion in absolute space4 ,when you once
 admit that the points are radically    
different entities for differing        
assumptions of rest1 then the orthodox  
formulae lose all their obviousness4    
,they were only obvious because you were
 really thinking of something else4     
,when discussing this topic you can only
 avoid paradox by taking refuge from the
 flood of criticism in the comfortable  
ark of no meaning4  ,the new theory     
provides a definition of the congruence 
of periods of time4 ,the prevalent view 
provides no such definition4 ,its       
position is that if we take such        
time-measurements so that certain       
familiar velocities which seem to us to 
be uniform are uniform1 then the laws of
 motion are true4 ,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-periods4 ,so in     
appealing to familiar phenomena it      

allows that there is some factor in     
nature which we can intellectually      
construct as a congruence theory4 ,it   
does not however say anything about it  
except that the laws of motion are then 
true4 ,suppose that with some expositors
 we cut out the reference to familiar   
velocities such as the rate of rotation 
of the earth4 ,we are then driven to    
admit that there is no meaning in       
temporal congruence except that certain 
assumptions make the laws of motion     
true4 ,such a statement is historically 
false4 ,king ,alfred the ,great was     
ignorant of the laws of motion1 but knew
 very well what he meant by the         
measurement of time1 and achieved his   
purpose by means of burning candles4    
,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 times4 ,uniformity in change  

is directly perceived1 and it follows   
that mankind perceives in nature factors
 from which a theory of temporal        
congruence can be formed4 ,the prevalent
 theory entirely fails to produce such  
factors4  ,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         
explanation4 ,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 body4 ,you   
must choose a body which is not rotating
 and has no acceleration4 ,for example  
they do not really apply to axes fixed  
in the earth because of the diurnal     
rotation of that body4 ,the law which   
fails when you assume the wrong axes as 
at rest is the third law1 that action   
and reaction are equal and opposite4    
,with the wrong axes uncompensated      
centrifugal forces and uncompensated    
composite centrifugal forces appear1 due
 to rotation4 ,the influence of these   

forces can be demonstrated by many facts
 on the earth's surface1 ,foucault's    
pendulum1 the shape of the earth1 the   
fixed directions of the rotations of    
cyclones and anticyclones4 ,it is       
difficult to take seriously the         
suggestion that these domestic phenomena
 on the earth are due to the influence  
of the fixed stars4 ,i cannot persuade  
myself to believe that a little star in 
its twinkling turned round ,foucault's  
pendulum in the ,paris ,exhibition of   
#ahfa4 ,of course anything is believable
 when a definite physical connexion has 
been demonstrated1 for example the      
influence of sunspots4 ,here all        
demonstration is lacking in the form of 
any coherent theory4 ,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-system4 ,for example1 consider the 
space of a time-system 4 ,there are sets
 of axes at rest in the space of 4      
,these are suitable dynamical axes4     

,also a set of axes in this space which 
is moving with uniform velocity without 
rotation is another suitable set4 ,all  
the moving points fixed in these moving 
axes are really tracing out parallel    
lines with one uniform velocity4 ,in    
other words they are the reflections in 
the space of  of a set of fixed axes in 
the space of some other time-system 4   
,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 properties4 ,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   
configuration4 ,thus the meaning of     
motion being what it is1 in order to    
describe the motion of any system of    
objects without changing the meaning of 
your terms as you proceed with your     

description1 you are bound to take one  
of these sets of axes as axes of        
reference2 though you may choose their  
reflections into the space of any       
time-system which you wish to adopt4 ,a 
definite physical reason is thereby     
assigned for the peculiar property of   
the dynamical group of axes4  ,on the   
orthodox theory the position of the     
equations of motion is most ambiguous4  
,the space to which they refer is       
completely undetermined and so is the   
measurement of the lapse of time4       
,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 time1 and something which
 it can call a system of forces1 and    
something which it can call masses1 so  
that these formulae may be satisfied4   
,the only reason--on this theory--why   
anyone should want to satisfy these     
formulae is a sentimental regard for    

,galileo1 ,newton1 ,euler and ,lagrange4
 ,the theory1 so far from founding      
science on a sound observational basis1 
forces everything to conform to a mere  
mathematical preference for certain     
simple formulae4  ,i do not for a moment
 believe that this is a true account of 
the real status of the ,laws of ,motion4
 ,these equations want some slight      
adjustment for the new formulae of      
relativity4 ,but with these adjustments1
 imperceptible in ordinary use1 the laws
 deal with fundamental physical         
quantities which we know very well and  
wish to correlate4  ,the measurement of 
time was known to all civilised nations 
long before the laws were thought of4   
,it is this time as thus measured that  
the laws are concerned with4 ,also they 
deal with the space of our daily life4  
,when we approach to an accuracy of     
measurement beyond that of observation1 
adjustment is allowable4 ,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 change4 ,it is for science
 to give an intellectual account of what
 is so evident in sense-awareness4 ,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     
,motion1 formulae completely unknown    
till the seventeenth century of our     
epoch4  ,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 congruence4 ,it  
gives an account of the meaning of the  
geometrical entities such as points1    
straight lines1 and volumes1 and        
connects the kindred ideas of extension 
in time and extension in space4 ,the    
theory satisfies the true purpose of an 
intellectual explanation in the sphere  
of natural philosophy4 ,this purpose is 

to exhibit the interconnexions of       
nature1 and to show that one set of     
ingredients in nature requires for the  
exhibition of its character the presence
 of the other sets of ingredients4  ,the
 false idea which we have to get rid of 
is that of nature as a mere aggregate of
 independent entities1 each capable of  
isolation4 ,according to this conception
 these entities1 whose characters are   
capable of isolated definition1 come    
together and by their accidental        
relations form the system of nature4    
,this system is thus thoroughly         
accidental2 and1 even if it be subject  
to a mechanical fate1 it is only        
accidentally so subject4  ,with this    
theory space might be without time1 and 
time might be without space4 ,the theory
 admittedly breaks down when we come to 
the relations of matter and space4 ,the 
relational theory of space is an        
admission that we cannot know space     
without matter or matter without space4 
,but the seclusion of both from time is 

still jealously guarded4 ,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 space4 ,also what we really
 observe in nature1 its colours and its 
sounds and its touches are secondary    
qualities2 in other words1 they are not 
in nature at all but are accidental     
products of the relations between nature
 and mind4  ,the explanation of nature  
which ,i urge as an alternative ideal to
 this accidental view of nature1 is that
 nothing in nature could be what it is  
except as an ingredient in nature as it 
is4 ,the whole which is present for     
discrimination is posited in            
sense-awareness as necessary for the    
discriminated parts4 ,an isolated event 
is not an event1 because every event is 
a factor in a larger whole and is       
significant of that whole4 ,there can be
 no time apart from space2 and no space 
apart from time2 and no space and no    

time apart from the passage of the      
events of nature4 ,the isolation of an  
entity in thought1 when we think of it  
as a bare 'it1' has no counterpart in   
any corresponding isolation in nature4  
,such isolation is merely part of the   
procedure of intellectual knowledge4    
,the laws of nature are the outcome of  
the characters of the entities which we 
find in nature4 ,the entities being what
 they are1 the laws must be what they   
are2 and conversely the entities follow 
from the laws4 ,we are a long way from  
the attainment of such an ideal2 but it 
remains as the abiding goal of          
theoretical science4     ,,chapter ,,vii
  ,,objects   ,the ensuing lecture is   
concerned with the theory of objects4   
,objects are elements in nature which do
 not pass4 ,the awareness of an object  
as some factor not sharing in the       
passage of nature is what ,i call       
'recognition4' ,it is impossible to     
recognise an event1 because an event is 
essentially distinct from every other   

event4 ,recognition is an awareness of  
sameness4 ,but to call recognition an   
awareness of sameness implies an        
intellectual act of comparison          
accompanied with judgment4 ,i use       
recognition for the non-intellectual    
relation of sense-awareness which       
connects the mind with a factor of      
nature without passage4 ,on the         
intellectual side of the mind's         
experience there are comparisons of     
things recognised and consequent        
judgments of sameness or diversity4     
,probably 'sense-recognition' would be a
 better term for what ,i mean by        
'recognition4' ,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-recognition4' ,i am quite
 willing to believe that recognition1 in
 my sense of the term1 is merely an     
ideal limit1 and that there is in fact  
no recognition without intellectual     
accompaniments of comparison and        

judgment4 ,but recognition is that      
relation of the mind to nature which    
provides the material for the           
intellectual activity4  ,an object is an
 ingredient in the character of some    
event4 ,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 event4 ,thus the    
theory of objects is the theory of the  
comparison of events4 ,events are only  
comparable because they body forth      
permanences4 ,we are comparing objects  
in events whenever we can say1 ',there  
it is again4' ,objects are the elements 
in nature which can 'be again4'         
,sometimes permanences can be proved to 
exist which evade recognition in the    
sense in which ,i am using that term4   
,the permanences which evade recognition
 appear to us as abstract properties    
either of events or of objects4 ,all the
 same they are there for recognition    
although undiscriminated in our         

sense-awareness4 ,the demarcation of    
events1 the splitting of nature up into 
parts is effected by the objects which  
we recognise as their ingredients4 ,the 
discrimination of nature is the         
recognition of objects amid passing     
events4 ,it is a compound of the        
awareness of the passage of nature1 of  
the consequent partition of nature1 and 
of the definition of certain parts of   
nature by the modes of the ingression of
 objects into them4  ,you may have      
noticed that ,i am using the term       
'ingression' to denote the general      
relation of objects to events4 ,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 object4 ,namely the event is what it
 is1 because the object is what it is2  
and when ,i am thinking of this         
modification of the event by the object1
 ,i call the relation between the two   
'the ingression of the object into the  
event4' ,it is equally true to say that 

objects are what they are because events
 are what they are4 ,nature is such that
 there can be no events and no objects  
without the ingression of objects into  
events4 ,although there are events such 
that the ingredient objects evade our   
recognition4 ,these are the events in   
empty space4 ,such events are only      
analysed for us by the intellectual     
probing of science4  ,ingression is a   
relation which has various modes4 ,there
 are obviously very various kinds of    
objects2 and no one kind of object can  
have the same sort of relations to      
events as objects of another kind can   
have4 ,we shall have to analyse out some
 of the different modes of ingression   
which different kinds of objects have   
into events4  ,but even if we stick to  
one and the same kind of objects1 an    
object of that kind has different modes 
of ingression into different events4    
,science and philosophy have been apt to
 entangle themselves in a simple-minded 
theory that an object is at one place at

 any definite time1 and is in no sense  
anywhere else4 ,this is in fact the     
attitude of common sense thought1 though
 it is not the attitude of language     
which is navely expressing the facts of 
experience4 ,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 object4 ,an object is ingredient
 throughout its neighbourhood1 and its  
neighbourhood is indefinite4 ,also the  
modification of events by ingression is 
susceptible of quantitative differences4
 ,finally therefore we are driven to    
admit that each object is in some sense 
ingredient throughout nature2 though its
 ingression may be quantitatively       
irrelevant in the expression of our     
individual experiences4  ,this admission
 is not new either in philosophy or     
science4 ,it is obviously a necessary   
axiom for those philosophers who insist 
that reality is a system4 ,in these     

lectures we are keeping off the profound
 and vexed question as to what we mean  
by 'reality4' ,i am maintaining the     
humbler thesis that nature is a system4 
,but ,i suppose that in this case the   
less follows from the greater1 and that 
,i may claim the support of these       
philosophers4 ,the same doctrine is     
essentially interwoven in all modern    
physical speculation4 ,as long ago as   
#ahdg ,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   
everywhere4 ,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 fact4 ,we can       
however illustrate the doctrine by the  
more familiar facts of life without     
recourse to the abstruse speculations of
 theoretical physics4  ,the waves as    
they roll on to the ,cornish coast tell 
of a gale in mid-,atlantic2 and our     

dinner witnesses to the ingression of   
the cook into the dining room4 ,it is   
evident that the ingression of objects  
into events includes the theory of      
causation4 ,i prefer to neglect this    
aspect of ingression1 because causation 
raises the memory of discussions based  
upon theories of nature which are alien 
to my own4 ,also ,i think that some new 
light may be thrown on the subject by   
viewing it in this fresh aspect4  ,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 events2 in a   
sense1 it is a more concentrated form4  
,for example1 the electron has a certain
 position in space and a certain shape4 
,perhaps it is an extremely small sphere
 in a certain test-tube4 ,the storm is a
 gale situated in mid-,atlantic with a  
certain latitude and longitude1 and the 
cook is in the kitchen4 ,i will call    
this special form of ingression the     
'relation of situation'2 also1 by a     

