Skip to main content

Full text of "Scientific thought"

See other formats 


International   Library  of  Psychology 
Philosophy    and     Scientific    Method 


Scientific  Thought 


Internationa]    Library   of  Psychology 
Philosophy    and     Scientific     Method 

General  Editor:  C.  K.  Ogden,  m.a. 

{Magdalene  College,  Cambridge) 

VOl  r  w/  S   Al  Rl  ADY   ARRANGED 

PHILOSOPHICAL  STUDIES         ....    by  G.  E.  MOORE,  Litt.D. 

THE    MISl  SE    OF  MIND by  Karin  Stephen 

i    Note  by  Henri  Bergson 
CONF1  ICT   AND    DREAM      ....      by  W.  II.  R.  Rivers,  F.R.S. 
PSYCHOLOGY    AND   POLITICS  .        .        .      by  W.   H.  R.  RIVERS,  F.R.S. 
PSYCHOLOGY    AND   ETHNOLOGY     .        .      by  W.    II.   R.   Rivers,  F.R.S. 
THE    ANALYSIS  OF   MATTER     .         .  by  Bertrand  RUSSELL,   F.R.S. 

IK ACTATUS  LOGICO-PHILOSOPHICUS  .         .        .by  L.  Wittgenstein 

Introduction  by  Bertrand  Russell 
MATHEMATICS   FOR   PHILOSOPHERS     .         .     by  G.  H.   Hardy,  F.R.S. 
PSYCHOLOGICAL  TYPES     .         .         .        .      by  C.  G.  Jung,  M.D.,  LL.D. 
THE   PSYCHOLOGY  OF  MYTHS         .        .     by  G.  Elliot  Smith,  F.R.S. 
THE   PHILOSOPHY'   OF  THE    UNCONSCIOUS         by  E.  von  Hartmann 

Introduction  by  Professor  G.  Elliot  Smith 
CHARACTER   AND   THE   UNCONSCIOUS         .      by  J.   H.  van  der  Hoop 

INDIVIDUAL   PSYCHOLOGY by  Alfred  Adler 

SCIENTIFIC   METHOD by  A.  V.  Ritchie 

THE   MEANING  OF  MEANING  .        .  by  C.  K.  Ogden  and  I.  A.  Richards 
THE   THEORY    OF    MEDICAL    DIAGNOSIS 

by  F.  G.  Crookshank,  M.D.,  F.R.C.P. 
THE  ELEMENTS  OF  PSYCHOTHERAPY     6y  William  Brown,  M.D.,  D.Sc. 
THE  MEASUREMENT   OF   EMOTION       .         .      by  W.  Whately  Smith 
Introduction  by  William  Brown 

EMOTION   AND    INSANITY by  S.   Thalbitzer 

Introduction  by  Professor  H.  H  off  ding 

THE   LAWS   OF   FEELING by  F.    Paulhan 

THE  PSYCHOLOGY   OF  MUSIC by  Edward  J.  Dent 

COLOUR-HARMONY by  James  Wood 

THE    DEVELOPMENT   OF  CHINESE   THOUGHT     by  Liang  Che-Chiao 

THE   HISTORY   OF   MATERIALISM d;  F.  A.   Lange 

THE   PRIMITIVE   MIND by  P.  Radin,  Ph.D. 

THE    PSYCHOLOGY    OF    PRIMITIVE    PEOPLES 

by  B.  Malinowski,  Ph.D.,  D.Sc. 
THE    STATISTICAL   METHOD    IN    ECONOMICS   AND    POLITICS 

by  P.   Sargant  Florence 
THE   PSYCHOLOGY   OF   REASONING        .        .  by  Eugenio  Rignano 

THE   PRINCIPLES  OF  CRITICISM    .         .        .  by  I.  A.  Richards 

THE   PHILOSOPHY   OF    'AS   IF'         .         .         .         .         by  H.  Vaihinger 


Scientific  Thought 


By 

C.    D.    pOAD 

M.A.,   Litt.D. 

Sometime    Fellow    of    Trinity    College,    Cambridge 

Professor  of  Philosophy  in  the  University  of  Bristol 

Author  of  "  Perception,  Physics  and  Reality  " 


y 


uT 


NEW   YORK 

HARCOURT,    BRACE   &  COMPANY,   INC. 

LONDON :  KEGAN  PAUL,  TRENCH,  TRUBNER  &  CO.,  LTD. 

I923 


V7? 


PRINTED   IN    GREAT   BRITAIN    BV 


THE   EDINBURGH    PRESS,    Q    A 


ND    II    YOUNG   STREET,    EDINBURGH. 


IN      PIAM      MEMORIAM 

IACOBI  MUDIE 

DUCIS    ILLIUS    DORSETIAE 

APUD  CONDISCIPULOS  IN  UNIVERSITATE  ANDREANA 

QUI    A.D.    MDCCCXCV  TAODUNI    SCOTORUM    NATUS 

A.D.  MDCCCCXVI   IN   PUGNA  AD  THESSALONICAM  OCCUBUIT 


.  .  .  Manibus  date  lilia  plenis  : 
Purpureos  spargam  flores,  animamque  nepotis 
His  saltern  accumulem  donis,  et  fungar  inani 
Munere. — Virgil,  Aeneid,  VI 


At  ego  tibi  sermone  isto  .  .  .  varias  fabulas  conseram, 
auresque  tuas  benevolas  lepido  susurro  permulceam, 
modo  si  papyram  JEgyptiam  argutia  Nilotici  calamo 
inscriptam  non  spreveris  inspicere  .  .  . — Apuleius, 
The  Golden  Ass 


PREFACE 

The  present  book  is  ultimately  based  on  a  course  of 
lectures  delivered  to  the  third  year  students  of  science 
at  the  University  of  Bristol  in  the  session  1920-21.  It 
is  an  admirable  custom,  which,  like  many  other  benefits, 
that  University  owes  to  my  distinguished  predecessor, 
Professor  Lloyd  Morgan,  that  all  students  of  science 
are  expected  to  attend  such  a  course  before  completing 
their  career.  It  seemed  worth  while  to  elaborate  the 
lectures,  to  remove  their  more  obvious  blemishes,  and 
to  present  them  to  a  wider  public. 

In  the  First  Part  I  have  started  with  the  highly 
sophisticated  concepts  of  the  classical  mathematical 
physics,  have  tried  to  express  them  clearly,  and 
have  then  discussed  the  modifications  which  recent 
advances  in  scientific  knowledge  have  necessitated  in 
these  concepts.  I  >  have  carried  this  account  to  the 
end  of  the  Second  Theory  of  Relativity.  I  have  not 
penetrated  into  the  still  more  revolutionary  speculations 
of  Weyl,  because  I  do  not  feel  that  I  yet  understand 
them  well  enough  myself  to  venture  to  explain  them 
to  others.  A  philosopher  who  regards  ignorance  of  a 
scientific  theory  as  a  sufficient  reason  for  not  writing 
about  it  cannot  be  accused  of  complete  lack  of  origin- 
ality, as  a  study  of  recent  philosophical  literature  will 
amply  prove. 

I  begin  with  an  Introduction,  which  states  what  I 
think  Philosophy  to  be   about,  and  how  I  think  it  to 


4  SCIENTIFIC   THOUGHT 

be  connected  with  the  special  sciences.  I  then  try  to 
explain  in  simple  terms  the  nature  and  objects  of 
Whitehead's  Principle  of  Extensive  Abstraction.  This 
seems  to  me  to  be  the  "  Prolegomena  to  every  future 
Philosophy  of  Nature."  It  is  quite  possible  to  explain 
its  motives  and  general  character  without  entering 
deeply  into  those  logico-mathematical  complications 
which  are  inevitable  when  it  is  applied  in  detail.  Next, 
greatly  daring,  I  have  discussed  the  difficult  problems 
which  centre  upon  the  general  notion  of  Time  and 
Change.  Here  I  have  tried  to  make  some  answer  to 
the  very  disturbing  arguments  by  which  Dr  M'Taggart 
has  claimed  to  disprove  the  reality  of  these  apparently 
fundamental  features  of  the  Universe.  After  this  the 
rest  of  the  First  Part  should  be  fairly  plain  sailing  to 
anyone  of  decent  general  education,  though  I  do  not 
pretend  that  it  can  be  understood  without  effort  by 
persons  who  are  unfamiliar  with  the  subjects  which  it 
treats. 

In  some  of  these  later  chapters  the  reader  will  find 
a  number  of  mathematical  formulas.  He  must  not  be 
frightened  of  them,  for  I  can  assure  him  that  they 
involve  no  algebraical  processes  more  advanced  than 
the  simple  equations  which  he  learnt  to  solve  at  his 
mother's  knee.  I  myself  can  make  no  claims  to  be 
a  mathematician  :  the  most  I  can  say  is  that  I  can 
generally  follow  a  mathematical  argument  if  I  take 
enough  time  over  it.  I  like  to  believe  that,  in  expound- 
ing the  Theory  of  Relativity,  a  clumsy  mathematician 
has  some  of  the  qualities  of  his  defects.  His  own  former 
difficulties  will  at  least  suggest  to  him  the  places  where 
others  are  likely  to  have  trouble. 

In  Part  II  we  start  afresh  at  a  quite  different  level. 
Here  I  try  to  point  out  the  sensible  and  perceptible 
facts   which    underlie   the    highly   abstract   concepts   of 


PREFACE  5 

science,  and  the  cruder,  but  still  highly  sophisticated, 
concepts  of  common-sense.  Beside  the  intrinsic  interest 
and  importance  of  this  topic  it  has  a  direct  bearing  on 
Part  I.  A  great  deal  of  the  difficulty  which  many 
people  have  in  accepting  the  newer  views  of  Space, 
Time  and  Motion,  arises  from  the  fact  that  they  regard 
the  traditional  concepts  as  perfectly  plain  and  obvious, 
whilst  they  feel  that  the  later  modifications  are  paradoxes, 
forced  on  them  vi  et  armis  by  a  few  inconvenient  and 
relatively  trivial  facts.  The  moment  we  recognise  how 
extraordinarily  remote  the  classical  concepts  are  from 
the  crude  facts  of  sense-experience,  from  which  they 
must  have  been  gradually  elaborated,  this  source  of 
incredulity  vanishes.  The  hold  of  the  tradition  is 
loosened  ;  and  we  are  prepared  to  consider  alternative, 
and  possibly  more  satisfactory,  conceptual  syntheses  of 
sensible  facts. 

I  have  tried  in  Part  II  to  focus  before  my  mind  what 
seems  to  me  to  be  the  most  important  work  that  has  been 
done  on  these  subjects  since  1914,  when  the  publication 
of  my  Perception,  Physics  and  Reality  unhappily  pre- 
cipitated a  European  war.  If  I  have  learnt  nothing 
else  since  then,  I  have  at  least  come  to  see  the  extreme 
complexity  of  the  problem  of  the  external  world  and  of 
our  supposed  knowledge  of  it.  My  obligations  to 
Moore,  Russell,  Whitehead  and  Stout  are  continual, 
and  will  be  perfectly  obvious  to  anyone  acquainted  with 
the  literature  of  the  subject.  I  here  make  my  grateful 
acknowledgments  to  them,  once  for  all.  To  a  less 
extent  I  have  been  influenced  by  Alexander  and  Dawes 
Hicks.  I  have  merely  mentioned  Dawes  Hicks's  theory 
of  appearance  and  then  left  it.  This  is  not  because  I 
think  it  either  impossible  or  unimportant,  but  because  I 
am  here  deliberately  trying  to  work  out  a  different  view, 
which  I  also  think  to  be  possible  and  important. 


6  SCIENTIFIC   THOUGHT 

I  cannot  claim  to  have  put  forward  any  new  and 
startling  theory  of  the  universe.  If  I  have  any  kind  of 
philosophical  merit,  it  is  neither  the  constructive  fertility 
of  an  Alexander,  nor  the  penetrating  critical  acumen  of 
a  Moore  ;  still  less  is  it  that  extraordinary  combination  of 
both  with  technical  mathematical  skill  which  character- 
ises Whitehead  and  Russell.  I  can  at  most  claim  the 
humbler  (yet  useful)  power  of  stating  difficult  things 
clearly  and  not  too  superficially. 

"  Excudcnt  alii  spirantia  mollius  aera, 
Credo  equidem  ;  vivos  ducent  de  marmore  vultus  ;  " 

but  I  hope  that  I  may  at  least  have  smolten  some  of  the 
metal  and  hewn  some  of  the  stone  which  others  will 
use  in  their  constructions. 

I  must  end  by  thanking  Dr  R.  S.  Paton  of  Perth 
for  kindly  reading  the  proofs  and  helping  me  with  the 
index;  Mr  E.  Harrison,  of  Trinity  College,  Cambridge, 
for  his  gallant  efforts  to  involve  my  dedication  in  "the 
decent  obscurity  of  a  learned  language "  ;  and  the 
printers  for  the  care  which  they  have  taken  in  printing 
what  must  have  been  a  rather  troublesome  piece  of 
work. 

C.  D.   BROAD. 

London,  Sept.  1922. 


CONTENTS 

PAGE 

Introduction  :    The   Subject-matter  of  Philosophy, 

and  its  relations  to  the  Special  Sciences     .  n 

PART   I 

THE  TRADITIONAL  CONCEPTS  OF  MATHEMATICAL 

PHYSICS,    AND    THEIR    GRADUAL     MODIFICATION 

WITHIN  THE  REGION  OF  PHYSICAL  SCIENCE 

CHAPTER 

I.  The  Traditional  Conception  of  Space,  and  the 

Principle  of  Extensive  Abstraction        .  .  26 

II.  The  General  Problem  of  Time  and  Change         .         53 

III.  The   Traditional    Kinematics,  and   its  gradual 

Modification  in  the  Region  of  Physics.     (1) 

The  Absolute  and  the  Relational  Theories     .         85 

IV.  Modification  of  the  Traditional  Kinematics  in 

the  Region  of  Physics — Continued.     (2)  The 
Special  Theory  of  Relativity         .         .         .114 

V.  The  Traditional  Kinetics,  and  its  gradual  Modifi- 
cation in  the  Region  of  Physics.  (1)  Newton's 
Laws  of  Motion  and  Gravitation     .         .         .       155 

VI.  Modification  of  the  Traditional  Kinetics — Con- 
tinued. (2)  The  General  Theory  of  Relativity. 
Summary  of  Part  I       ....  179 


8  SCIENTIFIC   THOUGHT 

PART    II 

THE  SENSATIONAL  AND  PERCEPTUAL  BASIS 
OF  OUR  SCIENTIFIC  CONCEPTS 

CHAPTER  PAGE 

VII.   Matter    and     its    Appearances  ;     Preliminary 

Definitions 227 

VIII.  The  Theory  of  Sensa,  and  the  Critical  Scientific 

Theory 239 

IX.  The    Positions    and   Shapes    of   Sensa   and   of 

Physical  Objects 284 

X.  The    Dates    and    Durations    of    Sensa   and   of 

Physical  Objects  and  Events      .  .         .       344 

XL  Sensible  and  Physical  Motion  ....       405 

XII.  Sensible  and  Physical  Space-Time     .         .         .        452 

XIII.  The  Physiological  Conditions  of  Sensations,  and 

the  Ontological  Status  of  Sensa    .  .  .        488 

Index 549 


PART   I 

THE  TRADITIONAL  CONCEPTS  OF  MATHEMATICAL 

PHYSICS,  AND   THEIR   GRADUAL   MODIFICATION 

WITHIN  THE  REGION  OF  PHYSICAL  SCIENCE 


Contents  of  Part  I 

Introduction. — The  Subject-matter  of  Philosophy,  and  its 
Relations  to  the  Special  Sciences 

CHAPTER 

I.  The  Traditional  Conception  of  Space,  and  the  Principle 
of  Extensive  Abstraction 

II.  The  General  Problem  of  Time  and  Change 

III.  The  Traditional  Kinematics  and  its  gradual  Modification 

within  the  Region  of  Physics,     (i)  The  Absolute  and 
the  Relational  Theories 

IV.  Modification  of  the  Traditional  Kinematics  in  the  Region 

of   Physics — Continued.      (2)    The    Special   Theory   of 
Relativity 

V.  The  Traditional  Kinetics  and  its  gradual  Modification  in 
the  Region  of  Physics.  (1)  Newton's  Laws  of  Motion 
and  of  Gravitation 

VI.  Modification  of  the  Traditional  Kinetics  —  Continued. 
(2)  The  General  Theory  of  Relativity.  Summary  of 
Part  I 


B 


SCIENTIFIC    THOUGHT 


INTRODUCTION 

"Noli,  Lector,  expectare  hoc  loco,  contra  Philosophiam 
aut  Philosophos  orationem  invectivam.  .  .  .  Distinguo  inter 
Philosophos  et  non  Philosophos,  et  inter  Philosophiam 
veram,  vitae  humanae  Magistram  sapientissimam,  humanae 
naturae  decus  singulare,  et  illam,  quae  jam  diu  pro  Philo- 
sophia  habita  est,  fucatam  et  garrulam  meretriculam." 

(Hobbes,  Leviathan,  Part  IV.  cap.  xlvi.) 

The  Subject-matter  of  Philosophy,  and  its  Relations 
to  the  special  Sciences 

I  shall  devote  this  introductory  chapter  to  stating  what 

I  think  Philosophy  is  about,  and  why  the  other  sciences 

are  important  to  it  and    it    is    important   to   the    other 

sciences.     A  very  large  number  of  scientists  will  begin 

such  a  book  as   this  with    the   strong   conviction    that 

Philosophy  is  mainly  moonshine,  and  with  the  gravest 

doubts  as  to  whether  it  has   anything  of  the  slightest 

importance  to  tell  them.     I  do  not  think  that  this  view 

of  Philosophy  is  true,  or  I  should  not  waste  my  time 

and  cheat  my  students  by  trying  to  teach  it.      But  I  do 

think   that  such  a  view   is  highly   plausible,   and    that 

the  proceedings  of  many  philosophers  have  given  the 

general  public  some  excuse  for  its  unfavourable  opinion 

of  Philosophy.     I  shall  therefore  begin  by  stating  the 

case  against  Philosophy  as  strongly  as   I  can,  and  shall 

then  try  to  show  that,  in  spite  of  all  objections,  it  really 

is  a  definite  science  with  a  distinct  subject-matter.     I 

shall  try  to  show  that  it  really  does  advance  and  that 

it  is  related  to  the  special  sciences  in  such  a  way  that 

ii 


12  SCIENTIFIC   THOUGHT 

the  co-operation  of  philosophers  and  scientists  is  of  the 
utmost  benefit  to  the  studies  of  both. 

I  think  that  an  intelligent  scientist  would  put  his 
case  against  Philosophy  somewhat  as  follows.  He 
would  say  :  "  Philosophers  discuss  such  subjects  as 
the  existence  of  God,  the  immortality  of  the  soul,  and 
the  freedom  of  the  will.  They  spin  out  of  their  minds 
fanciful  theories,  which  can  neither  be  supported  nor 
refuted  by  experiment.  No  two  philosophers  agree,  and 
no  progress  is  made.  Philosophers  are  still  discussing 
with  great  heat  the  same  questions  that  they  discussed 
in  Greece  thousands  of  years  ago.  What  a  poor  show 
does  this  make  when  compared  with  mathematics  or  any 
of  the  natural  sciences  !  Here  there  is  continual  steady 
progress  ;  the  discoveries  of  one  age  are  accepted  by 
the  next,  and  become  the  basis  for  further  advances 
in  knowledge.  There  is  controversy  indeed,  but  it  is 
fruitful  controversy  which  advances  the  science  and 
ends  in  definite  agreement  ;  it  is  not  the  aimless 
wandering  in  a  circle  to  which  Philosophy  is  condemned. 
Does  this  not  very  strongly  suggest  that  Philosophy 
is  either  a  mere  playing  with  words,  or  that,  if  it  has 
a  genuine  subject-matter,  this  is  beyond  the  reach  of 
human  intelligence?" 

Our  scientist  might  still  further  strengthen  his  case 
by  reflecting  on  the  past  history  of  Philosophy  and  on 
the  method  by  which  it  is  commonly  taught  to  students. 
He  will  remind  us  that  most  of  the  present  sciences 
started  by  being  mixed  up  with  Philosophy,  that  so 
long  as  they  kept  this  connexion  they  remained  misty 
and  vague,  and  that  as  soon  as  their  fundamental 
principles  began  to  be  discovered  they  cut  their  dis- 
reputable associate,  wedded  the  experimental  method, 
and  settled  down  to  the  steady  production  of  a  strapping 
family  of  established  truths.  Mechanics  is  a  case  in 
point.  So  long  as  it  was  mixed  up  with  Philosophy  it 
made  no  progress  ;  when  the  true  laws  of  motion  were 
discovered  by  the  experiments  and  reasoning  of  Galileo 


INTRODUCTION  13 

it  ceased  to  be  part  of  Philosophy  and  began  to  develop 
into  a  separate  science.  Does  this  not  suggest  that  the 
subject-matter  of  Philosophy  is  just  that  ever-diminishing 
fragment  of  the  universe  in  which  the  scientist  has  not 
yet  discovered  laws,  and  where  we  have  therefore  to  put 
up  with  guesses?  Are  not  such  guesses  the  best  that 
Philosophy  has  to  offer  ;  and  will  they  not  be  swept 
aside  as  soon  as  some  man  of  genius,  like  Galileo  or 
Dalton  or  Faraday,  sets  the  subject  on  the  sure  path  of 
science? 

Should  our  scientist  talk  to  students  of  Philosophy 
and  ask  what  happens  at  their  lectures,  his  objections 
will  most  likely  be  strengthened.  The  answer  may  take 
the  classical  form  :  "  He  tells  us  what  everyone  knows 
in  language  that  no  one  can  understand."  But,  even 
if  the  answer  be  not  so  unfavourable  as  this,  it  is  not 
unlikely  to  take  the  form:  "We  hear  about  the  views 
of  Plato  and  Kant  and  Berkeley  on  such  subjects  as  the 
reality  of  the  external  world  and  the  immortality  of  the 
soul."  Now  the  scientist  will  at  once  contrast  this  with 
the  method  of  teaching  in  his  own  subject,  and  will  be 
inclined  to  say,  if  e.g.  he  be  a  chemist:  "We  learn 
what  are  the  laws  of  chemical  combination  and  the 
structure  of  the  Benzene  nucleus,  we  do  not  worry  our 
heads  as  to  what  exactly  Dalton  thought  or  Kekule  said. 
If  philosophers  really  know  anything  about  the  reality 
of  the  external  world  why  do  they  not  say  straight- 
forwardly that  it  is  real  or  unreal,  and  prove  it?  The 
fact  that  they  apparently  prefer  to  discuss  the  divergent 
views  of  a  collection  of  eminent  '  back-numbers  '  on 
the  question  strongly  suggests  that  they  know  that  there 
is  no  means  of  answering  it,  and  that  nothing  better 
than  groundless  personal  opinions  can  be  offered." 

I  have  put  these  objections  as  strongly  as  I  can,  and 
I  now  propose  to  see  just  how  much  there  is  in  them. 
First,  as  to  the  alleged  unprogressive  character  of 
Philosophy.  This  is,  I  think,  an  illusion  ;  but  it  is 
a  very  natural  one.     Let  us  take  the  question   of  the 


14  SCIENTIFIC   THOUGHT 

reality  of  the  external  world  as  an  example.  Common- 
sense  says  that  chairs  and  tables  exist  independently 
of  whether  anyone  happens  to  perceive  them  or  not. 
We  study  Berkeley  and  find  him  claiming  to  prove 
that  such  things  can  only  exist  so  long  as  they  are 
perceived  by  someone.  Later  on  we  read  some  modern 
realist,  like  Alexander,  and  we  are  told  that  Berkeley 
was  wrong,  and  that  chairs  and  tables  can  and  do  exist 
unperceived.  We  seem  merely  to  have  got  back  to 
where  we  started  from,  and  to  have  wasted  our  time. 
But  this  is  not  really  so,  for  two  reasons,  (i)  What  we 
believe  at  the  end  of  the  process  and  what  we  believed  at 
the  beginning  are  by  no  means  the  same,  although  we 
express  the  two  beliefs  by  the  same  form  of  words. 
The  original  belief  of  common-sense  was  vague,  crude 
and  unanalysed.  Berkeley's  arguments  have  forced 
us  to  recognise  a  number  of  distinctions  and  to  define 
much  more  clearly  what  we  mean  by  the  statement  that 
chairs  and  tables  exist  unperceived.  What  we  find  is 
that  the  original  crude  belief  of  common-sense  consisted 
of  a  number  of  different  beliefs,  mixed  up  with  each 
other.  Some  of  these  may  be  true  and  others  false. 
Berkeley's  arguments  really  do  refute  or  throw  grave 
doubt  on  some  of  them,  but  they  leave  others  standing. 
Now  it  may  be  that  those  which  are  left  are  enough  to 
constitute  a  belief  in  the  independent  reality  of  external 
objects.  If  so  this  final  belief  in  the  reality  of  the 
external  world  is  much  clearer  and  subtler  than  the 
verbally  similar  belief  with  which  we  began.  It  has  been 
purified  of  irrelevant  factors,  and  is  no  longer  a  vague 
mass  of  different  beliefs  mixed  up  with  each  other. 

(ii)  Not  only  will  our  final  belief  differ  in  content 
from  our  original  one,  it  will  also  differ  in  certainty. 
Our  original  belief  was  merely  instinctive,  and  was  at 
the  mercy  of  any  sceptical  critic  who  chose  to  cast 
doubts  on  it.  Berkeley  has  played  this  part.  Our  final 
belief  is  that  part  or  that  modification  of  our  original 
one  that  has  managed  to  survive  his  criticisms.     This 


INTRODUCTION  15 

does  not  of  course  prove  that  it  is  true  ;  there  may  be 
other  objections  to  it.  But,  at  any  rate,  a  belief  that 
has  stood  the  criticisms  of  an  acute  and  subtle  thinker, 
like  Berkeley,  is  much  more  likely  to  be  true  than  a 
merely  instinctive  belief  which  has  never  been  criticised 
by  ourselves  or  anyone  else.  Thus  the  process  which 
at  first  sight  seemed  to  be  merely  circular  has  not  really 
been  so.  And  it  has  certainly  not  been  useless  ;  for  it 
has  enabled  us  to  replace  a  vague  belief  by  a  clear  and 
analysed  one,  and  a  merely  instinctive  belief  by  one 
that  has  passed  through  the  fire  of  criticism. 

The  above  example  will  suggest  to  us  a  part  at  least 
of  what  Philosophy  is  really  about.  Common-sense 
constantly  makes  use  of  a  number  of  concepts,  in  terms 
of  which  it  interprets  its  experience.  It  talks  of  things 
of  various  kinds  ;  it  says  that  they  have  places  and  dates, 
that  they  change,  and  that  changes  in  one  cause  changes 
in  others,  and  so  on.  Thus  it  makes  constant  use  of 
such  concepts  or  categories  as  thinghood,  space,  time, 
change,  cause,  etc.  Science  takes  over  these  concepts 
from  common-sense  with  but  slight  modification,  and 
uses  them  in  its  work.  Now  we  can  and  do  use 
concepts  without  having  any  very  clear  idea  of  their 
meaning  or  their  mutual  relations.  I  do  not  of  course 
suggest  that  to  the  ordinary  man  the  words  substance, 
cause,  change,  etc.,  are  mere  meaningless  noises,  like 
Jabberwock  or  Snark.  It  is  clear  that  we  mean  some- 
thing, and  something  different  in  each  case,  by  such 
words.  If  we  did  not  we  could  not  use  them  con- 
sistently, and  it  is  obvious  that  on  the  whole  we  do 
consistently  apply  and  withhold  such  names.  But  it 
is  possible  to  apply  concepts  more  or  less  successfully 
when  one  has  only  a  very  confused  idea  as  to  their 
meaning.  No  man  confuses  place  with  date,  and  for 
practical  purposes  any  two  men  agree  as  a  rule  in  the 
places  that  they  assign  to  a  given  object.  Nevertheless, 
if  you  ask  them  what  exactly  they  mean  by  place  and 
date,  they  will  be  puzzled  to  tell  you. 


16  SCIENTIFIC   THOUGHT 

Now  the  most  fundamental  task  of  Philosophy  is  to 
take  the  concepts  that  we  daily  use  in  common  life  and 
science,  to  analyse  them,  and  thus  to  determine  their 
precise  meanings  and  their  mutual  relations.  Evidently 
this  is  an  important  duty.  In  the  first  place,  clear  and 
accurate  knowledge  of  anything  is  an  advance  on  a 
mere  hazy  general  familiarity  with  it.  Moreover,  in 
the  absence  of  clear  knowledge  of  the  meanings  and 
relations  of  the  concepts  that  we  use,  we  are  certain 
sooner  or  later  to  apply  them  wrongly  or  to  meet  with 
exceptional  cases  where  we  are  puzzled  as  to  how  to 
apply  them  at  all.  For  instance,  we  all  agree  pretty 
well  as  to  the  place  of  a  certain  pin  which  we  are 
looking  at.  But  suppose  we  go  on  to  ask  :  "  Where  is 
the  image  of  that  pin  in  a  certain  mirror  ;  and  is  it  in 
this  place  (whatever  it  may  be)  in  precisely  the  sense 
in  which  the  pin  itself  is  in  its  place?"  We  shall  find 
the  question  a  very  puzzling  one,  and  there  will  be  no 
hope  of  answering  it  until  we  have  carefully  analysed 
what  we  mean  by  being  in  a  place. 

Again,  this  task  of  clearing  up  the  meanings  and 
determining  the  relations  of  fundamental  concepts  is 
not  performed  to  any  extent  by  any  other  science. 
Chemistry  uses  the  notion  of  substance,  geometry  that 
of  space,  and  mechanics  that  of  motion.  But  they 
assume  that  you  already  know  what  is  meant  by 
substance  and  space  and  motion.  So  you  do  in  a  vague 
way  ;  and  it  is  not  their  business  to  enter,  more 
than  is  necessary  for  their  own  special  purposes,  into 
the  meaning  and  relations  of  these  concepts  as  such. 
Of  course  the  special  sciences  do  in  some  measure  clear 
up  the  meanings  of  the  concepts  that  they  use.  A 
chemist,  with  his  distinction  between  elements  and 
compounds  and  his  laws  of  combination,  has  a  clearer 
idea  of  substance  than  an  ordinary  layman.  But  the 
special  sciences  only  discuss  the  meanings  of  their 
concepts  so  far  as  this  is  needful  for  their  own  special 
purposes.     Such  discussion  is  incidental  to  them,  whilst 


INTRODUCTION  17 

it  is  of  the  essence  of  Philosophy,  which  deals  with  such 
questions  for  their  own  sake.  Whenever  a  scientist 
begins  to  discuss  the  concepts  of  his  science  in  this 
thorough  and  disinterested  way  we  begin  to  say  that  he 
is  studying,  not  so  much  Chemistry  or  Physics,  as  the 
Philosophy  of  Chemistry  or  Physics.  It  will  therefore 
perhaps  be  agreed  that,  in  the  above  sense  of  Philosophy, 
there  is  both  room  and  need  for  such  a  study,  and  that 
there  is  no  special  reason  to  fear  that  it  will  be  beyond 
the  compass  of  human  faculties. 

At  this  point  a  criticism  may  be  made  which  had 
better  be  met  at  once.  It  may  be  said  :  "  By  your  own 
admission  the  task  of  Philosophy  is  purely  verbal  ;  it 
consists  entirely  of  discussions  about  the  meanings  of 
words."  This  criticism  is  of  course  absolutely  wide  of 
the  mark.  When  we  say  that  Philosophy  tries  to  clear 
up  the  meanings  of  concepts  we  do  not  mean  that  it  is 
simply  concerned  to  substitute  some  long  phrase  for 
some  familiar  word.  Any  analysis,  when  once  it  has 
been  made,  is  naturally  expressed  in  words  ;  but  so  too 
is  any  other  discovery.  When  Cantor  gave  his  defini- 
tion of  Continuity,  the  final  result  of  his  work  was 
expressed  by  saying  that  you  can  substitute  for  the 
word  "continuous"  such  and  such  a  verbal  phrase. 
But  the  essential  part  of  the  work  was  to  find  out  exactly 
what  properties  are  present  in  objects  when  we  predicate 
continuity  of  them,  and  what  properties  are  absent 
when  we  refuse  to  predicate  continuity.  This  was 
evidently  not  a  question  of  words  but  of  things  and 
their  properties. 

Philosophy  has  another  and  closely  connected  task. 
We  not  only  make  continual  use  of  vague  and 
unanalysed  concepts.  We  have  also  a  number  of  un- 
criticised  beliefs,  which  we  constantly  assume  in 
ordinary  life  and  in  the  sciences.  We  constantly 
assume,  e.g.  that  every  event  has  a  cause,  that  nature 
obeys  uniform  laws,  that  we  live  in  a  world  of  objects 
whose  existence  and  behaviour  are  independent  of  our 


18  SCIENTIFIC   THOUGHT 

knowledge  of  them,  and  so  on.  Now  science  takes  over 
these  beliefs  without  criticism  from  common-sense,  and 
simply  works  with  them.  We  know  by  experience, 
however,  that  beliefs  which  are  very  strongly  held  may 
be  mere  prejudices.  Negroes  find  it  very  hard  to 
believe  that  water  can  become  solid,  because  they  have 
always  lived  in  a  warm  climate.  Is  it  not  possible  that 
we  believe  that  nature  as  a  whole  will  always  act 
uniformly  simply  because  the  part  of  nature  in  which 
the  human  race  has  lived  has  happened  to  act  so  up 
to  the  present?  All  such  beliefs  then,  however  deeply 
rooted,  call  for  criticism.  The  first  duty  of  Philosophy 
is  to  state  them  clearly  ;  and  this  can  only  be  done 
when  we  have  analysed  and  defined  the  concepts  that 
they  involve.  Until  you  know  exactly  what  you  mean 
by  change  and  cause  you  cannot  know  what  is  meant 
by  the  statement  that  every  change  has  a  cause.  And 
not  much  weight  can  be  attached  to  a  person's  most 
passionate  beliefs  if  he  does  not  know  what  precisely  he 
is  passionately  believing.  The  next  duty  of  Philosophy 
is  to  test  such  beliefs  ;  and  this  can  only  be  done  by 
resolutely  and  honestly  exposing  them  to  every  objection 
that  one  can  think  of  oneself  or  find  in  the  writings  of 
others.  We  ought  only  to  go  on  believing  a  proposition 
if,  at  the  end  of  this  process,  we  still  find  it  impossible 
to  doubt  it.  Even  then  of  course  it  may  not  be  true, 
but  we  have  at  least  done  our  best. 

These  two  branches  of  Philosophy — the  analysis 
and  definition  of  our  fundamental  concepts,  and  the 
clear  statement  and  resolute  criticism  of  our  fundamental 
beliefs — I  call  Critical  Philosophy.  It  is  obviously  a 
necessary  and  a  possible  task,  and  it  is  not  performed 
by  any  other  science.  The  other  sciences  use  the 
concepts  and  assume  the  beliefs  ;  Critical  Philosophy 
tries  to  analyse  the  former  and  to  criticise  the  latter. 
Thus,  so  long  as  science  and  Critical  Philosophy 
keep  to  their  own  spheres,  there  is  no  possibility  of 
conflict    between    them,    since    their   subject-matter    is 


INTRODUCTION  19 

quite  different.  Philosophy  claims  to  analyse  the 
general  concepts  of  substance  and  cause,  e.g.;  it  does 
not  claim  to  tell  us  about  particular  substances,  like 
gold,  or  about  particular  laws  of  causation,  as  that 
aqua  regia  dissolves  gold.  Chemistry,  on  the  other 
hand,  tells  us  a  great  deal  about  the  various  kinds  of 
substances  in  the  world,  and  how  changes  in  one  cause 
changes  in  another.  But  it  does  not  profess  to  analyse 
the  general  concepts  of  substance  or  causation,  or  to 
consider  what  right  we  have  to  assume  that  every  event 
has  a  cause. 

It  should  now  be  clear  why  the  method  of  Philosophy 
is  so  different  from  that  of  the  natural  sciences.  Ex- 
periments are  not  made,  because  they  would  be  utterly 
useless.  If  you  want  to  find  out  how  one  substance 
behaves  in  presence  of  another  you  naturally  put  the 
two  together,  vary  the  conditions,  and  note  the  results. 
But  no  experiment  will  clear  up  your  ideas  as  to  the 
meaning  of  cause  in  general  or  of  substance  in  general. 
Again,  all  conclusions  from  experiments  rest  on  some 
of  those  very  assumptions  which  it  is  the  business  of 
Philosophy  to  state  clearly  and  to  criticise.  The  experi- 
menter assumes  that  nature  obeys  uniform  laws,  and 
that  similar  results  will  follow  always  and  everywhere 
from  sufficiently  similar  conditions.  This  is  one  of  the 
assumptions  that  Philosophy  wants  to  consider  critically. 
The  method  of  Philosophy  thus  resembles  that  of  pure 
mathematics,  at  least  in  the  respect  that  neither  has  any 
use  for  experiment. 

There  is,  however,  a  very  important  difference.  In 
pure  mathematics  we  start  either  from  axioms  which  no 
one  questions,  or  from  premises  which  are  quite  explicitly 
assumed  merely  as  hypotheses  ;  and  our  main  interest 
is  to  deduce  remote  consequences.  Now  most  of  the 
tacit  assumptions  of  ordinary  life  and  of  natural  science 
claim  to  be  true  and  not  merely  to  be  hypotheses,  and 
at  the  same  time  they  are  found  to  be  neither  clear 
nor  self-evident  when    critically  reflected    upon.      Most 


20  SCIENTIFIC   THOUGHT 

mathematical  axioms  are  very  simple  and  clear,  whilst 
most  other  propositions  which  men  strongly  believe  are 
highly  complex  and  confused.  Philosophy  is  mainly 
concerned,  not  with  remote  conclusions,  but  with  the 
analysis  and  appraisement  of  the  original  premises. 
For  this  purpose  analytical  power  and  a  certain  kind  of 
insight  are  necessary,  and  the  mathematical  method  is 
not  of  much  use. 

Now  there  is  another  kind  of  Philosophy  ;  and,  as 
this  is  more  exciting,  it  is  what  laymen  generally  under- 
stand by  the  name.  This  is  what  I  call  Speculative 
Philosophy.  It  has  a  different  object,  is  pursued  by  a 
different  method,  and  leads  to  results  of  a  different 
degree  of  certainty  from  Critical  Philosophy.  Its 
object  is  to  take  over  the  results  of  the  various  sciences, 
to  add  to  them  the  results  of  the  religious  and  ethical 
experiences  of  mankind,  and  then  to  reflect  upon  the 
whole.  The  hope  is  that,  by  this  means,  we  may  be 
able  to  reach  some  general  conclusions  as  to  the  nature 
of  the  Universe,  and  as  to  our  position  and  prospects 
in  it. 

There  are  several  points  to  be  noted  about  Speculative 
Philosophy,  (i)  If  it  is  to  be  of  the  slightest  use  it 
must  presuppose  Critical  Philosophy.  It  is  useless  to 
take  over  masses  of  uncriticised  detail  from  the  sciences 
and  from  the  ethical  and  religious  experiences  of  men. 
We  do  not  know  what  they  mean,  or  what  degree  of 
certainty  they  possess  till  they  have  been  clarified  and 
appraised  by  Critical  Philosophy.  It  is  thus  quite 
possible  that  the  time  for  Speculative  Philosophy  has 
not  yet  come  ;  for  Critical  Philosophy  may  not  have 
advanced  far  enough  to  supply  it  with  a  firm  basis.  In 
the  past  people  have  tended  to  rush  on  to  Speculative 
*  Philosophy,  because  of  its  greater  practical  interest. 
The  result  has  been  the  production  of  elaborate  systems 
which  may  quite  fairly  be  described  as  moonshine.  The 
discredit  which  the  general  public  quite  rightly  attaches 
to   these  hasty  attempts  at  Speculative    Philosophy  is 


INTRODUCTION  21 

reflected  back  on  Critical  Philosophy,  and  Philosophy 
as  a  whole  thus  falls  into  undeserved  disrepute. 

(ii)  At  the  best  Speculative  Philosophy  can  only 
consist  of  more  or  less  happy  guesses,  made  on  a  very 
slender  basis.  There  is  no  hope  of  its  reaching  the 
certainty  which  some  parts  of  Critical  Philosophy  might 
quite  well  attain.  Now  speculative  philosophers  as  a 
class  have  been  the  most  dogmatic  of  men.  They  have 
been  more  certain  of  everything  than  they  had  a  right 
to  be  of  anything. 

(iii)  A  man's  final  view  of  the  Universe  as  a  whole, 
and  of  the  position  and  prospects  of  himself  and  his 
fellows,  is  peculiarly  liable  to  be  biased  by  his  hopes 
and  fears,  his  likes  and  dislikes,  and  his  judgments  of 
value.  One's  Speculative  Philosophy  tends  to  be  in- 
fluenced to  an  altogether  undue  extent  by  the  state  of 
one's  liver  and  the  amount  of  one's  bank-balance.  No 
doubt  livers  and  bank-balances  have  their  place  in  the 
Universe,  and  no  view  of  it  which  fails  to  give  them 
their  due  weight  is  ultimately  satisfactory.  But  their 
due  weight  is  considerably  less  than  their  influence  on 
Speculative  Philosophy  might  lead  one  to  suspect.  But, 
if  we  bear  this  in  mind  and  try  our  hardest  to  be 
"ethically  neutral,"  we  are  rather  liable  to  go  to  the 
other  extreme  and  entertain  a  theory  of  the  Universe 
which  renders  the  existence  of  our  judgments  of  value 
unintelligible. 

A  large  part  of  Critical  Philosophy  is  almost  exempt 
from  this  source  of  error.  Our  analysis  of  truth  and 
falsehood,  or  of  the  nature  of  judgment,  is  not  very 
likely  to  be  influenced  by  our  hopes  and  fears.  Yet 
even  here  there  is  a  slight  danger  of  intellectual  dis- 
honesty. We  sometimes  do  our  Critical  Philosophy, 
with  half  an  eye  on  our  Speculative  Philosophy,  and 
accept  or  reject  beliefs,  or  analyse  concepts  in  a  certain 
way,  because  we  feel  that  this  will  fit  in  better  than  any 
alternative  with  the  view  of  Reality  as  a  whole  that  we 
happen  to  like. 


22  SCIENTIFIC   THOUGHT 

(iv)  Nevertheless,  if  Speculative  Philosophy  re- 
members its  limitations,  it  is  of  value  to  scientists,  in 
its  methods,  if  not  in  its  results.  The  reason  is  this. 
In  all  the  sciences  except  Psychology  we  deal  with 
objects  and  their  changes,  and  leave  out  of  account 
as  far  as  possible  the  mind  which  observes  them.  In 
Psychology,  on  the  other  hand,  we  deal  with  minds 
and  their  processes,  and  leave  out  of  account  as  far  as 
possible  the  objects  that  we  get  to  know  by  means  of. 
them.  A  man  who  confines  himself  to  either  of  these 
subjects  is  likely  therefore  to  get  a  very  one-sided  view 
of  the  world.  The  pure  natural  scientist  is  liable  to 
forget  that  minds  exist,  and  that  if  it  were  not  for 
them  he  could  neither  know  nor  act  on  physical  objects. 
The  pure  psychologist  is  inclined  to  forget  that  the 
main  business  of  minds  is  to  know  and  act  upon 
objects ;  that  they  are  most  intimately  connected 
with  certain  portions  of  matter ;  and  that  they  have 
apparently  arisen  gradually  in  a  world  which  at  one 
time  contained  nothing  but  matter.  Materialism  is 
the  characteristic  speculative  philosophy  of  the  pure 
natural  scientist,  and  subjective  idealism  that  of  the 
pure  psychologist.  To  the  scientist  subjective  idealism 
seems  a  fairy  tale,  and  to  the  psychologist  materialism 
seems  sheer  lunacy.  Both  are  right  in  their  criticisms, 
but  neither  sees  the  weakness  of  his  own  position.  The 
truth  is  that  both  these  doctrines  commit  the  fallacy  of 
over-simplification  ;  and  we  can  hardly  avoid  falling 
into  some  form  of  this  unless  at  some  time  we  make  a 
resolute  attempt  to  think  synoptically  of  all  the  facts. 
Our  results  may  be  trivial  ;  but  the  process  will  at  least 
remind  us  of  the  extreme  complexity  of  the  world,  and 
teach  us  to  reject  any  cheap  and  easy  philosophical 
theory,  such  as  popular  materialism  or  popular  theology.* 

Before  ending  this  chapter  I  will  say  a  word  about 
the  three  sciences  which  are  commonly  thought  to  be 

1  Theology,  whether  "natural"  ox  "revealed,"  is  a  form  of  Speculative 
Philosophy,  in  our  sense  of  the,  word..      So,  too,  is  Atheism. 


INTRODUCTION  23 

specially  philosophical.  These  are  Logic,  Ethics,  and 
Psychology.  Logic  simply  is  the  most  fundamental 
part  of  Critical  Philosophy.  It  deals  with  such  concepts 
as  truth,  implication, probability,  class,  etc.  In  fact  it  may 
be  defined  as  the  science  which  deals  with  propositional 
forms,  their  parts,  their  qualities,  and  their  relations. 
Its  business  is  to  analyse  and  classify  forms,  and  to 
consider  the  formal  relations  that  can  subsist  between 
them.  Now  all  science  consists  of  definite  propositions, 
and  each  of  these  is  of  one  of  the  forms  which  Logic 
studies  ;  but  it  is  not  the  business  of  any  other  science 
explicitly  to  discuss  propositional  forms.  Similarly  all 
science  is  full  of  inferences,  good  and  bad,  and  all 
inference  depends  on  relations  that  are  supposed  to 
subsist  between  premises  and  conclusion.  But  it  is 
for  Logic,  and  for  it  alone,  to  decide  what  relations  do 
in  fact  justify  inference,  and  whether  these  relations  do 
actually  subsist  in  a  given  case.  Thus  Logic  is  that 
part  of  Critical  Philosophy  which  deals  with  the  most 
general  and  pervasive  of  all  concepts,  and  with  those 
fundamental  beliefs  which  form  the  "connective  tissue" 
of  all  knowledge. 

The  greater  part  of  Ethics  again  is  simply  a  branch 
of  Critical  Philosophy.  It  is  a  fact  that  we  not  only 
believe  that  such  and  such  events  happen,  but  that 
we  also  pass  judgments  of  approval  or  disapproval  on 
certain  of  them.  Such  judgments  use  peculiar  con- 
cepts, like  good  and  bad,  right  and  wrong,  duty,  etc. 
A  very  important  part  of  Ethics  is  the  attempt  to 
analyse  and  define  these  peculiarly  obscure  notions 
which  we  all  use  so  gaily  in  everyday  life.  Again, 
there  are  a  great  many  judgments  of  value  which  many 
people  assume  as  certain  ;  e.g.  Pleasure  is  good,  It 
is  wrong  to  tell  lies,  A  man  has  a  right  to  do  what 
he  likes  with  his  own,  and  so  on.  Another  important 
part  of  Ethics  is  the  attempt  to  state  such  judgments 
clearly,  and  then  to  see  what  evidence,  if  any,  there 
is    for   them.       Thus,    Ethics    is    that    part   of  Critical 


24  SCIENTIFIC   THOUGHT 

Philosophy  which  analyses  the  concepts  and  criticises 
the  presuppositions  that  we  use  in  our  judgments  of 
approval  and  disapproval. 

Psychology,  as  it  seems  to  me,  is  not  a  part  of 
Philosophy  at  all,  but  is  simply  one  of  the  special 
sciences.  This  is  shown  by  the  fact  that,  unlike  Logic 
and  Ethics,  it  argues  inductively  from  experiment  and 
observation,  though  the  observation  takes  the  peculiar 
form  of  introspection.  It  is,  however,  a  very  peculiar 
kind  of  special  science.  It  is  obvious  that  Chemistry  and 
Physics  are  much  more  like  each  other  than  either  of 
them  is  like  Psychology.  The  reason  is  that  the  two 
former  sciences  treat  two  rather  different  but  very 
pervasive  sets  of  material  properties,  whilst  the  latter 
deals  with  minds,  which  apparently  occupy  a  unique 
and  strangely  isolated  position  in  the  Universe.  Or, 
again,  we  may  say  that  Psychology  deals  with  what 
is  relatively  private,  whilst  all  the  other  natural  sciences 
deal  with  what  is  relatively  public.  If,  now  it  should 
be  asked  why  Psychology  has  been  supposed  to  be 
specially  connected  with  Philosophy,  I  think  that  the 
following  answers  will  be  fairly  satisfactory. 

(i)  Psychology  supplies  Critical  Philosophy  with  a 
number  of  concepts  as  raw  material  for  analysis  and 
criticism.  Such  are  the  concepts  of  mind,  self,  con- 
sciousness, instinct,  sensation,  perception,  etc.  Now  these 
notions  we  all  admit  to  be  highly  confused  and  obscure, 
whereas  we  are  inclined  to  think — until  we  learn  better — 
that  there  is  no  particular  difficulty  about  such  concepts 
as  place,  date,  matter,  cause,  etc.,  which  we  use  in  the 
other  sciences.  Thus  a  great  part  of  any  standard 
book  on  Psychology  does  in  fact  consist  of  attempts 
to  analyse  and  define  certain  concepts,  and  this  is  of 
course  Critical  Philosophy. 

(ii)  When  we  try  to  clear  up  the  meanings  of 
physical  concepts  like  place,  date,  matter,  etc.,  we  often 
find  that  a  reference  to  the  processes  by  which  they 
come  to  be  known  is  essential,  and  that  they  owe  part 


INTRODUCTION  25 

of  their  obscurity  to  the  abstractions  which  science  and 
common-sense  have  made.  Thus,  in  doing  Critical 
Philosophy,  we  do  constantly  have  to  appeal  to  facts 
which  belong  to  Psychology,  even  when  we  are  not 
primarily  dealing  with  psychological  concepts.* 

(iii)  In  Speculative  Philosophy  we  ought,  no  doubt, 
to  take  into  account  the  results  of  all  the  sciences.  But, 
owing  to  the  unique  subject-matter  of  Psychology,  we 
shall  go  hopelessly  wrong  if  we  omit  it,  whilst  we  shall 
not  go  so  hopelessly  wrong  if  we  omit  one  of  the 
sciences  of  matter,  such  as  Mineralogy  or  Botany. 

For  these  reasons  we  may  admit  that  Psychology 
is  of  peculiar  importance  to  Philosophy,  though  we 
must  deny  that  it  is  a  part  of  Philosophy,  like  Logic 
and  Ethics. 

The  present  book  deals  wholly  with  Critical 
Philosophy,  and  only  with  a  small  part  of  that.  It  is 
concerned  almost  entirely  with  an  attempt  to  clear  up 
some  of  the  concepts  used  in  the  natural  sciences.  It 
does  not  deal  even  with  all  these,  e.g.  very  little  is  said 
about  causation.  The  reason  is  that  I  did  not  want  to 
deal  with  purely  logical  questions  ;  and  it  is  hardly 
possible  to  discuss  causation  adequately  without  going 
into  the  question  of  induction,  in  which  causation  is 
commonly  thought  to  play  an  important  part. 

Additional  works  that  may  be  consulted  with  profit  : 

F.  H.  BRADLEY,  Appearance  and  Reality,  Introduction. 

H.  Sidgwick,  Philosophy  :   its  Scope  and  Relations. 

B.  A.  W.  Russell,  Our  Knowledge  of  the  External  World, 

Lectures  I.  and  II. 
J.  Grote,  Exploratio  Philosofihica,  Part  I.  Caps.  I.  and  II. 
Descartes,  Rules  for  the  Direction  of  the  Mind. 
,,  Discourse  on  Method. 

*  It  is  also  true  that  we  cannot  give  a  complete  treatment  of  Logic 
(especially  the  subjects  of  Inference  and  Probability)  without  referring  to 
minds  and  their  special  limitations. 


CHAPTER  I 

"When  I  use  a  word,"  Humpty-Dumpty  said  in  rather 
a  scornful  tone,  "it  means  just  what  I  choose  it  to  mean 
— neither  more  nor  less." 

"The  question  is,"  said  Alice,  "whether  you  can  make 
words  mean  so  many  different  things." 

"The  question  is,"  said  Humpty-Dumpty,  "which  is  to 
be  Master — that's  all." 

(Lewis  Carroll,  Through  the  Looking-Glass.) 

The  Traditional  Conception  of  Space,  and  the  Principle 
of  Extensive  Abstraction 

It  is  not  ultimately  possible  to  treat  Space,  Time,  and 

Matter,  as  used  in  physical  science,  in   isolation   from 

each    other  ;    for    we    shall    see    that    they    are   closely 

bound  together  in  their  very  natures.     This  is,  however, 

a  comparatively   recent  discovery  ;  and  the  traditional 

view,  with  which  most  of  us  still  work  in  daily  life,  is 

that  Space  and  Time,  at  any  rate,  can  be  adequately 

analysed  in  isolation  from  each  other  and  from  matter. 

As  this  is  the  familiar  view,  it  seems  best  to  start  from  it 

and  gradually  to  point  out  and  remove  its  imperfections. 

In  any  case  we  must  start  somewhere ;  and  the  fact  that 

the  three  concepts  in  question  have  so  long  been  treated 

as  separable  without  serious  practical  error  shows  that, 

to  a  great  extent,  they  are  separable.     The  truth  is  that 

what  is  logically  most  primitive  in  nature  is  not  what 

is  now  most  familiar  to  us,  and  therefore  it  is  better  for 

didactic  purposes  to  start  with  the  logically  derivative 

but  practically  familiar,  and  work  back  to  the  logically 

primitive  but  practically  unfamiliar.      For  example,  the 

immediate   data   of  sense,    like   coloured    patches,    are 

logically  prior  to  the  notion  of  physical  objects,  which 

26 


TRADITIONAL   CONCEPT   OF   SPACE  27 

persist,  and  combine  many  qualities  ;  yet  the  latter  is 
much  the  more  familiar  notion  to  us.  I  shall  start  then 
from  the  traditional  conception  of  Space. 

Unquestionably  we  think  of  Space  in  ordinary  life 
and  in  science  as  a  single  great  box  or  container  in 
which  all  physical  objects  are  kept  and  in  which  all 
physical  processes  go  on.  It  is  true  that  many  books 
on  Mechanics  do  lip-service  to  a  different  view  of  Space, 
which  makes  it  consist  of  relations  between  bits  of  matter. 
But  this  conception  is  forgotten  as  soon  as  the  author 
has  worked  off  that  particular  chapter,  and  ever  after- 
wards he  and  his  readers  use  the  "box"  theory  of 
Space.  We  shall  deal  with  this  alternative  view  at  a 
much  later  stage.  Again,  we  shall  see  later  that  the 
notion  of  a  single  box  needs  overhauling,  but  we  shall 
not  be  able  to  appreciate  why  this  is  so  until  we  have 
considered  the  connexion  of  Space  with  Time. 

For  the  present  then,  we  shall  take  the  common 
practical  view  of  Space  as  a  single  box  "with  no  sides 
to  it,"  in  which  the  things  and  events  of  the  physical 
world  move  and  have  their  being.  The  first  point  to 
notice  is  that,  when  people  talk  of  Space  and  spaces, 
they  may  be  using  these  correlative  terms  in  two 
different  senses,  (i)  When  we  talk  of  Berkeley  Square 
as  one  space  and  Grosvenor  Square  as  a  different  one, 
we  simply  mean  that  they  are  two  different  regions 
which  do  not  overlap,  but  which  are  both  parts  of  the 
single  Space  of  nature.  We  do  not  mean  that  they 
are  different  kinds  of  Space.  Neither  Berkeley  Square 
nor  Grosvenor  Square  is  a  Space — for  neither  is  a  box 
containing  the  whole  of  nature  ;  but  each  of  them  is  a 
space,  in  the  sense  of  a  part  of  such  a  box. 

(ii)  On  the  other  hand,  when  mathematicians  talk  of 
Euclidean  and  non-Euclidean  Spaces,  they  are  discussing 
different  possible  kinds  of  Space,  and  not  different  spaces 
like  the  two  London  Squares  which  are  parts  of  the 
Space  of  nature,  of  whatever  kind  that  may  be.  The 
word  Space  is  thus  used  (a)  as  a  proper  name,  in  which 


28  SCIENTIFIC   THOUGHT 

case  it  is  equivalent  to  the  phrase  "  tJic  Space  of  nature, 
of  whatever  kind  that  may  be"  ;  and  (/;)  as  a  general 
name,  in  which  case  it  connotes  the  property  of  being 
a  Space,  and  denotes  all  the  various  wholes  of  that  kind, 
such  as  Euclidean  Space,  Lobatchewskian  Space,  and 
so  on.  Finally,  every  kind  of  Space  has  parts,  which 
are  spaces,  but  not  of  course  Spaces. 

As  a  matter  of  history  the  concept  of  Space  in 
general  sprang  from  the  investigation  of  the  Space  of 
nature.  Euclid  certainly  meant  his  axioms  to  describe 
the  Space  in  which  we  live  and  move.  But,  on  further 
reflection,  two  very  important  facts  emerged,  (i)  The 
validity  of  Euclid's  deductions  does  not  depend  in  any 
way  on  this  assumption  being  true,  (ii)  We  can  con- 
ceive of  extended  wholes  which  are  continuous  and 
have  several  dimensions,  like  the  Space  of  nature,  but 
which  yet  differ  from  the  Euclidean  kind  of  Space  in 
many  of  their  properties.  We  decide  then  to  call  any 
whole  that  sufficiently  resembles  the  Space  of  nature 
a  Space,  but  we  allow  that  there  are  many  possible 
wholes  which  agree  to  this  extent  and  yet  differ  in 
their  remaining  properties.  Mathematicians  at  first 
only  made  timid  modifications  in  Euclid's  axioms,  but 
as  boldness  grew  with  familiarity,  they  gradually  con- 
sidered what,  from  the  Euclidean  point  of  view,  were 
wilder  and  wilder  kinds  of  Space. 

The  important  thing  for  us  to  notice  is  that  the  pro- 
positions of  any  system  of  pure  geometry  are  merely 
hypothetical.  They  simply  state  that  such  and  such 
propositions  follow  from  the  axioms,  when  the  terms 
employed  are  defined  by  the  definitions  and  postulates 
of  the  system.  We  ought  not  to  say  that  the  angles 
of  a  triangle  are  together  equal  to  two  right  angles, 
but  that,  if  a  triangle  be  in  the  Space  defined  by 
Euclid's  axioms,  this  will  follow.  This  fact  is  hidden 
from  the  beginner  in  mathematics,  because  (a)  the 
Space  of  nature  is  commonly  assumed  to  be  Euclidean, 
and    (6)    figures   are   commonly   used    in    proving  pro- 


TRADITIONAL   CONCEPT   OF   SPACE         29 

positions.  But  the  truth  is  that  figures  in  geometry 
are  used  only  as  illustrations,  like  statistics  in  the  late 
Mr  Chamberlain's  tariff-reform  speeches.  They  play 
no  logical  part  in  the  proof,  as  is  shown  by  the  fact 
that  a  proposition  about  circles  can  be  proved  just  as 
conclusively  with  a  rough  circle  drawn  in  chalk  on  a 
blackboard  as  with  an  accurate  circle  drawn  with  a 
pair  of  compasses.  The  real  premises  of  the  proof  are 
the  axioms  of  the  system,  and  the  definitions  of  the 
terms  which  we  are  arguing  about. 

When  these  facts  are  once  grasped  it  is  easy  to 
see  the  connexion  between  the  Space  of  physics  and 
the  Spaces  of  pure  geometry.  We  have  arrived,  by 
whatever  means,  at  the  concept  of  one  physical  Space 
— the  single  sideless  box  in  which  all  the  phenomena 
of  nature  are  kept.  This  has  various  characteristic  pro- 
perties, such  as  continuity,  three  dimensions,  etc. 
From  this  the  pure  mathematician  generalises.  He 
takes  a  selection  of  these  properties  as  the  defining 
marks  of  Space  in  general  ;  and  then,  by  varying  the 
remaining  properties,  conceives  various  kinds  of  Space 
and  works  out  their  geometry.  At  that  stage,  and  not 
till  then,  the  question  can  be  put :  "  Of  what  kind  is  the 
Space  of  nature?"  "Which  of  the  various  possible 
Spaces  accords  best  with  the  Space  of  physics?" 

This  is  the  question:  "In  what  kind  of  a  box  is 
nature  contained?"  It  turns  out  not  to  be  quite  so 
simple  as  asking  whether  one's  clothes  are  in  a  port- 
manteau, a  trunk,  or  a  Gladstone  bag.  In  the  first 
place,  the  actual  entanglement  of  physical  Space  with 
Time  and  with  Matter  becomes  highly  relevant  at  this 
point.  For  instance,  our  geometry  and  our  physics 
are  constructed  to  deal  with  different  but  intimately 
connected  factors  in  nature,  which  are  not  met  with 
in  isolation.  It  is  therefore  conceivable  that  several 
different  systems  of  geometry  will  equally  fit  the  spatial 
side  of  nature  provided  that  suitable  modifications  be 
made  in  the  forms  of  physical  laws.     Apart  from  this, 


30  SCIENTIFIC   THOUGHT 

there  is  the  purely  mathematical  question  as  to  whether 
the  difference  between  Euclidean  and  certain  kinds  of 
non-Euclidean  geometry  be  not  merely  a  difference  in 
the  conventions  for  measuring  a  single  kind  of  Space. 
The  first  kind  of  complication  is  roughly  comparable 
to  the  possibility  of  a  box  which  changes  its  shape 
according  to  the  way  in  which  we  pack  our  clothes  in 
it.  If  some  bluff,  downright  person  (such  as  an  Oxford 
tutor)  then  asks  whether  your  box  is  a  trunk  or  a  port- 
manteau, and  insists  on  "a  plain  answer  to  a  plain 
question,"  there  is  likely  to  be  misunderstanding.  It 
is  not  so  easy  to  illustrate  the  second  kind  of  complica- 
tion mentioned  above,  but  perhaps  the  following  analogy 
will  be  of  use.  The  difference  of  temperature  between 
two  places  might  be  defined  either  by  the  difference  in 
length  of  a  certain  column  of  mercury  when  held  at  the 
two  places,  or  by  the  difference  in  pressure  of  a  certain 
volume  of  gas  when  it  is  transferred  from  one  place  to 
the  other.  When  temperature-difference  is  measured 
by  the  first  convention,  two  pairs  of  points  may  have 
the  same  temperature- difference  ;  when  it  is  measured 
by  the  second  convention  the  same  two  pairs  may  have 
different  temperature-differences.  There  is  no  question 
of  right  or  wrong  in  the  matter ;  we  just  take  two 
different  measures  of  temperature-difference,  one  of 
which  is  more  convenient  for  one  purpose  and  the 
second  for  another  purpose.  Substitute  "distance 
between  two  points"  for  "  temperature  -  difference 
between  two  places,"  and  you  have  a  case  where  two 
different  systems  of  geometry  mean,  not  two  Spaces, 
but  two  alternative  ways  of  measuring  a  single  Space. 