double use of the word 'situation1' ,i  
will call the event in which an object  
is situated 'the situation of the       
object4' ,thus a situation is an event  
which is a relatum in the relation of   
situation4 ,now our first impression is 
that at last we have come to the simple 
plain fact of where the object really   
is2 and that the vaguer relation which  
,i call ingression should not be muddled
 up with the relation of situation1 as  
if including it as a particular case4   
,it seems so obvious that any object is 
in such and such a position1 and that it
 is influencing other events in a       
totally different sense4 ,namely1 in a  
sense an object is the character of the 
event which is its situation1 but it    
only influences the character of other  
events4 ,accordingly the relations of   
situation and influencing are not       
generally the same sort of relation1 and
 should not be subsumed under the same  
term 'ingression4' ,i believe that this 
notion is a mistake1 and that it is     

impossible to draw a clear distinction  
between the two relations4  ,for        
example1 ,where was your toothache8 ,you
 went to a dentist and pointed out the  
tooth to him4 ,he pronounced it         
perfectly sound1 and cured you by       
stopping another tooth4 ,which tooth was
 the situation of the toothache8 ,again1
 a man has an arm amputated1 and        
experiences sensations in the hand which
 he has lost4 ,the situation of the     
imaginary hand is in fact merely thin   
air4 ,you look into a mirror and see a  
fire4 ,the flames that you see are      
situated behind the mirror4 ,again at   
night you watch the sky2 if some of the 
stars had vanished from existence hours 
ago1 you would not be any the wiser4    
,even the situations of the planets     
differ from those which science would   
assign to them4  ,anyhow you are tempted
 to exclaim1 the cook is in the kitchen4
 ,if you mean her mind1 ,i will not     
agree with you on the point2 for ,i am  
only talking of nature4 ,let us think   

only of her bodily presence4 ,what do   
you mean by this notion8 ,we confine    
ourselves to typical manifestations of  
it4 ,you can see her1 touch her1 and    
hear her4 ,but the examples which ,i    
have given you show that the notions of 
the situations of what you see1 what you
 touch1 and what you hear are not so    
sharply separated out as to defy further
 questioning4 ,you cannot cling to the  
idea that we have two sets of           
experiences of nature1 one of primary   
qualities which belong to the objects   
perceived1 and one of secondary         
qualities which are the products of our 
mental excitements4 ,all we know of     
nature is in the same boat1 to sink or  
swim together4 ,the constructions of    
science are merely expositions of the   
characters of things perceived4         
,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 characters4 ,the situations

 of the perceived manifestations of her 
bodily presence have only a very general
 relation to the situations of the      
molecules1 to be determined by          
discussion of the circumstances of      
perception4  ,in discussing the         
relations of situation in particular and
 of ingression in general1 the first    
requisite is to note that objects are of
 radically different types4 ,for each   
type 'situation' and 'ingression' have  
their own special meanings which are    
different from their meanings for other 
types1 though connexions can be pointed 
out4 ,it is necessary therefore in      
discussing them to determine what type  
of objects are under consideration4     
,there are1 ,i think1 an indefinite     
number of types of objects4 ,happily we 
need not think of them all4 ,the idea of
 situation has its peculiar importance  
in reference to three types of objects  
which ,i call sense-objects1 perceptual 
objects and scientific objects4 ,the    
suitability of these names for the three

 types is of minor importance1 so long  
as ,i can succeed in explaining what ,i 
mean by them4  ,these three types form  
an ascending hierarchy1 of which each   
member presupposes the type below4 ,the 
base of the hierarchy is formed by the  
sense-objects4 ,these objects do not    
presuppose any other type of objects4 ,a
 sense-object is a factor of nature     
posited by sense-awareness which 7i71 in
 that it is an object1 does not share in
 the passage of nature and 7ii7 is not a
 relation between other factors of      
nature4 ,it will of course be a relatum 
in relations which also implicate other 
factors of nature4 ,but it is always a  
relatum and never the relation itself4  
,examples of sense-objects are a        
particular sort of colour1 say          
,cambridge blue1 or a particular sort of
 sound1 or a particular sort of smell1  
or a particular sort of feeling4 ,i am  
not talking of a particular patch of    
blue as seen during a particular second 
of time at a definite date4 ,such a     

patch is an event where ,cambridge blue 
is situated4 ,similarly ,i am not       
talking of any particular concert-room  
as filled with the note4 ,i mean the    
note itself and not the patch of volume 
filled by the sound for a tenth of a    
second4 ,it is natural for us to think  
of the note in itself1 but in the case  
of colour we are apt to think of it     
merely as a property of the patch4 ,no  
one thinks of the note as a property of 
the concert-room4 ,we see the blue and  
we hear the note4 ,both the blue and the
 note are immediately posited by the    
discrimination of sense-awareness which 
relates the mind to nature4 ,the blue is
 posited as in nature related to other  
factors in nature4 ,in particular it is 
posited as in the relation of being     
situated in the event which is its      
situation4  ,the difficulties which     
cluster around the relation of situation
 arise from the obstinate refusal of    
philosophers to take seriously the      
ultimate fact of multiple relations4 ,by

 a multiple relation ,i mean a relation 
which in any concrete instance of its   
occurrence necessarily involves more    
than two relata4 ,for example1 when     
,john likes ,thomas there are only two  
relata1 ,john and ,thomas4 ,but when    
,john gives that book to ,thomas there  
are three relata1 ,john1 that book1 and 
,thomas4  ,some schools of philosophy1  
under the influence of the ,aristotelian
 logic and the ,aristotelian philosophy1
 endeavour to get on without admitting  
any relations at all except that of     
substance and attribute4 ,namely all    
apparent relations are to be resolvable 
into the concurrent existence of        
substances with contrasted attributes4  
,it is fairly obvious that the          
,leibnizian monadology is the necessary 
outcome of any such philosophy4 ,if you 
dislike pluralism1 there will be only   
one monad4  ,other schools of philosophy
 admit relations but obstinately refuse 
to contemplate relations with more than 
two relata4 ,i do not think that this   

limitation is based on any set purpose  
or theory4 ,it merely arises from the   
fact that more complicated relations are
 a bother to people without adequate    
mathematical training1 when they are    
admitted into the reasoning4  ,i must   
repeat that we have nothing to do in    
these lectures with the ultimate        
character of reality4 ,it is quite      
possible that in the true philosophy of 
reality there are only individual       
substances with attributes1 or that     
there are only relations with pairs of  
relata4 ,i do not believe that such is  
the case2 but ,i am not concerned to    
argue about it now4 ,our theme is       
,nature4 ,so long as we confine         
ourselves to the factors posited in the 
sense-awareness of nature1 it seems to  
me that there certainly are instances of
 multiple relations between these       
factors1 and that the relation of       
situation for sense-objects is one      
example of such multiple relations4     
,consider a blue coat1 a flannel coat of

 ,cambridge blue belonging to some      
athlete4 ,the coat itself is a          
perceptual object and its situation is  
not what ,i am talking about4 ,we are   
talking of someone's definite           
sense-awareness of ,cambridge blue as   
situated in some event of nature4 ,he   
may be looking at the coat directly4 ,he
 then sees ,cambridge blue as situated  
practically in the same event as the    
coat at that instant4 ,it is true that  
the blue which he sees is due to light  
which left the coat some inconceivably  
small fraction of a second before4 ,this
 difference would be important if he    
were looking at a star whose colour was 
,cambridge blue4 ,the star might have   
ceased to exist days ago1 or even years 
ago4 ,the situation of the blue will not
 then be very intimately connected with 
the situation 7in another sense of      
'situation'7 of any perceptual object4  
,this disconnexion of the situation of  
the blue and the situation of some      
associated perceptual object does not   

require a star for its exemplification4 
,any looking glass will suffice4 ,look  
at the coat through a looking glass4    
,then blue is seen as situated behind   
the mirror4 ,the event which is its     
situation depends upon the position of  
the observer4  ,the sense-awareness of  
the blue as situated in a certain event 
which ,i call the situation1 is thus    
exhibited as the sense-awareness of a   
relation between the blue1 the          
percipient event of the observer1 the   
situation1 and intervening events4 ,all 
nature is in fact required1 though only 
certain intervening events require their
 characters to be of certain definite   
sorts4 ,the ingression of blue into the 
events of nature is thus exhibited as   
systematically correlated4 ,the         
awareness of the observer depends on the
 position of the percipient event in    
this systematic correlation4 ,i will use
 the term 'ingression into nature' for  
this systematic correlation of the blue 
with nature4 ,thus the ingression of    

blue into any definite event is a part  
statement of the fact of the ingression 
of blue into nature4  ,in respect to the
 ingression of blue into nature events  
may be roughly put into four classes    
which overlap and are not very clearly  
separated4 ,these classes are 7i7 the   
percipient events1 7ii7 the situations1 
7iii7 the active conditioning events1   
7iv7 the passive conditioning events4   
,to understand this classification of   
events in the general fact of the       
ingression of blue into nature1 let us  
confine attention to one situation for  
one percipient event and to the         
consequent rles of the conditioning     
events for the ingression as thus       
limited4 ,the percipient event is the   
relevant bodily state of the observer4  
,the situation is where he sees the     
blue1 say1 behind the mirror4 ,the      
active conditioning events are the      
events whose characters are particularly
 relevant for the event 7which is the   
situation7 to be the situation for that 

percipient event1 namely the coat1 the  
mirror1 and the state of the room as to 
light and atmosphere4 ,the passive      
conditioning events are the events of   
the rest of nature4  ,in general the    
situation is an active conditioning     
event2 namely the coat itself1 when     
there is no mirror or other such        
contrivance to produce abnormal effects4
 ,but the example of the mirror shows us
 that the situation may be one of the   
passive conditioning events4 ,we are    
then apt to say that our senses have    
been cheated1 because we demand as a    
right that the situation should be an   
active condition in the ingression4     
,this demand is not so baseless as it   
may seem when presented as ,i have put  
it4 ,all we know of the characters of   
the events of nature is based on the    
analysis of the relations of situations 
to percipient events4 ,if situations    
were not in general active conditions1  
this analysis would tell us nothing4    
,nature would be an unfathomable enigma 

to us and there could be no science4    
,accordingly the incipient discontent   
when a situation is found to be a       
passive condition is in a sense         
justifiable2 because if that sort of    
thing went on too often1 the rle of the 
intellect would be ended4  ,furthermore 
the mirror is itself the situation of   
other sense-objects either for the same 
observer with the same percipient event1
 or for other observers with other      
percipient events4 ,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        
situations4  ,this is a fundamental     
principle of science which it has       
derived from common sense4  ,i now turn 
to perceptual objects4 ,when we look at 
the coat1 we do not in general say1     
,there is a patch of ,cambridge blue2   
what naturally occurs to us is1 ,there  

is a coat4 ,also the judgment that what 
we have seen is a garment of man's      
attire is a detail4 ,what we perceive is
 an object other than a mere            
sense-object4 ,it is not a mere patch of
 colour1 but something more2 and it is  
that something more which we judge to be
 a coat4 ,i will use the word 'coat' as 
the name for that crude object which is 
more than a patch of colour1 and without
 any allusion to the judgments as to its
 usefulness as an article of attire     
either in the past or the future4 ,the  
coat which is perceived--in this sense  
of the word 'coat'--is what ,i call a   
perceptual object4 ,we have to          
investigate the general character of    
these perceptual objects4  ,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 event1 but is the   
situation of a variety of sense-objects 
for a variety of percipient events4 ,for
 example1 for any one percipient event1 

the situation of a sense-object of sight
 is apt also to be the situations of    
sense-objects of sight1 of touch1 of    
smell1 and of sound4 ,furthermore this  
concurrence in the situations of        
sense-objects has led to the body--i4e4 
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 situation4    
,this interplay is especially the case  
between touch and sight4 ,there is a    
certain correlation between the         
ingressions of sense-objects of touch   
and sense-objects of sight into nature1 
and in a slighter degree between the    
ingressions of other pairs of           
sense-objects4 ,i call this sort of     
correlation the 'conveyance' of one     
sense-object by another4 ,when you see  
the blue flannel coat you subconsciously
 feel yourself wearing it or otherwise  
touching it4 ,if you are a smoker1 you  
may also subconsciously be aware of the 

faint aroma of tobacco4 ,the peculiar   
fact1 posited by this sense-awareness of
 the concurrence of subconscious        
sense-objects along with one or more    
dominating sense-objects in the same    
situation1 is the sense-awareness of the
 perceptual object4 ,the perceptual     
object is not primarily the issue of a  
judgment4 ,it is a factor of nature     
directly posited in sense-awareness4    
,the element of judgment comes in when  
we proceed to classify the particular   
perceptual object4 ,for example1 we say1
 ,that is flannel1 and we think of the  
properties of flannel and the uses of   
athletes' coats4 ,but that all takes    
place after we have got hold of the     
perceptual object4 ,anticipatory        
judgments affect the perceptual object  
perceived by focussing and diverting    
attention4  ,the perceptual object is   
the outcome of the habit of experience4 
,anything which conflicts with this     
habit hinders the sense-awareness of    
such an object4 ,a sense-object is not  

the product of the association of       
intellectual ideas2 it is the product of
 the association of sense-objects in the
 same situation4 ,this outcome is not   
intellectual2 it is an object of        
peculiar type with its own particular   
ingression into nature4  ,there are two 
kinds of perceptual objects1 namely1    
'delusive perceptual objects' and       
'physical objects4' ,the situation of a 
delusive perceptual object is a passive 
condition in the ingression of that     
object into nature4 ,also the event     
which is the situation will have the    
relation of situation to the object only
 for one particular percipient event4   
,for example1 an observer sees the image
 of the blue coat in a mirror4 ,it is a 
blue coat that he sees and not a mere   
patch of colour4 ,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 event4 ,namely  
we are to look for them in the          

investigations of medical psychologists4
 ,the ingression into nature of the     
delusive sense-object is conditioned by 
the adaptation of bodily events to the  
more normal occurrence1 which is the    
ingression of the physical object4  ,a  
perceptual object is a physical object  
when 7i7 its situation is an active     
conditioning event for the ingression of
 any of its component sense-objects1 and
 7ii7 the same event can be the         
situation of the perceptual object for  
an indefinite number of possible        
percipient events4 ,physical objects are
 the ordinary objects which we perceive 
when our senses are not cheated1 such as
 chairs1 tables and trees4 ,in a way    
physical objects have more insistent    
perceptive power than sense-objects4    
,attention to the fact of their         
occurrence in nature is the first       
condition for the survival of complex   
living organisms4 ,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      
objects4 ,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 objects4   
,for example1 stray smells1 sounds1     
colours and more subtle nameless        
sense-objects4 ,there is no perception  
of physical objects without perception  
of sense-objects4 ,but the converse does
 not hold3 namely1 there is abundant    
perception of sense-objects             
unaccompanied by any perception of      
physical objects4 ,this lack of         
reciprocity in the relations between    
sense-objects and physical objects is   
fatal to the scholastic natural         
philosophy4  ,there is a great          
difference in the rles of the situations
 of sense-objects and physical objects4 
,the situations of a physical object are
 conditioned by uniqueness and          
continuity4 ,the uniqueness is an ideal 

limit to which we approximate as we     
proceed in thought along an abstractive 
set of durations1 considering smaller   
and smaller durations in the approach to
 the ideal limit of the moment of time4 
,in other words1 when the duration is   
small enough1 the situation of the      
physical object within that duration is 
practically unique4  ,the identification
 of the same physical object as being   
situated in distinct events in distinct 
durations is effected by the condition  
of continuity4 ,this condition of       
continuity is the condition that a      
continuity of passage of events1 each   
event being a situation of the object in
 its corresponding duration1 can be     
found from the earlier to the later of  
the two given events4 ,so far as the two
 events are practically adjacent in one 
specious present1 this continuity of    
passage may be directly perceived4      
,otherwise it is a matter of judgment   
and inference4  ,the situations of a    
sense-object are not conditioned by any 

such conditions either of uniqueness or 
of continuity4 ,in any durations however
 small a sense-object may have any      
number of situations separated from each
 other4 ,thus two situations of a       
sense-object1 either in the same        
duration or in different durations1 are 
not necessarily connected by any        
continuous passage of events which are  
also situations of that sense-object4   
,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     
events4 ,in one respect this is also a  
tautology4 ,for the physical object is  
nothing else than the habitual          
concurrence of a certain set of         
sense-objects in one situation4         
,accordingly when we know all about the 
physical object1 we thereby know its    
component sense-objects4 ,but a physical
 object is a condition for the          
occurrence of sense-objects other than  

those which are its components4 ,for    
example1 the atmosphere causes the      
events which are its situations to be   
active conditioning events in the       
transmission of sound4 ,a mirror which  
is itself a physical object is an active
 condition for the situation of a patch 
of colour behind it1 due to the         
reflection of light in it4  ,thus the   
origin of scientific knowledge is the   
endeavour to express in terms of        
physical objects the various rles of    
events as active conditions in the      
ingression of sense-objects into nature4
 ,it is in the progress of this         
investigation that scientific objects   
emerge4 ,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 event4 ,their    
relations to each other are also        
characterised by a certain simplicity   
and uniformity4 ,finally the characters 

of the observed physical objects and    
sense-objects can be expressed in terms 
of these scientific objects4 ,in fact   
the whole point of the search for       
scientific objects is the endeavour to  
obtain this simple expression of the    
characters of events4 ,these scientific 
objects are not themselves merely       
formulae for calculation2 because       
formulae must refer to things in nature1
 and the scientific objects are the     
things in nature to which the formulae  
refer4  ,a scientific object such as a  
definite electron is a systematic       
correlation of the characters of all    
events throughout all nature4 ,it is an 
aspect of the systematic character of   
nature4 ,the electron is not merely     
where its charge is4 ,the charge is the 
quantitative character of certain events
 due to the ingression of the electron  
into nature4 ,the electron is its whole 
field of force4 ,namely the electron is 
the systematic way in which all events  
are modified as the expression of its   

ingression4 ,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 electron4 ,we may if we   
please term the mere charge the         
electron4 ,but then another name is     
required for the scientific object which
 is the full entity which concerns      
science1 and which ,i have called the   
electron4  ,according to this conception
 of scientific objects1 the rival       
theories of action at a distance and    
action by transmission through a medium 
are both incomplete expressions of the  
true process of nature4 ,the stream of  
events which form the continuous series 
of situations of the electron is        
entirely self-determined1 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 cogredient1 and the flux of 
their positions in their corresponding  

durations4 ,this is the foundation of   
the denial of action at a distance2     
namely the progress of the stream of the
 situations of a scientific object can  
be determined by an analysis of the     
stream itself4  ,on the other hand the  
ingression of every electron into nature
 modifies to some extent the character  
of every event4 ,thus the character of  
the stream of events which we are       
considering bears marks of the existence
 of every other electron throughout the 
universe4 ,if we like to think of the   
electrons as being merely what ,i call  
their charges1 then the charges act at a
 distance4 ,but this action consists in 
the modification of the situation of the
 other electron under consideration4    
,this conception of a charge acting at a
 distance is a wholly artificial one4   
,the conception which most fully        
expresses the character of nature is    
that of each event as modified by the   
ingression of each electron into nature4
 ,the ether is the expression of this   

systematic modification of events       
throughout space and throughout time4   
,the best expression of the character of
 this modification is for physicists to 
find out4 ,my theory has nothing to do  
with that and is ready to accept any    
outcome of physical research4  ,the     
connexion of objects with space requires
 elucidation4 ,objects are situated in  
events4 ,the relation of situation is a 
different relation for each type of     
object1 and in the case of sense-objects
 it cannot be expressed as a two-termed 
relation4 ,it would perhaps be better to
 use a different word for these         
different types of the relation of      
situation4 ,it has not however been     
necessary to do so for our purposes in  
these lectures4 ,it must be understood  
however that1 when situation is spoken  
of1 some one definite type is under     
discussion1 and it may happen that the  
argument may not apply to situation of  
another type4 ,in all cases however ,i  
use situation to express a relation     

between objects and events and not      
between objects and abstractive         
elements4 ,there is a derivative        
relation between objects and spatial    
elements which ,i call the relation of  
location2 and when this relation holds1 
,i say that the object is located in the
 abstractive element4 ,in this sense1 an
 object may be located in a moment of   
time1 in a volume of space1 an area1 a  
line1 or a point4 ,there will be a      
peculiar type of location corresponding 
to each type of situation2 and location 
is in each case derivative from the     
corresponding relation of situation in a
 way which ,i will proceed to explain4  
,also location in the timeless space of 
some time-system is a relation          
derivative from location in             
instantaneous spaces of the same        
time-system4 ,accordingly location in an
 instantaneous space is the primary idea
 which we have to explain4 ,great       
confusion has been occasioned in natural
 philosophy by the neglect to           

distinguish between the different types 
of objects1 the different types of      
situation1 the different types of       
location1 and the difference between    
location and situation4 ,it is          
impossible to reason accurately in the  
vague concerning objects and their      
positions without keeping these         
distinctions in view4 ,an object is     
located in an abstractive element1 when 
an abstractive set belonging to that    
element can be found such that each     
event belonging to that set is a        
situation of the object4 ,it will be    
remembered that an abstractive element  
is a certain group of abstractive sets1 
and that each abstractive set is a set  
of events4 ,this definition defines the 
location of an element in any type of   
abstractive element4 ,in this sense we  
can talk of the existence of an object  
at an instant1 meaning thereby its      
location in some definite moment4 ,it   
may also be located in some spatial     
element of the instantaneous space of   

that moment4  ,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 end4  ,by these definitions  
location in elements of instantaneous   
spaces is defined4 ,these elements      
occupy corresponding elements of        
timeless spaces4 ,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 element4  ,it is not     
every object which can be located in a  
moment4 ,an object which can be located 
in every moment of some duration will be
 called a 'uniform' object throughout   
that duration4 ,ordinary physical       
objects appear to us to be uniform      

objects1 and we habitually assume that  
scientific objects such as electrons are
 uniform4 ,but some sense-objects       
certainly are not uniform4 ,a tune is an
 example of a non-uniform object4 ,we   
have perceived it as a whole in a       
certain duration2 but the tune as a tune
 is not at any moment of that duration  
though one of the individual notes may  
be located there4  ,it is possible      
therefore that for the existence of     
certain sorts of objects1 e4g4          
electrons1 minimum quanta of time are   
requisite4 ,some such postulate is      
apparently indicated by the modern      
quantum theory and it is perfectly      
consistent with the doctrine of objects 
maintained in these lectures4  ,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 nature4 

,we can intellectually distinguish even 
subtler and subtler types of objects4   
,here ,i reckon subtlety as meaning     
seclusion from the immediate            
apprehension of sense-awareness4        
,evolution in the complexity of life    
means an increase in the types of       
objects directly sensed4 ,delicacy of   
sense-apprehension means perceptions of 
objects as distinct entities which are  
mere subtle ideas to cruder             
sensibilities4 ,the phrasing of music is
 a mere abstract subtlety to the        
unmusical2 it is a direct               
sense-apprehension to the initiated4    
,for example1 if we could imagine some  
lowly type of organic being thinking and
 aware of our thoughts1 it would wonder 
at the abstract subtleties in which we  
indulge as we think of stones and bricks
 and drops of water and plants4 ,it only
 knows of vague undifferentiated        
feelings in nature4 ,it would consider  
us as given over to the play of         
excessively abstract intellects4 ,but   

then if it could think1 it would        
anticipate2 and if it anticipated1 it   
would soon perceive for itself4  ,in    
these lectures we have been scrutinising
 the foundations of natural philosophy4 
,we are stopping at the very point where
 a boundless ocean of enquiries opens   
out for our questioning4  ,i agree that 
the view of ,nature which ,i have       
maintained in these lectures is not a   
simple one4 ,nature appears as a complex
 system whose factors are dimly         
discerned by us4 ,but1 as ,i ask you1   
,is not this the very truth8 ,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       
formulated8 ,the aim of science is to   
seek the simplest explanations of       
complex facts4 ,we are apt to fall into 
the error of thinking that the facts are
 simple because simplicity is the goal  
of our quest4 ,the guiding motto in the 
life of every natural philosopher should

 be1 ,seek simplicity and distrust it4  
,,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   
them4 ,they have made us think4 ,but    
when we have admitted so far1 we are    
most of us faced with a distressing     
perplexity4 ,what is it that we ought to
 think about8 ,the purport of my lecture
 this afternoon will be to meet this    
difficulty and1 so far as ,i am able1 to
 set in a clear light the changes in the
 background of our scientific thought   
which are necessitated by any           
acceptance1 however qualified1 of       
,einstein's main positions4 ,i remember 
that ,i am lecturing to the members of a
 chemical society who are not for the   
most part versed in advanced            
mathematics4 ,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 acceptance4  
,of course1 the detailed deductions are 
important1 because unless our colleagues
 the astronomers and the physicists find
 these predictions to be verified we can
 neglect the theory altogether4 ,but we 
may now take it as granted that in many 
striking particulars these deductions   
have been found to be in agreement with 
observation4 ,accordingly the theory has
 to be taken seriously and we are       
anxious to know what will be the        
consequences of its final acceptance4   
,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 theory4 ',space      
caught bending' appeared on the         
news-sheet of a well-known evening      
paper4 ,this rendering is a terse but   

not inapt translation of ,einstein's own
 way of interpreting his results4 ,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 own1 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 explained4 ,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 production4  ,to put         
ourselves in the position to assimilate 
and to criticise any change in ultimate 
scientific conceptions we must begin at 
the beginning4 ,so you must bear with me
 if ,i commence by making some simple   
and obvious reflections4 ,let us        
consider three statements1 7i7          
',yesterday a man was run over on the   
,chelsea ,embankment1' 7ii7             
',cleopatra's ,needle is on the ,charing