So  much  for  the  distinction  between  the  one  Space 
of  the  natural  scientist  and  the  many  Spaces  of  the 
mathematician.  Let  us  now  ask  ourselves  :  What  is 
the  irreducible  minimum  of  properties  that  the  ordinary 
scientist  ascribes  to  the  Space  of  nature?  (i)  He  holds 
that  it  is  in  some  sense  continuous,  and  that  it  has 
three  dimensions.     We  need  not  go  into  the  accurate 


TRADITIONAL   CONCEPT   OF   SPACE         31 

mathematical  definitions  of  continuity  and  dimensions. 
Roughly  we  mean  by  the  former  that  any  two  spaces 
that  do  not  overlap  are  at  once  separated  and  joined  by 
another  space,  and  that  all  these  spaces  are  parts  of  the 
one  big  Space  of  nature.  By  saying  that  Space  has 
three  dimensions  we  roughly  mean  that  three  inde- 
pendent bits  of  information  are  needed  to  fix  the  position 
of  a  point. 

(ii)  Again,  the  scientist  and  the  ordinary  layman 
draw  a  sharp  distinction  between  Space  and  the  things 
in  Space.  They  hold  that  Space,  as  such,  never  causes 
anything.  Mere  position  has  no  effect  on  any  property 
of  matter.  If  we  move  a  bit  of  matter  about,  it  may  of 
course  change  in  shape  or  size.  The  mercury  column 
of  a  thermometer  will  do  this  if  we  move  it  from  outside 
the  window  to  a  place  near  the  fire.  But  the  traditional 
view  is  that  the  mere  change  in  position  is  not  enough 
to  account  for  this.  The  length  has  changed  because 
the  mercury  has  altered  its  position  with  respect  to 
certain  matter  in  Space.  The  complete  inactivity  of 
Space  is,  I  think,  for  the  plain  man  the  mark  that  dis- 
tinguishes it  from  matter  in  Space.  Whenever  it  seems 
to  break  down  we  feel  perplexed  and  uncomfortable.  I 
can  illustrate  this  in  two  ways,  (a)  On  the  older 
theories  of  physics  there  was  supposed  to  be  a  peculiar 
kind  of  matter,  called  Ether,  that  filled  all  Space.  On 
these  theories  the  Ether  was  supposed  to  produce  all 
kinds  of  effects  on  ordinary  matter,  and  it  became  almost 
a  family  pet  with  certain  physicists.  As  physics  has 
advanced,  less  and  less  has  been  found  for  the  Ether  to 
do.  In  proportion  as  this  has  happened  physicists  have 
begun  to  ask:  "Do  we  mean  by  the  Ether  anything 
more  than  empty  Space?"  On  Lorentz's  theory  of 
electro-dynamics,  it  is  difficult  to  see  that  the  Ether  is 
anything  but  the  concept  of  absolute  Space  ;  and  that 
eminent  scientist's  attitude  towards  it  recalls  Mrs 
Micawber's  statement  that  she  "will  never  desert 
Mr  Micawber." 


32  SCIENTIFIC  THOUGHT 

(/>)  Conversely,  many  mathematicians  have  con- 
ceived Spaces  in  which  difference  of  position  does  make 
a  difference  to  the  shapes  and  sizes  of  bodies,  and  have 
successfully  explained  physical  phenomena  thereby. 
Prof.  Clifford  is  one  example,  and  Einstein,  in  his  theory 
of  gravitation,  is  another.  But  we  do  not  as  yet  feel 
comfortable  with  the  theories  of  this  type,  however  well 
they  may  explain  the  facts,  because  they  seem  to  involve 
the  action  of  Space  on  matter,  and  this  seems  to  upset 
all  means  of  distinguishing  between  the  two.  The 
average  intelligent  physicist  will  accept  from  the 
mathematician  any  kind  of  Space  that  fits  the  observ- 
able facts,  so  long  as  it  does  not  act  on  matter.  But 
the  wilder  kind  of  Spaces  that  the  pure  mathematician 
can  offer  him  he  refuses  to  accept  as  Spaces  at  all, 
because  it  is  part  of  what  he  means  by  Space  that  it 
shall  be  indifferent  to,  and  thus  distinguishable  from, 
its  content.  It  may  be  that  we  ought  not  to  accept 
this  objection  as  ultimate,  because  the  sharp  separation 
between  the  three  concepts  of  Space,  Time,  and  Matter 
has  all  the  appearance  of  being  artificial  ;  but  in  the 
present  chapter  we  are  confining,  ourselves  to  the  tradi- 
tional view. 

Space  then,  at  present,  is  to  be  thought  of  as  a  single 
infinite,  three-dimensional  receptacle,  in  which  all  the 
events  of  nature  have  their  being,  but  which  is  indifferent 
to  them.  If  we  reflect,  we  shall  see  that  the  evidence  for 
the  existence  of  such  an  object  is  by  no  means  obvious. 
We  can  neither  see  nor  touch  empty  spaces  ;  what  we 
see  and  touch  are  bits  of  matter.  Now  of  course  most 
things  in  which  scientists  believe  cannot  be  perceived 
by  the  senses  ;  no  one  can  see  or  touch  a  hydrogen 
atom  or  a  light-wave.  Such  objects  are  inferred  by  the 
scientist  from  the  perceptible  effects  which  they  are 
supposed  to  produce.  But  Space  is  not  even  in  this 
position.  For,  as  we  saw,  the  essence  of  Space  on  the 
traditional  view,  is  that  it  does  not  produce  any  effects. 
Obviously  then  the  existence  of  Space  cannot  be  inferred 


TRADITIONAL   CONCEPT   OF   SPACE         33 

from  its  supposed  perceptible  effects,  since  it  is  not 
supposed  to  have  any.  If  then  Space  is  neither  per- 
ceived nor  inferred,  whence  do  we  get  the  concept  of  it? 

In  dealing  with  both  Space  and  Time  there  are  two 
distinct  sets  of  concepts  used,  which  we  might  call 
distributive  and  collective.  The  collective  properties  of 
Space  and  Time  are  those  that  belong  to  them  as 
individual  wholes.  Thus  the  questions  of  how  we  come 
to  believe  that  there  is  one  Space,  that  it  is  Euclidean, 
that  it  can  be  distinguished  from  the  matter  in  it,  and 
so  on,  are  questions  concerning  collective  properties  of 
space.  On  the  other  hand,  there  are  certain  concepts 
that  apply,  not  so  much  to  Space  as  an  individual 
whole,  as  to  every  bit  of  space.  These  are  distributive 
properties,  such  as  divisibility,  order  of  points  on  lines, 
and  so  on.  In  this  and  the  next  chapter  we  shall 
confine  ourselves  to  distributive  properties  of  Space  and 
Time  respectively  ;  it  is  only  at  a  much  later  stage  that 
the  question  of  one  Space  or  Time,  and  its  distinction 
from  things  or  events  in  it  can  be  faced. 

Now  all  the  distributive  properties  that  we  ascribe 
to  Space  have  their  root  in  certain  facts  that  we  can 
directly  observe  in  our  fields  of  view,  and  to  a  less 
extent,  in  our  fields  of  touch.  Whenever  I  open  my 
eyes  I  am  aware  of  a  variously  coloured  field.  This  is 
extended,  or  spread  out,  and  this  extendedness  is  the 
root  of  my  notion  of  surfaces  and  volumes.  Again, 
within  the  total  field  certain  specially  coloured  patches 
will  stand  out  against  a  background  ;  e.g.  there  might 
be  two  green  patches,  which  are  in  fact  the  visual 
appearances  of  a  pair  of  trees.  Such  patches  have 
shapes  and  sizes  ;  and  here  we  have  the  sensible  basis 
of  the  concepts  of  definite  figures.  Then,  between  any 
two  such  outstanding  patches  there  will  always  be  an 
extended  background  with  a  different  colour,  which  at 
once  joins  and  separates  the  patches.  If,  e.g.  we  are 
in  fact  looking  at  two  trees,  standing  up  against  a 
cloudless    sky,    our   field    of  view   will   consist   of  two 


34  SCIENTIFIC   THOUGHT 

characteristically  shaped  green  patches  separated  and 
surrounded  by  a  blue  extension.  In  the  visual  field 
there  is  nothing  to  correspond  to  the  notion  of  empty 
space,  for  the  whole  field  is  occupied  by  some  colour  or 
other.  Still,  the  visual  experience  that  we  have  been 
describing  does  suffice  to  give  us,  in  a  rough  form,  the 
distributive  concepts  of  extension,  shape,  size,  between- 
ness,  and  continuity.  And  it  suggests,  though  it  does 
not  by  itself  actually  give  us,  another  concept.  A  field 
of  view  does  not  come  sharply  to  an  end  at  its  edges. 
It  fades  gradually  away,  and  the  details  become  less 
and  less  definite  the  further  they  are  from  the  centre. 
Thus  there  is  nothing  in  the  experience  to  suggest  that 
the  field  of  view  is  an  independent  complete  whole  ;  it 
rather  presents  itself  as  a  fragment  of  something  bigger. 
This  suggestion  is  strengthened  by  the  fact  that  when 
we  move  our  heads  slightly  the  new  field  of  view  is  only 
slightly  different  from  the  old  one.  Some  details  that 
were  distinct  have  become  less  so,  others  that  were 
indistinct  have  become  clearer  ;  a  little  that  was  present 
has  vanished  and  a  little  that  was  not  present  has  been 
added  at  the  extreme  edges  ;  but  the  bulk  of  the  field 
has  scarcely  altered.  This  confirms  the  feeling  that 
any  field  of  view  is  only  a  fragment  of  a  larger  whole, 
and  I  believe  that  it  is  one  of  the  roots  of  the  limitless 
character  which  we  ascribe  to  Space. 

Much  the  same  concepts  are  crudely  presented  to  us 
in  our  tactual  fields.  When  I  grasp  anything  it  feels 
extended,  and  some  things  feel  bigger  than  others. 
Again,  if  the  thing  has  projections,  I  can  feel  them 
as  standing  out  from  a  background  of  "  feeling"  in  the 
same  kind  of  way  in  which  the  green  patches  stand  out 
from  the  blue  background  in  the  visual  field.  But  there 
are  certain  peculiar  facts  connected  with  touch,  and 
more  especially  with  touch  in  conjunction  with  move- 
ment, which  are  the  germ  of  the  distinction  between 
empty  and  filled  spaces.  Had  we  been  confined  to 
sight  it  is  difficult  to  see  how  we  could  have  reached 


TRADITIONAL   CONCEPT   OF   SPACE         35 

this  distinction,  since  the  visual  field,  as  we  have 
already  said,  is  everywhere  full  of  colour,  (i)  If  I  put 
my  hand  on  the  top  of  an  open  tin  box  I  get  a  peculiar 
sensation.  I  feel  a  cold,  sharp  outline,  and,  although 
it  would  not  be  true  to  say  that  there  is  no  felt  back- 
ground within  and  without  this,  yet  it  is  true  to  say  that 
it  is  neutral  and  indefinite  as  compared  with  the  blue 
background  of  the  visual  field  in  our  example,  (ii) 
Suppose  I  move  my  fingers  along  the  edge  of  a  ruler. 
I  have  a  series  of  kinesthetic  sensations  accompanied 
by  a  series  of  tactual  sensations.  Suppose  I  continue 
the  movement  until  my  finger  gets  to  the  end  of  the 
ruler,  and  still  continue  it  afterwards.  The  tactual 
sensations  cease,  but  the  kinesthetic  sensations  go  on 
just  as  before.  The  ceasing  of  the  tactual  sensations 
is  the  basis  of  the  concept  of  emptiness  ;  the  persistence 
of  the  kinesthetic  sensations  is  the  basis  of  the  concept 
that  extension  goes  on  in  spite  of  the  absence  of  extended 
matter. 

Many  of  these  remarks,  which  are  here  just  thrown 
out,  will  need  to  be  more  fully  developed  when  we 
come  to  deal  with  the  collective  attributes  of  Space.  In 
the  meanwhile  we  notice  that  all  the  information  gained 
in  this  way  is  extremely  crude,  as  compared  with  the 
concepts  that  we  use  in  •geometry  and  apply  in  physics. 
We  see  and  feel  finite  surfaces  and  lumps  of  complicated 
shapes,  not  the  unextended  points  and  the  lines  without 
breadth  of  the  geometers.  And  the  spatial  relations 
that  we  can  immediately  recognise  between  outstanding 
patches  in  our  fields  of  view  are  equally  crude.  They 
are  not  relations  between  points  and  straight  lines,  but 
between  rough  surfaces  and  volumes.  All  that  I  am 
maintaining  is  that  these  crude  objects  of  sense-aware- 
ness do  have  properties  that  are  evidently  spatial,  and 
that  we  can  see  in  them  the  germs  of  the  refined  notions 
of  points,  straight  lines,  etc.  The  question  is  :  "  How- 
are  the  refined  terms  and  their  accurately  definable 
relations,  which  we  use  in  our  mathematics  and  physics, 


36  SCIENTIFIC   THOUGHT 

but  cannot  perceive  with  our  senses,  connected  with 
the  crude  lumps  or  surfaces  and  their  rough  relations, 
which  we  actually  do  sense?" 

The  real  problem  is  this.  The  relations  of  rough  finite 
volumes,  such  as  we  can  perceive,  are  of  unmanageable 
complexity.  Again,  the  continuity  and  boundlessness 
of  Space,  as  suggested  to  us  by  our  sense-experiences, 
are  vaguely  felt,  not  intellectually  grasped.  In  this 
state  it  is  impossible  to  lay  down  their  laws  or  to  reason 
about  them.  What  we  want  to  do  is  to  analyse 
finite  figures  and  their  fearfully  complicated  perceptible 
relations  into  sets  of  terms  with  simpler  and  more  manage- 
able relations.  If  we  can  do  this  successfully  we  shall 
have  killed  two  birds  with  one  stone.  We  shall  have 
done  full  justice  to  the  spatial  properties  of  what  we 
can  perceive  ;  for  our  analysis  is  supposed  to  be 
exhaustive.  And,  on  the  other  hand,  we  shall  be  able 
to  grasp  these  properties  and  to  reason  about  them 
in  a  way  that  was  impossible  while  they  remained  in 
the  crude  unanalysed  state  in  which  we  meet  them 
in  sense-awareness.  I  will  give  examples  of  what  I 
mean,  starting  with  very  crude  ones,  and  gradually 
working  up  to  more  refined  cases. 

(i)  If  I  want  to  measure  an  irregular  piece  of  ground 
I  first  try  to  divide  it  up  into  triangles.  Why?  Because 
the  triangle  is  a  simple  figure,  and  the  areas  of  all 
triangles  are  connected  with  their  linear  dimensions 
by  a  single  simple  law.  Moreover,  I  can  exhaustively 
analyse  any  rectilinear  figure  into  triangles.  Thus, 
instead  of  having  to  apply  a  different  principle  of 
mensuration  to  every  different  rectilinear  figure,  I  can 
treat  them  all  by  this  analysis  in  accordance  with  one 
simple  law. 

(ii)  The  notion  of  the  distance  between  two  finite 
bodies  is  clearly  indefinite  ;  so  too  is  that  of  the  direction 
of  the  line  joining  them.  For  there  is  no  one  distance 
and  no  one  direction  in  such  a  case.  Yet  evidently 
there    is   a  certain   relation   between   two  such    bodies, 


TRADITIONAL   CONCEPT   OF   SPACE         37 

which  I  can  perceive,  and  should  like  to  be  able  to  treat 
mathematically.  Two  trees  are  at  different  perceptible 
distances  from  a  third,  and  one  pair  of  them  may 
define  a  different  perceptible  direction  from  another  pair. 
Thus  there  are  crude  perceptible  relations  of  distance 
and  direction,  which  we  should  like  to  be  able  to  express 
accurately  and  to  treat  scientifically.  Now  we  notice 
that  the  smaller  we  take  our  patches  or  lumps  the  less 
is  the  inaccuracy  in  the  notion  of  the  distance  between 
them  or  the  direction  determined  by  them.  Still,  so 
long-  as  they  have  any  area  or  volume,  the  theoretical 
difficulty  remains.  What  we  should  like  to  be  able 
to  do  would  be  to  cut  up  our  finite  areas  and  volumes 
into  sets  of  parts  of  no  size,  as  we  cut  up  our  irregular 
rectilinear  figure  into  a  set  of  triangles  that  exactly  make 
it  up,  and  to  regard  the  crude  complex  relations  between 
the  finite  wholes  as  compounded  out  of  the  simple  and 
definite  relations  between  these  unextended  parts. 

Now  this  second  example  shows  us  an  important 
general  principle  and  an  important  general  difficulty, 
both  of  which  extend  beyond  Space  and  apply  equally 
to  Time  and  Matter.  We  find  that  the  relations 
between  objects  become  simpler  and  more  manageable 
as  the  objects  become  smaller.  We  therefore  want  to 
analyse  finite  objects  and  their  relations  into  smaller 
and  smaller  parts,  and  their  simpler  and  simpler 
relations.  But  we  find  that  when  we  try  to  pursue 
this  course  to  the  bitter  end  we  land  in  a  difficulty. 
The  relations  do  not  become  really  definite  and  manage- 
able till  we  have  come  to  parts  with  no  size  or  events 
with  no  duration.  And  here  we  are  faced  with  a  dis- 
continuity. What  we  perceive  is  always  objects  with 
some  magnitude  and  duration,  and  the  relations  that 
our  perception  tells  us  about  are  always  between  such 
objects.  Have  we  any  right  to  believe  that  finite 
objects  consist  of  parts  of  no  magnitude,  or  that  such 
parts,  if  they  exist  at  all,  will  have  relations  in  the 
least  like  those  which    hold    between    finite   areas   and 


38  SCIENTIFIC   THOUGHT 

volumes?  A  point  is  something  different  in  kind  from 
a  volume  or  area,  however  small.  We  know  what 
we  mean  when  we  say  that  a  big  area  can  be  cut  up 
into  smaller  ones  ;  but  it  is  not  at  all  clear  what  we 
mean  when  we  say  that  it  can  be  cut  up  into  points. 
The  one  thing  that  is  certain  is  that  the  sense  in  which 
points  are  parts  of  volumes  must  be  different  from  the 
sense  in  which  little  volumes  are  parts  of  bigger  ones. 
The  latter  sense  of  part  and  whole  is  one  that  we  find 
exemplified  among  perceived  objects.  The  former  is 
not,  and  we  are  bound  to  define  it  before  we  can  feel 
comfortable  in  using  points  and  instants. 

We  commonly  slur  over  this  difficulty  by  entertain- 
ing two  incompatible  notions  of  points,  and  using  them 
alternately  as  convenience  requires.  This  expedient 
is  not  unfamiliar  to  theologians,  and  to  business  men 
returning  their  incomes  for  purposes  of  taxation.  When 
we  want  to  talk  of  an  area  as  analysable  into  points  we 
think  of  points  as  little  volumes.  If  we  feel  qualms 
about  this  we  usually  suppress  them  with  the  excuse 
which  Midshipman  Easy's  nurse  gave  for  her  baby, 
that  "after  all,  it  was  a  very  little  one."  When  we 
want  to  think  of  points  as  having  exactly  definite 
distances  we  take  them  to  have  "  position  but  no 
magnitude,"  as  Euclid  put  it.  Now  nothing  will  make 
these  two  conceptions  of  points  consistent  with  each 
other.  Either  points  are  extended  or  they  are  not. 
If  they  are  not,  how  can  they  fit  together  along  their 
sides  and  edges  (which  they  will  not  possess)  to  make 
a  finite  volume  or  area?  If  they  are,  in  what  sense 
can  you  talk  of  the  distance  between  them,  or  of  the 
direction  determined  by  a  pair  of  them  ?  To  call  them 
infinitesimal  volumes  or  areas  only  darkens  counsel  ; 
for  the  word  infinitesimal  here  only  serves  to  cover  the 
attempt  to  combine  these  two  incompatible  qualities. 

The  method  by  which  such  difficulties  as  these 
have  been  overcome  is  due  to  Whitehead,  who  has 
lately  worked  it  out  in  full  detail   in   his  Principles  of 


TRADITIONAL   CONCEPT   OF   SPACE         39 

Natural  Knozv/edge,  and  his  Concept  of  Nature,  two 
epoch-making  works.  To  explain  it  in  full  would  take 
us  into  regions  of  mathematical  logic  which  I  do  not 
propose  to  penetrate  in  the  present  book.  But  the 
problem  is  so  important,  and  the  method  is  of  such 
general  application  in  bridging  the  gaps  between  the 
crude  facts  of  sense  and  the  refined  concepts  of  mathe- 
matical physics  that  I  shall  give  a  sketch  of  it. 

The  first  thing  to  notice  is  that  it  does  not  in  the 
least  matter  to  science  what  is  the  inner  nature  of  a  term, 
provided  it  will  do  the  work  that  is  required  of  it.     If 
we  can   give  a   definition    of  points    which   will    make 
them  fulfil  a  certain  pair  of  conditions,  it  will  not  matter 
though    points   in    themselves    should    turn    out   to    be 
entities   of  a   very   different   kind    from   what   we   had 
supposed  them  to  be.     The  two  conditions  are  (i)  that 
points  must  have  to  each  other  the   kind   of  relations 
which    geometry    demands  ;  and    (ii)   that   points   must 
have  to  finite  areas  and  volumes  such  a  relation  that  a 
reasonable   sense  can    be    given  to  the  statement  that 
such  areas  and  volumes  can  be  exhaustively  analysed 
into   sets   of  points.      Any   entity   that    answers    these 
conditions  will  do  the  work  of  a  point,  and  may  fairly 
be  called  a  point,   no   matter  what   its  other  properties 
may  be.     This  important  fact,  that  what  really  matters 
to  science  is  not  the  inner  nature  of  objects  but  their 
mutual  relations,   and  that  any  set  of  terms  with   the 
right  mutual    relations  will   answer   all   scientific   pur- 
poses as  well  as  any  other  set  with    the   same  sort  of 
relations,    was   first   recognised     in    pure    mathematics. 
Whitehead's  great  merit  is  to  have  applied  it  to  physics. 
I  will  first  illustrate  it  from  pure  mathematics,  and 
then  consider   its  application  to   our  present  problem. 
Consider    such    irrational    numbers    as    ^2   and    ^3. 
Why  do  we  call  them  numbers  ?     Simply  because  they 
obey    the    formal    laws  of  addition    and  multiplication 
which  integers,  like  2  and  3,  obey  ;  i.e.   because   they 
have   to   each    other    relations   with    the    same    formal 


40  SCIENTIFIC   THOUGHT 

properties  as  the  relations  that  hold  between  integers. 
Now  numbers  like  *J2  and  ^3  were  at  first  defined  as 
the  limits  of  certain  series  of  rational  numbers.  Thus 
+J2  was  defined  as  the  limit  of  the  series  of  rational 
fractions  whose  squares  are  less  than  2.  Similarly  ^3 
was  defined  as  the  limit  of  the  series  of  rational  fractions 
whose  squares  are  less  than  3.  Then  you  can  define 
what  you  are  going  to  mean  by  the  addition  and 
multiplication  of  such  limits.  These  will  be  new 
senses  of  addition  and  multiplication.  The  sign  + 
does  not  stand  for  the  same  relation  when  we  talk  of 
*Ji  +  ^3  as  when  we  talk  of  2  +  3.  But  addition  and 
multiplication,  in  the  new  senses,  have  the  same  formal 
properties    as  they  have  when  used    in    the  old  sense. 

Thus,  e.g.  s/~+  \/3  =  \^3+  \/2  just  as  2  +  3  =  3  +  2- 
We  have  extended  the  meaning  of  addition  and 
multiplication ;  but,  as  they  have  precisely  the  same 
logical  properties  in  both  senses,  no  harm  is  done  by 
using  the  same  name  for  both,  and  talking  of  the 
addition  and  multiplication  of  irrationals.  Consequently 
there  is  no  harm  in  calling  *J '2  and  ^3  numbers;  for 
we  agreed  that  any  set  of  entities  were  to  count  as 
numbers,  provided  they  had  to  each  other  relations  with 
the  same  logical  properties  as  the  relations  between 
familiar  numbers,  like  2  and  3,  possess.  Now  all 
reasoning  depends  entirely  on  the  logical  or  formal 
properties  of  the  objects  reasoned  about,  and  therefore 
we  can  henceforth  reason  about  irrationals  as  if  they 
were  ordinary  numbers. 

In  exactly  the  same  way,  if  we  can  define  objects 
which  have  to  each  other  relations  with  the  same  formal 
properties  as  the  relations  between  geometrical  points, 
these  objects  will  do  all  the  work  of  points,  and  can  be 
called  points,  whatever  their  internal  structure  may  be. 
Once  this  is  grasped  an  initial  difficulty  can  be  re- 
moved. We  are  apt  to  think  of  points  as  internally 
simple,  because  they  are  said  to  have  no  parts  and 
no    magnitude.     But   none   of    the    uses   to   which    we 


TRADITIONAL   CONCEPT   OF   SPACE         41 

put  points  in  geometry  or  physics  depend  on  this 
supposed  internal  simplicity.  The  usefulness  of  points 
depends  entirely  on  the  fact  that  any  pair  of  them 
define  a  unique  relation  with  very  simple  logical 
properties,  viz.,  the  straight  line  joining  them.  Now 
we  see  that  any  terms  whatever  that  are  related  to 
each  other  by  a  relation  with  these  properties  will  do 
this  part  of  the  work  of  points.  Hence  we  must  not  be 
surprised  if  we  should  find  that  points  are  not  really 
simple,  but  have  a  complex  internal  logical  structure. 
This  is  what  we  shall  find.  But  we  shall  also  find 
that,  in  spite  of  the  logical  complexity  of  points,  a 
clear  sense  can  be  given  to  the  statement  that  they 
have  no  parts  and  no  magnitude. 

We  can  now  go  a  step  further.  I  said  that  irrationals 
used  to  be  defined  as  the  limits  of  certain  series  of 
rationals.  They  are  not  so  defined  nowadays.  Why 
is  this?  The  answer  is  that,  if  we  define  them  in  this 
way,  it  is  not  certain  that  there  is  anything  answering 
to  the  definition.  ^2  is  said  to  be  the  limit  of  the 
series  of  rationals  whose  squares  are  less  than  2.  But 
how  do  you  know  that  this  series  has  a  limit  at  all  ;  i.e. 
roughly  speaking,  how  do  you  know  that  there  exists 
a  number  which  the  series  continually  approaches,  but 
never  reaches?  The  fact  is  that  we  do  not  know  it  and 
cannot  prove  it.  It  follows  that,  if  we  define  irrationals 
in  this  way,  it  is  not  certain  that  there  are  any  irra- 
tionals ;  aJ '2  might  be  a  symbol  which  stands  for  nothing 
at  all,  like  the  phrase  "The  present  King  of  France," 
which  has  a  meaning  but  no  application.  We  want 
therefore  to  °ret  a  definition  that  shall  amount  to  much 
the  same  thing  as  the  definition  by  limits,  but  shall  not 
leave  us  in  any  doubt  as  to  the  existence  of  something 
answering  to  it. 

Now  very  much  the  same  difficulty  arises  over  points. 
I  will  put  it  in  this  way.  We  are  naturally  tempted  to 
define  points  as  the  limits  of  certain  series  of  areas  or 
volumes,  just  as  we  defined  irrationals  as  the  limits  of 

D 


42  SCIENTIFIC   THOUGHT 

certain  series  of  rationals.  And  these  attempted  defini- 
tions are  steps  in  the  right  direction.  But  they  are  not 
ultimately  satisfactory,  because  they  leave  the  existence 
of  points,  as  of  irrationals,  doubtful.  Let  me  illustrate 
this  with  regard  to  points.  We  saw  that,  as  we  take 
smaller  and  smaller  areas  or  volumes,  the  spatial  rela- 
tions between  them  become  simpler  and  more  definite. 
Now  we  can  imagine  a  series  of  areas  or  volumes,  one 
inside  the  other,  like  a  nest  of  Chinese  boxes.  Suppose, 
e.g.  that  it  was  a  set  of  concentric  spheres.  As  you  pass 
to  smaller  and  smaller  spheres  in  the  series  you  get  to 
things  that  have  more  and  more  approximately  the 
relations  which  points  have  in  geometry.  You  might 
therefore  be  tempted  to  define  a  point,  such  as  the 
common  centre  of  the  spheres,  as  the  limit  of  this  series 
of  spheres  one  inside  the  other.  But  at  once  the  old 
difficulty  would  arise  :  "Is  there  any  reason  to  suppose 
that  this  series  has  a  limit?"  Admittedly  it  has  no 
last  term  ;  you  can  go  on  finding  spheres  within  spheres 
indefinitely.  But  the  mere  fact  that  it  does  not  have  a 
last  term  is  no  proof  that  it  does  have  a  limit.  The 
limit  of  an  endless  series  might  be  described  as  the  first 
term  that  comes  after  all  the  terms  of  the  endless  series. 
But  this  implies  that  the  series  in  question  forms  part 
of  some  bigger  series  ;  otherwise  there  is  no  beyond. 
Now  it  is  not  at  all  obvious  that  our  endless  series  of 
concentric  spheres  does  form  part  of  any  bigger  series, 
or  that  there  is  any  term  that  comes  after  every  sphere 
in  it.  Hence  there  is  no  certainty  that  points,  defined 
as  the  limits  of  such  series,  exist. 

How  is  such  a  difficulty  to  be  overcome?  It  was  first 
overcome  for  irrational  numbers,  and  Whitehead  then 
showed  that  it  might  be  dealt  with  in  the  same  way  for 
points.  The  solution  will  at  first  sight  strike  those  who 
are  unfamiliar  with  it  as  a  mere  tour  de  force ;  neverthe- 
less it  is  perfectly  valid,  and  really  does  the  trick. 
Instead  of  defining  *J2  as  the  limit  of  the  series  of 
rational    numbers  whose  squares  are  less  than  2,   it  is 


TRADITIONAL   CONCEPT   OF   SPACE         43 

defined  as  this  series  itself.  That  is  *J2  is  defined  as 
the  series  of  all  rational  numbers  whose  squares  are 
less  than  2.  There  is  no  doubt  that  there  is  such  a 
thing  as  ^2,  so  defined.  For  there  certainly  are  rational 
numbers,  like  1  and  1*2  and  2*5,  and  so  on.  And  it 
is  certain  that  the  squares  of  some  of  them  are  less  than 
2,  that  the  squares  of  others  of  them  are  greater  than  2, 
and  that  the  squares  of  none  of  them  are  equal  to  2. 
It  is  therefore  certain  that  there  is  a  definite  class  of 
rationals  whose  squares  are  less  than  2,  and  that  it 
has  an  infinite  number  of  members.  It  is  equally 
certain  that  the  numbers  in  this  class  form  a  series, 
when  arranged  in  order  of  magnitude.  Thus  there  is 
no  doubt  of  the  existence  of  the  series  which  is  said  to 
be  the  meaning  of  sj2. 

But  the  difficulty  that  will  be  felt  at  first  will  be  a 
different  one.  The  reader  will  be  inclined  to  say:  "I 
don't  doubt  that  ^/2,  as  defined  by  you,  exists  ;  what 
I  very  gravely  doubt  is  whether,  as  defined  by  you,  it 
is  what  I  or  anyone  else  mean  by  ^2,  By  1J2  I  under- 
stand a  certain  number  of  a  peculiar  kind  ;  I  do  not 
mean  a  series  of  numbers  or  of  anything  else."  The 
answer  to  that  difficulty  is  that  series  of  this  kind  will 
serve  every  purpose  for  which  irrationals,  like  ^2  and 
^3,  are  used  in  mathematics.  You  can  define  addition 
and  multiplication  for  such  series,  and  they  have  exactly 
the  same  logical  properties  as  the  addition  and  multipli- 
cation of  integers  or  of  rational  fractions.  Lastly,  taking 
this  definition  of  ^2,  you  can  give  a  perfectly  definite 
meaning  to  the  statement  that  the  length  of  the  diagonal 
of  a  square,  whose  side  is  of  unit  length,  is  represented 
by  *J2.  The  position  is  therefore  this.  The  definition 
of  irrationals  defines  something  that  certainly  exists. 
And  this  something  has  all  the  formal  properties  and 
will  do  all  the  work  of  irrationals.  The  sole  objection 
to  it  is  that  it  is  paradoxical,  in  so  far  as  it  assigns  a 
complex  internal  structure  to  irrationals  which  we  did 
not  suspect  them  of  having.     But  that  objection  is  really 


44 


SCIENTIFIC   THOUGHT 


unimportant,  because  of  the  general  principle  that  in 
science  it  is  only  the  logical  properties  of  the  relations 
between  our  terms  that  matter,  and  not  their  internal 
logical  structure.  The  objection  is  just  a  prejudice  to 
be  got  over,  like  our  feeling  that  the  inhabitants  of 
Australia  must  be  precariously  hanging  on  to  the  earth 
by  suction,  like  tlies  on  a  ceiling. 

Now  we  deal  with  the  difficulty  about  points  in  an 
exactly  similar  way.  We  should  like  to  say  that  points 
are  the  limits  of  series  of  smaller  and  smaller  volumes, 
one  inside  the  other,  like  Chinese  boxes.  But  we 
cannot  feel  any  confidence  that  such  series  have  limits 
and  therefore  that  points,  so  defined,  exist.  Now  there 
is  no  doubt  that  such  series  themselves  exist ;  ordinary 
perception  makes  us  acquainted  with  their  earlier  and 
bigger  terms,  and  the  assumption  that  Space  is  con- 
tinuous guarantees  the  later  ones.  We  see,  on  reflection, 
that  it  is  of  the  very  nature  of  any  area  or  volume  to 
have  parts  that  are  themselves  areas  or  volumes.  We, 
therefore,  boldly  define  points,  not  as  the  limits  of  such 
series,  but  as  such  series  themselves.  This  is  exactly 
like  the  procedure  adopted  in  defining  irrationals. 

There  are  certain  additional  difficulties  of  detail  in 
defining  points,  which  do  not  arise  in  defining  irrationals. 

I  will  just  indicate  them  and 
refer  the  reader  to  Whitehead  for 
the  complete  solution  of  them, 
(i)  There  may  be  a  great  many 
different  series  of  converging 
volumes  which  would  all  com- 
monly be  said  to  converge  to  the 
same  point.  This  is  illustrated 
for  areas  in  the  figure  above, 
where  the  series  of  circles  and  the  series  of  squares 
might  equally  be  taken  to  define  the  point  which  is 
their  common  centre.  Now,  of  course,  the  point  cannot 
reasonably  be  identified  with  one  of  these  series  rather 
than  with  another.     We,  therefore,  define  the  point,  not 


TRADITIONAL   CONCEPT   OF   SPACE         45 

as  any  one  of  these  series  of  converging  volumes,  but  as 
the  class  of  all  the  volumes  in  any  of  the  series  that  would 
commonly  be  said  to  converge  to  the  point,  (ii)  Not 
all  series  of  converging  volumes  converge  to  points  ; 
some  converge  to  lines,  and  others  to  areas.  An  ex- 
ample of  a  series  of  areas  converging  to  a  straight 
line  is  illustrated  below.  (It  should  be  noticed  that, 
although  for  simplicity  of  drawing  I  have  always  taken 
series  of  areas  in  my  diagrams,  the  fundamental  fact 
is  series  of  volumes,  and  areas  need  definition,  like  points 
and  lines.) 

The  general  principle  is,  however,  always  the  same. 
Points,  straight  lines  and  areas  are  all  defined  as  series 
of  converging  volumes.     But  the  series  that  define  points 


differ  in  certain  assignable  ways  from  those  that  define 
straight  lines,  and  these  in  turn  differ  in  certain  assign- 
able ways  from  those  which  define  areas.  Ordinary 
perception  gives  us  examples  of  each  kind  of  series, 
and  the  only  difficulty  is  to  state  in  formal  logical  terms 
these  differences  which  we  can  all  vaguely  see  and  feel. 
To  do  this  properly  is,  of  course,  a  very  hard  job,  but  it 
can  be  and  has  been  done.  Many  of  these  additional 
complications  arise  because  Space  has  three  dimensions, 
whilst  the  series  of  real  numbers  has  only  one.  Conse- 
quently, as  a  matter  of  history,  moments  of  Time  were 
defined  in  this  way  before  points  of  Space.  Time  forms 
a  one-dimensional  series,  like  the  real  numbers,  and, 
therefore  presents  an  easier  problem  than  Space  for  this 
method. 

Before  going  further  I  want  to  remove  a  legitimate 
ground  of  doubt  which  will  probably  be  in  the  minds 
of  most  careful  readers  to  whom  the  subject  is  new. 
Many  will  say:   "This  is  no  doubt   highly  ingenious, 


46  SCIENTIFIC  THOUGHT 

but  are  we  not  merely   moving-  in  a  circle?     May  not 
the  theory  be  summed   up   by    saying   that  points  are 
those  series  of  volumes  that  converge  to  points?     If  so, 
are  we  not  plainly  using  the  notion  of  point  in  order  to 
define  it?"     This  would  of  course  be  a  fatal  objection 
if  it  were  well  founded,  but  it  is  not.     The  theory  may 
roughly  be  summed  up  in   the  statement  that  a  point 
is  a  series  of  volumes  that  would   commonly  be   said  to 
converge  to  that  point.     The  whole  question  is  whether 
the  common  phrase  "converging  to  the  point/"  really 
involves  a  reference  to  points.      If  it  does  the  definition 
of  points  is  circular  and  useless  ;  if  it  does  not  there  is 
no  vicious  circle  in  the  theory.     Now  the  essence  of  the 
theory  is  that  it  can  state  the  meaning  of  such  phrases 
as    "converging  to  a   point"   in   terms  which   involve 
nothing  but  volumes  and  their  relations  to  each  other. 
We  see  certain  series  of  volumes  which  we  say  "con- 
verge to  a  point,"  e.g.  series  of  concentric  spheres.     We 
see  other  series  of  volumes  of  which  we  do  not  say  this. 
Here  is  a  perceptible  difference  in  perceptible  objects. 
This  difference,  which  can   be  seen   and   felt,  must  be 
expressible  in  terms  of  volumes  and  their  relations  to 
each  other.     It  cannot  really  involve  a  relation  to  some- 
thing that  can  neither  be  seen  nor  felt,  such  as  a  point. 
Thus  a  series  of  volumes  is  said  to  converge  to  a  point 
simply  and  solely   because  of  certain   relations  which 
hold  between  the  volumes  of  the  series.     Another  series 
of  volumes  is  said  not  to  converge  to  a  point  simply  and 
solely  because  certain  other  relations  exist  between  the 
volumes  of  this  series.     These  relations,  as  well  as  their 
terms,   are  perceptible,   and    this    is    how   we   come   to 
distinguish  two  such  series.     It  only  remains  to  state 
the  differences  of  relation,  which  can  thus  be  seen  and 
felt,  in  definite  terms  that  can  be  grasped  by  the  intellect. 
This  the   present  theory  does.     For  example,  a  series 
of  confocal  conicoids  could  be  defined  as  one  whose 
members  cut  each  other  at  right  angles  ;  a  definition 
which  makes  no  mention   of  their  common   focus,  but 


TRADITIONAL   CONCEPT   OF   SPACE         47 

simply  mentions  a  relation  which  the  members  of  the 
series  have  to  each  other.  There  is  thus  no  circularity 
in  the  definition  of  points  by  this  method. 

The  method  which  we  have  been  sketching,  by  which 
the  accurate  concepts   of  science  are  defined  in   terms 
of  perceptible  objects  and  their  perceptible  relations,  is 
called  by  Whitehead  the  Principle  of  Extensive  Abstrac- 
tion.    Our  next  question  is:  Do  points,   lines,  etc.,  as 
defined  by  Extensive  Abstraction,  fulfil  the  conditions 
that  we   laid  down    for  them  at  the   beginning?     The 
first  was  that  they  must  have  to   each    other  the   sort 
of  relations  that  points,  etc.,  are  said  to  have  to  each 
other    in    geometry.     For    instance,    two    points    must 
define  a  unique  relation  with  certain  logical  properties, 
viz.,    the    straight   line   that  joins   them.     Intersecting 
straight  lines  must  define  planes,  and  so  on.      Points, 
straight  lines,  and  planes,  defined  as  above,  do  in  fact 
have  relations  of  this  kind  to  each  other.     The  detailed 
proof  of  this  must  here  be  taken  on  trust,  but  I  shall 
take  one  example  to  indicate  roughly  the  way  in  which 
these   results   come   about.     Take    two   different   series 
of  concentric  spheres,  one  in  one  place  and  the  other  in 
another.     Choose  any   sphere  out  of  one  set  and  any 
sphere  out  of  another.     There  will  be  a  certain  crude 
perceptible    relation    between    them.      For    instance,   as 
shown  in  the  diagram   below,  there  will   be  a  volume 


which  connects  and  contains  both  of  them,  which  does 
not  wholly  contain  any  pair  of  larger  spheres  in  the  two 
series,  but  more  than  contains  any  pair  of  smaller  spheres 
in  the  two  series. 

Let  us  call  this  the  containing  volume  of  the  selected 
pair.     As  we  take  smaller  and  smaller  pairs  of  spheres 


48  SCIENTIFIC  THOUGHT 

from  the  two  series  it  is  easy  to  see  that  the  corre- 
sponding- containing  volumes  form  a  series  of  Chinese 
boxes  of  the  usual  kind.  Now  this  series  of  containing 
volumes  is  obviously  of  the  sort  that  defines  a  straight 
line.  Our  two  series  of  spheres  are  of  the  sort  that 
define  points  ;  the  points  that  they  define  are  what  we 
commonly  call  the  centres  of  the  two  systems.  And 
it  is  easy  to  see  roughly  that  the  line  defined  by  the 
series  of  containing  volumes  is  what  we  call  the  line 
joining  the  two  centres.  Of  course,  for  accurate  mathe- 
matical treatment,  many  more  refinements  are  needed  ; 
but  I  hope  that  the  example  will  suffice  to  show  in  a 
rough  way  how  points,  as  defined  by  us,  determine 
straight  lines,  as  defined  by  us. 

The  second  condition  which  points  had  to  fulfil  was 
that  it  must  be  possible  to  give  a  clear  meaning  to  the 
statement  that  finite  volumes  and  areas  can  be  completely 
analysed  into  sets  of  points.  Now  we  can  see  at  once 
that,  whatever  a  point  may  be,  it  is  certain  that  it  cannot 
be  part  of  a  volume  in  the  sense  in  which  a  little  volume 
can  be  part  of  a  bigger  one.  The  latter  is  the  funda- 
mental relation  ;  it  holds  only  between  finite  volumes, 
and  it  is  perceptible.  In  this  sense  points,  however 
defined,  could  not  be  parts  of  volumes.  Divide  a 
volume  as  long  as  you  like  and  you  will  get  nothing 
but  smaller  volumes.  Put  points  together  as  much  as 
you  like  (if  this  permission  conveys  anything  to  you)  and 
you  will  not  get  any  volume,  however  small.  In  fact  the 
whole  notion  of  ''putting  together"  points  is  absurd, 
for  it  tries  to  apply  to  points  a  relation  which  can  only 
hold  between  volumes  or  areas.  To  put  together  means 
to  place  so  that  the  edges  touch  ;  and  a  point,  having 
no  area  or  volume,  has  no  edges.  We  see  then  that, 
whatever  definition  we  give  of  points,  we  must  not 
expect  them  to  be  parts  of  volumes  in  the  plain  straight- 
forward sense  in  which  the  Great  Court  is  part  of  the 
college  buildings  of  Trinity.  It  is  therefore  no  special 
objection    to   our   definition    of   points    that   points,    as 


TRADITIONAL   CONCEPT   OF   SPACE         49 

defined  by  us,   could  not  be    parts    of  volumes  in  the 
plain  straightforward  sense. 

The  sense  in  which  a  point  p  is  contained  in  a 
volume  v  is  roughly  the  following.  We  say  that  p  is 
contained  in  v  if,  after  a  certain  „---, 

volume  has  been  reached  in  the 
series  that  defines  p,  all  sub- 
sequent volumes  in  this  series 
are  parts,   in    the   plain  straight-  --—' 

forward  sense,  of  the  volume  v.     The  diagram  illustrates 
this  definition. 

The  sense  in  which  any  volume  can  be  exhaustively 
analysed  into  points  is  roughly  the  following :  Any 
pair  of  volumes  of  which  both  are  contained  in  v,  but 
of  which  neither  is  wholly  contained  in  the  other,  belong 
to  series  which  define  different  points,  both  of  which  are 
contained  in  v  in  the  sense  just  defined.  Of  course  both 
these  definitions  need  further  refinements  to  cover  all 
cases  that  can  arise. 

Now  what  precisely  has  been  accomplished  by  all 
this?  We  have  shown  the  exact  connexion  between 
what  we  can  and  do  perceive,  but  cannot  deal  with 
mathematically,  and  what  we  can  and  do  deal  with 
mathematically,  but  cannot  perceive.  We  perceive 
volumes  and  surfaces,  and  we  perceive  certain  relations 
between  them,  viz.,  that  they  intersect,  or  that  one  is 
contained  in  the  other,  or  that  they  are  separated  and 
both  contained  in  some  third  volume  or  surface.  We 
do  not  perceive  the  points  without  volume  and  the  lines 
without  breadth,  in  terms  of  which  geometry  and  physics 
are  stated  and  worked  out.  On  the  one  hand,  we  cannot 
make  geometry  into  a  deductive  science  at  all  except 
in  terms  of  points,  etc.  On  the  other  hand,  we  want 
to  be  able  to  apply  geometry  to  the  actual  world,  and 
not  to  treat  it  as  a  mere  mathematical  fairy  tale.  It  is 
essential  therefore  that  the  connexion  between  what  we 
perceive,  but  cannot  directly  treat  mathematically,  and 
what  we  cannot  perceive,  but  can   treat  mathematically, 


50  SCIENTIFIC   THOUGHT 

should  be  made  clear.  This  is  what  we  have  tried  to 
do,  following-  the  method  of  Extensive  Abstraction  laid 
down  and  worked  out  by  Whitehead. 

It  seems  to  me  that  the  more  we  reflect  the  more 
clearly  we  see  that  something  like  the  course  that  we 
have  followed  is  necessary  if  the  application  of  geometry 
(and  also  of  rational  mechanics)  to  the  real  world  is  to 
be  justified.  The  world  of  pure  mathematics  with  its 
points,  straight  lines,  and  planes,  its  particles,  instants, 
and  momentary  configurations,  has  an  appearance  of 
unnatural  smoothness  and  tidiness,  as  compared  with 
the  rough  complexity  of  the  perceptible  world.  Yet 
the  laws  of  geometry  and  mechanics  came  out  of  the 
study  of  that  world,  and  return  to  it  in  the  form  of 
applied  mathematics.  What  I  have  tried  to  do  is  to 
show  in  rough  outline  how  the  two  are  connected,  in 
the  hope  that  the  reader  may  be  encouraged  to  consult 
the  original  authorities  to  learn  how  the  same  method 
establishes  the  connexion  in  the  minutest  details. 

I  think  that  possibly  two  difficulties  may  still  remain 
in  the  reader's  mind,  (i)  He  may  say  :  "  Men  used 
geometry  for  thousands  of  years,  and  applied  it,  and 
yet  they  knew  nothing  of  these  definitions  of  points, 
straight  lines,  and  planes."  I  answer  that  this  is 
perfectly  true,  and  that  it  perfectly  illustrates  the 
difference  between  the  special  sciences  and  Critical 
Philosophy.  Certainly  people  used  the  concepts  of 
point  and  straight  line,  and  used  them  correctly  as  the 
results  show.  But  equally  certainly  they  had  the  most 
confused  ideas  as  to  what  they  meant  by  points  and 
straight  lines,  and  could  not  have  explained  why  a 
geometry  stated  in  terms  of  these  and  their  relations 
should  apply  so  accurately  to  a  world  in  which  nothing 
of  the  kind  was  perceptible.  It  is  the  business  of  Critical 
Philosophy  not  to  rest  content  with  the  successful  use 
of  such  concepts,  but  to  disentangle  their  meaning  and 
thus  determine  the  limits  within  which  they  can  safely 
be  employed. 


TRADITIONAL   CONCEPT   OF   SPACE         51 

(ii)  The  second  question  that  may  be  asked  is  :  "  Do 
points,  straight  lines,  etc.,  really  exist  in  the  same  sense 
as  volumes,  or  are  they  merely  convenient  and  perhaps 
indispensable  fictions?"  This  seems  to  me  to  be 
an  important  point,  on  which  even  authorities  like 
Mr  Russell  often  speak  with  a  strangely  uncertain 
voice.  (Probably  Mr  Russell  calls  certain  things, 
which  he  thinks  can  be  defined  in  this  kind  of  way, 
"fictions,"  from  the  same  motives  as  led  Mr  Pope, 
according  to  Dr  Johnson,  to  write  the  lines  : — 

"  Let  modest  FOSTER,  if  he  will,  excel 
Ten  metropolitans  in  preaching  well.") 

The  right  answer  to  the  question  appears  to  me  to  be 
the  following:  Points,  etc.,  as  defined  by  us,  are  not 
fictions  ;  they  are  not  made  by  our  minds,  but  discovered 
by  them,  just  as  America  was  discovered,  and  not 
created,  by  Columbus's  voyage.  On  the  other  hand, 
they  do  not  exist  in  precisely  the  same  sense  in  which 
finite  volumes  exist.  They  are  real  in  their  own  kind, 
but  it  is  a  different  kind  from  that  of  volumes.  It  is 
through  no  mere  accidental  limitation  of  our  senses  that 
we  cannot  perceive  the  points  and  straight  lines  of  the 
geometers,  whilst  we  can  see  and  feel  volumes.  Only 
particulars  can  be  perceived  by  the  senses  ;  and  points 
are  not  particulars.  They  are  classes  of  series  of 
volumes,  or,  to  be  more  accurate,  are  the  logical 
sums  of  such  classes.  The  volumes  and  the  series 
of  volumes  that  define  points  exist  quite  literally, 
and  the  earlier  and  bigger  terms  of  these  series  can  be 
perceived.  The  points  themselves  are  rather  compli- 
cated logical  functions  of  these.  They  exist  in  the 
sense  that  they  are  determinate  functions  of  real  series 
of  actually  existing  particulars. 

Perhaps  an  illustration  from  another  region  will 
make  their  mode  of  being  clearer  to  some  people.  The 
curve  called  a  cycloid  is  traced  out  by  a  point  on  the 
circumference  of  a  circle  when  the  latter  rolls  along  a 


52  SCIENTIFIC   THOUGHT 

Straight  line.  Now  the  arches  of  Westminster  Bridge 
are  cycloidal,  and  can  therefore  be  regarded  as  due  to 
the  rolling  of  a  certain  circle  on  a  certain  straight  line. 
Now  suppose  we  were  asked  whether  this  circle  actually 
exists  or  is  a  mere  fiction.  In  one  sense  I  answer  that 
it  does  not  exist.  So  far  as  I  know,  no  physical  circle 
actually  rolled  at  some  date  in  the  world's  history 
on  a  physical  straight-edge  to  produce  the  arches  of 
Westminster  Bridge.  On  the  other  hand,  the  circle  is 
not  a  mere  fiction.  The  cycloidal  arches  really  do  exist, 
and  the  circle  corresponding  to  them  is  completely 
determined  by  the  shape  and  size  of  these  arches.  This 
connexion  is  a  real  fact,  absolutely  independent  of  our 
minds  and  their  operations.  I  therefore  say  that  the 
circle  exists,  in  the  sense  that  it  is  a  determinate  function 
of  the  arches,  which  exist  in  the  ordinary  sense.  Points, 
straight  lines,  etc.,  as  defined  by  us,  exist  in  the  same 
sense  as  the  circle  determined  by  the  arches  of  West- 
minster Bridge  ;  the  particular  series  of  volumes  which 
define  points  exist  in  the  same  sense  as  the  arches 
themselves. 

Additional     works     that     may    be     consulted    with 
profit : 

A.  N.  Whitehead,  Principles  of  Natural  Knowledge,  Part  III. 
„  Concept  of  Nature,  Cap.  IV. 


CHAPTER   II 

Alice  sighed  wearily.  "  I  think  you  might  do  something 
better  with  the  time,"  she  said,  "than  waste  it  asking  riddles 
with  no  answers." 

"  If  you  knew  Time  as  well  as  I  do,"  said  the  Hatter,  "  you 
wouldn't  talk  about  wasting  it." 

(Lewis  Carroll,  Alice  in  Wonderland.) 

The  General  Problem  of  Time  and  Change 

We  have  now  said  as  much  about  Space  as  can  be 
said  with  profit  before  its  relations  to  Time  and  Matter 
have  been  dealt  with.  We  have  shown  at  least  how 
the  concepts,  such  as  points,  lines,  planes,  etc.,  which 
are  needed,  whatever  view  we  finally  take  of  Space, 
are  connected  with  the  rough,  untidy  facts  that  we 
can  perceive.  We  have  not,  however,  explained  why 
there  is  supposed  to  be  one  single  Space  in  which 
all  the  events  of  nature  are  located,  nor  how  things 
have  places  assigned  to  them  in  it.  This  can  only  be 
done  at  a  later  stage.  In  the  meanwhile  I  propose  to 
treat  the  concepts  of  Time  and  Change,  as  they  appear 
at  the  same  level  of  thought. 

At  first  sight  the  problems  of  Time  look  very  much 
like  those  of  Space,  except  that  the  single  dimension 
of  Time,  as  compared  with  the  three  of  Space,  seems  to 
promise  greater  simplicity.  We  shall  point  out  these 
analogies  at  the  beginning  ;  but  we  shall  find  that  they 
are  somewhat  superficial,  and  that  Time  and  Change 
are  extremely  difficult  subjects,  in  which  spatial  analogies 
help  us  but  little. 

The  physicist  conceives  Time  in  much  the  same  way 
as  he  conceives  Space.     lust  as  he  distinguishes  Space 

53 


54  SCIENTIFIC  THOUGHT 

from  the  matter  in  it,  so  he  distinguishes  Time  from 
events.  Again,  mere  difference  of  position  in  Time  is 
supposed  to  have  no  physical  consequences.  It  is  true 
that,  if  I  go  out  without  my  overcoat  at  2  a.m.,  I  shall 
probably  catch  cold;  whilst,  if  I  do  so  at  2  p.m.,  I 
shall  probably  take  no  harm.  But  this  difference  is 
never  ascribed  to  the  mere  difference  in  date,  but  to 
the  fact  that  different  conditions  of  temperature  and 
dampness  will  be  contemporary  with  my  two  expeditions. 
Again,  Time,  like  Space,  is  supposed  to  be  continuous, 
and  physicists  suppose  (or  did  so  until  quite  lately)  that 
there  is  a  single  time-series  in  which  all  the  events  of 
nature  take  place.  This  series  is  of  one  dimension,  so 
that,  as  far  as  appears  at  present,  Time  is  like  a  very 
simple  Space  consisting  of  a  single  straight  line. 

Just  as  we  treat  our  geometry  in  terms  of  unextended 
points  and  their  relations,  so  we  treat  our  chronometry 
in  terms  of  moments  without  duration  and  their  relations. 
Duration  in  Time  corresponds  to  extension  in  Space. 
Now,  just  as  we  never  perceive  points  or  even  unex- 
tended particles,  so  we  are  never  aware  of  moments  or 
of  momentary  events.  What  we  are  aware  of  is  finite 
events  of  various  durations.  By  an  event  I  am  going 
to  mean  anything  that  endures  at  all,  no  matter  how 
long  it  lasts  or  whether  it  be  qualitatively  alike  or 
qualitatively  different  at  adjacent  stages  in  its  history. 
This  is  contrary  to  common  usage,  but  common  usage 
has  nothing  to  recommend  it  in  this  matter.  We 
usually  call  a  flash  of  lightning  or  a  motor  accident 
an  event,  and  refuse  to  apply  this  name  to  the  history 
of  the  cliffs  at  Dover.  Now  the  only  relevant  difference 
between  the  flash  and  the  cliffs  is  that  the  former  lasts 
for  a  short  time  and  the  latter  for  a  long  time.  And 
the  only  relevant  difference  between  the  accident  and 
the  cliffs  is  that,  if  successive  slices,  each  of  one  second 
long,  be  cut  in  the  histories  of  both,  the  contents  of  a 
pair  of  adjacent  slices  may  be  very  different  in  the  first 
case  and  will  be  very  similar  in  the  second  case.     Such 


TIME   AND   CHANGE  55 

merely  quantitative  differences  as  these  give  no  good 
ground  for  calling  one  bit  of  history  an  event  and 
refusing  to  call  another  bit  of  history  by  the  same  name. 
Now  the  temporal  relations  which  we  perceive  among 
events  are  similar  to  the  relations  of  partial  or  complete 
overlapping  which  we  can  perceive  in  the  case  of  two 
extended  objects,  like  a  pair  of  sticks.  The  possible 
time-relations  between  two  events  can  be  completely 
represented  by  taking  a  single  straight  line,  letting 
"  left-to-right "  on  this  stand  for  "  earlier  and  later," 
and  taking  two  stretches  on  this  line  to  represent  a 
pair  of  finite  events.  Let  AB  and  CD  be  two  events 
of  which  the  latter  lasts  the  longer  ;  then  the  possible 
temporal  relations  between  the  two  are  represented  by 
the  nine  figures  given  below. 

y    tf) 


(/)     . 

C 

D 

'       A       B 

(2)       .          ? 

D 

1   '      A        B 

(3)       .    C    . 

D 

'   '      A        B 

(4)      C         , 

D 

A         B 

D 


A        B 

.    D 


A        B 

D 


■*    (6) 

->    (7) 


A  8 

D 


B 


>  (8) 

►  (9) 


The  most  general  kinds  of  relation  between  finite 
events  are  those  of  partial  precedence  and  partial 
subsequence  ;  the  rest  can  be  defined  in  terms  of  these. 
From  these  crude  perceptible  data  and  their  crude 
perceptible  relations  the  concepts  of  momentary  events 
and  moments  can  be  obtained,  and  their  exact  relations 
determined,  by  the  Method  of  Extensive  Abstraction. 
I  believe  that,  as  a  matter  of  history,  one  of  the  first 
successful  applications  of  the  method  was  made  by 
Dr  Norbert  Wiener  to  this  very  problem. 

The  motives  that  lead  us  to  apply  Extensive 
Abstraction  to  Time  are  the  same  as  those  which  lead 
us  to  apply  it  to  Space.  As  scientists  our  main  interest 
is  to  discover  laws  connecting  events  of  one  kind  with 
events   of  other   kinds   at   different   times.     Now,   just 


56  SCIENTIFIC  THOUGHT 

as  the  geometrical  relations  of  finite  volumes,  as  such, 
are  of  unmanageable  complexity,  so  are  the  causal 
relations  of  events  of  finite  duration.  There  is  no 
simple  relation  between  the  contents  of  one  hour  and 
the  contents  of  another.  But  the  shorter  we  make 
our  events  the  simpler  become  the  relations  between 
them.  So,  finally,  we  state  our  laws  in  terms  of  so- 
called  "momentary  events"  and  their  exact  relations, 
and  we  "analyse"  finite  events  into  sets  of  momentary 
ones,  and  explain  their  relations  in  terms  of  those  of 
their  momentary  "parts."  Everything  that  has  been 
said  of  this  procedure  in  geometry  applies,  mutatis 
mutandis )  to  its  use  in  physics.  Momentary  "events" 
are  not  really  events,  any  more  than  points  are  little 
volumes.  A  momentary  event  is  not  "  part  of"  a  finite 
one  in  the  plain  straightforward  sense  in  which  the 
event  of  a  minute  is  part  of  the  event  that  occupies 
a  certain  hour.  The  meanings  of  all  these  concepts, 
and  their  relations,  have  to  be  given  in  terms  of 
perceptible  entities  and  their  relations,  by  means  of 
Extensive  Abstraction. 

What  we  have  been  saying  is  most  excellently 
illustrated  by  the  science  of  Mechanics.  What  we 
want  to  deal  with  there  is  the  movements  of  finite 
bodies,  like  wheels  and  planets  ;  and  we  want  to  treat 
their  changes  of  position  and  motion  over  long  periods 
of  time.  To  do  this  we  have  first  to  analyse  the  finite 
bodies  into  unextended  particles,  and  then  to  analyse 
the  finite  events  into  momentary  ones.  The  laws  of 
Mechanics  are  only  simple  when  they  state  relations 
between  momentary  configurations  of  one  set  of  par- 
ticles and  a  later  or  earlier  configuration  of  the  same 
or  another  set  of  particles.  The  gap  between  the 
perceptible  facts,  that  we  are  trying  to  describe  and 
predict,  and  the  imperceptible  concepts  and  relations, 
in  terms  of  which  we  have  to  treat  the  facts,  is  bridged 
by  Extensive  Abstraction,  applied  both  to  extension 
in   Space  and  to  duration   in   Time.       Mechanics    is  a 


TIME   AND   CHANGE  57 

kind  of  geometry  of  events,  which  has  to  take  account 
of  both  their  spatial  and  their  temporal  characteristics. 
Geometry  is  the  kind  of  mechanics  which  results  when 
we  confine  ourselves  to  a  single  moment,  and  omit  the 
temporal  characteristics  of  events.  These  are,  of  course, 
only  rough  general  statements  ;  but  they  are  perhaps 
illuminating,  and  they  will  be  more  fully  explained 
later. 

So  far,  the  analogy  between  Time  and  Space  has 
seemed  to  work  very  well.  Duration  has  corresponded 
to  length,  before  and  after  to  right  and  left,  and 
simultaneity  to  complete  mutual  overlapping.  But,  if 
we  reflect  a  little  more  carefully,  we  shall  see  that  the 
analogy  between  before  and  after  and  right  and  left 
is  not  so  illuminating  as  it  seems  at  first  sight.  The 
peculiarity  of  a  series  of  events  in  Time  is  that  it  has 
not  only  an  intrinsic  order  but  also  an  intrinsic  sense. 
Three  points  on  a  straight  line  have  an  intrinsic  order, 
i.e.  B  is  between  A  and  C,  or  C  is  between  B  and 
A,  or  A  is  between  C  and  B.  This  order  is  independent 
of  any  tacit  reference  to  something  traversing  the  line 
in  a  certain  direction.  By  difference  of  sense  I  mean 
the  sort  of  difference  which  there  is  between,  say, 
ABC  and  CBA.  Now  the  points  on  a  straight  line 
do  not  have  an  intrinsic  sense.  A  sense  is  only 
assigned  to  them  by  correlation  with  the  left  and  right 
hands  of  an  imaginary  observer,  or  by  thinking  of  a 
moving  body  traversing  the  line  in  such  a  way  that 
its  presence  at  A  is  earlier  than  its  presence  at  B, 
and  the  latter  is  earlier  than  its  presence  at  C.  In 
fact,  if  we  want  a  spatial  analogy  to  Time,  it  is  not 
enough  to  use  a  straight  line  ;  we  need  a  straight  line 
with  a  fixed  sense,  i.e.  the  sort  of  thing  which  we 
usually  represent  by  a  line  with  an  arrow-head  on  it. 
Now  the  points  on  straight  lines  do  not  have  any 
intrinsic  sense,  and  so  the  meaning  of  the  arrow-head 
is  only  supplied  by  reference  to  something  which  is  at 
one  point  before  it  gets  to  another.     Thus  to  attempt 


58  SCIENTIFIC   THOUGHT 

to  understand  before  and  after  by  analogy  with  a 
directed  line  is  in  the  end  circular,  since  the  line  only 
gets  its  sense  through  a  tacit  correlation  with  a  series 
of  events  in  Time. 