 ,cross ,embankment1' and 7iii7 ',there 
are dark lines in the ,solar ,spectrum4'
 ,the first statement about the accident
 to the man is about what we may term an
 'occurrence1' a 'happening1' or an     
'event4' ,i will use the term 'event'   
because it is the shortest4 ,in order to
 specify an observed event1 the place1  
the time1 and character of the event are
 necessary4 ,in specifying the place and
 the time you are really stating the    
relation of the assigned event to the   
general structure of other observed     
events4 ,for example1 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 ,strand4  
,the point which ,i want to make is     
this3 ,nature is known to us in our     
experience as a complex of passing      
events4 ,in this complex we discern     
definite mutual relations between       
component events1 which we may call     
their relative positions1 and these     
positions we express partly in terms of 

space and partly in terms of time4 ,also
 in addition to its mere relative       
position to other events1 each          
particular event has its own peculiar   
character4 ,in other words1 nature is a 
structure of events and each event has  
its position in this structure and its  
own peculiar character or quality4  ,let
 us now examine the other two statements
 in the light of this general principle 
as to the meaning of nature4 ,take the  
second statement1 ',cleopatra's ,needle 
is on the ,charing ,cross ,embankment4' 
,at first sight we should hardly call   
this an event4 ,it seems to lack the    
element of time or transitoriness4 ,but 
does it8 ,if an angel had made the      
remark some hundreds of millions of     
years ago1 the earth was not in         
existence1 twenty millions of years ago 
there was no ,thames1 eighty years ago  
there was no ,thames ,embankment1 and   
when ,i was a small boy ,cleopatra's    
,needle was not there4 ,and now that it 
is there1 we none of us expect it to be 

eternal4 ,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    
needless4 ,what it comes to is this3    
,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 character1 
namely the character of being the       
situations of ,cleopatra's ,needle4 ,day
 by day and hour by hour we can find a  
certain chunk in the transitory life of 
nature and of that chunk we say1 ',there
 is ,cleopatra's ,needle4' ,if we define
 the ,needle in a sufficiently abstract 
manner we can say that it never changes4
 ,but a physicist who looks on that part
 of the life of nature as a dance of    
electrons1 will tell you that daily it  
has lost some molecules and gained      
others1 and even the plain man can see  
that it gets dirtier and is occasionally

 washed4 ,thus the question of change in
 the ,needle is a mere matter of        
definition4 ,the more abstract your     
definition1 the more permanent the      
,needle4 ,but whether your ,needle      
change or be permanent1 all you mean by 
stating that it is situated on the      
,charing ,cross ,embankment1 is that    
amid the structure of events you know of
 a certain continuous limited stream of 
events1 such that any chunk of that     
stream1 during any hour1 or any day1 or 
any second1 has the character of being  
the situation of ,cleopatra's ,needle4  
,finally1 we come to the third          
statement1 ',there are dark lines in the
 ,solar ,spectrum4' ,this is a law of   
nature4 ,but what does that mean8 ,it   
means merely this4 ,if any event has the
 character of being an exhibition of the
 solar spectrum under certain assigned  
circumstances1 it will also have the    
character of exhibiting dark lines in   
that spectrum4  ,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 own4 ,the aim of science is to 
express the relations between their     
characters in terms of the mutual       
structural relations between the events 
thus characterised4 ,the mutual         
structural relations between events are 
both spatial and temporal4 ,if you think
 of them as merely spatial you are      
omitting the temporal element1 and if   
you think of them as merely temporal you
 are omitting the spatial element4 ,thus
 when you think of space alone1 or of   
time alone1 you are dealing in          
abstractions1 namely1 you are leaving   
out an essential element in the life of 
nature as known to you in the experience
 of your senses4 ,furthermore there are 
different ways of making these          
abstractions which we think of as space 
and as time2 and under some             
circumstances we adopt one way and under
 other circumstances we adopt another   

way4 ,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     
circumstances4 ,and equally what we mean
 by time under one set of circumstances 
is not what we mean by time under       
another set of circumstances4 ,by saying
 that space and time are abstractions1  
,i do not mean that they do not express 
for us real facts about nature4 ,what ,i
 mean is that there are no spatial facts
 or temporal facts apart from physical  
nature1 namely that space and time are  
merely ways of expressing certain truths
 about the relations between events4    
,also that under different circumstances
 there are different sets of truths     
about the universe which are naturally  
presented to us as statements about     
space4 ,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 
circumstances4 ,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    
time8' ,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 ether1 the    
perihelion of mercury1 and the positions
 of the stars in the neighbourhood of   
the sun1 have been solved by reference  
to this purely relative significance of 
space and time4  ,i want now to recall  
your attention to ,cleopatra's ,needle1 
which ,i have not yet done with4 ,as you
 are walking along the ,embankment you  
suddenly look up and say1 ',hullo1      
there's the ,needle4' ,in other words1  
you recognise it4 ,you cannot recognise 
an event2 because when it is gone1 it is
 gone4 ,you may observe another event of
 analogous character1 but the actual    
chunk of the life of nature is          
inseparable from its unique occurrence4 

,but a character of an event can be     
recognised4 ,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 ,needle4 ,things which we  
thus recognise ,i call objects4 ,an     
object is situated in those events or in
 that stream of events of which it      
expresses the character4 ,there are many
 sorts of objects4 ,for example1 the    
colour green is an object according to  
the above definition4 ,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 situated4 ,for this purpose we can
 mainly concentrate on two types of     
objects1 which ,i will call material    
physical objects and scientific objects4
 ,a material physical object is an      
ordinary bit of matter1 ,cleopatra's    
,needle for example4 ,this is a much    
more complicated type of object than a  
mere colour1 such as the colour of the  

,needle4 ,i call these simple objects1  
such as colours or sounds1              
sense-objects4 ,an artist will train    
himself to attend more particularly to  
sense-objects where the ordinary person 
attends normally to material objects4   
,thus if you were walking with an       
artist1 when you said ',there's         
,cleopatra's ,needle1' perhaps he       
simultaneously exclaimed ',there's a    
nice bit of colour4' ,yet you were both 
expressing your recognition of different
 component characters of the same event4
 ,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 situations4   
,for example1 when we know that there is
 a blazing fire 7i4e4 material and      
scientific objects undergoing various   
exciting adventures amid events7 and    

opposite to it a mirror 7which is       
another material object7 and the        
positions of a man's face and eyes      
gazing into the mirror1 we know that he 
can perceive the redness of the flame   
situated in an event behind the         
mirror--thus1 to a large extent1 the    
appearance of sense-objects is          
conditioned by the adventures of        
material objects4 ,the analysis of these
 adventures makes us aware of another   
character of events1 namely their       
characters as fields of activity which  
determine the subsequent events to which
 they will pass on the objects situated 
in them4 ,we express these fields of    
activity in terms of gravitational1     
electromagnetic1 or chemical forces and 
attractions4 ,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 events4 ,i mean  
molecules and electrons4 ,these objects 
are not recognised in isolation4 ,we    

cannot well miss ,cleopatra's ,needle1  
if we are in its neighbourhood2 but no  
one has seen a single molecule or a     
single electron1 yet the characters of  
events are only explicable to us by     
expressing them in terms of these       
scientific objects4 ,undoubtedly        
molecules and electrons are             
abstractions4 ,but then so is           
,cleopatra's ,needle4 ,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 nothing4 ,it merely means that its  
existence is only one factor of a more  
concrete element of nature4 ,so an      
electron is abstract because you cannot 
wipe out the whole structure of events  
and yet retain the electron in          
existence4 ,in the same way the grin on 
the cat is abstract2 and the molecule is
 really in the event in the same sense  
as the grin is really on the cat's face4
 ,now the more ultimate sciences such as
 ,chemistry or ,physics cannot express  

their ultimate laws in terms of such    
vague objects as the sun1 the earth1    
,cleopatra's ,needle1 or a human body4  
,such objects more properly belong to   
,astronomy1 to ,geology1 to             
,engineering1 to ,archaeology1 or to    
,biology4 ,chemistry and ,physics only  
deal with them as exhibiting statistical
 complexes of the effects of their more 
intimate laws4 ,in a certain sense1 they
 only enter into ,physics and ,chemistry
 as technological applications4 ,the    
reason is that they are too vague4      
,where does ,cleopatra's ,needle begin  
and where does it end8 ,is the soot part
 of it8 ,is it a different object when  
it sheds a molecule or when its surface 
enters into chemical combination with   
the acid of a ,london fog8 ,the         
definiteness and permanence of the      
,needle is nothing to the possible      
permanent definiteness of a molecule as 
conceived by science1 and the permanent 
definiteness of a molecule in its turn  
yields to that of an electron4 ,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 them4  ,again when we seek  
definitely to express the relations of  
events which arise from their           
spatio-temporal structure1 we           
approximate to simplicity by            
progressively diminishing the extent    
7both temporal and spatial7 of the      
events considered4 ,for example1 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 relation4 
,but suppose we progressively diminish  
the time considered to a second1 to a   
hundredth of a second1 to a thousandth  
of a second1 and so on4 ,as we pass     
along such a series we approximate to an
 ideal simplicity of structural         
relations of the pairs of events        
successively considered1 which ideal we 

call the spatial relations of the       
,needle to the barge at some instant4   
,even these relations are too           
complicated for us1 and we consider     
smaller and smaller bits of the ,needle 
and of the barge4 ,thus we finally reach
 the ideal of an event so restricted in 
its extension as to be without extension
 in space or extension in time4 ,such an
 event is a mere spatial point-flash of 
instantaneous duration4 ,i call such an 
ideal event an 'event-particle4' ,you   
must not think of the world as          
ultimately built up of event-particles4 
,that is to put the cart before the     
horse4 ,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 structure4
 ,we can express the properties of this 
structure in terms of the ideal limits  
to routes of approximation1 which ,i    
have termed event-particles4            