Now  the  intrinsic  sense  of  a  series  of  events  in  Time 
is  essentially  bound  up  with  the  distinction  between 
past,  present,  and  future.  A  precedes  B  because  A  is 
past  when  B  is  present.  We  may  begin  by  asking 
whether  there  is  any  spatial  analogy  to  the  distinction 
of  past,  present,  and  future.  We  shall  find  that  there 
is,  but  that  once  more  it  is  not  ultimately  useful,  because 
it  involves  a  reference  to  these  very  temporal  character- 
istics on  which  it  is  supposed  to  throw  light.  The 
obvious  analogy  to  Now  in  Time  is  Here  in  Space. 

Here  is  primarily  the  name  of  a  certain  region  in 
the  continuum  of  possible  positions  that  one's  body 
can  take  up.  When  Here,  is  used  as  a  predicate,  as 
when  I  say,  "So  and  so  is  here,"  I  mean  that  so  and 
so  is  within  a  region  whose  boundaries  I  can  reach 
with  little  or  no  walking.  The  peculiarity  of  Here  is 
its  peculiar  kind  of  ambiguity.  Here,  as  used  by  me, 
is  understood  to  describe  a  different  region  from  that 
which  is  described  by  the  same  word,  as  used  by  you. 
As  used  by  me,  it  means  "  near  me"  ;  as  used  by  you 
it  means  "near  you."  It  is  thus  a  word  which  has  a 
partially  different  meaning  as  used  by  every  different 
observer,  simply  because  an  essential  part  of  its  mean- 
ing is  a  relation  to  the  particular  observer  who  is 
using  it. 

We  must  notice,  however,  that  Here  has  a  second 
ambiguity.  It  not  only  has  a  different  meaning  as 
used  by  you  and  by  me  at  the  same  time,  it  also  has 
a  different  meaning  as  used  by  either  of  us  at  different 
times.  By  Here  I  always  mean  that  region  which  is 
near  me  at  the  time  of  speaking.  This  difference  of 
meaning  at  two  moments  need  not  betray  itself  by  a 
difference  of  application,  though  it  often  does.  If  I 
stand    still    for   five    minutes   the    region    which    I   call 


TIME   AND   CHANGE  59 

Here  at  the  end  of  the  time  will  be  the  same  as  that 
which  I  called  Here  at  the  beginning  ;  but,  if  I  have 
moved,  the  difference  in  meaning  will  also  be  accom- 
panied by  a  difference  in  application. 

We  can,  of  course,  extract  a  general  meaning  of 
"  hereness  "  ;  it  means  "nearness  to  an  observer  who 
uses  the  word  Here,  at  the  time  when  he  uses  it."  But 
obviously  Here  is  a  descriptive  phrase  with  a  double 
ambiguity,  since  it  refers  both  to  a  certain  person  and 
to  a  certain  date  in  his  history,  and  does  not  become 
definite  till  these  two  blanks  have  been  filled  in  by  the 
context. 

It  is  evident  then  that  Here  is  not  going  to  help  us 
to  understand  Now,  since  it  contains  an  essential  refer- 
ence to  Now.  We  must  therefore  treat  past,  present, 
and  future  on  their  own  account,  without  expecting  any 
help  from  spatial  analogies.  Now,  the  present  does 
have  a  systematic  ambiguity  such  as  we  noticed  in 
Here.  Whether  it  contains  an  essential  reference  to 
the  particular  observer  who  uses  it  I  will  not  now 
discuss.  The  traditional  view  is  that  it  is  neutral  as 
between  various  observers,  but  we  shall  later  see  reason 
to  doubt  this.  However  this  may  be,  it  is  certainly 
ambiguous  in  another  sense.  Every  place  to  which 
an  observer's  body  can  go  is  a  possible  Here.  In  the 
same  way  every  event  either  is,  has  been  or  will  be 
Now,  on  the  ordinary  view,  provided  it  be  short  enough 
to  fall  into  what  psychologists  call  a  Specious  Present. 

We  are  naturally  tempted  to  regard  the  history  of 
the  world  as  existing  eternally  in  a  certain  order  of 
events.  Along  this,  and  in  a  fixed  direction,  we  imagine 
the  characteristic  of  presentness  as  moving,  somewhat 
like  the  spot  of  light  from  a  policeman's  bull's-eye 
traversing  the  fronts  of  the  houses  in  a  street.  What 
is  illuminated  is  the  present,  what  has  been  illuminated 
is  the  past,  and  what  has  not  yet  been  illuminated  is 
the  future.  The  fact  that  the  spot  is  of  finite  area 
expresses  the  fact  that  the  Specious   Present  is  not  a 


60  SCIENTIFIC   THOUGHT 

mere  point  but  is  of  finite,  though  short,  duration. 
Such  analogies  may  be  useful  for  some  purposes,  but 
it  is  clear  that  they  explain  nothing.  On  this  view 
the  series  'of  events  has  an  intrinsic  order,  but  no 
intrinsic  sense.  It  gains  a  sense,  and  we  become  able 
to  talk  of  one  event  as  earlier  than  another,  and  not 
merely  of  one  event  as  between  two  others,  because  the 
attribute  of  presentness  moves  along  the  series  in  a 
fixed  direction.  But,  in  the  first  place,  the  lighting  of 
the  characteristic  of  presentness  now  on  one  event 
and  now  on  another  is  itself  an  event,  and  ought 
therefore  to  be  itself  a  part  of  the  series  of  events,  and 
not  simply  something  that  happens  to  the  latter  from 
outside.  Again,  if  events  have  no  intrinsic  sense  but 
only  an  intrinsic  order,  what  meaning  can  we  give  to 
the  assertion  that  the  characteristic  of  presentness 
traverses  the  series  of  events  in  a  fixed  direction  ?  All 
that  we  can  mean  is  that  this  characteristic  is  present  at 
B  when  it  is  past  at  A.  Thus  all  the  problems  which 
the  policeman's  bull's-eye  analogy  was  invented  to 
solve  are  simply  taken  out  of  other  events  to  be  heaped 
on  that  particular  series  of  events  which  is  the  move- 
ment of  the  bull's-eye. 

The  difficulties  that  we  have  found  in  this  particular 
analogy  are  of  very  wide  range.  For  instance,  it  is 
extremely  tempting  to  try  to  resolve  the  difference 
between  past,  present,  and  future  into  differences  in 
the  cognitive  relations  of  our  minds  to  different  events 
in  a  series  which  has  intrinsic  order  but  no  intrinsic 
sense.  Let  us  confine  ourselves,  for  the  sake  of  sim- 
plicity, to  events  that  fall  within  the  knowledge  of  a 
certain  observer  O.  Undoubtedly  O  has  a  different 
kind  of  cognitive  relation  to  those  events  which  he 
calls  present  from  that  which  he  has  to  those  which 
he  calls  past  and  to  those  which  he  calls  future.  About 
future  events  he  can  only  guess  or  make  inferences  by 
analogy  with  the  past.  Some  present  events  he  can 
directly  perceive  with    his  senses.      Some   past  events 


TIME   AND   CHANGE  61 

he  knows  by  direct  memory,  which  is  quite  a  different 
kind  of  experience  from  sense-perception.  It  is  tempt- 
ing to  suppose  that  these  are  not  simply  interesting 
facts  about  past,  present,  and  future,  but  are  what  we 
mean  by  these  three  temporal  distinctions.  Can  such 
a  theory  be  made  to  work? 

Clearly  we  cannot  simply  define  an  event  as  present 
for  O  if  O  can  perceive  it  or  if  it  is  contemporary  with 
something  that  O  can  perceive.  For  we  shall  then 
have  to  define  an  event  as  past  for  O  if  O  cannot  per- 
ceive it  but  can  either  remember  it  or  remember  some- 
thing contemporary  with  it.  Now,  of  course,  every 
event  that  falls  within  O's  knowledge  has  these  two 
incompatible  relations  to  O  ;  though,  as  we  put  it,  it 
has  them  at  different  times.  He  can  first  perceive, 
but  not  remember  the  event,  and  can  then  remember 
but  not  perceive  it.  Hence  these  cognitive  character- 
istics do  not  suffice  to  distinguish  a  past  from  a  present 
event,  since  every  event  that  O  knows  of  has  both  these 
relations  to  him.  If  you  add  that  an  event  always  has 
the  perceptual  relation  to  O  before  it  has  the  memory 
relation,  you  only  mean  that  the  event  of  remembering 
something  is  present  when  the  event  of  perceiving  it 
is  past,  and  you  have  simply  defined  present  and  past 
for  O's  objects  in  terms  of  present  and  past  for  his 
cognitive  acts.  If  you  then  try  to  define  the  latter  in 
terms  of  different  relations  to  O's  acts  of  introspection, 
you  simply  start  on  an  infinite  regress,  in  which  past 
and  present  remain  obstinately  undefined  at  any  place 
where  you  choose  to  stop. 

It  does  not  of  course  follow  that  past  and  present 
in  external  Nature  may  not  be  reducible  to  certain 
relations  between  objective  events  and  minds  which 
observe  them  ;  but  it  does  follow  that  these  charac- 
teristics cannot  be  analysed  away  in  this  manner  out 
of  Reality  as  a  whole,  which  of  course  includes  observing 
minds  as  well  as  what  they  observe. 

The   difficulty   about    past,    present,    and    future    in 


62  SCIENTIFIC   THOUGHT 

general  can  be  summed  up  in  two  closely  connected 
paradoxes,  (i)  Every  event  has  all  these  characteristics, 
and  yet  they  are  inconsistent  with  each  other.  And  (ii) 
events  change  in  course  of  time  with  respect  to  these 
characteristics.  Now  we  believe  ourselves  to  under- 
stand change  in  things,  but  to  talk  of  events  changing 
seems  almost  unintelligible.  The  connexion  between 
the  two  paradoxes  is,  of  course,  that  we  get  into  the 
second  directly  we  take  the  obvious  step  to  avoid  the 
first. 

We  have  plenty  of  experience  of  things  which 
appear  to  have  incompatible  characteristics,  such  as 
redness  and  greenness,  or  greatness  and  smallness.  As 
a  rule  we  remove  this  apparent  inconsistency  by  point- 
ing out  that  the  facts  have  been  stated  elliptically,  and 
that  really  a  relation  is  involved.  In  the  first  example 
we  say  that  what  has  been  omitted  is  a  relation  to  two 
different  times.  The  full  statement  is  that  the  thing 
is  red  at  one  time  and  green  at  another,  and  there  is 
no  inconsistency  in  this.  In  the  second  example  we 
have  no  need  even  to  bring  in  a  relation  to  two  different 
times.  It  is  enough  to  point  out  that  the  predicates 
great  and  small  themselves  tacitly  assume  relations  ; 
so  that  the  full  statement  is  that  the  thing  is  at  once 
great  as  compared  with  one  object  and  small  as  com- 
pared with  another.  In  one  of  these  two  ways  we 
always  proceed  when  we  have  to  deal  with  the  apparent 
co-inherence  of  incompatible  predicates  in  a  single 
subject.  We  therefore  naturally  try  one  of  these 
expedients  to  deal  with  the  fact  that  every  event  is 
past,  present,  and  future,  and  that  these  predicates  are 
incompatible. 

It  seems  natural  and  childishly  simple  to  treat  the 
problem  in  the  way  in  which  we  treated  the  thing  that 
was  both  red  and  green.  We  say  :  "  Of  course  the 
event  E  has  futurity  for  a  certain  stretch  of  time,  then 
it  has  presentness  for  a  short  subsequent  stretch,  and 
it    has    pastness     at   all    other    moments."       Now   the 


TIME   AND   CHANGE  63 

question  at  once  arises:  "Can  we  treat  the  change  of 
an  event  in  respect  to  its  temporal  qualities  as  just  like 
the  change  of  a  thing  with  respect  to  qualities  like  red 
and  green  ?  " 

To  answer  this  question  we  must  try  to  see  what 
we  mean  when  we  say  that  a  certain  thing  T  changes 
from  red  to  green.  So  far  as  I  can  see,  our  meaning 
is  somewhat  as  follows  :  There  is  a  certain  long-lasting 
event  in  the  history  of  the  world.  This  stands  out  in 
a  noticeable  way  from  other  events  which  overlap  it 
wholly  or  partly.  If  successive  short  sections  in  time 
be  taken  of  this  long  event,  adjacent  sections  have 
spatial  continuity  with  each  other,  and  predominant 
qualitative  resemblance  to  each  other.  On  these 
grounds  the  whole  long  event  is  treated  as  the  history 
of  a  single  thing  T.  But,  although  adjacent  short 
sections  are  predominantly  alike  in  their  qualities,  there 
may  be  adjacent  sections  which  differ  very  markedly 
in  some  quality,  such  as  colour.  If  you  can  cut  the 
history  of  the  thing  in  a  certain  moment,  such  that  a 
slice  of  its  history  before  that  is  red  and  a  slice  after 
that  is  green,  we  say  that  the  thing  T  has  changed 
from  red  to  green  at  that  moment.  To  say  that  a  thing 
changes,  thus  simply  means  that  its  history  can  be 
cut  up  into  a  series  of  adjacent  short  slices,  and  that 
two  adjacent  slices  may  have  qualitative  differences. 

Can  we  treat  the  change  of  an  event  from  futurity, 
through  presentness,  to  pastness  in  the  way  in  which 
we  have  treated  the  change  of  a  thing  (say  a  signal 
lamp)  from  red  to  green?  I  think  it  is  certain  that  we 
cannot ;  for  two  closely  connected  reasons.  In  the 
first  place,  the  attempt  would  be  circular,  because  the 
change  of  things  will  be  found  on  further  analysis  to 
involve  the  change  of  events  in  respect  to  their  temporal 
characteristics.  We  have  assumed  that  the  history 
of  our  signal  lamp  can  be  analysed  into  a  series  of 
shorter  adjacent  events,  and  that  it  was  true  of  a  certain 
pair  of  these  that  the   earlier   was    red   and   the   later 


<>4  SCIENTIFIC  THOUGHT 

green.  But  to  say  that  this  series  of  events  passes  from 
earlier  to  later  (which  is  necessary  if  we  are  to  dis- 
tinguish between  a  change  from  red  to  green  and  a 
change  from  green  to  red)  simply  means  that  the  red 
sections  are  past  when  the  green  ones  are  present  and 
that  the  red  ones  are  present  when  the  green  ones  are 
future.  Thus  the  notion  of  the  history  of  the  lamp  as 
divisible  into  a  series  of  sections,  following  each  other 
in  a  certain  direction,  depends  on  the  fact  that  each 
of  these  sections  itself  changes  from  future,  through 
present,  to  past.  It  would  therefore  be  circular  to 
attempt  to  analyse  changes  in  events  in  the  way  in 
which  we  have  analysed  changes  in  things,  since  the 
latter  imply  the  former. 

Apart  from  this  objection,  we  can  see  directly  that 
the  change  of  events  cannot  be  treated  like  the  changes 
of  things.  Let  us  take  a  short  section  of  the  history 
of  the  lamp,  small  enough  to  fall  into  a  Specious 
Present,  and  such  that  the  light  from  the  lamp  is  red 
throughout  the  whole  of  this  section.  This  short  event 
was  future,  became  present,  and  then  became  past.  If 
we  try  to  analyse  this  change  in  the  way  in  which  we 
analysed  the  change  of  the  lamp  from  red  to  green 
we  shall  have  to  proceed  as  follows  :  We  shall  have 
to  divide  this  red  event  into  shorter  successive  sections, 
and  say  that  the  latest  of  these  have  futurity,  the  middle 
ones  presentness,  and  the  earliest  ones  pastness.  Now 
this  analysis  obviously  does  not  fit  the  facts.  For  the 
fact  is  that  the  whole  event  was  future,  became  present, 
and  is  now  past.  Clearly  no  analysis  which  splits  up 
the  event  into  successive  sections  with  different  charac- 
teristics is  going  to  account  for  the  change  in  the 
temporal  attributes  of  the  event  as  a  whole. 

We  see  then  that  the  attempt  to  reconcile  the  in- 
compatible temporal  qualities  of  the  same  event  by 
appealing  to  change,  in  the  ordinary  sense  of  the  word, 
is  both  circular  and  ineffective.  The  circularity  becomes 
specially  glaring  when  put  in  the  following  way  :    The 


TIME   AND   CHANGE  65 

changes  of  things  are  changes  in  Time  ;  but  the  change 
of  events  or  of  moments  from  future,  through  present, 
to  past,  is  a  change  <?/"Time.  We  can  hardly  expect  to 
reduce  changes  of  Time  to  changes  in  Time,  since  Time 
would  then  need  another  Time  to  change  in,  and  so  on 
to  infinity. 

We  seem,  therefore,  to  be  forced  back  to  the  other 
type  of  solution,  viz.,  that  the  predicates,  past,  present, 
and  future,  are  of  their  very  nature  relational,  like  large 
and  small.  Unfortunately  we  have  already  had  occasion 
to  look  at  some  solutions  of  this  type — the  policeman's 
bull's-eye  and  the  different  cognitive  relations — and  the 
omens  are  not  very  favourable. 

If  we  reflect,  we  shall  notice  that  there  are  two  quite 
different  senses  in  which  an  entity  can  be  said  to  change 
its  relational  properties.  An  example  of  the  first  is 
where  Tom  Smith,  the  son  of  John  Smith,  becomes 
taller  than  his  father.  An  example  of  the  second  is 
where  Tom  Smith  ceases  to  be  the  youngest  son  of 
John  Smith,  and  becomes  the  last  son  but  one.  What 
is  the  difference  between  these  two  cases?  In  the  first 
we  have  two  partially  overlapping  life-histories,  T  and 
J.  If  we  cut  up  both  into  successive  short  sections  we 
find  that  the  earlier  sections  of  T  have  the  relation  of 
"shorter  than"  to  the  contemporary  sections  of  J, 
whilst  the  later  sections  of  T  have  the  relation  of 
"taller  than  "  to  the  contemporary  sections  of  J.  In 
the  second  we  have  quite  a  different  state  of  affairs. 
When  we  say  that  T  is  the  youngest  son  of  J  we  mean 
that  there  is  no  entity  in  the  universe  of  which  it  is  true 
to  say  both  that  it  is  a  son  of  J  and  that  it  is  younger 
than  T.  When  we  say  that  T  has  ceased  to  be  the 
youngest  son  of  J  we  mean  that  the  universe  does 
contain  an  entity  of  which  it  is  true  to  say  both  that 
it  is  a  son  of  J  and  that  it  is  younger  than  T.  In  the 
first  case  then,  we  simply  have  a  difference  of  relation 
between  different  corresponding  sections  of  two  existing 
long  events.     In  the  latter,  the  difference  is  that  a  certain 


66  SCIENTIFIC   THOUGHT 

entity  has  changed  its  relational  properties  because  a 
second  entity,  which  did  not  formerly  exist  (and  there- 
fore could  stand  in  no  relation  whatever  to  T),  has  begun 
to  exist,  and  consequently  to  stand  in  certain  relations 
to  T,  who  is  a  member  of  the  same  universe  as  it. 

Now  it  is  obvious  that  the  change  that  happens  to 
an  event  when  it  ceases  to  be  present  and  becomes  past 
is  like  the  change  of  Tom  Smith  when  he  ceases  to  be 
the  youngest  son  of  John  Smith  ;  and  the  continuous 
retreat  of  an  event  into  the  more  and  more  remote  past 
is  like  the  successive  departure  of  Tom  from  being  the 
"baby"  of  the  family,  as  John  Smith  (moved  by  the 
earnest  exhortations  of  the  Bishop  of  London)  produces 
more  and  more  children.  A  Specious  Present  of  mine 
is  just  the  last  thin  slice  that  has  joined  up  to  my  life- 
history.  When  it  ceases  to  be  present  and  becomes 
past  this  does  not  mean  that  it  has  changed  its  relations 
to  anything  to  which  it  was  related  when  it  was  present. 
It  will  simply  mean  that  other  slices  have  been  tacked 
on  to  my  life-history,  and,  with  their  existence,  relations 
have  begun  to  hold,  which  could  not  hold  before  these 
slices  existed  to  be  terms  to  these  relations.  To  put 
the  matter  in  another  way  :  When  an  event,  which  was 
present,  becomes  past,  it  does  not  change  or  lose  any 
of  the  relations  which  it  had  before  ;  it  simply  acquires 
in  addition  new  relations  which  it  could  not  have  before, 
because  the  terms  to  which  it  now  has  these  relations 
were  then  simply  non-entities. 

It  will  be  observed  that  such  a  theory  as  this  accepts 
the  reality  of  the  present  and  the  past,  but  holds  that 
the  future  is  simply  nothing  at  all.  Nothing  has 
happened  to  the  present  by  becoming  past  except  that 
fresh  slices  of  existence  have  been  added  to  the  total 
history  of  the  world.  The  past  is  thus  as  real  as  the 
present.  On  the  other  hand,  the  essence  of  a  present 
event  is,  not  that  it  precedes  future  events,  but  that 
there  is  quite  literally  nothing  to  which  it  has  the  relation 
of  precedence.     The  sum    total    of  existence  is  always 


TIME   AND   CHANGE  67 

increasing,  and  it  is  this  which  gives  the  time-series  a 
sense  as  well  as  an  order.  A  moment  t  is  later  than 
a  moment  t'  if  the  sum  total  of  existence  at  t  includes 
the  sum  total  of  existence  at  t'  together  with  some- 
thing more. 

We  are  too  liable  to  treat  change  from    future  to 
present  as  if  it  were  analogous  to  change  from  present 
to  past  or  from  the  less  to  the  more  remote  past.     This 
is,  I  believe,  a  profound  mistake.      I  think  that  we  must 
recognise   that   the  word    "change"  is    used    in    three 
distinct   senses,   of  which  the  third  is  the  most  funda- 
mental.      These   are   (i)    Change    in    the    attributes   of 
things,  as  where  the  signal  lamp  changes  from  red  to 
green  ;  (ii)  Change  in  events  with  respect  to  pastness, 
as  where  a  certain  event  ceases  to  be  present  and  moves 
into  the  more  and  more  remote  past ;  and  (iii)  Change 
from  future  to  present.      I  have  already  given  an  analysis 
of  the  first  two  kinds  of  change.      It  is  clear  that  they 
both    depend    on    the    third    kind.       We   analysed   the 
change  in  colour  of  the  signal  lamp  to  mean  that  a  red 
section  of  its  history  was  followed  by  a  green  section  of 
its  history.     This  is  sufficient  analysis  for  a  past  change 
of  quality,  dealt  with   reflectively  in   retrospect.     But, 
when  we   say  that  the   red  section  precedes    the  green 
section,  we  mean   that  there  was  a  moment  when  the 
sum  total  of  existence  included  the  red  event  and  did 
not  include  the  green  one,  and  that  there  was  another 
moment  at  which  the  sum  total  of  existence  included  all 
that  was  included  at  the  first  moment  and  also  the  green 
event.     Thus   a   complete   analysis   of    the    qualitative 
changes  of  things  is  found  to  involve  the  coming  into 
existence  of  events. 

Similarlv  we  have  seen  that  the  second  kind  of 
change  involves  the  third.  For  the  change  of  an  event 
from  present  to  past  turned  out  to  depend  on  the  fact 
the  sum  total  of  existence  increases  beyond  the  limits 
which  it  had  when  our  given  event  came  into  existence. 
Let  us  call  the  third  kind  of  change  Becoming.     It 


()8  SCIENTIFIC   THOUGHT 

is  now  quite  evident  that  becoming  cannot  be  analysed 
into  either  of  the  two  other  kinds  of  change,  since  they 
both  involve  it.  Moreover,  we  can  see  by  direct  in- 
spection that  becoming  is  of  so  peculiar  a  character 
that  it  is  misleading  to  call  it  change.  When  we  say 
that  a  thing  changes  in  quality,  or  that  an  event  changes 
in  pastness,  we  are  talking  of  entities  that  exist  both 
before  and  after  the  moment  at  which  the  change  takes 
place.  But,  when  an  event  becomes,  it  comes  into 
existence;  and  it  was  not  anything  at  all  until  it  had 
become.  You  cannot  say  that  a  future  event  is  one 
that  succeeds  the  present ;  for  a  present  event  is  defined 
as  one  that  is  succeeded  by  nothing.  We  can  put  the 
matter,  at  choice,  in  one  of  two  ways.  We  can  either 
say  that,  since  future  events  are  non-entities,  they  cannot 
stand  in  any  relations  to  anything,  and  therefore  cannot 
stand  in  the  relation  of  succession  to  present  events. 
Or,  conversely,  we  can  say  that,  if  future  events  succeeded 
present  events,  they  would  have  the  contradictory  pro- 
perty of  succeeding  something  that  has  no  successor, 
and  therefore  they  cannot  be  real. 

It  has  long  been  recognised  that  there  are  two 
unique  and  irreducible,  though  intimately  connected 
types  of  judgment.  The  first  asserts  that  S  is  or  exists  ; 
and  is  called  an  existential  judgment.  The  second 
asserts  that  S  is  so  and  so,  or  has  such  and  such  a 
characteristic.  This  may  be  called  a  characterising  judg- 
ment. The  connexion  between  the  two  is  that  a  thing 
cannot  be  so  and  so  without  being,  and  that  it  cannot  be 
without  being  so  and  so  *  Meinong,  with  the  resources 
of  the  German  tongue  at  his  disposal,  coins  the  con- 
venient words  Sein  and  Sosein.  Now  it  seems  to  me 
that  we  have  got  to  recognise  a  third  equally  fundamental 
and  irreducible  type  of  judgment,  viz.,  one  of  the  form  : 
S  becomes  or  comes  into  existence.  Let  us  call  these 
genetic  judgments.  I  think  that  much  of  the  trouble 
about   Time   and    Change    comes    from    our    obstinate 

*  Uber  die  Stellung  der  Gegenstandstheorie,  and  elsewhere. 


TIME   AND   CHANGE  69 

attempts  to  reduce  such  judgments  to  the  characterising 
form.  Any  judgment  can  be  verbally  reduced  to  this 
form.  We  can  reduce  "  S  is  "  to  "  S  is  existent."  But 
the  reduction  is  purely  verbal,  and  those  who  take  it 
seriously  land  in  the  sloughs  of  the  Ontological  Argu- 
ment. Similarly  "S  is  future  "  is  verbally  a  judgment 
that  ascribes  a  characteristic  to  an  event  S.  But,  if  we 
are  right,  this  must  be  a  mistake ;  since  to  have  a 
characteristic  implies  to  exist  (at  any  rate  in  the  case  of 
particulars,  like  events),  and  the  future  does  not  exist  so 
long  as  it  is  future. 

Before  passing  on  there  is  one  more  verbal  ambiguity 
to  be  noted.  The  same  word  is  is  used  absolutely  in 
the  existential  judgment  "S  is,"  and  as  a  connective 
tie  in  the  characterising  judgment  "S  is  P."  Much 
the  same  is  true  of  the  word  becomes.  We  say  "S 
becomes,"  and  we  say  "S  becomes  P."  The  latter 
type  of  judgment  expresses  qualitative  change,  the 
former  expresses  coming  into  existence. 

The  relation  between  existence  and  becoming  (and 
consequently  between  characterisation  and  becoming) 
is  very  intimate.  Whatever  is  has  become,  and  the 
sum  total  of  the  existent  is  continually  augmented  by 
becoming.  There  is  no  such  thing  as  ceasing  to  exist ; 
what  has  become  exists  henceforth  for  ever.  When  we 
say  that  something  has  ceased  to  exist  we  only  mean 
that  it  has  ceased  to  be  present;  and  this  only  means 
that  the  sum  total  of  existence  has  increased  since  any 
part  of  the  history  of  the  thing  became,  and  that  the 
later  additions  contain  no  events  sufficiently  alike  to 
and  sufficiently  continuous  with  the  history  of  the  thing 
in  question  to  count  as  a  continuation  of  it.  For  com- 
plete accuracy  a  slight  modification  ought  to  be  made 
in  the  statement  that  "whatever  is  has  become."  Long 
events  do  not  become  bodily,  only  events  short  enough 
to  fall  in  Specious  Presents  become,  as  wholes.  Thus 
the  becoming  of  a  long  event  is  just  the  successive 
becoming  of  its  shorter  sections.     We  shall  have  to  go 


70  SCIENTIFIC   THOUGHT 

more  fully  into  the  question  of  Specious  Presents  at  a 
later  stage. 

We  are  left  with  two  problems  which  we  may  hope 
that  the  previous  discussions  will  help  us  to  solve. 
(i)  If  the  future,  so  long  as  it  is  future,  be  literally 
nothing  at  all,  what  are  we  to  say  of  judgments  which 
profess  to  be  about  the  future?  And  (ii)  What,  in  the 
end,  is  our  answer  to  the  original  difficulty  that  every 
event  is  past,  present,  and  future,  and  that  these 
characteristics  are  mutually  incompatible? 

(i)  Undoubtedly  we  do  constantly  make  judgments 
which  profess  to  be  about  the  future.  Weather  fore- 
casts, nautical  almanacs,  and  railway  time-tables,  are 
full  of  such  judgments.  Admittedly  no  judgment 
about  the  future  is  absolutely  certain  (with  the  possible 
exception  of  the  judgment  that  there  will  always  be 
events  of  some  kind  or  other)  ;  but  this  is  irrelevant  for 
our  present  purpose.  No  historical  judgment  about 
the  past  is  absolutely  certain  either  ;  and,  in  any  case, 
our  question  is  not  whether  we  can  have  certain 
knowledge  about  the  future,  but  is  the  prior  question  : 
What  are  we  really  talking  about  when  we  profess  to 
make  judgments  about  the  future,  and  what  do  we  mean 
by  the  truth  or  falsity  of  such  judgments? 

We  cannot  attempt  to  answer  these  questions  till 
we  have  cleared  up  certain  points  about  the  nature  of 
judgments  in  general.  First,  we  must  notice  that  the 
question:  "What  is  a  certain  judgment  about?"  is 
ambiguous.  It  may  mean:  "What  is  the  subject  or 
subjects  of  the  judgment?  "  or  :  "  To  what  fact  does  the 
judgment  refer?"  The  fact  to  which  a  judgment  refers 
is  the  fact  that  renders  it  true  or  false.  It  is  true,  if  it 
has  the  peculiar  relation  of  concordance  to  the  fact 
to  which  it  refers  ;  and  false,  if  it  has  the  relation  of 
discordance  to  this  fact.  Discordance,  I  think,  is  a 
positive  relation  which  is  incompatible  with  concord- 
ance ;  it  is  not  the  mere  absence  of  concordance.  I 
see    no    reason    to    suppose    that    the    reference    of   a 


TIME   AND   CHANGE  71 

judgment  to  a  fact  is  a  third  independent  relation  over 
and  above  the  relations  of  concordance  and  discordance. 
I  take  it  to  be  just  the  disjunction  "  concordance-or- 
discordance  "  ;  and  I  suppose  that  to  say  that  J  refers  to 
F  simply  means  that  F  is  the  fact  which  either  makes  J 
true  by  concording  with  it  or  false  by  discording 
with  it. 