,accordingly event-particles are        
abstractions in their relations to the  
more concrete events4 ,but then by this 
time you will have comprehended that you
 cannot analyse concrete nature without 
abstracting4 ,also ,i repeat1 the       
abstractions of science are entities    
which are truly in nature1 though they  
have no meaning in isolation from       
nature4  ,the character of the          
spatio-temporal structure of events can 
be fully expressed in terms of relations
 between these more abstract            
event-particles4 ,the advantage of      
dealing with event-particles is that    
though they are abstract and complex in 
respect to the finite events which we   
directly observe1 they are simpler than 
finite events in respect to their mutual
 relations4 ,accordingly they express   
for us the demands of an ideal accuracy1
 and of an ideal simplicity in the      
exposition of relations4 ,these         
event-particles are the ultimate        
elements of the four-dimensional        

space-time manifold which the theory of 
relativity presupposes4 ,you will have  
observed that each event-particle is as 
much an instant of time as it is a point
 of space4 ,i have called it an         
instantaneous point-flash4 ,thus in the 
structure of this space-time manifold   
space is not finally discriminated from 
time1 and the possibility remains open  
for diverse modes of discrimination     
according to the diverse circumstances  
of observers4 ,it is this possibility   
which makes the fundamental distinction 
between the new way of conceiving the   
universe and the old way4 ,the secret of
 understanding relativity is to         
understand this4 ,it is of no use       
rushing in with picturesque paradoxes1  
such as ',space caught bending1' if you 
have not mastered this fundamental      
conception which underlies the whole    
theory4 ,when ,i say that it underlies  
the whole theory1 ,i mean that in my    
opinion it ought to underlie it1 though 
,i may confess some doubts as to how far

 all expositions of the theory have     
really understood its implications and  
its premises4  ,our measurements when   
they are expressed in terms of an ideal 
accuracy are measurements which express 
properties of the space-time manifold4  
,now there are measurements of different
 sorts4 ,you can measure lengths1 or    
angles1 or areas1 or volumes1 or times4 
,there are also other sorts of measures 
such as measurements of intensity of    
illumination1 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 time4 ,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 manifold4 ,for example1 in a        
rectangular field you start from one    
corner at a given time1 you measure a   
definite distance along one side1 you   

then strike out into the field at right 
angles1 and then measure a definite     
distance parallel to the other pair of  
sides1 you then rise vertically a       
definite height and take the time4 ,at  
the point and at the time which you thus
 reach there is occurring a definite    
instantaneous point-flash of nature4 ,in
 other words1 your four measurements    
have determined a definite              
event-particle belonging to the         
four-dimension space-time manifold4     
,these measurements have appeared to be 
very simple to the land-surveyor and    
raise in his mind no philosophic        
difficulties4 ,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 earth4 ,suppose that they     
construe the operations of the ,english 
land-surveyors in reference to the space
 natural to a being on ,mars1 namely a  
,martio-centric space in which that     
planet is fixed4 ,the earth is moving   

relatively to ,mars and is rotating4 ,to
 the beings on ,mars the operations1    
construed in this fashion1 effect       
measurements of the greatest            
complication4 ,furthermore1 according to
 the relativistic doctrine1 the         
operation of time-measurement on earth  
will not correspond quite exactly to any
 time-measurement on ,mars4  ,i have    
discussed this example in order to make 
you realise that in thinking of the     
possibilities of measurement in the     
space-time manifold1 we must not confine
 ourselves merely to those minor        
variations which might seem natural to  
human beings on the earth4 ,let us make 
therefore the general statement that    
four measurements1 respectively of      
independent types 7such as measurements 
of lengths in three directions and a    
time71 can be found such that a definite
 event-particle is determined by them in
 its relations to other parts of the    
manifold4  ,if 7p1 p1 p1 p7 be a set of 
measurements of this system1 then the   

event-particle which is thus determined 
will be said to have p1 p1 p1 p as its  
co-ordinates in this system of          
measurement4 ,suppose that we name it   
the p-system of measurement4 ,then in   
the same p-system by properly varying   
7p1 p1 p1 p7 every event-particle that  
has been1 or will be1 or instantaneously
 is now1 can be indicated4 ,furthermore1
 according to any system of measurement 
that is natural to us1 three of the     
co-ordinates will be measurements of    
space and one will be a measurement of  
time4 ,let us always take the last      
co-ordinate to represent the            
time-measurement4 ,then we should       
naturally say that 7p1 p1 p7 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     
manifold4 ,that manifold is all that    
there is for the determination of the   
meaning of space and time4 ,we have got 

to determine the meaning of a           
space-point in terms of the             
event-particles of the four-dimensional 
manifold4 ,there is only one way to do  
this4 ,note that if we vary the time and
 take times with the same three space   
co-ordinates1 then the event-particles1 
thus indicated1 are all at the same     
point4 ,but seeing that there is nothing
 else except the event-particles1 this  
can only mean that the point 7p1 p1 p7  
of the space in the p-system is merely  
the collection of event-particles 7p1 p1
 p1 p71 where p is varied and 7p1 p1 p7 
is kept fixed4 ,it is rather            
disconcerting to find that a point in   
space is not a simple entity2 but it is 
a conclusion which follows immediately  
from the relative theory of space4      
,furthermore the inhabitant of ,mars    
determines event-particles by another   
system of measurements4 ,call his system
 the q-system4 ,according to him 7q1 q1 
q1 q7 determines an event-particle1 and 
7q1 q1 q7 determines a point and q a    

time4 ,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 point4 ,thus the q-space 
for the man on ,mars is quite different 
from the p-space for the land-surveyor  
on earth4  ,so far in speaking of space 
we have been talking of the timeless    
space of physical science1 namely1 of   
our concept of eternal space in which   
the world adventures4 ,but the space    
which we see as we look about is        
instantaneous space4 ,thus if our       
natural perceptions are adjustable to   
the p-system of measurements we see     
instantaneously all the event-particles 
at some definite time p1 and observe a  
succession of such spaces as time moves 
on4 ,the timeless space is achieved by  
stringing together all these            
instantaneous spaces4 ,the points of an 
instantaneous space are event-particles1
 and the points of an eternal space are 
strings of event-particles occurring in 

succession4 ,but the man on ,mars will  
never perceive the same instantaneous   
spaces as the man on the earth4 ,this   
system of instantaneous spaces will cut 
across the earth-man's system4 ,for the 
earth-man there is one instantaneous    
space which is the instantaneous        
present1 there are the past spaces and  
the future spaces4 ,but the present     
space of the man on ,mars cuts across   
the present space of the man on the     
earth4 ,so that of the event-particles  
which the earth-man thinks of as        
happening now in the present1 the man on
 ,mars thinks that some are already past
 and are ancient history1 that others   
are in the future1 and others are in the
 immediate present4 ,this break-down in 
the neat conception of a past1 a        
present1 and a future is a serious      
paradox4 ,i call two event-particles    
which on some or other system of        
measurement are in the same             
instantaneous space 'co-present'        
event-particles4 ,then it is possible   

that ,a and ,b may be co-present1 and   
that ,a and ,c may be co-present1 but   
that ,b and ,c may not be co-present4   
,for example1 at some inconceivable     
distance from us there are events       
co-present with us now and also         
co-present with the birth of ,queen     
,victoria4 ,if ,a and ,b are co-present 
there will be some systems in which ,a  
precedes ,b and some in which ,b        
precedes ,a4 ,also there can be no      
velocity quick enough to carry a        
material particle from ,a to ,b or from 
,b to ,a4 ,these different              
measure-systems with their divergences  
of time-reckoning are puzzling1 and to  
some extent affront our common sense4   
,it is not the usual way in which we    
think of the ,universe4 ,we think of one
 necessary time-system and one necessary
 space4 ,according to the new theory1   
there are an indefinite number of       
discordant time-series and an indefinite
 number of distinct spaces4 ,any        
correlated pair1 a time-system and a    

space-system1 will do in which to fit   
our description of the ,universe4 ,we   
find that under given conditions our    
measurements are necessarily made in    
some one pair which together form our   
natural measure-system4 ,the difficulty 
as to discordant time-systems is partly 
solved by distinguishing between what ,i
 call the creative advance of nature1   
which is not properly serial at all1 and
 any one time series4 ,we habitually    
muddle together this creative advance1  
which we experience and know as the     
perpetual transition of nature into     
novelty1 with the single-time series    
which we naturally employ for           
measurement4 ,the various time-series   
each measure some aspect of the creative
 advance1 and the whole bundle of them  
express all the properties of this      
advance which are measurable4 ,the      
reason why we have not previously noted 
this difference of time-series is the   
very small difference of properties     
between any two such series4 ,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 light4 ,now light    
takes about fifty minutes to get round  
the earth's orbit2 and the earth takes  
rather more than #ag1eca half-hours to  
do the same4 ,hence all the effects due 
to this motion are of the order of the  
ratio of one to the square of #aj1jjj4  
,accordingly an earth-man and a sun-man 
have only neglected effects whose       
quantitative magnitudes all contain the 
factor #a_/aj4 ,evidently such effects  
can only be noted by means of the most  
refined observations4 ,they have been   
observed however4 ,suppose we compare   
two observations on the velocity of     
light made with the same apparatus as we
 turn it through a right angle4 ,the    
velocity of the earth relatively to the 
sun is in one direction1 the velocity of
 light relatively to the ether should be
 the same in all directions4 ,hence if  
space when we take the ether as at rest 

means the same thing as space when we   
take the earth as at rest1 we ought to  
find that the velocity of light         
relatively to the earth varies according
 to the direction from which it comes4  
,these observations on earth constitute 
the basic principle of the famous       
experiments designed to detect the      
motion of the earth through the ether4  
,you all know that1 quite unexpectedly1 
they gave a null result4 ,this is       
completely explained by the fact that1  
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 moving4  ,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 example1 the laws of the   
electromagnetic field1 and the law of   
gravitation4 ,let us take the law of    

gravitation as an example4 ,its         
formulation is as follows3 ,two material
 bodies attract each other with a force 
proportional to the product of their    
masses and inversely proportional to the
 square of their distances4 ,in this    
statement the bodies are supposed to be 
small enough to be treated as material  
particles in relation to their          
distances2 and we need not bother       
further about that minor point4 ,the    
difficulty to which ,i want to draw your
 attention is this3 ,in the formulation 
of the law one definite time and one    
definite space are presupposed4 ,the two
 masses are assumed to be in            
simultaneous positions4  ,but what is   
simultaneous in one time-system may not 
be simultaneous in another time-system4 
,so according to our new views the law  
is in this respect not formulated so as 
to have any exact meaning4 ,furthermore 
an analogous difficulty arises over the 
question of distance4 ,the distance     
between two instantaneous positions1    

i4e4 between two event-particles1 is    
different in different space-systems4   
,what space is to be chosen8 ,thus again
 the law lacks precise formulation1 if  
relativity is accepted4 ,our problem is 
to seek a fresh interpretation of the   
law of gravity in which these           
difficulties are evaded4 ,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 nature1 namely to    
events4 ,also in order to find the ideal
 simplicity of expressions of the       
relations between events1 we restrict   
ourselves to event-particles4 ,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 manifold4   
,these event-particles are the various  
situations of the material particle4 ,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 time4  ,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 other4 ,think of 
the path as a whole4 ,what              
characteristic has that path got which  
would not be shared by any other        
slightly varied path8 ,we are asking for
 more than a law of gravity4 ,we want   
laws of motion and a general idea of the
 way to formulate the effects of        
physical forces4  ,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 path4 ,in so doing 
we are acting in conformity with the    
whole trend of scientific thought during
 the last hundred years1 which has more 
and more concentrated attention on the  
field of force as the immediate agent in

 directing motion1 to the exclusion of  
the consideration of the immediate      
mutual influence between two distant    
bodies4 ,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 manifold4 ,i bring in a
 fundamental physical idea which ,i call
 the 'impetus' to express this physical 
field4 ,the event-particle ,e is related
 to any neighbouring event-particle ,p  
by an element of impetus4 ,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 ,e4
 ,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 manifold4 ,i

 cannot attach any clear conception to  
his interpretation of space and time4   
,my formulae differ slightly from his1  
though they agree in those instances    
where his results have been verified4 ,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 discovery4  ,einstein showed  
how to express the characters of the    
assemblage of elements of impetus of the
 field surrounding an event-particle ,e 
in terms of ten quantities which ,i will
 call ,j#aa1 ,j#ab 7,j#ba71 ,j#bb1      
,j#bc7;,j#cb71 etc4 ,it will be noted   
that there are four spatio-temporal     
measurements relating ,e to its         
neighbour ,p1 and that there are ten    
pairs of such measurements if we are    
allowed to take any one measurement     
twice over to make one such pair4 ,the  
ten ,j's depend merely on the position  
of ,e in the four-dimensional manifold1 
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 ,p4 ,the numerical values of the   
,j's will depend on the system of       
measurement adopted1 but are so adjusted
 to each particular system that the same
 value is obtained for the element of   
impetus between ,e and ,p1 whatever be  
the system of measurement adopted4 ,this
 fact is expressed by saying that the   
ten ,j's form a 'tensor4' ,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 announced4  ,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 ,e4 ,the       
potential is practically what is meant  
by the ordinary gravitation potential1  
when we express ourselves in terms of   

the ,euclidean space in reference to    
which the attracting mass is at rest4   
,the associate-potential is defined by  
the modification of substituting the    
direct distance for the inverse distance
 in the definition of the potential1 and
 its calculation can easily be made to  
depend on that of the old-fashioned     
potential4 ,thus the calculation of the 
,j's--the coefficients of impetus1 as ,i
 will call them--does not involve       
anything very revolutionary in the      
mathematical knowledge of physicists4   
,we now return to the path of the       
attracted particle4 ,we add up all the  
elements of impetus in the whole path1  
and obtain thereby what ,i call the     
'integral impetus4' ,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 lose1 if the    
particle wobbled out of it into a small 
extremely near alternative path4        
,mathematicians would express this by   