Now  people  make  many  judgments,  which  have 
nothing  to  do  with  the  future,  but  are  nevertheless 
apparently  about  objects  which  do  not,  in  fact,  exist. 
Many  English  peasants,  in  the  Middle  Ages,  must 
have  made  the  judgments  "Puck  exists"  or  "Puck 
has  turned  the  milk."  And  the  latter  of  these,  of 
course,  implies  the  former.  I  will  assume  (in  spite 
of  Sir  Conan  Doyle)  that  Puck  does  not  in  fact  exist. 
What  were  these  men  referring  to,  in  our  sense  of  the 
word?  To  answer  this  we  have  simply  to  ask:  What 
fact  made  their  judgments  false?  The  answer  is  that 
it  is  the  negative  fact  that  no  part  of  the  universe  was 
characterised  by  the  set  of  characteristics  by  which 
they  described  Puck  to  themselves.  Their  judgment 
boils  down  to  the  assertion  that  some  part  of  the  existent 
is  characterised  by  this  set  of  characteristics,  and  it  is 
false  because  it  discords  with  the  negative  fact  that  the 
set  in  question  characterises  no  part  of  the  universe. 
Naturally  they  did  not  know  that  this  was  what  their 
judgment  referred  to,  or  they  would  not  have  made  it. 
But,  in  our  sense  of  reference,  there  is  no  reason  why 
a  person  who  makes  a  judgment  should  know  what  it 
refers  to. 

Now  it  would  obviously  be  absurd  to  say  that  what 
these  men  were  talking  about  was  the  negative  fact  that 
no  part  of  the  universe  has  the  characteristics  which 
they  ascribe  to  Puck.  Hence  we  see  the  need  of  dis- 
tinguishing between  what  a  judgment  refers  to  and 
what  the  person  who  makes  the  judgment  is  talking 
about.  What  they  were  talking  about  was  a  certain 
set  of  characteristics,  viz.,  those  by  which  they  described 


yi  SCIENTIFIC   THOUGHT 

Puck  to  themselves.  This  may  be  called  the  logical 
subject  of  their  judgment.  It  is  something  real  and 
independent  of  the  judging  mind  ;  having  the  kind  of 
reality  and  independence  which  is  characteristic  of  uni- 
versals,  and  not,  of  course,  that  which  is  characteristic 
of  particular  existents.  Thus,  although  there  is  no 
such  being  as  Puck,  people  who  profess  to  be  judging 
about  him  are  not  judging  about  nothing  (for  they  are 
judging  about  a  set  of  characteristics  which  is  itself 
real,  though  it  does  not  happen  to  characterise  any 
particular  existent).  Nor  are  they  referring  to  nothing 
(for  they  are  referring — though  they  do  not  know  it — 
to  an  important  negative  fact  about  the  existent). 

Since  the  non-existence  of  Puck  is  compatible  with 
the  fact  that  the  judgment  "Puck  exists"  is  an 
intelligible  statement  about  something  real,  we  may 
hope  that  the  non-existence  of  the  future  may  prove 
to  be  compatible  with  the  existence  and  intelligibility 
of  judgments  which  profess  to  be  about  the  future. 
Up  to  a  point  the  two  kinds  of  judgment  can  be  treated 
in  much  the  same  way.  The  judgment  which  is  gram- 
matically about  "Puck"  proves  to  be  logically  about 
the  set  of  characteristics  by  which  the  assertor  describes 
Puck  to  himself.  Similarly  the  judgment,  "To-morrow 
will  be  wet,"  which  is  grammatically  about  "to-morrow," 
is  logically  about  the  characteristic  of  wetness.  The 
non-existence  of  to-morrow  is  therefore  consistent 
with  the  fact  that  the  judgment  is  about  something. 

Still  there  is  one  very  important  difference  between 
the  two  kinds  of  judgment.  Judgments  like  "Puck 
exists"  are  not  only  about  something;  they  also  refer 
to  some  fact  which  makes  them  true  or  false.  This 
fact  may  be  negative,  but  it  is  a  real  fact  about  the 
existent  world.  If  we  ask  what  fact  judgments  ostensibly 
about  the  future  refer  to,  we  must  answer  that  there  is 
no  such  fact.  If  I  judge  to-day  that  to-morrow  will 
be  wet,  the  only  fact  which  this  judgment  can  refer 
to,  in  our  sense  of  the  word,  is  the  fact  which  renders 


TIME  AND   CHANGE  73 

it  true  or  false.  Now  it  is  obvious  that  this  fact  is 
the  wetness  or  fineness  of  to-morrow  when  to-morrow 
comes.  To-day,  when  I  make  the  judgment,  there  is 
no  such  fact  as  the  wetness  of  to-morrow  and  there  is 
no  such  fact  as  the  fineness  of  to-morrow.  For  these 
facts  can  neither  of  them  begin  to  be  till  to-morrow 
begins  to  be,  which  does  not  happen  till  to-morrow 
becomes  to-day.  Thus  judgments  which  profess  to  be 
about  the  future  do  not  refer  to  any  fact,  whether 
positive  or  negative,  at  the  time  when  they  are  made. 
They  are  therefore  at  that  time  neither  true  nor  false. 
They  will  become  true  or  false  when  there  is  a  fact 
for  them  to  refer  to  ;  and  after  this  they  will  remain 
true  or  false,  as  the  case  may  be,  for  ever  and  ever. 
If  you  choose  to  define  the  word  judgment  in  such  a 
way  that  nothing  is  to  be  called  a  judgment  unless  it 
be  either  true  or  false,  you  must  not,  of  course,  count 
"judgments"  that  profess  to  be  about  the  future  as 
judgments.  If  you  accept  the  latter,  you  must  say  that 
the  Law  of  Excluded  Middle  does  not  apply  to  all 
judgments.  If  you  reject  them,  you  may  say  that  the  Law 
of  Excluded  Middle  applies  to  all  genuine  judgments  ; 
but  you  must  add  that  "judgments  "  which  profess  to  be 
about  the  future  are  not  genuine  judgments  when  they 
are  made,  but  merely  enjoy  a  courtesy  title  by  antici- 
pation, like  the  eldest  sons  of  the  higher  nobility 
during  the  lifetime  of  their  fathers.  For  convenience, 
I  shall  continue  to  speak  of  them  as  judgments. 

So  far  then,  we  have  determined  two  facts  about 
judgments  which  profess  to  be  concerned  with  the 
future.  (a)  They  are  about  something,  viz.,  some 
characteristic  or  set  of  characteristics  ;  and  {b)  they  do 
not  refer  to  any  fact  at  the  time  when  they  are  made. 
This  is  clearly  not  a  complete  analysis.  Two  further 
points  need  to  be  cleared  up.  (a)  If  such  judgments 
when  made  do  not  refer  to  anything,  how  is  it  that, 
if  certain  events  become,  the  judgment  is  verified,  and, 
if  other  events  become,  it  is  refuted?     (b)  If  such  judg- 


74  SCIENTIFIC   THOUGHT 

ments   are    about   characteristics,    what    precisely    is    it 
that  they  assert  about  these  characteristics  ? 

(a)  Suppose  I  judge  to-day  that  to-morrow  will  be 
wet.       Nothing   that   may    happen    to-morrow    will    be 
relevant  to  this  judgment  except  the  state  of  the  weather, 
and  nothing  will  then  make  it  true  except  the  wetness 
of  the  weather.     This  is  true  enough,   but  it  does  not 
prove    that    the  judgment    refers    to    any    fact,    in    our 
sense   of  reference.     With  any  judgment  we   can    tell 
what  kind  of  fact  will   verify  or  refute  it,  as  soon   as 
we  know  what  the  judgment  is  about  and  what  kind 
of  assertion  it  makes.     But  no  amount  of  inspection  of 
a  judgment  itself  will  show  us  the  particular  fact  which 
makes  it  true  if  it  is  true  and  false  if  it  is  false.     There 
is    therefore    no    inconsistency    between    the    statement 
that   we    can    know   at   once  what   kind  of  fact   would 
verify  a  judgment  about  the  future,  and  the  statement 
that  such  judgments  do  not  refer  to  any  fact  when  made. 
(if)  As  regards  any  judgment  we  have  to  consider 
not   only   what    it   is   about,    but   also   what   it   asserts 
about  its  subject  or  subjects.     These  two  questions  are 
not  altogether  free  from  ambiguity,  and  this  ambiguity 
must   be   cleared    up    before    we    consider    the    special 
question  as  to  what  judgments  that  profess  to  be  about 
the  future  assert,      (i)  There  is  the  confusion  between 
what  a  judgment  is  about  and  what  it  refers  to.     This 
we  have  already  dealt  with.      (2)  There  is  the  distinc- 
tion between  what  a  judgment  is  ostensibly  about  and 
what  it  is  really  about.      If  you  had  asked  a  peasant, 
who  said  that  Puck  had  turned  the  milk,  what  he  was 
talking  about,  he  would  have  said  that  he  was  talking 
about   a    certain    individual    fairy.      This    is    what    the 
judgment   professes   to    be   about.      What   it  is    really 
about    is    a    certain    set    of   characteristics.       Roughly 
speaking,  we  may  say  that  what  a  judgment  professes 
to    be    about    can    be    determined    by    a    grammatical 
analysis  of  the  sentence  in  which  the  judgment  is  ex- 
pressed.   Although  there  is  always  a  connexion  between 


TIME  AND   CHANGE  75 

the  grammatical  structure  of  a  sentence  and  the  logical 
structure  of  a  judgment,  it  is  highly  dangerous  to  sup- 
pose that  what  the  sentence  is  grammatically  about 
is  the  name  of  what  the  judgment  is  logically  about. 
(3)  When  these  two  confusions  have  been  set  aside 
and  we  are  quite  definitely  dealing  with  the  judgment, 
and  neither  with  the  fact  to  which  it  refers  nor  the 
sentence  which  expresses  it,  there  is  still  a  difficulty  as 
to  how  much  is  to  be  included  under  the  head  of  what 
the  judgment  is  about  and  how  much  is  to  be  included 
under  the  head  of  what  the  judgment  asserts.  Take 
first  a  very  simple  characterising  judgment,  like  "  3 
is  a  prime."  What  is  this  about,  and  what  does  it 
assert?  We  should  all  agree  that  it  is  at  any  rate 
about  the  number  3.  But  is  it  about  the  characteristic 
of  primeness  too?  If  you  say  Yes,  what  is  there  left 
for  it  to  assert?  If  you  say  No,  how  can  you  face  the 
obviously  equivalent  judgment  "  Primeness  is  a  charac- 
teristic of  3 "  ?  Exactly  the  same  kind  of  difficulty 
arises  over  a  relational  proposition,  like  "  3  is  greater 
than  2."  We  should  all  at  this  time  of  day  agree  that 
it  is  at  least  about  the  numbers  2  and  3.  But  is  it  or 
is  it  not  about  the  relation  of  greater?  I  think  that  we 
must  say  that  the  former  judgment  is  about  primeness 
as  much  as  it  is  about  the  number  3,  and  that  the 
latter  is  about  the  relation  of  greater  as  much  as  it  is 
about  the  numbers  2  and  2.  Really  it  is  as  misleading 
to  say  that  the  first  asserts  primeness  as  to  say  that  it 
asserts  3.  The  minimum  that  it  asserts  is  the  prime- 
ness of  3.  Similar  remarks  apply  to  the  second.  If 
we  like  to  use  the  useful  word  tie,  which  Mr  W.  E. 
Johnson*  has  lately  introduced  into  logic,  we  might  say 
that  the  first  judgment  is  about  the  number  3  and  the 
characteristic  of  primeness,  and  asserts  that  they  are 
connected  by  the  characterising  tie.  The  second  is 
about  the  numbers  3  and  2  and  the  relation  greater, 
and  asserts  that  they  are  connected   by  the   relational 

*  Logic,  vol.  i. 


76  SCIENTIFIC   THOUGHT 

tie  in  the  order  3  to  2.  But  we  might  equally  well 
distinguish  different  kinds  of  assertion,  and  say  that 
the  first  is  about  the  number  3  and  the  characteristic 
of  primeness,  and  makes  a  characterising  assertion 
about  them.  In  the  case  of  the  second  we  should 
talk  of  a  relating  assertion. 

So  far  we  have  purposely  chosen  examples  which 
are  about  timeless  objects,  like  numbers.  Let  us  now 
take  the  series  of  judgments  :  "  It  has  rained,"  "  It  is 
raining,"  and  "  It  will  rain,"  which  are  about  events, 
and  contain  an  essential  reference  to  time.  The  first 
may  be  analysed  as  follows:  "There  is  an  event  which 
is  characterised  by  raininess,  and  the  sum  total  of  exist- 
ence when  the  judgment  is  made  includes  all  and  more 
than  all  which  it  includes  when  this  event  becomes."  The 
second  may  be  analysed  as  follows  :  "  There  is  an  event 
which  is  characterised  by  raininess,  and  the  sum  total  of 
existence  is  the  same  when  this  event  becomes  and  when 
the  judgment  is  made."  Thus  judgments  about  the  past 
and  the  present  can  be  analysed  into  judgments  which 
involve  the  four  familiar  types  of  assertion— the  exist- 
ential, the  characterising,  the  genetic,  and  the  relational. 
But  the  judgment  that  it  will  rain  cannot  be  analysed 
in  a  similar  way.  It  cannot  mean  anything  that  begins 
with  the  statement:  "There  is  an  event,"  for  the  only 
events  that  there  are  are  the  events  that  have  become  up 
to  the  time  when  the  assertion  is  made  ;  the  sum  total 
of  existence  does  not  contain  future  events.  We  can 
only  restate  the  judgment  in  the  form  :  "The  sum  total 
of  existence  will  increase  beyond  what  it  is  when  the 
judgment  is  made,  and  some  part  of  what  will  become 
will  be  characterised  by  raininess."  We  cannot  then 
analyse  will  away,  as  we  can  has  been  and  is  now.  Every 
judgment  that  professes  to  be  about  the  future  would 
seem  then  to  involve  two  peculiar  and  not  further 
analysable  kinds  of  assertion.  One  of  these  is  about 
becoming ;  it  asserts  that  further  events  will  become. 
The  other  is  about  some  characteristic  ;  it  asserts  that 


TIME  AND   CHANGE  77 

this  will  characterise  some  of  the  events  which  will 
become.  If  then  we  ask :  What  are  judgments  which 
profess  to  be  about  future  events  really  about?  the 
answer  would  seem  to  be  that  they  are  about  some 
characteristic  and  about  becoming.  And  if  it  be  asked  : 
What  do  such  judgments  assert?  the  only  answer  that 
I  can  give  is  that  they  assert  that  the  sum  total  of 
existence  will  increase  through  becoming,  and  that  the 
characteristic  in  question  will  characterise  some  part  of 
what  will  become.  These  answers  are  compatible  with 
the  non-existence  of  the  future.  The  only  "constitu- 
ents" of  the  judgment,  when  it  is  made,  are  the 
characteristic  —  which  has  the  kind  of  reality  which 
universals  possess  —  and  the  concept  of  becoming. 
About  these  the  judgment  makes  certain  assertions 
of  a  quite  peculiar  and  not  further  analysable  kind. 
Something  called  to-morrow  is  not  a  constituent  of  judg- 
ments which  are  grammatically  about  "  to-morrow,"  any 
more  than  an  individual  called  Puck  is  a  constituent  of 
judgments  which  profess  to  be  about  "  Puck." 

I  have  thus  tried  to  show  that  there  is  an  extreme 
difference  between  judgments  which  profess  to  be  about 
future  events  and  these  which  are  about  past  or  present 
events.  The  former,  when  made,  do  not  refer  to  any- 
thing, and  therefore  are  not  literally  true  or  false, 
though  it  is  possible  for  anyone  who  understands  their 
meaning  to  see  what  kind  of  fact  will  eventually  make 
them  true  or  false  as  the  case  may  be.  Again,  is  now 
and  has  been  need  not  be  taken  as  new  and  ultimate 
types  of  assertion,  but  will  be  apparently  must  be  so 
taken.  Nevertheless,  although  the  future  is  nothing 
and  although  judgments  which  profess  to  be  about 
future  events  refer  to  nothing,  they  are  not  about 
nothing.  They  are  about  some  characteristic  and 
about  becoming  ;  and,  so  far  as  I  can  see,  they  make  an 
unique  and  not  further  analysable  kind  of  assertion 
about  these  terms. 

There  are  just  two  points  that  I  want  to  make  before 


78  SCIENTIFIC  THOUGHT 

leaving  this  subject,  (a)  Of  course  there  are  plenty  of 
ex  post  facto  statements  which  nominally  involve  the 
existence  of  future  events.  We  can  say  that  the  Battle 
of  Hastings  was  future  to  Edward  the  Confessor.  Such 
statements  need  no  special  analysis.  We  merely  mean 
that  the  sum  total  of  existence  now  includes  the  Battle 
of  Hastings,  and  that  when  Edward  the  Confessor's 
death  became  it  did  not  include  this  battle.  We,  who 
live  after  both  events,  are  dealing  with  two  parts  of  the 
existent,  which  can  and  do  stand  in  various  relations 
to  each  other  ;  and  so  there  is  no  kind  of  difficulty  in 
giving  a  meaning  to  the  statement. 

(/>)  It  is  commonly  held  that  there  can  be  no  certain 
knowledge  about  the  future,  but  that  all  judgments 
which  profess  to  be  about  it  consist  of  more  or  less 
probable  conjectures  made  by  analogy  with  the  past. 
Now  we  do  not  always  recognise  how  odd  our  certainty 
about  this  is  on  the  assumption  that  the  future  really  is 
something  that  has  "  future  existence"  as  the  past  really 
is  something  that  has  "past  existence."  We  have 
immediate,  and  not  merely  inferential,  knowledge  about 
some  past  events  by  direct  memory.  Hence  mere 
difference  in  date  between  the  act  of  cognition  and  an 
event  does  not  necessarily  prevent  the  event  from  being 
an  object  to  the  act.  If  the  future  exist,  and  be  just 
that  part  of  the  existent  which  succeeds  the  present,  it 
is  difficult  to  see  why  a  present  act  of  cognition  might 
not  know  an  event  which  is  later  than  itself,  just  as 
it  can  know  some  events  which  are  earlier  than  itself. 
Why  should  we  not  have  direct  anticipations  of  some 
future  events,  just  as  we  have  direct  memories  of  some 
past  ones,  if  the  future  were  of  the  same  general  nature  as 
the  past,  and  simply  differed  from  it  by  standing  in  the 
converse  temporal  relation  to  the  present?  Still  more, 
why  should  all  claims  to  direct  knowledge  of  future 
events  be  regarded  as  so  wildly  paradoxical? 

These  facts  become  plausible  on  two  theories  about 
the  future,  one  of  which  we  have  rejected,  and  the  other 


TIME  AND   CHANGE  79 

of  which  is  our  own.  Obviously  if  to  be  future  just 
means  to  be  incapable  of  being  directly  cognised,  direct 
cognition  of  future  events  could  be  ruled  out  as  a  con- 
tradiction in  terms.  We  have,  however,  examined  and 
rejected  this  view  of  the  future.  But  the  impossibility 
of  absolutely  certain  knowledge  about  the  future  follows 
equally  from  our  theory.  We  can  be  absolutely  certain 
that  an  event  has  the  characteristic  C  only  if  we  are 
directly  acquainted  with  this  event  and  can  notice  the 
characteristic  in  it.  Now  we  can  be  directly  acquainted 
only  with  somethings  not  with  a  mere  non-entity.  On 
our  view  we  cannot  stand  in  the  relation  of  direct  ac- 
quaintance to  future  events,  for  the  same  reason  which 
prevents  us  from  robbing  a  Highlander  of  his  breeks. 
We  can  stand  in  this  relation  to  present  events  (in  sense- 
awareness)  and  to  past  events  (in  genuine  memory), 
because  such  events  are  parts  of  the  sum  total  of 
existence  when  the  cognition  in  question  takes  place. 

(ii)  The  last  question  that  we  have  to  deal  with  is 
the  alleged  difficulty  that  every  event  is  past,  present, 
and  future  ;  that  these  characteristics  are  incompatible  ; 
and  that  there  is  no  way  of  reconciling  them  which 
does  not  either  involve  an  infinite  regress,  in  which 
the  same  difficulty  recurs  at  every  stage,  or  a  vicious 
circle.  This  argument  has  been  used  by  Dr  M  'Taggart* 
as  a  ground  for  denying  the  reality  of  Time.  It  is 
certainly  the  best  of  the  arguments  which  have  been 
used  for  this  purpose ;  since  it  really  does  turn  on 
features  which  are  peculiar  to  Time,  and  not,  like  most 
of  the  others,  on  difficulties  about  continuity  and  infinity 
which  vanish  with  a  knowledge  of  the  relevant  mathe- 
matical work  on  the  subject.  Do  the  results  of  our 
earlier  discussions  in  this  chapter  help  us  to  remove 
this  supposed  contradiction  ? 

Let  us  take  M'Taggart's  example  of  the  death  of 
Queen  Anne,  as  an  event  which  is  supposed  to  combine 
the  incompatible  characteristics  of  pastness,  presentness, 

*   The  Unreality  of  Time,  Mind,  N.S.,  1908. 


80  SCIENTIFIC  THOUGHT 

and  futurity.      In   the  first  place,  we  may  say  at  once 
that,  on  our  view,   futurity  is  not  and  never  has  been 
literallv  a  characteristic  of  the  event  which  is  character- 
ised as  the  death  of  Queen  Anne.     Before  Anne  died 
there  was  no  such  event  as  Anne's  death,  and  "nothing" 
can  have  no  characteristics.     After  Anne  died  the  sum 
total  of  existent  reality  does  contain  Anne's  death,  but  this 
event  then  has  the  characteristic  of  pastness.     No  doubt 
I  can  say  "Anne's  death  was  future  to  William   III." 
But  I  simply  mean  that,  so  long  as  William  III  was 
alive,  there  was  no  event  characterised  as  the  death  of 
Anne  ;  and  that  afterwards,  as  the  sum  total  of  existence 
increased   by   becoming,    it  contained   both  the   events 
of  William's  life  and  the  event  of  Anne's  death.     Anne's 
death  succeeded  William's  life  so  soon  as  Anne's  death 
existed  at  all,  and  it  succeeds   it  henceforth  for  ever  ; 
but    it   did    not    succeed    it   while    William    was   alive, 
because    it   had    not   become,    was    not   anything,    and 
therefore   could   not  have  any  characteristics  or  stand 
in    any    relations.       But   it    might    be    said    that   Anne 
herself  or  William  III  might  have  made  the  judgment: 
"Queen   Anne's  death  is  future";    that  this   is  a  true 
judgment  on  their  parts;  and  that  it  cannot  be  explained 
in   the   same  way  as    my  ex  post  facto  judgment   that 
Queen  Anne's  death  was  future.     To  this  I  answer  that 
the  existence  and  the  truth  of  William's  judgment  do 
not  imply  that  there  ever  was  an  event  which  has  the 
two  characteristics  of  futurity  and  of  being  the  death 
of  Anne.     When    William   made  this  judgment  there 
was   no  event  for  it  to   refer  to  ;    for  the  event  which 
afterwards  became,  and  was  the  death  of  Anne,  had  not 
then   become   and  was   not  anything.     What   William 
did  was    to   make  a  peculiar   kind    of  assertion    about 
becoming   and   about   the   characteristic   of    being    the 
death  of  Oueen  Anne.     He  asserted  that  the  sum  total 
of  existence  would  increase  by  further  becoming,  and 
that  some  part  of  what  would  thus  be  added  would  be 
characterised   as   the   death    of   his   sister-in-law.       He 


TIME   AND   CHANGE  81 

was  neither  talking  about  nor  referring  to  that  particular 
event  which  did  in  fact  eventually  become,  and  which, 
when  it  became,  was  in  fact  characterised  as  the  death 
of  Anne.  For,  when  he  made  his  judgment,  there  was 
no  such  event  in  the  whole  of  reality  for  him  to  talk 
about  or  to  refer  to.  Thus  the  first  thing  that  we  have 
to  say  with  regard  to  M'Taggart's  argument  is  that 
no  event  ever  does  have  the  characteristic  of  futurity. 
When  we  say  that  a  certain  event  is  future,  the  sentence 
which  expresses  our  judgment  is  no  doubt  of  the  same 
form  as  when  we  say  that  a  certain  book  is  green. 
We  are  therefore  tempted  to  treat  the  former  judgment 
as  a  characterising  judgment,  like  the  latter  ;  and  to 
suppose  that  the  only  difference  between  them  is  that 
one  asserts  the  characteristic  of  "futurity"  whilst  the 
other  asserts  the  characteristic  of  greenness.  From 
what  has  gone  before  we  conclude  that  the  former 
judgment  is  not  really  a  characterising  judgment  at 
all,  and  that  there  is  no  characteristic  of  "futurity." 
Judgments  which  appear  to  characterise  events  as  future 
make  a  peculiar  kind  of  assertion  about  some  ordinary 
characteristic  {e.g.  wetness  or  fineness)  ;  they  do  not 
make  an  ordinary  characterising  assertion  about  a 
certain  event  and  a  peculiar  kind  of  characteristic  (viz. , 
"futurity"). 

Is  there  anything  contradictory  in  the  fact  that 
Queen  Anne's  death  has  been  present  and  is  now  past? 
There  very  well  might  be  if  we  had  to  take  the  change 
of  an  event  in  respect  to  the  characteristics  of  present- 
ness  and  pastness  as  analogous  to  the  change  of  a 
signal  lamp  in  respect  to  the  characteristics  of  red 
and  green.  But  we  have  seen  that  this  cannot  be  done, 
and  that  the  second  kind  of  change  depends  on  the 
first.  When  Queen  Anne's  death  became,  it  came 
into  relations  with  all  that  had  already  become,  and 
to  nothing  else,  because  there  was  nothing  else  for  it 
to  be  related  to.  All  these  relations  it  retains  hence- 
forth  for   ever.      As   more   events  become    it   acquires 


82  SCIENTIFIC   THOUGHT 

further  relations,  which  it  did  not  have,  and  could  not 
have  had  while  those  events  were  non-existent.  This 
is  all  that  ever  happens  to  the  event  in  question. 
Suppose  we  now  ask  ourselves  the  question  :  "  Does 
anything  that  was  true  of  Anne's  death  when  it  first 
became  get  false  of  it  afterwards,  through  further 
becoming?  And,  if  so,  does  this  raise  any  logical 
difficulty?"  Here  we  must  draw  a  distinction,  (i) 
All  the  relations  which  Anne's  death  entered  into  with 
the  sum  total  of  reality,  as  it  was  when  this  event  first 
became,  persist  eternally  for  ever  afterwards,  and  are 
wholly  unaffected  by  anything  else  that  may  be  added 
on  to  this  sum  total  by  further  becoming.  Hence  no 
true  proposition  about  these  will  ever  become  false, 
and  no  false  proposition  about  them  will  ever  become 
true.  (2)  As  further  events  become  they  automatically 
enter  into  various  relations  with  Anne's  death,  which 
thus  acquires  additional  relations  and  becomes  a  con- 
stituent in  additional  facts.  If  e.g.  my  Lord  Bolingbroke 
swore  when  he  heard  of  Anne's  death,  it  is  clear  that 
something  subsequently  became  true  of  the  death  which 
was  not  true  of  it  when  it  first  became.  When  Lord 
Bolingbroke  had  sworn  it  became  true  of  Queen  Anne's 
death  that  it  caused  a  certain  event  in  his  lordship's 
life.  And  this  was  not  true  of  Queen  Anne's  death 
before  Lord  Bolingbroke  had  heard  of  it,  and  had 
thereby  been  caused  to  swear.  Thus  something,  which 
was  not  true  of  Queen  Anne's  death  when  it  became, 
is  afterwards  rendered  true  of  it  by  the  becoming  of 
Lord  Bolingbroke's  oath. 

Now  we  are  inclined  to  think  that  to  say  that  some- 
thing, which  was  not  true  of  an  event,  subsequently 
became  true  of  it,  is  equivalent  to  saying  that  something 
which  was  false  of  the  event,  became  true  of  it.  This 
is,  I  think,  a  mistake;  for  "not-true"  is  a  wider  term 
than  "  false."  Suppose  we  compare  the  two  statements  : 
"It  is  not  true  that  Queen  Anne's  death  caused  the 
earthquake  at  Lisbon,"  and  :  "  It  is  not  true  that  Queen 


TIME  AND   CHANGE  83 

Anne's  death,  when  it  happened,  had  caused  Lord 
Bolingbroke  to  swear."  In  the  former  "not-true" 
is  equivalent  to  "false."  For  it  means  that  there  is 
a  certain  negative  fact  (containing  both  the  death  and 
the  earthquake  as  constituents)  which  discords  with 
the  judgment  that  the  first  caused  the  second.  But  the 
latter  does  not  mean  that  at  the  time  of  Anne's  death 
there  was  a  negative  fact,  containing  Anne's  death  and 
Bolingbroke's  oath  as  constituents,  and  discording  with 
the  judgment  that  the  death  causes  the  oath.  For, 
when  Anne's  death  became,  there  was  no  such  entity 
as  Lord  Bolingbroke's  oath,  and  therefore  no  fact  of 
which  this  is  a  constituent.  What  happens  when  Lord 
Bolingbroke  swears  is  not  that  something  which  was 
false  of  Anne's  death  becomes  true  of  it,  but  that  some- 
thing becomes  true  of  Anne's  death  which  was  before 
neither  true  nor  false  of  it. 

Now  I  do  not  think  that  the  laws  of  logic  have 
anything  to  say  against  this  kind  of  change  ;  and,  if 
they  have,  so  much  the  worse  for  the  laws  of  logic, 
for  it  is  certainly  a  fact.  What  the  laws  of  identity, 
contradiction,  and  excluded  middle,  between  them  assert 
is  that  any  proposition  is  either  true  or  false,  cannot 
be  both,  and  cannot  alter  in  this  respect.  They  do  not 
assert  (and,  if  they  do,  they  must  be  amended)  that 
the  number  of  propositions,  is  eternally  fixed  ;  they  only 
assert  that  it  cannot  be  diminished.  But  it  may  be 
increased,  and  it  is  continually  increased  by  the  process 
of  becoming  which  continually  augments  the  sum  total 
of  existence  and  thereby  the  sum  total  of  positive  and 
negative  facts.  Or,  to  put  it  in  another  way,  the  laws 
of  logic  apply  to  a  fixed  universe  of  discourse,  and  we 
can  at  any  moment  get  a  fixed  universe  of  discourse 
by  taking  the  sum  total  of  reality  up  to  that  moment. 
But  the  universe  of  actual  fact  is  continually  increasing 
through  the  becoming  of  fresh  events  ;  and  changes 
in  truth,  which  are  mere  increases  in  the  number  of  truths 
through  this  cause,  are  logically  unobjectionable. 


84  SCIENTIFIC  THOUGHT 

I  can  hardly  hope  that  what  I  have  been  saying 
about  Time  and  Change  will  satisfy  most  of  my  readers, 
or  indeed,  that  it  is  more  than  a  shadow  of  the  truth, 
if  that.  It  is  admitted  that  this  is  the  hardest  knot 
in  the  whole  of  philosophy.  The  Dean  of  Carlisle 
judiciously  remarks  that  "we  cannot  understand  Time, 
but  we  shall  not  understand  it  better  by  talking  nonsense 
about  it."  In  the  hope  that  I  have  not  darkened  counsel 
by  words  without  understanding,  I  leave  this  most  diffi- 
cult subject,  to  return  at  a  later  stage  to  the  questions 
of  one  or  many  time  series,  the  entanglement  of  Time 
with  Space,  and  the  placing  and  dating  of  events. 