saying1 that the integral impetus is    
stationary for an infinitesimal         
displacement4 ,in this statement of the 
law of motion ,i have neglected the     
existence of other forces4 ,but that    
would lead me too far afield4  ,the     
electromagnetic theory has to be        
modified to allow for the presence of a 
gravitational field4 ,thus ,einstein's  
investigations lead to the first        
discovery of any relation between       
gravity and other physical phenomena4   
,in the form in which ,i have put this  
modification1 we deduce ,einstein's     
fundamental principle1 as to the motion 
of light along its rays1 as a first     
approximation which is absolutely true  
for infinitely short waves4 ,einstein's 
principle1 thus partially verified1     
stated in my language is that a ray of  
light always follows a path such that   
the integral impetus along it is zero4  
,this involves that every element of    
impetus along it is zero4  ,in          
conclusion1 ,i must apologise4 ,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 physics4 ,i do not allow that     
physical phenomena are due to oddities  
of space4 ,also ,i have added to the    
dullness of the lecture by my respect   
for the audience4 ,you would have       
enjoyed a more popular lecture with     
illustrations of delightful paradoxes4  
,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 researches4      
,,chapter ,,ix  ,,the ,,ultimate        
,,physical ,,concepts   ,the second     
chapter of this book lays down the first
 principle to be guarded in framing our 
physical concept4 ,we must avoid vicious
 bifurcation4 ,nature is nothing else   
than the deliverance of sense-awareness4
 ,we have no principles whatever to tell
 us what could stimulate mind towards   
sense-awareness4 ,our sole task is to   

exhibit in one system the characters and
 inter-relations of all that is         
observed4 ,our attitude towards nature  
is purely 'behaviouristic1' so far as   
concerns the formulation of physical    
concepts4  ,our knowledge of nature is  
an experience of activity 7or passage74 
,the things previously observed are     
active entities1 the 'events4' ,they are
 chunks in the life of nature4 ,these   
events have to each other relations     
which in our knowledge differentiate    
themselves into space-relations and     
time-relations4 ,but this               
differentiation between space and time1 
though inherent in nature1 is           
comparatively superficial2 and space and
 time are each partial expressions of   
one fundamental relation between events 
which is neither spatial nor temporal4  
,this relation ,i call 'extension4' ,the
 relation of 'extending over' is the    
relation of 'including1' either in a    
spatial or in a temporal sense1 or in   
both4 ,but the mere 'inclusion' is more 

fundamental than either alternative and 
does not require any spatio-temporal    
differentiation4 ,in respect to         
extension two events are mutually       
related so that either 7i7 one includes 
the other1 or 7ii7 one overlaps the     
other without complete inclusion1 or    
7iii7 they are entirely separate4 ,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 properties4     
,such fallacies can be avoided by taking
 account of two elements in our         
experience1 namely1 7i7 our             
observational 'present1' and 7ii7 our   
'percipient event4'  ,our observational 
'present' is what ,i call a 'duration4' 
,it is the whole of nature apprehended  
in our immediate observation4 ,it has   
therefore the nature of an event1 but   
possesses a peculiar completeness which 
marks out such durations as a special   
type of events inherent in nature4 ,a   

duration is not instantaneous4 ,it is   
all that there is of nature with certain
 temporal limitations4 ,in              
contradistinction to other events a     
duration will be called infinite and the
 other events are finite#aj4 ,in our    
knowledge of a duration we distinguish  
7i7 certain included events which are   
particularly discriminated as to their  
peculiar individualities1 and 7ii7 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 duration4 ,the 
duration as a whole is signified#aa by  
that quality of relatedness 7in respect 
to extension7 possessed by the part     
which is immediately under observation2 
namely1 by the fact that there is       
essentially a beyond to whatever is     
observed4 ,i mean by this that every    
event is known as being related to other
 events which it does not include4 ,this
 fact1 that every event is known as     
possessing the quality of exclusion1    

shows that exclusion is as positive a   
relation as inclusion4 ,there are of    
course no merely negative relations in  
nature1 and exclusion is not the mere   
negative of inclusion1 though the two   
relations are contraries4 ,both         
relations are concerned solely with     
events1 and exclusion is capable of     
logical definition in terms of          
inclusion4  #aj ,cf4 note on            
'significance1' pp4 #aig1 #aih4  #aa    
,cf4 ,ch4 ,,iii1 pp4 #ea et seq4        
,perhaps the most obvious exhibition of 
significance is to be found in our      
knowledge of the geometrical character  
of events inside an opaque material     
object4 ,for example we know that an    
opaque sphere has a centre4 ,this       
knowledge has nothing to do with the    
material2 the sphere may be a solid     
uniform billiard ball or a hollow       
lawn-tennis ball4 ,such knowledge is    
essentially the product of significance1
 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 structure4  ,some     
criticisms on ',the ,principles of      
,natural ,knowledge' show that          
difficulty has been found in            
apprehending durations as real          
stratifications of nature4 ,i think that
 this hesitation arises from the        
unconscious influence of the vicious    
principle of bifurcation1 so deeply     
embedded in modern philosophical        
thought4 ,we observe nature as extended 
in an immediate present which is        
simultaneous but not instantaneous1 and 
therefore the whole which is immediately
 discerned or signified as an           
inter-related system forms a            
stratification of nature which is a     
physical fact4 ,this conclusion         
immediately follows unless we admit     
bifurcation in the form of the principle
 of psychic additions1 here rejected4   
,our 'percipient event' is that event   
included in our observational present   

which we distinguish as being in some   
peculiar way our standpoint for         
perception4 ,it is roughly speaking that
 event which is our bodily life within  
the present duration4 ,the theory of    
perception as evolved by medical        
psychology is based on significance4    
,the distant situation of a perceived   
object is merely known to us as         
signified by our bodily state1 i4e4 by  
our percipient event4 ,in fact          
perception requires sense-awareness of  
the significations of our percipient    
event together with sense-awareness of a
 peculiar relation 7situation7 between  
certain objects and the events thus     
signified4 ,our percipient event is     
saved by being the whole of nature by   
this fact of its significations4 ,this  
is the meaning of calling the percipient
 event our standpoint for perception4   
,the course of a ray of light is only   
derivatively connected with perception4 
,what we do perceive are objects as     
related to events signified by the      

bodily states excited by the ray4 ,these
 signified events 7as is the case of    
images seen behind a mirror7 may have   
very little to do with the actual course
 of the ray4 ,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 welfare4 ,the whole world of      
events is signified1 but there are some 
which exact the death penalty for       
inattention4  ,the percipient event is  
always here and now in the associated   
present duration4 ,it has1 what may be  
called1 an absolute position in that    
duration4 ,thus one definite duration is
 associated with a definite percipient  
event1 and we are thus aware of a       
peculiar relation which finite events   
can bear to durations4 ,i call this     
relation 'cogredience4' ,the notion of  
rest is derivative from that of         
cogredience1 and the notion of motion is
 derivative from that of inclusion      

within a duration without cogredience   
with it4 ,in fact motion is a relation  
7of varying character7 between an       
observed event and an observed duration1
 and cogredience is the most simple     
character or subspecies of motion4 ,to  
sum up1 a duration and a percipient     
event are essentially involved in the   
general character of each observation of
 nature1 and the percipient event is    
cogredient with the duration4  ,our     
knowledge of the peculiar characters of 
different events depends upon our power 
of comparison4 ,i call the exercise of  
this factor in our knowledge            
'recognition1' and the requisite        
sense-awareness of the comparable       
characters ,i call 'sense-recognition4' 
,recognition and abstraction essentially
 involve each other4 ,each of them      
exhibits an entity for knowledge which  
is less than the concrete fact1 but is a
 real factor in that fact4 ,the most    
concrete fact capable of separate       
discrimination is the event4 ,we cannot 

abstract without recognition1 and we    
cannot recognise without abstraction4   
,perception involves apprehension of the
 event and recognition of the factors of
 its character4  ,the things recognised 
are what ,i call 'objects4' ,in this    
general sense of the term the relation  
of extension is itself an object4 ,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 event2 namely1 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 object4   
,even so1 there are different types of  
objects1 and statements which are true  
of objects of one type are not in       
general true of objects of other types4 
,the objects with which we are here     
concerned in the formulation of physical
 laws are material objects1 such as bits
 of matter1 molecules and electrons4 ,an
 object of one of these types has       
relations to events other than those    

belonging to the stream of its          
situations4 ,the fact of its situations 
within this stream has impressed on all 
other events certain modifications of   
their characters4 ,in truth the object  
in its completeness may be conceived as 
a specific set of correlated            
modifications of the characters of all  
events1 with the property that these    
modifications attain to a certain focal 
property for those events which belong  
to the stream of its situations4 ,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 object4 ,but the     
object cannot really be separated from  
its field4 ,the object is in fact       
nothing else than the systematically    
adjusted set of modifications of the    
field4 ,the conventional limitation of  
the object to the focal stream of events
 in which it is said to be 'situated' is
 convenient for some purposes1 but it   

obscures the ultimate fact of nature4   
,from this point of view the antithesis 
between action at a distance and action 
by transmission is meaningless4 ,the    
doctrine of this paragraph is nothing   
else than another way of expressing the 
unresolvable multiple relation of an    
object to events4  ,a complete          
time-system is formed by any one family 
of parallel durations4 ,two durations   
are parallel if either 7i7 one includes 
the other1 or 7ii7 they overlap so as to
 include a third duration common to     
both1 or 7iii7 are entirely separate4   
,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 duration4 ,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-systems4 ,its divergence from      

,einstein's concept of nature will be   
briefly indicated later4  ,the          
instantaneous spaces of a given         
time-system are the ideal 7non-existent7
 durations of zero temporal thickness   
indicated by routes of approximation    
along series formed by durations of the 
associated family4 ,each such           
instantaneous space represents the ideal
 of nature at an instant and is also a  
moment of time4 ,each time-system thus  
possesses an aggregate of moments       
belonging to it alone4 ,each            
event-particle lies in one and only one 
moment of a given time-system4 ,an      
event-particle has three characters#ab3 
7i7 its extrinsic character which is its
 character as a definite route of       
convergence among events1 7ii7 its      
intrinsic character which is the        
peculiar quality of nature in its       
neighbourhood1 namely1 the character of 
the physical field in the neighbourhood1
 and 7iii7 its position4  #ab ,cf4 pp4  
#hb et seq4  ,the position of an        

event-particle arises from the aggregate
 of moments 7no two of the same family7 
in which it lies4 ,we fix our attention 
on one of these moments which is        
approximated to by the short duration of
 our immediate experience1 and we       
express position as the position in this
 moment4 ,but the event-particle        
receives its position in moment ,m in   
virtue of the whole aggregate of other  
moments ,m'1 ,m''1 etc41 in which it    
also lies4 ,the differentiation of ,m   
into a geometry of event-particles      
7instantaneous points7 expresses the    
differentiation of ,m by its            
intersections with moments of alien     
time-systems4 ,in this way planes and   
straight lines and event-particles      
themselves find their being4 ,also the  
parallelism of planes and straight lines
 arises from the parallelism of the     
moments of one and the same time-system 
intersecting ,m4 ,similarly the order of
 parallel planes and of event-particles 
on straight lines arises from the       

time-order of these intersecting        
moments4 ,the explanation is not given  
here#ac4 ,it is sufficient now merely to
 mention the sources from which the     
whole of geometry receives its physical 
explanation4  #ac ,cf4 ,principles of   
,natural ,knowledge1 and previous       
chapters of the present work4  ,the     
correlation of the various momentary    
spaces of one time-system is achieved by
 the relation of cogredience4 ,evidently
 motion in an instantaneous space is    
unmeaning4 ,motion expresses a          
comparison between position in one      
instantaneous space with positions in   
other instantaneous spaces of the same  
time-system4 ,cogredience yields the    
simplest outcome of such comparison1    
namely1 rest4  ,motion and rest are     
immediately observed facts4 ,they are   
relative in the sense that they depend  
on the time-system which is fundamental 
for the observation4 ,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-system4 
,in this way each time-system possesses 
its own permanent timeless space        
peculiar to it alone1 and each such     
space is composed of timeless points    
which belong to that time-system and to 
no other4 ,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 times1 in which points and  
moments have different meanings4  ,the  
source of order has already been        
indicated and that of congruence is now 
found4 ,it depends on motion4 ,from     
cogredience1 perpendicularity arises2   
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 7cf4 loc4 cit474     
,the resulting formulae are those for   
the electromagnetic theory of           