Additional  works  which  may  be  consulted  with  profit  : 

B.  A.  W.    Russell,  Our  Knowledge  of  the  External  World, 

Lecture  IV. 
A.  N.  Whitehead,  Concept  0/ 'Nature,  Cap.  III. 
J.    M.   E.    M'TaGGART,    The  Relation   of  Time  and  Eternity 

(Mind,  N.S.,  vol.  xviii.  No.  71). 
„      The  Unreality  of  Time  (MlND,  N.S.,  xvii.,  1908). 
H.  Bergson,  Time  and  Free- Will. 
„  Matter  and  Memory. 


CHAPTER   III 

"  Its  eyebrows  (of  a  vivid  green) 
Have  never,  never  yet  been  seen  ; 
But  Scientists,  who  ought  to  know, 
Assure  us  that  it  must  be  so. 
Oh,  let  us  never,  never  doubt 
What  no  one  can  be  sure  about ! " 

(H.  Belloc,  The  Microbe.) 

The  Traditional  Kinematics,  and  its  Gradual  Modifica- 
tion in  the  Region  of  Physics,  (i)  The  Absolute 
and  the  Relational  Theories 

We  have  now   dealt  with  the   traditional    concepts  of 

Space   and    Time,   and   we    might  turn    next   either   to 

Matter  or  to  Motion.     I  propose  to  treat  the  classical 

doctrine   of    Motion    before    touching   the    problem    of 

Matter.     As  we  all    know,  the  concept  of  Motion  has 

been   the    subject   of  constant  discussion  by  physicists 

and    mathematicians  for  centuries,  and  in  recent  years 

the  classical  kinematics  has  been  profoundly  modified, 

owing   to   circumstances    that    have   arisen    within    the 

region  of  Physics  itself.     The  older  arguments  between 

supporters  of  Absolute  and    Relative   Motion,  and  the 

later  ones  about  the  Theory  of  Relativity,  are  essentially 

pieces  of  Critical  Philosophy  in  our  sense  of  the  word. 

Thus    we    may    fairly    say   that,    as    regards    Motion, 

physicists   have   been    their   own    philosophers,    forced 

into   this   unwelcome   position   by   their  own    domestic 

difficulties.     Now  this  is  not  so  in  the  case  of  Matter. 

The   difficulties   about    Matter,    which    show   the    need 

for    radical   philosophic   criticism    of  that   concept,  are 

not   indigenous   to    Physics    itself.     They  arise    in    the 

main    when    we    begin    to   take    into   account   the   way 

85 


86  SCIENTIFIC   THOUGHT 

in  which  we  get  to  know  matter  through  sensation. 
It  is  the  apparent  conflict  between  what  our  sensations 
tell  us  and  what  Physics  teaches  about  matter,  com- 
bined with  the  fact  that  our  sensations  are  after  all 
the  only  ultimate  source  of  all  our  alleged  information 
on  the  subject,  which  compels  us  to  indulge  in 
philosophical  criticism.  The  moment  we  begin  this 
criticism  we  find  that  it  will  lead  us  very  far  afield,  and 
that  we  cannot  stop  till  we  have  profoundly  modified 
the  traditional  concepts  of  Space,  Time,  and  Motion 
too.  Now  I  hope  to  be  able  to  show  that  these 
modifications,  which  are  forced  on  us  as  philosophers 
when  we  begin  to  deal  with  the  concept  of  Matter,  are 
of  somewhat  the  same  kind  as  those  which  Physicists 
have  had  to  make  for  purely  domestic  reasons.  If  this 
can  be  shown,  even  in  rough  outline,  it  will  greatly 
strengthen  the  case  for  the  newer  views  of  Space,  Time, 
Motion,  and  Matter.  There  is  much  in  these  views 
which  is  at  first  sight  highly  paradoxical  and  upsetting 
to  common-sense,  so  that  it  is  of  some  advantage  even  to 
the  scientist  to  know  that  they  can  be  justified  on  wider 
grounds  than  the  special  needs  of  his  science.  On  the 
other  hand,  it  is  always  a  comfort  to  the  philosopher 
to  know  that  he  is  not  simply  bombinans  in  vacuo,  but 
is  working  on  lines  which  have  been  found  to  lead 
to  useful  results  in  some  concrete  region  of  science. 

This  book  is  written  primarily  for  scientists  who 
are  interested  in  philosophy,  and  secondarily  for  philo- 
sophers who  are  interested  in  science.  It  has  therefore 
been  my  plan  to  diverge  as  gradually  as  possible  from 
the  concepts  that  are  most  familiar  to  scientists.  Now, 
for  the  reasons  given,  the  philosophic  criticism  of  the 
concept  of  Motion  is  more  familiar  to  most  scientists 
than  the  criticism  of  the  concept  of  Matter.  It  therefore 
seems  right  to  treat  the  former  before  the  latter.  I 
am  going,  then,  to  deal  at  present  with  the  purely 
physical  arguments  which  have  gradually  undermined 
the    traditional    Kinematics    and    replaced    it   by    that 


THE  TRADITIONAL   KINEMATICS  87 

of  the  Theory  of  Relativity.     In  spite  of  many  excellent 
(and    more,    execrable)     popular    works     which     have 
appeared  in   the   last  few  years,    I   think  there   is  still 
room  for  a  restatement  of  these  arguments.     To  many 
scientific  readers  they  will  of  course  be  perfectly  familiar, 
but  it  will  do  no  harm  to  the  reader  who  is  primarily  a 
philosopher  to  put  himself  au  courant  with  the  present 
position    in    Physics  before  going  further.       At  a  con- 
siderably later  stage,  when  we  have  seen  what  modifica- 
tions in  the  traditional  concepts  of  Space  and  Time  are 
forced  on  us  by  our  criticisms  of  the  traditional  concept 
of  Matter,  we  shall  return  to  the  present  subject,  and  try 
to  connect  the  physical  with  the  philosophical  doctrines. 
We  have  at  least   four  general    kinematic  concepts 
to  consider,  viz.,  the  Absolute  Theory  of  Motion,  the 
Relational    Theory  of   Motion,   the  Special   Theory  of 
Relativity,  and  the  General  Theory  of  Relativity.     This 
is    approximately   the   historical  order   in    which    these 
concepts  have  arisen  in  Physics  since  the  Renaissance. 
We   must    remember,    however,    that    the   controversy 
between  the  Absolute  and  the  Relational   Theories  of 
Motion  had  a  long  history  before  ever  modern  Mechanics 
was  founded  by  Galileo,  Descartes,  Huyghens,  Newton, 
and    Leibniz.       This     controversy    was    inherited    by 
Mechanics,  and  the  opposite  sides  were  upheld  by  two 
such  eminent   contemporaries  as  Newton  and  Leibniz. 
I  shall  treat  the  concepts  in  their  historical  order,  putting 
the  Absolute   Theory  before  the  Relational  Theory   of 
Motion.       But,  when    the   various   theories   have    been 
clearly  stated  and  the  pros  and  cons  have  been  weighed, 
a  further  task  will  confront  us,   viz.,   to  try  to  exhibit 
their  logical  order  and  interconnexions.      I  must  confess 
that  I  have  not  seen  a  satisfactory  account  of  this  point 
in   any   work  on   the   subject.     It  seems   commonly  to 
be  assumed  that  the   logical  order  has  been  the  same 
as   the    historical,    and    that   the    successive    kinematic 
concepts  have  represented  a  steady  development  of  the 
doctrine   that  motion   is    purely  relative.     Yet  some  of 


88  SCIENTIFIC   THOUGHT 

the  chief  exponents  of  the  General  Theory  of  Relativity, 
which  is  the  latest  phase  of  kinematics,  use  language 
which  seems  to  imply  a  thoroughly  Absolute  Theory. 
We  hear  of  "  kinks"  in  Space  or  in  Space-Time,  and 
we  are  told  that  they  modify  the  motions  of  matter, 
or  that  matter  consists  of  such  "kinks."  All  this  is 
extremely  puzzling  after  one  has  been  led  to  believe 
by  the  same  writers  that  the  General  Theory  of 
Relativity  is  the  final  triumph  of  the  Relational  Theory 
of  Motion.  I  think  we  shall  find  that  the  logical 
connexions  are  not  so  simple  as  we  have  been  told  ; 
and  it  will  certainly  be  useful  to  do  our  best  to  throw 
some  light  on  this  dim  spot.  We  cannot,  however, 
profitably  discuss  this  question  until  we  have  seen  what 
precisely  the  various  theories  assert. 

The  Absolute  and  Relational  Theories  of  Motion.  In 
the  last  two  chapters  we  have  been  discussing  the 
traditional  concepts  of  Space  and  Time.  Now  the 
kinematic  concept  which  strictly  corresponds  to  these 
is  that  of  Absolute  Motion.  In  accordance  with  the 
traditional  concepts  of  Space,  Time,  and  Matter,  the 
three  are  largely  independent  entities.  The  traditional 
view  does  not  as  a  rule  go  very  deeply  into  the  question 
of  their  mutual  relations,  but  I  think  the  following 
would  be  a  fair  statement  of  what  it  tacitly  assumes 
on  this  subject :  Time  could  have  existed  without  Space 
or  Matter;  Space  could  not  have  existed  without  Time, 
but  it  could  have  existed  without  Matter  ;  Matter  could 
not  have  existed  without  both  Space  and  Time.  Space 
needs  Time  in  order  to  endure,  but  the  only  connexion 
is  that  all  points  of  Space  endure  unchanged  for  ever. 
Matter  needs  Time  in  order  to  endure,  and  it  needs 
Space  in  order  to  have  place  and  shape,  which  are 
essential  to  it.  With  Matter  there  begins  the  possibility 
of  Motion  ;  Matter  need  not  have  moved,  but  as  a  fact 
it  does  so  from  time  to  time. 

The  alternative  between  the  Absolutist  and  the 
Relationist  Theory  of  Time  may  be  illustrated  as  follows  : 


THE   TRADITIONAL   KINEMATICS  89 

We  say  that  the  Battle  of  Hastings  precedes  the  Battle 
of  Waterloo  by  a  certain  amount,  viz.,  749  years.  The 
two  battles  are  events  in  the  world's  history,  and  the 
Absolutist  and  the  Relationist  agree  that  a  certain 
temporal  relation  subsists  between  them,  and  that  it 
has  a  certain  measure  in  terms  of  the  usual  units.  The 
whole  question  between  them  as  to  Time  is  the  follow- 
ing :  Is  this  relation  simple,  direct,  and  unanalysable, 
connecting  the  two  events  in  question  and  nothing  else, 
or  is  it  a  complex  compounded  out  of  other  relations 
which  involve  other  terms  in  addition  to  the  two  events? 
The  former  alternative  is  taken  by  the  Relationist,  the 
latter  by  the  Absolutist.  On  the  former  view  there  is 
not  something  called  Time  which  could  exist  even 
though  there  had  been  no  events  ;  Time  just  consists 
of  the  relations  of  before  and  after  among  events.  These 
relations  have  various  magnitudes  which  can  be  measured 
by  comparison  with  the  temporal  relation  between  some 
standard  pair  of  events,  such  as  the  successive  occupa- 
tions of  the  same  position  on  a  dial  by  the  hands  of  a 
suitably  standardised  clock. 

The  Absolutist,  on  the  other  hand,  holds  that  the 
temporal  relations  between  events  are  not  direct  and 
unanalysable ;  they  are  really  compounded  out  of 
relations  of  two  wholly  different  kinds.  On  this  view 
there  is  something  called  Time  which  is  composed  of 
simple  entities  called  moments  ;  and  it  is  only  moments 
which  can  strictly  be  said  to  be  before  or  after  each 
other.  There  is  further  a  certain  peculiar  relation 
between  events  and  moments  which  is  denoted  by  the 
word  at.  At  is  a.  many-one  relation,  i.e.  many  different 
events  can  be  at  the  same  moment  but  no  momentary 
event  can  be  at  more  than  one  moment.  The  Absolutist 
analyses  the  statement  that  the  Battle  of  Hastings 
precedes  the  Battle  of  Waterloo  by  749  years  into 
the  three  following  propositions:  (1)  The  Battle  of 
Hastings  happened  at  a  certain  moment  tv  (2)  The 
Battle  of  Waterloo  happened  at  a  certain  moment  t%. 

G 


90  SCIENTIFIC   THOUGHT 

(3)  The  moment  fl  eternally  precedes  the  moment  t2 
by  749  years.  (I  am  neglecting  the  fact  that  both 
battles  took  up  a  finite  time  and  therefore  did  not  liter- 
ally happen  at  two  moments.  This  is  not  important  for 
the  present  purpose,  and  can  quite  easily  be  dealt  with 
on  either  theory.) 

It  is  important  to  notice  that  the  traditional  Absolu- 
tist and  the  traditional  Relationist  agree  in  holding  that 
there  is  something  that  can  be  called  the  dates  of  the 
two  battles  and  something  that  can  be  called  the  time- 
lapse  between  them.  Neither  of  them  would  admit  that 
the  same  pair  of  events  could  stand  in  several  different 
temporal  relations  ;  that,  for  instance,  they  might  be 
both  contemporary  and  yet  one  earlier  than  the  other, 
or  again  that  they  might  precede  each  other  by  several 
different  amounts.  They  agree  that  there  is  one  and 
only  one  temporal  relation  between  a  given  pair  of 
events,  and  they  only  differ  as  to  the  right  analysis  of 
this  relation.  It  is  important  to  notice  this,  because  it 
is  here  that  the  Theory  of  Relativity  differs  from  both 
of  them.  For,  as  we  shall  see,  this  theory  denies  that 
there  is  a  single  relation  which  can  be  called  the  time- 
lapse  between  a  given  pair  of  events. 

Now  that  we  have  got  the  difference  between  the 
Absolute  Theory  of  Time  and  the  Relational  Theory 
clear  we  can  briefly  consider  the  arguments  between 
them.  These  fall  into  two  classes,  viz.,  those  which 
apply  directly  to  Time  and  those  which  apply  to  it  only 
indirectly  through  the  question  of  Motion.  Absolute 
motion  implies  absolute  Time  and  Space,  though  there 
will,  of  course,  be  relative  motion  even  if  there  be 
absolute  Time  and  Space.  The  Absolute  Theory  does 
not  deny  relative  motion,  but  simply  asserts  that  all 
relative  motion  is  the  appearance  of  absolute  motions. 
The  arguments  for  and  against  these  theories,  which 
depend  on  motion,  may  be  reserved  for  the  moment, 
and  we  will  now  consider  those  which  apply  directly 
to  Time. 


THE  TRADITIONAL  KINEMATICS  91 

The  main  merit  of  the  Relational  Theory  is  that  it 
is  simpler  and  keeps  closer  to  the  observable  facts.  We 
can  observe  events,  and  if  two  events  fall  into  the  same 
specious  present,  or  if  one  is  sensed  and  the  other 
remembered,  we  can  directly  observe  the  temporal 
relation  between  them.  We  cannot  perceive  moments 
of  Time.  Nor  can  we  say  that  they  are  hypothetical 
entities,  like  atoms  and  electrons,  which  we  also  cannot 
perceive.  We  accept  the  latter  because  there  are  certain 
sensible  facts  which  we  can  explain  with  them  and  can- 
not easily  explain  without  them.  But,  whilst  electrons 
are  supposed  to  be  causes  with  sensible  effects,  bare 
moments  are  not  supposed  to  do  anything  or  to  produce 
any  effects,  sensible  or  otherwise. 

Undoubtedly  there  is  something  more  than  mere 
relations  in  Time.  We  have  already  seen  that  the  Time 
series  has  a  definite  intrinsic  sense,  and  that  this  arises 
because  there  is  a  continual  addition  to  the  sum  total 
of  existence,  whilst  nothing  that  has  ever  existed  ceases 
to  do  so  save  in  a  derivative  and  analysable  sense. 
Even  though  there  were  no  "change"  in  the  ordinary 
sense  of  the  word,  i.e.  if  every  fresh  slice  of  existence 
were  qualitatively  indistinguishable  from  all  its  pre- 
decessors, there  would  be  this  continual  becoming. 
But,  so  long  as  this  absolute  feature  in  Time  is  recog- 
nised, there  seems  no  objection  to  the  Relative  Theory 
as  such.  If  it  has  to  be  rejected,  it  will  not  be  in  favour 
of  the  Absolute  Theory  but  in  favour  of  something  still 
more  relativistic  than  itself. 

A  minor  objection  to  the  Relational  Theory  of  Time, 
as  stated  in  most  mechanics  books,  is  that  it  is  incom- 
plete. Relativists,  as  well  as  other  people,  constantly 
talk  in  practice  of  moments  and  of  several  events 
happening  at  the  same  moment.  For  the  Absolutist, 
of  course,  such  statements  are  literal  expressions  of  fact. 
For  the  Relativist  they  cannot  be  so,  since  he  does  not 
literally  believe  in  the  existence  of  moments.  It  is 
therefore  his  duty  to  give  a  definition  of  what  he  means 


92  SCIENTIFIC.   THOUGHT 

by  "moments,"  which  shall  (a)  be  compatible  with  his 
theory,  and  (/>)  compatible  with  the  common  usage  of 
this  word  by  himself  and  others.  This  duty  he  invari- 
ably shirks.  The  problem  can,  however,  be  solved  by 
the  Method  of  Extensive  Abstraction.  Two  applications 
of  it  will  be  needed:  (i)  to  define  momentary  events 
in  terms  of  finite  events  and  their  relations  of  partial 
overlapping",  and  (2)  to  define  moments.  A  moment  is 
eventually  defined  as  a  class  of  contemporary  momentary 
events.  Thus  the  objection  under  discussion  is  not 
intrinsic  to  the  Relative  Theory  of  Time,  but  only  to 
the  common  presentment  of  it. 

Let  us  now  consider  the  difference  between  the 
Absolute  and  the  Relational  theories  of  Space.  This 
is  much  the  same  as  the  difference  between  the  two 
theories  of  Time.  It  is,  I  think,  harder  to  accept  a 
purely  relative  theory  of  Space,  because  of  certain 
additional  complications  which  turn  up  here.  On  the 
Relational  Theory  spatial  relations  directly  connect  bits 
of  matter,  e.g.  the  theory  says  that  Cambridge  is 
60  miles  N.N.E.  of  London,  and  takes  this  to  be  a 
direct  relation  between  the  two  towns.  The  Absolute 
theory  would  analyse  the  fact  into  three  propositions, 
viz.  :  (1)  London  is  at  a  certain  point  px  of  Absolute 
Space ;  (2)  Cambridge  is  at  a  certain  point  p.,  of 
Absolute  Space  ;  and  (3)  p2  is  60  miles  N.N.E.  of  py* 
The  Absolute  Theory  thus  assumes  certain  entities, 
which  may  be  called  geometrical  points,  in  addition  to 
matter  ;  spatial  relations  directly  connect  these.  They 
only  indirectly  connect  pieces  of  matter  in  so  far  as 
these  are  at  the  geometrical  points  in  question. 

Now  there  is  an  additional  complication  in  the  case 
of  Space  which  is  not  present  with  Time.  Events 
always  have  the  same  temporal  relations  to  each  other ; 
the  Battle  of  Hastings  always  precedes  the  Battle  of 
Waterloo  by  749  years  when  the  latter  Battle  has  once 
become.     But  bits  of  matter  move  about ;  consequently 

*  I  am  neglecting  here  the  motion  of  the  earth. 


THE   TRADITIONAL   KINEMATICS  93 

statements  about  the  distance  from  one  bit  of  matter 
to  another  or  about  the  relative  position  of  two  bits  of 
matter  are  ambiguous.  A  train  travelling  from  London 
to  Edinburgh  by  the  East  Coast  Route  is  sometimes 
to  the  East  of  London  and  sometimes  to  the  West  of 
it,  and  is  constantly  at  different  distances  from  it.  The 
way  in  which  the  Absolute  Theory  deals  with  these 
facts  is  the  following :  It  holds  that  the  points  of 
Absolute  Space  have  to  each  other  purely  geometrical 
relations  which  are  wholly  independent  of  Time.  It 
puts  the  burden  of  change  on  the  relation  at,  which 
connects  bits  of  matter  with  points  of  Space.  What 
it  says  is  that  at,  in  the  present  sense,  is  a  three-term 
relation  which  always  connects  a  bit  of  matter,  a 
geometrical  point,  and  a  moment  of  Time.  The 
simplest  statement  that  you  can  make  about  the  position 
of  a  bit  of  matter  is  that  it  is  at  such  and  such  a 
point  at  such  and  such  a  moment.  Another  way  of 
putting  it  is  that  the  presence  of  a  bit  of  matter  at  a 
geometrical  point  is  an  event,  and  that,  like  all  events, 
this  occupies  a  certain  moment  of  Absolute  Time.  The 
relation  of  being  at  a  point  at  a  moment  is  held  to 
have  certain  properties,  which  are  just  worth  mention- 
ing. (1)  Two  bits  of  matter  cannot  be  at  the  same 
point  at  the  same  moment.  This  property  expresses 
the  impenetrability  of  matter.  (2)  One  bit  of  matter 
cannot  be  at  two  different  points  at  the  same  moment. 
(The  only  alleged  exception  to  this  is  the  Body  and  Blood 
of  Christ  in  the  Celebration  of  the  Eucharist.)  (3)  If  one 
bit  of  matter  is  at  two  different  points  at  two  different 
moments  it  must  be  at  a  continuous  series  of  inter- 
mediate points  at  the  intermediate  moments.  This 
expresses  the  fact  that  bits  of  matter  do  not  suddenly 
leave  one  place  and  afterwards  turn  up  at  another 
without  following  a  path  from  the  first  to  the  second. 
(4)  Every  bit  of  matter  is  at  some  point  or  other  at  all 
moments.  This  expresses  the  indestructibility  of  matter. 
Now   all   these    propositions    certainly   express    im- 


04  SCIENTIFIC  THOUGHT 

portant  alleged  facts  which  arc  commonly  believed  to 
he  true  of  matter,  and  any  theory  must  contain  them 
in  some  form.  On  the  Relational  Theory  of  Space 
it  is  clear  that  they  will  need  a  great  deal  of  rein- 
terpretation,  since  that  theory  believes  neither  in 
geometrical  points,  nor  in  moments,  in  the  literal  senses 
of  those  words.  It  follows  that  if  the  Relational  Theory 
of  Space  is  to  be  of  the  slightest  use,  it  must  give 
meanings  to  all  these  statements  which  (a)  shall  not 
imply  the  literal  existence  of  points  or  moments,  and 
(/>)  shall  nevertheless  be  equivalent  in  practice  to 
these  propositions.  I  need  scarcely  say  that  writers  of 
mechanics  books,  who  start  by  telling  their  readers  that 
Space  is  relative,  never  attempt  to  recast  these  state- 
ments in  terms  of  their  theory,  and  never  even  mention 
or  apparently  recognise  the  need  of  doing  so. 

Now  this  fact,  that  things  move  about,  at  once 
introduces  a  difficulty  into  the  notion  of  distance  and 
relative  position  on  the  Relational  Theory.  We  very 
often  need  to  know  the  distance  between  one  thing  at 
one  moment  and  another  thing  at  another  moment. 
When  we  try  to  measure  the  velocity  of  anything  it 
is  evidently  necessary  to  know  the  distance  between 
one  piece  of  matter  at  the  time  of  starting  and  another 
piece  of  matter  at  the  time  of  arrival.  Again,  if  we 
use  a  measuring  rod  which  has  to  be  taken  up  and 
laid  down  several  times  between  A  and  B,  it  is  clear 
that  what  we  directly  measure  is  neither  the  distance 
between  A  and  B  at  tx  (the  moment  when  we  begin  to 
measure)  nor  the  distance  between  A  and  B  at  tt  (the 
moment  when  we  cease  to  measure).  If  in  certain 
cases  the  measured  distance  is  held  to  agree  with  the 
momentary  distance  this  must  be  a  matter  of  inference, 
and  it  will  be  necessary  for  the  Relational  Theory  to 
state  and  justify  the  assumptions  made  and  the  conven- 
tions used  in  drawing  these  inferences. 

Now  the  Absolute  Theory  can,  of  course,  give  a 
perfectly   definite    meaning   to   the    distance    between    a 


THE  TRADITIONAL   KINEMATICS  95 

body  at  one  moment  and  the  same  or  a  different  body 
at  another  moment.  What  it  says  is  that  the  distance 
required  is  the  distance  between  the  place  where  the 
one  body  was  at  the  first  moment  and  the  place  where 
the  other  body  is  at  the  second  moment.  In  ordinary 
life  we  do  constantly  use  this  phraseology  ;  but  we 
forget  that,  whilst  it  has  a  literal  meaning  on  the 
Absolute  Theory,  it  needs  to  be  given  a  meaning  on 
the  Relative  Theory.  For,  on  that  theory,  the  primary 
meaning  of  distance  is  distance  between  two  bodies  at 
the  same  moment.  And,  as  soon  as  this  is  seen,  we 
see  further  that  the  relative  theory  of  Space  cannot  be 
complete  without  some  criterion  of  simultaneity  at 
different  places.  This  example  brings  out  rather  well 
the  characteristic  merits  and  defects  of  each  type  of 
theory.  The  Absolute  Theory  does  give  a  definite 
meaning  to  the  notion  of  distance  between  two  bodies 
at  different  moments  ;  but,  since  we  certainly  cannot 
perceive  points  of  Absolute  Space,  it  fails  to  explain 
how  we  ever  know  that  we  are  measuring  distance  in 
the  sense  defined.  On  the  other  hand  the  Relational 
Theory  gives  a  clear  meaning  only  to  the  notion  of 
distance  between  two  bodies  at  the  same  moment  ;  and 
this  is  not  enough  for  practical  or  scientific  purposes. 
But  it  does  stick  to  bodies,  that  is  to  things  that  we  can 
actually  perceive  and  deal  with. 

It  is  pretty  evident  that  the  Relational  Theory 
suffers  from  not  being  thorough  enough,  and  not  fully 
recognising  its  responsibilities.  It  ought  to  start  with 
events,  and  to  take  the  relation  of  distance  between 
contemporary  events  as  fundamental.  The  notion  of 
bodies  and  of  the  distances  between  bodies  at  different 
times  will  have  to  be  built  on  this  basis  ;  you  cannot 
take  either  Space  or  Time  or  Matter  as  something  given. 
There  is  a  common  matrix  out  of  which  the  concepts 
of  all  three  are  developed  by  experience  and  reflection 
thereon.  The  Relational  Theory  needs  to  define  some 
sense  of  Space,  which  shall  still  be  relative  but  shall  not 


96  SCIENTIFIC   THOUGHT 

be  merely  momentary.  Science  and  common-sense 
require  a  Space  which  shall  be  timeless,  in  the  sense 
of  enduring  unchanged  throughout  Time  :  a  collection 
of  momentary  Spaces  is  not  enough.  It  is  one  of  the 
great  merits  of  Whitehead  to  have  grasped  this  point. 
The  Absolute  Theory  does  offer  us  a  timeless  Space  ; 
but,  as  this  can  neither  be  perceived  nor  inferred 
causally  from  what  is  perceptible,  it  is  rather  like 
the  offer  of  a  gold  brick  or  a  Castle  in  Spain.  The 
Relational  Theory  (whatever  may  be  its  pretensions) 
only  offers  us  a  collection  of  momentary  Spaces. 
This  has  at  least  two  disadvantages:  (i)  that  strictly 
momentary  relations  between  bodies  can  no  more 
be  directly  observed  than  distances  between  points  of 
Absolute  Space  ;  and  (2)  that  motion  becomes,  not 
change  of  position  within  a  Space,  but  a  movement  out 
of  one  momentary  Space  into  another  momentary  Space. 
The  Relational  Theory  can  hardly  solve  these  unsettled 
problems  without  raising  precisely  those  questions 
which  lead  on  to  the  Special  Theory  of  Relativity. 

We  will  now  desert  the  subject  of  Absolute  v. 
Relative  Space,  as  such,  for  the  present,  and  consider 
those  arguments  on  the  subject  which  depend  on  the 
question  of  Absolute  v.  Relative  Motion.  It  is  doubtful 
whether  people  would  ever  have  worried  their  heads 
greatly  about  Absolute  Space  and  Time,  had  it  not  been 
that  there  seemed  to  be  very  grave  difficulties  about 
purely  relative  motion.  The  question  has  really  arisen 
twice  in  the  history  of  modern  physics,  first  at  the 
foundation  of  the  classical  dynamics  by  Galileo  and 
Newton,  and  then  again  in  connexion  with  electro- 
dynamics in  quite  recent  years. 

It  is  usual  for  scientific  writers  with  a  tincture  of 
philosophy  to  talk  as  if  plain  common-sense  unhesitat- 
ingly holds  motion  to  be  purely  relative,  and  as  if 
it  were  only  persons  debauched  by  metaphysics  who 
believe  in  absolute  motion.  This  is  of  course  a  pro- 
found mistake.     It  is  indeed  true   that  the    plain  man 


THE   TRADITIONAL   KINEMATICS  97 

does  not  mean  by  motion  absolute  motion  as  defined 
by  Newton.  But  he  is  perhaps  even  more  shocked  by 
the  theory  that  all  motion  is  purely  relative,  when  once 
the  logical  consequences  of  that  theory  are  explained 
to  him.  Naturally,  the  scientific  theories  both  of 
absolute  and  of  relative  motion  are  highly  abstract 
intellectual  analyses  of  facts  which  the  plain  man  is 
content  to  see  and  feel  without  analysing.  Still,  it 
would  not  be  going  too  far  to  say  that  the  analysis 
offered  by  the  absolute  theory  seems  to  common-sense 
nearer  to  the  facts  than  that  proposed  by  the  Relationists. 
This  is  hidden  by  the  very  half-hearted  and  obscure 
way  in  which  most  Relationists  state  their  views  ;  in 
practice  it  is  almost  as  difficult  to  take  a  consistently 
relational  view  about  motion  as  it  is  to  bear  constantly 
in  mind  the  fact  that  men  at  the  antipodes  do  not  have 
the  uncomfortable  feeling  that  we  should  have  if  we 
were  hanging  head  downwards  with  our  feet  fixed  to 
the  ceiling.  Let  us  then  try  to  state  the  two  theories 
clearly  and  to  draw  their  logical  consequences.  Absolute 
motion  is  the  passing  of  a  body  from  one  point  of 
Absolute  Space  to  another.  Absolute  rest  is  the 
remaining  of  a  body  at  a  point  of  Absolute  Space. 
Relative  motion  has  the  same  meaning  on  both 
theories  ;  it  is  just  a  change  in  the  relative  positions 
of  two  bodies.  The  difference  about  it  is  that  the 
Relationists  say  that  all  motion  simply  is  a  change  in 
the  spatial  relations  of  one  body  to  others,  whilst  the 
Absolutists  say  that  there  is  absolute  as  well  as  relative 
motion  and  that  the  two  must  be  distinguished  from 
each  other.  On  the  Absolute  Theory  all  relative  motion 
implies  absolute  motion,  and  is  the  appearance  of  it  to 
us,  but  a  knowledge  of  relative  motion  does  not  suffice 
to  determine  unambiguously  the  absolute  motions 
involved.  Thus,  suppose  that  A  and  B  are  two  bodies, 
and  that  u  is  the  rate  at  which  the  distance  between 
them  is  increasing.  Then  u  is  a  relative  velocity.  The 
Absolutist  says  that  it  must  be  due  to  absolute  motions 


98  SCIENTIFIC   THOUGHT 

in  A  or   in    B  or  in  both,  and   that  all  that  we  can   say 
about  thorn  is  that  their  difference  is  equal  to  u. 