relativity1 or1 as it is now termed1 the
 restricted theory4 ,but there is this  
vital difference3 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 7in distinction from the          
extensional structure of events74 ,it   
simply marks the fact that our          
congruence determination embraces both  
times and spaces in one universal       
system1 and therefore if two arbitrary  
units are chosen1 one for all spaces and
 one for all times1 their ratio will be 
a velocity which is a fundamental       
property of nature expressing the fact  
that times and spaces are really        
comparable4  ,the physical properties of
 nature are expressed in terms of       
material objects 7electrons1 etc474 ,the
 physical character of an event arises  
from the fact that it belongs to the    
field of the whole complex of such      
objects4 ,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 events4  ,the             
spatio-temporal measurableness of nature
 arises from 7i7 the relation of        
extension between events1 and 7ii7 the  
stratified character of nature arising  
from each of the alternative            
time-systems1 and 7iii7 rest and motion1
 as exhibited in the relations of finite
 events to time-systems4 ,none of these 
sources of measurement depend on the    
physical characters of finite events as 
exhibited by the situated objects4 ,they
 are completely signified for events    
whose physical characters are unknown4  
,thus the spatio-temporal measurements  
are independent of the objectival       
physical characters4 ,furthermore the   
character of our knowledge of a whole   
duration1 which is essentially derived  
from the significance of the part within
 the immediate field of discrimination1 
constructs it for us as a uniform whole 
independent1 so far as its extension is 

concerned1 of the unobserved characters 
of remote events4 ,namely1 there is a   
definite whole of nature1 simultaneously
 now present1 whatever may be the       
character of its remote events4 ,this   
consideration reinforces the previous   
conclusion4 ,this conclusion leads to   
the assertion of the essential          
uniformity of the momentary spaces of   
the various time-systems1 and thence to 
the uniformity of the timeless spaces of
 which there is one to each time-system4
  ,the analysis of the general character
 of observed nature set forth above     
affords explanations of various         
fundamental observational facts3 77 ,it 
explains the differentiation of the one 
quality of extension into time and      
space4 77 ,it gives a meaning to the    
observed facts of geometrical and       
temporal position1 of geometrical and   
temporal order1 and of geometrical      
straightness and planeness4 77 ,it      
selects one definite system of          
congruence embracing both space and     

time1 and thus explains the concordance 
as to measurement which is in practice  
attained4 77 ,it explains 7consistently 
with the theory of relativity7 the      
observed phenomena of rotation1 e4g4    
,foucault's pendulum1 the equatorial    
bulge of the earth1 the fixed senses of 
rotation of cyclones and anticyclones1  
and the gyro-compass4 ,it does this by  
its admission of definite               
stratifications of nature which are     
disclosed by the very character of our  
knowledge of it4 77 ,its explanations of
 motion are more fundamental than those 
expressed in 772 for it explains what is
 meant by motion itself4 ,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   
observation4 ,this motion expresses a   
real relation of the object to the rest 
of nature4 ,the quantitative expression 
of this relation will vary according to 
the time-system selected for its        

expression4  ,this theory accords no    
peculiar character to light beyond that 
accorded to other physical phenomena    
such as sound4 ,there is no ground for  
such a differentiation4 ,some objects we
 know by sight only1 and other objects  
we know by sound only1 and other objects
 we observe neither by light nor by     
sound but by touch or smell or          
otherwise4 ,the velocity of light varies
 according to its medium and so does    
that of sound4 ,light moves in curved   
paths under certain conditions and so   
does sound4 ,both light and sound are   
waves of disturbance in the physical    
characters of events2 and 7as has been  
stated above1 p4 #ahh7 the actual course
 of the light is of no more importance  
for perception than is the actual course
 of the sound4 ,to base the whole       
philosophy of nature upon light is a    
baseless assumption4 ,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 units4 ,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 field4 ,this        
completely disposes of any necessity for
 differentiating light from other       
physical phenomena as possessing any    
peculiar fundamental character4  ,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      
thought4 ,otherwise there is no meaning 
to the concept of one presentation of   
your extended measuring rod ,,ab4 ,why  
not ,,ab where ,b is the end ,b five    
minutes later8 ,measurement presupposes 
for its possibility nature as a         

simultaneity1 and an observed object    
present then and present now4 ,in other 
words1 measurement of extended nature   
requires some inherent character in     
nature affording a rule of presentation 
of events4 ,furthermore congruence      
cannot be defined by the permanence of  
the measuring rod4 ,the permanence is   
itself meaningless apart from some      
immediate judgment of self-congruence4  
,otherwise how is an elastic string     
differentiated from a rigid measuring   
rod8 ,each remains the same             
self-identical object4 ,why is one a    
possible measuring rod and the other not
 so8 ,the meaning of congruence lies    
beyond the self-identity of the object4 
,in other words measurement presupposes 
the measurable1 and the theory of the   
measurable is the theory of congruence4 
,furthermore the admission of           
stratifications of nature bears on the  
formulation of the laws of nature4 ,it  
has been laid down that these laws are  
to be expressed in differential         

equations which1 as expressed in any    
general system of measurement1 should   
bear no reference to any other          
particular measure-system4 ,this        
requirement is purely arbitrary4 ,for a 
measure-system measures something       
inherent in nature2 otherwise it has no 
connexion with nature at all4 ,and that 
something which is measured by a        
particular measure-system may have a    
special relation to the phenomenon whose
 law is being formulated4 ,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-system4 ,the field can of     
course be expressed in any              
measure-systems1 but the particular     
reference will remain as the simple     
physical explanation4   ,,note3 ,,on    
,,the ,,greek ,,concept ,,of ,a ,,point 
,the preceding pages had been passed for
 press before ,i had the pleasure of    

seeing ,sir ,t4 ,l4 ,heath's ,euclid in 
,greek#ad4 ,in the original ,euclid's   
first definition is       1   4  ,i have
 quoted it on p4 #hf in the expanded    
form taught to me in childhood1 'without
 parts and without magnitude4' ,i should
 have consulted ,heath's ,english       
edition--a classic from the moment of   
its issue--before committing myself to a
 statement about ,euclid4 ,this is      
however a trivial correction not        
affecting sense and not worth a note4 ,i
 wish here to draw attention to ,heath's
 own note to this definition in his     
,euclid in ,greek4 ,he summarises ,greek
 thought on the nature of a point1 from 
the ,pythagoreans1 through ,plato and   
,aristotle1 to ,euclid4 ,my analysis of 
the requisite character of a point on   
pp4 #hi and #ij is in complete agreement
 with the outcome of the ,greek         
discussion4  #ad ,camb4 ,univ4 ,press1  
#aibj4   ,,note3 ,,on ,,significance    
,,and ,,infinite ,,events  ,the theory  
of significance has been expanded and   

made more definite in the present       
volume4 ,it had already been introduced 
in the ,principles of ,natural          
,knowledge 7cf4 subarticles #c4c to #c4h
 and #af4a1 #af4b1 #ai4d1 and articles  
#bj1 #ba74 ,in reading over the proofs  
of the present volume1 ,i come to the   
conclusion that in the light of this    
development my limitation of infinite   
events to durations is untenable4 ,this 
limitation is stated in article #cc of  
the ,principles and at the beginning of 
,chapter ,,iv 7p4 #gd7 of this book4    
,there is not only a significance of the
 discerned events embracing the whole   
present duration1 but there is a        
significance of a cogredient event      
involving its extension through a whole 
time-system backwards and forwards4 ,in 
other words the essential 'beyond' in   
nature is a definite beyond in time as  
well as in space cf4 pp4 #ec1 #aid4     
,this follows from my whole thesis as to
 the assimilation of time and space and 
their origin in extension4 ,it also has 

the same basis in the analysis of the   
character of our knowledge of nature4   
,it follows from this admission that it 
is possible to define point-tracks i4e4 
the points of timeless spaces as        
abstractive elements4 ,this is a great  
improvement as restoring the balance    
between moments and points4 ,i still    
hold however to the statement in        
subarticle #ce4d of the ,principles that
 the intersection of a pair of          
non-parallel durations does not present 
itself to us as one event4 ,this        
correction does not affect any of the   
subsequent reasoning in the two books4  
,i may take this opportunity of pointing
 out that the 'stationary events' of    
article #eg of the ,principles are      
merely cogredient events got at from an 
abstract mathematical point of view4    
,,index  ,in the case of terms of       
frequent occurrence1 only those         
occurrences are indexed which are of    
peculiar importance for the elucidation 
of meaning4    ,a or an1 #aa            

,abraham1 #aje    ,absolute position1   
#aje1 #ajf1 #aad1 #ahh    ,abstraction1 
#cc1 #cg1 #afh1 #aga1 #agc2             
extensive1 #fe1 #gi1 #he    ,abstractive
 element1 #hd2     set1 #fa1 #gi        
,action at a distance1 #aei1 #aij       
,action by transmission1 #aei1 #aij     
,active conditions1 #aeh    ,activity1  
field of1 #agj1 #aha    ,adjunction1    
#aja    ,aggregate1 #bc    ,alexander1  
,prof41 viii    ,alexandria1 #ga        
,alfred the ,great1 #acg                
,anticipation1 #fi    ,anti-prime1 #hh  
,apparent nature1 #ca1 #ci    ,area1    
#ii2     momental1 #ajc2     vagrant1   
#ajc    ,aristotelian logic1 #aej       
,aristotle1 #af1 #ag1 #ah1 #bd1 #aig    
,associate-potential1 #ahc    ,atom1 #ag
    ,attribute1 #ba1 #bf1 #aej          
,awareness1 #c    ,axiom1 #cf1 #aba     
,axioms of congruence1 #abh et seqq4    
,bacon1 ,francis1 #gh                   
,behaviouristic1 #ahe    ,bergson1 #ed  
,berkeley1 #bh    ,between1 #fd         
,beyond1 #ahf1 #aih    ,bifurcation1 vi1

 #cj1 #ahe1 #ahg    ,boundary1 #ajj2    
moment1 #fc2     particle1 #ajj         
,broad1 ,c4 ,d41 viii     ,calculation1 
formula of1 #de1 #aeh    ,cambridge1 #ig
    ,causal nature1 #ca1 #ci            
,causation1 #ca1 #adf    ,centrifugal   
force1 #ach    ,change1 uniformity of1  
#adj    ,character1 extrinsic1 #hb1 #hi1
 #ij1 #aac1 #aia2     intrinsic1 #hj1   
#hb1 #ij1 #aac1 #aia    ,charge1 #afj   
,closure of nature1 #d    ,coefficient  
of drag1 #acc    ,coefficients of       
impetus1 #ahc    ,cogredience1 #aaj1    
#ahh    ,coherence1 #bi    ,comparison1 
#abd1 #abe1 #adc1 #ahi    ,complex1 #ac 
,conceptual nature1 #de2     space1 #if 
,concrete facts1 #afg1 #aga1 #ahi       
,conditioning events1 #aeb              
,conditions1 active1 #aeh               
,congruence1 #fe1 #if1 #aah1 #abj1 #abg1
 #aif    ,continuity1 #aeg2             
,dedekindian1 #ajb2     of events1 #gf2 
of nature1 #ei1 #gf    ,convention1 #aba
    ,convergence1 #fb1 #gi2     law of1 
#hb    ,conveyance1 #aed1 #aee          

,co-present1 #agg    ,covering1 #hc     
,creative advance1 #agh    ,critical    
velocity1 #aic1 #aie    ,curvature of   
space-time1 #ahb    ,cyclone1 #aid      
,dedekindian continuity1 #ajb           
,definite1 #ec1 #aid1 #aih              
,delusions1 #ca1 #ch    ,delusive       
perceptual object1 #aec    ,demarcation 
of events1 #add    ,demonstrative       
phrase1 #f    ,descriptive phrase1 #f1  
#aj    ,differential equations1 #aif    
,discrimination1 #ad1 #ej1 #add         
,diversification of nature1 #ae         
,duddington1 ,mrs1 #dg    ,duration1    
#cg1 #ec1 #ee1 #ahf    ,durations1      
families of1 #ei1 #gc1 #aij             
,dynamical axes1 #ach     ,einstein1    
vii1 #ajb1 #aca1 #afd1 #afe1 #aha1 #ahb1
 #ahc1 #ahd1 #aia    ,electromagnetic   
field1 #agi    ,electron1 #cj1 #adf1    
#aeh1 #aga    ,element1 #ag2            
abstractive1 #hd    ,elliptical         
phraseology1 #g    ,empty space1 #ade   
,entity1 #e1 #ac    ,equal in           
abstractive force1 #hc    ,error1 #fh   

,ether1 #ah1 #gh1 #afj2     material1   
#gh2     of events1 #gh    ,euclid1 #he1
 #id1 #aig    ,euler1 #adj    ,event1   
#ae1 #eb1 #ge1 #afe2     percipient1    
#ajg1 #aeb1 #ahf    ,event-particle1    
#hf1 #ic1 #id1 #agb1 #aia    ,events1   
conditioning1 #aeb2     continuity of1  
#gf2     demarcation of1 #add2     ether
 of1 #gh2     infinite1 #aig1 #aih2     
limited1 #gd2     passage of1 #cd2      
signified1 #eb2     stationary1 #aih2   
stream of1 #afg2     structure of1 #eb1 
#aff    ,exclusion1 #ahf                
,explanation1 #ig1 #ada    ,extended    
nature1 #aif    ,extension1 #bb1 #eh1   
#ge1 #ahe    ,extensive abstraction1    
#fe1 #gi1 #he    ,extrinsic character1  
#hb1 #hi1 #ij1 #aac1 #aia2              
properties1 #fb     ,fact1 #ab1 #ac     
,factors1 #ab1 #ac1 #ae    ,facts1      
concrete1 #afg1 #aga    ,family of      
durations1 #ei1 #fc1 #gc2     of        
moments1 #fc    ,faraday1 #adf          
,field1 gravitational1 #aig2     of     
activity1 #agj1 #aha2     physical1 #aij

    ,finite truths1 #ab    ,fitzgerald1 
#acc    ,formula of calculation1 #de1   
#aeh    ,foucault1 #ach1 #aid           
,four-dimensional manifold1 #hf         
,fresnel1 #acc    ,future1 the1 #gb1    
#agg     ,galileo1 #aci    ,geometrical 
order1 #aid    ,geometry1 #cf2          
metrical1 #abi    ,gravitation1 #agi et 
seqq4    ,gravitational field1 #aig     
,greek philosophy1 #af2     thought1    
#aig    ,gyro-compass1 #aid     ,heath1 
,sir ,t4 ,l41 #aig    ,here1 #ajg       
,idealists1 #gj    ,immediacy1 #eb2     
of perception1 #gb    ,impetus1 #aha1   
#ahb2     coefficients of1 #ahc2        
integral1 #ahc    ,inclusion1 #ahf      
,individuality1 #ac    ,infinite events1
 #aig1 #aih    ,inge1 ,dr1 #dh          
,ingredient1 #ad    ,ingression1 #add1  
#ade1 #adh1 #aeb    ,inherence1 #hc     
,inside1 #ajf    ,instant1 #cc1 #ce1 #eg
    ,instantaneous plane1 #ia2          
present1 #gb2     spaces1 #hf1 #ij1 #agg
    ,instantaneousness1 #ef1 #eg        
,intersection1 locus of1 #ij            

,intrinsic character1 #hj1 #hb1 #ij1    
#aac1 #aia2     properties1 #fb         
,ionian thinkers1 #ai    ,irrelevance1  
infinitude of1 #ab    ,irrevocableness1 
#ce1 #cg    ,it1 #h     ,julius ,caesar1
 #cf    ,junction1 #gf1 #aja            
,kinetic energy1 #aje2     symmetry1    
#abi    ,knowledge1 #bh1 #cb            
,lagrange1 #adj    ,larmor1 #aca    ,law
 of convergence1 #hb    ,laws of motion1
 #acg1 #aci2     of nature1 #aif        
,leibnizian monadology1 #aej    ,level1 
#ia1 #ib    ,light1 #aie2     ray of1   
#ahh2     velocity of1 #aca    ,limit1  
#eg    ,limited events1 #gd             
,location1 #afj1 #afa    ,locke1 #bg    
,locus1 #ajb2     of intersection1 #ij  
,london1 #ig    ,lorentz1 ,h4 ,a41 #aca1
 #acc    ,lossky1 #dg     ,manifold1    
four-dimensional1 #hf2     space-time1  
#agc    ,material ether1 #gh2           
object1 #afi    ,materialism1 #dc1 #gj  
,matrix1 #aaf    ,matter1 #af1 #ag1 #ai1
 #bj1 #bf    ,maxwell1 #aca1 #acc       
,measurableness1 #aif2     of nature1   

#aic    ,measurement1 #if1 #abj1 #agd1  
#aif2     of time1 #fe1 #adj            
,measure-system1 #aif    ,memory1 #fh   
,metaphysics1 #bh1 #cb    ,metrical     
geometry1 #abi    ,michelson-,morley1   
#aie    ,milton1 #ce    ,mind1 #bg1 #bh 
,minkowski1 viii1 #aca    ,molecule1    
#cb1 #aga    ,moment1 #eg1 #fj1 #hh     
,momental area1 #ajc2     route1 #ajc   
,momentum1 #aje    ,motion1 #aje1 #aad1 
#aag1 #abg1 #ahh1 #aib    ,multiplicity1
 #bb     ,natural philosophy1 #bi1 #cj  
,natural science1 philosophy of1 #df    
,nature1 #c2     apparent1 #ca1 #ci2    
causal1 #ca1 #ci2     conceptual1 #de2  
continuity of1 #ei1 #gf2                
discrimination of1 #add2     extended1  
#aif2     laws of1 #aif2     passage of1
 #ed2     stratification of1 #aid1 #aif2
     system of1 #adf    ,newton1 #bg1   
#acf1 #aci1 #adj     ,object1 #gg1 #abe1
 #adc1 #afi1 #ahi2     delusive         
perceptual1 #aee2     material1 #afi2   
perceptual1 #aec2     physical1 #aee1   
#aeg2     scientific1 #aeh1 #afi2       

uniform1 #afb    ,occupation1 #bb1 #cd1 
#cf1 #ajj1 #aja    ,order1 source of1   
#aib2     spatial1 #ie1 #aid2           
temporal1 #fd1 #ie1 #aid                
,organisation of thought1 #gi           
,outside1 #fc1 #ajj     ,paradox1 #aib  
,parallel1 #fc1 #abg2     durations1    
#aij    ,parallelism1 #ie1 #aia         
,parallelogram1 #abg    ,paris1 #hg1    
#ach    ,parliament1 #abj    ,part1 #ad1
 #ae1 #eh    ,passage of events1 #cd2   
of nature1 #ed    ,past1 the1 #gb1 #agg 
,perception1 #c    ,perceptual objects1 
#adi1 #aec    ,percipience1 #bh         
,percipient event1 #ajg1 #aeb1 #ahf1    
#ahg    ,period of time1 #ea            
,permanence1 #add    ,perpendicularity1 
#aag1 #abg1 #aic    ,philosophy1 #a2    
natural1 #bi1 #cj2     of natural       
science1 #df2     of the sciences1 #b   
,physical field1 #aij2     object1 #aee1
 #aef1 #aeg    ,physics1 speculative1   
#cj    ,place1 #ea    ,plane1 #aia2     
instantaneous1 #ia    ,plato1 #af1 #ag1 
#ah1 #bd1 #aig    ,poincar1 #aba1 #abb1 

#abc    ,point1 #ce1 #hi1 #ia1 #aad1    
#agc1 #agf    ,point-flash1 #agb1 #agc  
,point of space1 #he    ,point1         
timeless1 #aib    ,point-track1 #aac1   
#aih    ,pompey1 #cf    ,position1 #hi1 
#ij1 #ib1 #ic1 #ii1 #aac1 #aia2         
absolute1 #aje1 #ajf1 #aad1 #ahh        
,potential1 #ahc2     associate-1 #ahc  
,predicate1 #ah    ,predication1 #ah    
,present1 the1 #fi1 #gb1 #agg2          
instantaneous1 #gb2     observational1  
#ahf    ,primary qualities1 #bg         
,prime1 #hh    ,process1 #ec1 #ed2      
of nature1 #ed    ,psychic additions1   
#bi1 #ahg    ,punct1 #ib1 #ic1 #id      
,pythagoreans1 #aig     ,quality1 #bg   
,quantum of time1 #afb    ,quantum      
theory1 #afb     ,ray of light1 #ahh    
,reality1 #cj2     of durations1 #ee1   
#ahg    ,recognition1 #abd1 #adc1 #ahi  
,rect1 #ia1 #ib    ,recurrence1 #ce     
,relative motion1 #aag2     velocity1   
#acj    ,relativity1 #afi2              
restricted theory of1 #aic    ,rest1    
#aje1 #aad1 #ahh1 #aib    ,rotation1    

#ach1 #aid    ,route1 #ii2     momental1
 #ajc2     straight1 #ajc    ,russell1  
,bertrand1 #aa1 #abb1 #abc              
,schelling1 #dg    ,science1 #b2        
metaphysical1 #cb    ,scientific        
objects1 #adi1 #aeh1 #afi    ,secondary 
qualities1 #bg    ,self-congruence1 #aif
    ,self-containedness of nature1 #d   
,sense-awareness1 #c1 #fg               
,sense-object1 #adi1 #agj               
,sense-perception1 #c1 #ad              
,sense-recognition1 #adc1 #ahi          
,series1 temporal1 #ff1 #gj1 #he1 #agh  
,set1 abstractive1 #fa1 #gi             
,significance1 #ea1 #ahf1 #ahg1 #ahh1   
#aid1 #aig1 #aih    ,signified events1  
#eb    ,simplicity1 #afc1 #agc          
,simultaneity1 #ec1 #ef1 #aif           
,situation1 #ae1 #gh1 #adg1 #adh1 #aeb1 
#afj1 #ahi    ,solid1 #ii1 #aja1 #ajb2  
vagrant1 #aja    ,sound1 #aie    ,space1
 #af1 #ag1 #ca1 #cc1 #gi2     empty1    
#ade2     timeless1 #hf1 #ajf1 #aad2    
uniformity of1 #aid    ,spaces1         
instantaneous1 #hf1 #ij                 

,space-system1 #agi    ,space-time      
manifold1 #agc    ,spatial-order1 #ie   
,spatio-temporal structure1 #agc        
,speculative demonstration1 #f          
,speculative physics1 #cj    ,standpoint
 for perception1 #ajg1 #ahh    ,station1
 #ajc1 #ajd1 #aac    ,stationary events1
 #aih    ,straight line1 #ia1 #aad1     
#aia2     route1 #ajc    ,stratification
 of nature1 #ahg1 #aid1 #aif    ,stream 
of events1 #afg    ,structure of events1
 #eb1 #aff    ,structure1               
spatio-temporal1 #agc    ,subject1 #ah  
,substance1 #af1 #ah1 #ai1 #aej         
,substratum1 #af1 #ah1 #ba    ,symmetry1
 #aah1 #abf2     kinetic1 #abi          
,system of nature1 #adf    ,system1     
time-1 #aib     ,tarner1 ,edward1 v1 #a 
,temporal order1 #fd1 #ie1 #aid         
,temporal series1 #ff1 #gj1 #he         
,tensor1 #ahb    ,terminus1 #d    ,the1 
#aa    ,theory1 quantum1 #afb    ,there1
 #aaj1 #ahi    ,this1 #aa    ,thought1  
#c1 #ad    ,timaeus1 the1 #ag1 #bj1 #bd 
,time1 #af1 #ag1 #ca1 #cc1 #di1 #gi2    

measurement of1 #adj2     quantum of1   
#afb2     transcendence of1 #ci         
,time-series1 #agh1 also cf4 ,temporal  
series    ,time-system1 see             
,time-series1 also #ia1 #ig1 #ajd1 #agi1
 #aib    ,timeless point1 #aib2         
space1 #hf1 #ajf1 #aad1 #agg            
,totality1 #hi    ,transcendence of     
time1 #ci    ,transmission1 #bf1 #bh2   
action by1 #aei1 #aij    ,tubes of      
force1 #adf     ,unexhaustiveness1 #ej  
,uniform object1 #afb    ,uniformity of 
change1 #adj2     of space1 #aid        
,vagrant area1 #ajc2     solid1 #aja    
,veblen and ,young1 #cf    ,velocity1   
critical1 #aic1 #aie2     of light1     
#aca1 #aie2     relative1 #acj          
,volume1 #ib1 #aja     ,when1 #ajg      
,where1 #ajg    ,whole1 #eh    ,within1 
#fc     ,young1 ,veblen and1 #cf