Now  the  point  at  which  the  purely  relative  theory  of 
motion  conflicts  with  common-sense  is  that  it  will  never 
allow  you  to  say  of  any  two  bodies  that  one  is  moving 
and  that  the  other  is  at  rest.  Distance  between  A  and 
B  is  a  perfectly  mutual  relation  ;  if  the  distance  between 
A  and  B  increases  at  a  certain  rate  the  distance  between 
B  and  A  ipso  facto  increases  at  the  same  rate.  If  then 
motion  just  means  rate  of  change  of  distance  between 
bodies  there  is  no  sense  in  saying  that  A  moves  and  B 
stands  still.  Suppose  now  that  I  am  the  body  A  and 
that  B  is  the  wall  of  the  room.  Common-sense  is 
perfectly  sure  that  I  move  and  that  the  wall  stands 
still.  But  for  the  consistent  Relativist  this  is  simply 
nonsense  ;  it  is  true  in  precisely  the  same  sense,  and 
in  the  only  sense  in  which  he  admits  motion,  that  the 
wall  moves  towards  me.  Thus  common-sense  seems 
here  to  be  much  more  on  the  side  of  the  Absolutist 
than  on  that  of  the  Relationist.  It  quite  admits  that, 
in  particular  cases,  it  is  difficult  or  impossible  to  tell  in 
what  proportions  a  particular  relative  motion  ought  to 
be  divided  between  the  two  bodies,  but  it  is  quite 
convinced  that  in  ever^  case  there  is  a  genuine  meaning 
in  the  question  :  What  is  the  real  velocity  of  each  body  ? 
This  question,  as  we  have  seen,  has  a  perfectly  definite 
meaning  on  the  Absolute  Theory,  but  its  meaning  is 
not  obvious  on  the  Relational  Theory. 

Of  course  I  do  not  regard  this  common-sense  objec- 
tion as  at  all  conclusive,  for  I  think  that  the  Relationist 
can  make  a  fairly  satisfactory  answer  to  it.  He  will 
say:  "You  think  that  certain  bodies  are  absolutely  at 
rest  and  others  in  motion,  not  because  there  is  really 
anything  but  relative  motion,  but  because  you  tacitly 
assume  a  certain  body  for  relating  all  others  to."  This 
body,  for  the  ordinary  man,  is  the  earth.  He  says 
that  the  wall  is  at  rest  because  it  does  not  move  relatively 
to   the    surface  of  the  earth  ;   he  says  that  he  himself 


THE   TRADITIONAL   KINEMATICS  99 

moves  because  he  does  change  his  position  with  respect 
to  this  body  of  reference.  It  is  very  easy  to  forget 
about  a  relation  altogether  if  we  always  tacitly  relate  to 
the  same  term  in  a  whole  series  of  judgments.  If  our 
common-sense  friend  replies  that  when  he  moves  he 
gets  tired,  whilst  when  other  things  move  and  he 
stands  still  he  does  not  get  tired,  the  Relativist  can 
easily  deal  with  this  objection.  He  will  say:  "All 
motion  is  relative,  and  all  relative  motions  are  equally 
genuine  facts  ;  but  they  do  not  all  have  the  same  effects. 
When  you  and  the  earth  move  relatively  to  each  other 
effects  are  produced  in  your  body,  but  when  you  rest 
relatively  to  the  earth  and  merely  move  with  respect  to 
other  things  which  are  themselves  in  motion  with 
respect  to  the  earth,  such  as  tram-cars,  no  such  effects 
are  produced.  This  is  just  a  law  of  nature  which  we 
have  to  recognise." 

So  far  the  Relationist  has  a  perfectly  good  case. 
It  is  when  we  come  to  deal  with  mechanics,  and 
particularly  with  rotation,  that  his  difficulties  begin 
to  accumulate.  We  will  deal  with  rotation  first, 
because  it  can  be  discussed  without  any  knowledge  of 
the  laws  of  mechanics,  and  because  it  furnished  Newton 
with  one  of  his  strongest  arguments  in  favour  of  absolute 
rotation.  Suppose  that  you  take  a  pail  of  water  and 
hang  it  up  by  a  string,  then  twist  the  string  a  number 
of  times  and  let  it  untwist  itself.  The  pail  will,  of 
course,  spin  rapidly  round  its  axis.  At  first  the  water 
will  not  spin,  but  gradually  it  will  take  up  the  spinning 
movement  of  the  pail,  and  eventually  the  water  and 
the  pail  will  be  spinning  as  one  rigid  body.  Now  stop 
the  pail.  The  water  will  go  on  spinning  for  some  time 
till  it  is  gradually  brought  to  rest  by  friction.  Now 
what  we  have  to  notice  is  this  :  At  the  beginning  of 
the  experiment,  i.e.  when,  in  ordinary  language,  the 
bucket  is  spinning  and  the  water  is  still  at  rest,  the 
water  has  its  maximum  velocity  of  rotation  with  respect 
to  the  pail.     And  at  this  stage  the  surface  of  the  water 


ioo  SCIENTIFIC   THOUGHT 

is  quite  flat.  At  the  second  stage  of  the  experiment, 
when,  in  ordinary  language,  we  should  say  that  the 
water  had  picked  up  the  speed  of  rotation  of  the  pail, 
the  water  has  no  rate  of  rotation  with  respect  to  the 
pail.  Yet  at  this  stage  the  surface  of  the  water  is 
depressed  in  the  middle,  so  that  it  becomes  a  paraboloid 
of  revolution.  Now  we  all  say  that  this  depression  is 
due  to  the  rotation  of  the  water.  But,  if  we  confine 
ourselves  to  relative  rotation,  we  see  that  the  depression 
was  nil  when  the  relative  rotation  was  a  maximum,  and 
that  it  was  a  maximum  when  the  relative  rotation  is  nil. 
If  we  now  pass  to  the  next  stage  of  the  experiment, 
where,  in  ordinary  language,  the  pail  has  been  brought 
to  rest  and  the  water  is  still  rotating,  we  have  again  a 
maximum  rate  of  relative  rotation,  but  this  is  now 
accompanied  by  a  maximum  depression  in  the  surface 
of  the  water.  Thus  there  seems  to  be  no  regular  con- 
nexion between  relative  rotation  and  depression  at  all  ; 
for  the  depression  can  be  a  maximum  both  when  there 
is  no  relative  rotation  and  when  the  relative  rotation  is 
a  maximum,  and  the  depression  can  be  nil  both  when 
there  is  maximum  relative  rotation — as  at  the  beginning 
— and  when  there  is  no  relative  rotation  —  as  at  the 
end  of  the  experiment. 

These  are  the  facts  which  led  Newton  to  hold  that 
we  must  distinguish  between  absolute  and  relative 
rotation.  The  argument  comes  to  this  :  If  we  take  all 
rotation  to  be  simply  and  solely  the  rotation  of  one  body 
with  respect  to  another  we  can  find  no  general  law 
connecting  rotation  with  depression.  Yet  we  are  all 
agreed  that  in  some  sense  the  depression  is  due  to 
the  rotation.  Newton's  suggestion  was  that  absolute 
rotation,  and  it  alone,  produces  physical  changes  like 
the  depression  of  the  water  in  the  pail  and  the  flattening 
of  the  earth  at  the  poles.  It  is  true  that  we  can  observe 
only  the  relative  rotations  of  bodies ;  but  these  are 
appearances  of  absolute  rotations,  and  by  studying  and 
measuring  such  physical    consequences   as   depression 


THE   TRADITIONAL   KINEMATICS  101 

and  flattening  we  can  ascribe  to  each  of  the  bodies  its 
proper  amount  of  absolute  motion. 

Now  of  course  the  facts  on  which  Newton  based 
his  argument  are  genuine  and  very  important.  But 
they  certainly  do  not  necessitate  Newton's  conclusion, 
although  that  is  no  doubt  one  way  of  explaining  them. 
They  can  equally  well  be  explained  without  recourse  to 
absolute  motion.  If  we  reflect,  we  shall  see  that  it  is 
logically  impossible  that  premises  which  are  wholly 
about  bodies,  such  as  water  and  pails,  and  about  their 
shapes  and  relative  motions,  could  necessitate  con- 
clusions about  something  entirely  different,  viz.,  Absolute 
Space  and  Absolute  Time.  By  a  logical  argument  you 
may  learn  of  new  relations  between  the  terms  that  are 
mentioned  in  the  premises,  but  you  cannot  possibly 
learn  about  the  existence  of  other  terms  of  a  quite 
different  kind  from  any  that  were  mentioned  in  the 
premises.  So  we  can  see  at  once,  from  purely  logical 
considerations,  that  Newton's  argument  cannot  neces- 
sitate a  belief  in  absolute  motion.  What  we  can 
legitimately  argue  is  that,  if  there  be  such  things  as 
absolute  Space,  Time,  and  Motion,  it  is  in  rotation  that 
they  first  disclose  themselves  by  producing  observable 
effects  in  matter,  and  that  by  studying  these  phenomena 
we  may  be  able  to  detect  the  presence  and  measure  the 
magnitude  of  the  absolute  motion  of  each  body. 

But,  as  I  have  said,  the  Relationist  can  interpret  the 
pail  experiment  in  terms  of  his  theory.  If  we  reflect 
carefully  on  the  results  of  that  experiment,  we  see  that 
all  that  it  tells  us  is  that  one  particular  relative  rotation 
is  not  connected  by  any  simple  law  with  the  depression 
of  the  water  in  the  pail.  It  shows  that  the  relative 
rotation  of  water  and  bucket  is  irrelevant.  It  does  not 
in  the  least  follow  that  no  relative  rotation  is  relevant. 
At  the  beginning  of  the  experiment  the  water  was  at 
rest  relatively  to  the  fixed  stars,  at  the  middle  it  was 
rotating,  and  at  the  end  it  was  again  at  rest  with  respect 
to  them.     What  the  Relationist  must  say  is  therefore 


102  SCIENTIFIC   THOUGHT 

the  following:  "There  is  nothing  but  relative  rotation, 
and  any  body  that  you  choose  to  mention  has  at  one 
and  the  same  time  all  sorts  of  different  relative  rotations  ; 
for  instance,  the  water  at  the  beginning  is  rotating  with 
respect  to  the  pail  and  is  at  rest  with  respect  to  the  fixed 
stars.  Each  of  these  states  of  motion  is  equally  real 
and  there  is  no  incompatibility  between  them,  because 
they  are  not  properties  of  the  water  alone  but  are 
relations  between  it  and  other  things.  It  is  no  more 
unreasonable  to  say  that  the  water  is  at  once  at  rest  and 
in  motion  than  it  is  to  say  that  a  man  is  at  once  a  father 
and  a  son  ;  it  only  seems  odd  because  we  are  haunted 
by  the  ghost  of  the  Absolute  Theory.  But  of  all  these 
various  equally  real  and  co-existing  motions  some  only 
are  connected  by  simple  laws  with  physical  changes  in 
the  water.  Relative  rotation  between  the  water  and  the 
fixed  stars  causes  depression  of  the  surface  of  the  latter  ; 
relative  rotation  between  the  water  and  the  walls  of  the 
pail  causes  no  such  depression  if  the  water  be  at  rest 
with  respect  to  the  fixed  stars."  This  answer  of  the 
Relationist  seems  to  me  to  be  perfectly  compatible 
with  all  the  facts  of  the  pail  experiment  and  to  be 
perfectly  consistent  with  itself. 

I  will  now  consider  certain  objections  which  have 
been  brought  against  this  interpretation  of  the  facts. 

(i)  It  is  sometimes  said:  Suppose  the  water  stayed 
still  and  that  the  fixed  stars  rotated  round  it ;  the  water 
would  be  moving  relatively  to  the  fixed  stars.  On  the 
above  explanation  the  water  ought  to  be  depressed. 
Is  it  reasonable  to  suppose  that  the  mere  rotation  of 
the  fixed  stars  would  have  any  effect  on  the  water  in 
the  pail?  This  objection  is  merely  silly  and  circular. 
It  is  based  on  an  assumption  which  has  a  meaning  on 
the  Absolute  Theory  and  no  meaning  at  all  on  the 
Relational  Theory.  On  the  Absolute  Theory  there  is 
a  sense  in  distinguishing  between  the  case  where  the 
water  rotates  and  the  stars  keep  still  and  the  case  where 
the  stars  rotate  and  the  water  keeps  still.      But  the  dis- 


THE   TRADITIONAL   KINEMATICS  103 

tinction  is  meaningless  on  the  Relational  Theory.  The 
argument  in  question  is  therefore  irrelevant  as  opposed 
to  the  Relational  Theory.  It  is  really  circular,  for  its 
premise  only  has  a  meaning  for  a  man  who  has  already 
rejected  the  Relative  Theory,  and,  therefore,  it  cannot 
consistently  be  used  as  an  argument  against  this 
theory. 

(2)  A  stronger  objection  is  the  following:  Even 
if  the  sky  had  always  been  covered  with  thick  clouds, 
so  that  the  fixed  stars  had  never  been  observed, 
we  could  still  have  discovered  that  the  earth  rotates, 
have  determined  its  axis,  and  have  measured  its  rate 
of  rotation  by  means  of  the  gyrostatic  compass  and 
Foucault's  pendulum.  What  is  it  that  we  discover  and 
measure  in  such  cases  if  it  be  not  the  absolute  rotation 
of  the  earth  ?  How  can  it  be  the  rotation  of  the  earth 
relative  to  the  fixed  stars,  since  they  do  not  come  into 
the  question  at  all?  I  think  that  this  objection  is 
fallacious,  but  it  needs  a  little  reflection  to  answer  it. 
I  will  take  the  case  of  Foucault's  pendulum  ;  and  neglect 
the  gyrostatic  compass,  which  is  harder  to  discuss 
without  mathematics.  It  will  suffice  to  say  that  the 
answer  that  I  shall  give  about  Foucault's  pendulum, 
if  valid  at  all,  will  apply  equally  to  the  gyrostatic 
compass. 

To  simplify  matters  we  will  suppose  that  the  compass 
is  hung  up  at  the  North  Pole  and  started  swinging. 
Make  a  chalk  mark  on  the  ground  where  the  plane  in 
which  the  pendulum  starts  swinging  cuts  the  earth. 
As  time  goes  on  you  will  find  that  the  pendulum  no 
longer  swings  in  this  plane  ;  if  you  draw  another  such 
chalk  line  it  will  make  an  angle  with  the  first.  In 
fact,  the  plane  will  slowly  rotate,  and  the  time  of  its 
rotation  will  be  twenty-four  hours.  If  this  experiment 
be  done  anywhere  else  on  the  earth,  analogous  results 
will  be  got.  The  actual  measurements  will  depend  on 
the  latitude,  and  it  will  be  found  that  they  are  all 
connected  with  each  other  and  with  the  latitude  by  a 


104  SCIENTIFIC   THOUGHT 

simple  law.  The  fact  to  be  noticed  is  that  what  has 
been  measured  in  all  cases  is  a  relative  rotation  between 
the  plane  of  swing-  of  the  pendulum  and  the  earth's 
surface.  Let  us  suppose  that  the  sky  were  always 
covered  with  thick  clouds  so  that  the  fixed  stars  coidd 
never  be  seen.  What  people  would  probably  have 
said  would  be  the  following:  "All  pendula  slowly 
rotate  their  planes  of  rotation  with  respect  to  the 
earth,  and  the  way  in  which  they  do  this  at  different 
places  follows  a  simple  law." 

Now,  if  motion  be  purely  relative,  this  is  precisely 
equivalent  to  saying  that  the  surface  of  the  earth  rotates 
with  respect  to  the  planes  of  swinging  pendula.  It 
follows  that  a  perfectly  clear  meaning  could  have  been 
given  to  the  rotation  of  the  earth  on  the  Relative 
Theory,  even  if  no  stars  had  ever  been  observed. 
Suppose  some  speculative  scientist  had  said:  "There 
may  be  other  bodies  beyond  those  thick  clouds  ;  if  so, 
does  the  earth  rotate  at  the  same  rate  with  respect  to 
them?"  Of  course,  no  answer  could  have  been  given. 
We  who  can  see  the  fixed  stars  know  that  the  planes 
in  which  pendula  swing  do  not  rotate  with  respect  to 
them,  and  we  therefore  know  that  the  rotation  of  the 
earth  or  of  any  other  body  with  respect  to  the  plane 
of  swing  of  a  pendulum  is  the  same  as  its  rotation 
with  respect  to  the  fixed  stars.  This  particular  fact 
of  nature  would,  of  course,  have  been  hidden  from  us 
if  we  had  never  seen  the  stars ;  but  otherwise  we 
should  be  in  exactly  the  same  position  as  we  are  in 
now.  We  can  say:  "The  earth  rotates  at  such  and 
such  a  rate  both  with  respect  to  the  fixed  stars  and 
with  respect  to  the  planes  of  pendula."  Men  who  had 
never  seen  the  fixed  stars  could  only  make  the  latter 
part  of  this  assertion.  We  know  an  extra  fact  which 
they  do  not,  but  what  each  of  us  knows  is  equally  about 
relative  rotation. 

(3)  The  third  objection  is  one  that  is  constantly 
mixed   up  with  the  one  that  has  just  been  discussed, 


THE   TRADITIONAL   KINEMATICS  105 

but  really  is  quite  different  from  it.  It  is  said:  "If 
there  were  no  fixed  stars  the  earth  could  not  be  rotating 
with  respect  to  them.  Now  you  say  that  it  is  rotation 
with  respect  to  the  fixed  stars  which  causes  the  flatten- 
ing of  the  earth  at  the  poles  and  the  depression  of  the 
water  in  a  rotating  pail.  Can  you  seriously  maintain 
that,  if  the  fixed  stars  were  annihilated,  the  earth  would 
become  perfectly  spherical  and  the  water  in  the  pail 
perfectly  flat?  You  certainly  ought  to  hold  this.  For 
you  say  that  the  cause  of  the  depression  of  the  water 
is  its  rotation  with  respect  to  the  fixed  stars.  If  the 
fixed  stars  ceased  to  exist,  this  relative  rotation  would 
ipso  facto  vanish  too.  The  alleged  cause  of  the  depres- 
sion having  thus  ceased  to  exist,  we  may  presume  that 
the  depression  itself  would  cease  too." 

Before  discussing  this  argument,  I  want  to  point 
out  its  precise  connexion  with  the  previous  one,  and 
the  cause  of  the  frequent  confusion  between  the  two. 
The  present  argument  deals  with  the  physical  causation 
of  such  phenomena  as  the  flattening  of  the  earth  at  the 
poles,  and  the  depression  of  the  water  in  a  spinning 
pail.  It  points  out  an  implication  of  the  Relational 
Theory  which  its  supporters  are  very  liable  to  forget. 
The  theory  says  that  the  cause  of  such  phenomena  is 
the  rotation  of  the  earth  or  the  pail  with  respect  to 
some  other  body  or  bodies.  Now,  if  this  is  to  be 
literally  true,  it  would  seem  that  the  existence  of  one 
at  least  of  the  assigned  bodies  of  reference  must  be  an 
essential  part  of  the  cause  of  the  physical  phenomena 
in  question.  Relationists  are  inclined  to  regard  the 
fixed  stars,  or  whatever  frame  of  reference  they  may 
happen  to  use,  as  mere  axes  of  reference,  and  in  no 
sense  causal  factors.  The  present  argument  shows 
that  this  is  inconsistent.  To  square  the  Relational 
Theory  with  the  facts,  it  is  necessary  to  hold  that  certain 
relative  motions  stand  out  from  all  others  in  producing 
observable  physical  consequences.  Now  these  out- 
standing relative  motions  are  those  which  bodies  have 

H 


106  SCIENTIFIC   THOUGHT 

witli  respect  to  certain  bits  of  matter,  such  as  the  fixed 
stars.  These  particular  bits  of  matter  are  thus  put  in 
a  unique  position  among  all  other  bodies.  Motion 
with  respect  to  any  one  of  this  particular  set  of 
bodies  produces  physical  phenomena  ;  otherwise  similar 
motions  with  respect  to  other  bodies  do  not  produce 
similar  physical  consequences.  Thus  the  existence  of 
this  privileged  set  of  bodies  is  an  essential  factor  in 
the  production  of  these  particular  physical  phenomena, 
and  we  have  no  right  to  suppose  that  these  phenomena 
would  continue  to  happen  if  all  the  bodies  in  this 
set  were  annihilated.  (It  is  not  necessary  to  suppose 
that  the  existence  of  any  one  member  of  the  set,  e.g. 
the  fixed  stars,  is  essential.  What  does  seem  to  be 
essential  is  that  there  should  be  at  least  one  member  of 
the  set,  though  it  is  immaterial  which  particular  one 
it  may  be.)  This  is  the  basis  of  the  present  argument, 
and  the  force  of  it  is  that  it  is  hard  to  believe  that 
the  existence  of  a  certain  privileged  set  of  bodies  is  a 
necessary  condition  of  the  flattening  of  the  earth  or  the 
depression  of  the  water. 

Now  the  previous  argument  was  not  about  physical 
causation,  but  was  about  the  meaning  of  and  the 
evidence  for  the  statement  that  the  earth  rotates.  It 
suggested  that,  since  we  could  know  that  the  earth 
rotates  and  measure  the  rate  at  which  it  does  so,  even 
though  we  had  never  seen  the  fixed  stars,  we  cannot 
mean  by  the  statement  that  the  earth  rotates  simply 
that  it  does  so  with  respect  to  the  fixed  stars.  And  it 
concluded  from  this  that,  when  we  talk  of  the  rotation 
of  the  earth,  we  must  mean  absolute  rotation,  and  that 
we  must  be  able  to  detect  and  measure  it  by  observations 
made  on  purely  terrestrial  bodies.  As  we  have  seen, 
the  premise  of  this  argument  and  the  first  part  of  its 
conclusion  are  true,  but  its  final  conclusion  does  not 
follow.  What  we  observe  in  these  purely  terrestrial 
experiments  is  still  relative  rotation,  and  what  men  who 
could  not  see  the  fixed  stars  would   mean  when   they 


THE   TRADITIONAL   KINEMATICS  107 

said  that  the  earth  revolved,  would  be  that  it  does  so 
with  respect  to  the  plane  of  a  swinging  pendulum. 
We  who  can  observe  the  fixed  stars  have  found  out  the 
additional  fact  that  the  rotation  of  the  earth  with  respect 
to  them  is  the  same  as  its  rotation  with  respect  to  a 
pendulum  swinging  at  the  North  Pole. 

The  arguments,  then,  are  entirely  different.  Why 
is  it  that  they  are  so  often  mixed  up?  I  think  the 
reason  is  the  following  :  It  is  thought  that,  since  you 
could  find  out  the  rotation  of  the  earth  without  knowing 
anything  about  the  fixed  stars,  therefore  the  fixed  stars 
cannot  be  an  essential  part  of  the  cause  of  such 
phenomena  as  the  flattening  of  the  earth.  This  is, 
however,  a  very  bad  argument.  We  can  find  out  a 
good  deal  about  the  symptoms  and  treatment  of 
influenza,  though  no  one  has  ever  seen  an  influenza 
germ.  This  does  not  prove  that  these  symptoms  do 
not  depend  on  a  germ,  or  that  they  would  not  cease 
altogether  if  the  germ  were  exterminated. 

Having  cleared  up  the  connexions,real  and  imaginary, 
between  these  two  arguments,  let  us  consider  the  second 
of  them.  Several  answers  might  be  made  to  it.  The 
first,  which  was  made  by  Mach,*  seems  to  me  to  be 
logically  sound,  and  to  contain  an  important  truth, 
though — as  I  shall  point  out  later — it  does  not  altogether 
satisfy  our  physical  instincts.  The  argument  that  we 
are  discussing  appeals  to  our  conviction  that  such 
remote  bodies  as  the  fixed  stars  cannot  really  be 
essential  factors  in  the  causation  of  purely  terrestrial 
phenomena  like  the  flattening  of  the  earth  and  the 
depression  of  the  water  in  the  pail.  Now  Mach's 
answer  is  to  say  that  this  conviction  is  a  mere  prejudice, 
and  to  point  out  how  this  prejudice  arose.  Mach  says 
that  we  have  really  not  the  least  idea  what  would 
happen  if  the  fixed  stars  were  annihilated,  and  that 
therefore  we  have  no  right  to  suppose  that  the  earth 
would  still  be  flattened  and  the  water  still   depressed 

*  Science  of  Mechanics. 


ioS  SCIENTIFIC   THOUGHT 

after  such  a  cosmic  upheaval.  Mach's  grounds  for 
this  assertion  seem  to  me  to  be  sound.  They  are  as 
follows  :  The  laws  of  motion  and  all  other  scientific 
laws  have  been  discovered  and  verified  in  a  world 
which,  as  a  matter  of  fact,  does  contain  the  fixed  stars. 
Our  laws  do  not  make  explicit  mention  of  these  bodies, 
because  they  have  been  a  constant  factor,  and  are 
assumed  to  be  going-  to  be  a  constant  factor  in  all 
predictions  which  we  make  by  means  of  these  laws. 
But,  though  constant  factors  need  not  be  mentioned, 
it  does  not  follow  that  they  are  causally  irrelevant. 
We  say  that  gas  lights  when  you  put  a  match  to  it  ; 
and  we  do  not  as  a  rule  mention  that  air  must  be 
present,  because  it  practically  always  is  present  when 
we  strike  matches  and  attempt  to  light  gas.  Never- 
theless this  constant  factor  is  as  relevant  as  the  matches 
and  the  gas,  and  if  we  argued  that  the  absence  of  air 
would  make  no  difference,  we  should  be  wrong.  You 
can  never  safely  assume  that  any  factor  which  has  been 
present  in  all  cases  under  which  a  law  has  been  verified 
is  irrelevant  to  the  truth  of  the  law,  until  you  have 
produced  a  definite  negative  instance  in  which  this  factor 
was  absent  and  the  law  was  nevertheless  found  still  to 
hold.  Now  we  obviously  cannot  remove  the  fixed 
stars,  spin  a  bucket,  and  see  whether  the  water  is  still 
depressed  in  the  middle.  Therefore  we  have  no  right 
to  feel  so  sure  that  it  still  would  be  depressed  in  the 
middle  if  there  were  no  fixed  stars. 

I  will  now  point  out  why  this  argument,  though 
logically  sound  and  based  on  an  important  general 
principle,  is  liable  to  leave  us  dissatisfied  as  physicists. 
Mach's  answer  accepts  the  view  that  the  flattening  of 
the  earth  and  the  depression  of  the  water  depend  on 
motion  relative  to  the  fixed  stars,  and  that  therefore  the 
existence  of  these  bodies  is  an  essential  factor  in  the 
causation  of  such  phenomena.  Now  we  must  notice 
that,  if  this  be  true,  a  very  peculiar  kind  of  physical 
causation    is  introduced.      It  is  of  such  a  kind  that,   if 


THE   TRADITIONAL   KINEMATICS  109 

there  were  much  of  it  in  the  world,  physics  and  all  other 
experimental  sciences  would  be  impossible.  It  is  a 
fundamental  assumption  in  all  our  practical  work  that 
the  more  distant  a  body  is  the  less  difference  it  makes 
to  the  physical  phenomena  in  a  given  region.  The 
chemist  assumes  that  practically  everything  that  goes 
on  outside  his  laboratory,  and  most  things  that  go  on 
outside  his  test-tube,  are  irrelevant  to  the  phenomena 
inside  his  test-tube.  We  are,  of  course,  prepared  to 
admit  that  possibly  everything  that  happens  anywhere 
has  some  influence  on  everything  else,  and  that  the 
more  delicate  we  make  our  experiments  the  less  we  can 
afford  to  treat  anything  as  irrelevant.  But,  unless  very 
distant  things  could  on  the  whole  be  safely  neglected, 
and  neglected  with  greater  safety  the  further  they  are 
away,  all  experimental  research  would  be  hopeless, 
because  no  phenomenon  would  be  even  approximately 
isolable  from  the  rest  of  the  world.  If  gravitational, 
electric,  and  magnetic  forces  varied  directly  instead  of 
inversely  with  the  square  of  the  distance,  there  would 
be  what  Mr  Mookerjee  very  justly  termed  "a  rare 
hullaballoo  or  pretty  kettle  of  fish. "  Now  Mach's  answer 
does  introduce  a  sort  of  physical  causation  which  is  of 
just  this  objectionable  kind.  The  fixed  stars  are  the 
most  distant  bodies  that  we  know  of,  and  yet  they  are 
an  essential  factor  in  causing  the  flattening  of  the  earth 
and  the  depression  of  the  water.  This  is  why  I  said 
that  the  implications  of  Mach's  answer  contradicted  our 
physical  instincts.  Of  course  it  is  quite  possible  that 
here  our  physical  instincts  are  mere  prejudices.  It  may 
well  be  that  all  the  known  laws  of  nature,  when  fully 
expressed,  involve  two  factors,  viz.,  those  that  we 
actually  mention  and  measure  on  the  one  hand,  and  the 
general  structure  of  the  stellar  universe  on  the  other. 
The  latter  has  kept  fairly  constant  up  to  the  present, 
and  so  we  have  come  to  no  harm  as  yet  by  neglecting 
it  and  confining  ourselves  entirely  to  the  first  factor. 
I  now  turn  to  a  second  possible  answer  to  the  present 


no  SCIENTIFIC  THOUGHT 

objection    to    the    Relational    Theory  of  motion.     I  am 
inclined    to    think    that    Mach's   answer  concedes  more 
than  is  necessary  to  the  opponent.     The  opponent  con- 
fines himself  to  the  fixed  stars,   argues  that  it  is  only 
rotations  with    respect   to    them    that    produce   physical 
consequences  on  the  Relational  Theory,  and  therefore 
confronts  the   Relationist  with  the  conclusion  that  the 
existence  of  the  fixed  stars  must  be  an  essential  factor 
in  the  production  of  these  physical  phenomena.     Mach 
accepts  this   as   a    fair    consequence   of  the    Relational 
Theory,   and   simply  argues  that  it  is   unobjectionable 
for  the   reasons    given  above.     This    seems  to   me  too 
big  a  concession.      I  pointed  out  that  every  body  has  at 
one  and  the  same  time  many  different  relative  motions, 
all  equally  real,  just  as  any  town   has  at  one  and  the 
same  time  any  number  of  different  "  distances."     There 
is  no  kind  of  contradiction  or  inconsistency  in  this  unless 
we    tacitly    smuggle    in    the    idea   of   absolute    motion. 
Now,  if  the  laws  of  Mechanics  be  true,  all  the  motions 
of  all  other  bodies  relative  to  (say)  the  fixed  stars  obey 
a   certain   set  of  rules,   viz.,   Newton's  laws  of  motion, 
or  whatever  modification  of  them   may  be  found  to  be 
necessary.     Suppose  that  a  whole  set  of  bodies  B1?  B2, 
.  .  .   Ba  obey  Newton's  laws  for  all  their  motions  with 
respect  to  the  fixed  stars.     Let  us  select  any  body  Br 
out  of  this  set.     Then  the  motions  of  any  other,   such 
as  B:,  with  respect  to  Br,  could  be  compounded   out  of 
the  motions  of  Bx  and  Br  with  respect  to  the  fixed  stars. 
But,  by  hypothesis,  the  motions  of  both  Bx  and  Br  with 
respect  to  the  fixed  stars  obey  Newton's  laws.      Hence 
the    motions    of   Ba  with  respect  to  Br  must  obey  laws 
which    are    merely    mathematical     transformations     of 
Newton's.      Precisely  the   same   remarks   apply   to   the 
motions  of  any  of  the  other  B's  with  respect  to  Br.     The 
standard  body  Br  might  be  as  wild  as  we  like,  it  might 
be  a  midge  dancing  in  the  sunlight  ;  still,  if  it  and  all 
other  bodies  obey  a  certain  set   of   rules  for   all  their 
movements   with  respect   to    the   fixed    stars,    all  other 


THE   TRADITIONAL   KINEMATICS  in 

bodies  will  obey  a  set  of  rules  for  their  movements  with 
respect  to  it.  No  doubt  these  rules  would  be  of  perfectly 
awful  complexity  if  we  had  chosen  a  midge  instead  of 
the  fixed  stars  as  our  body  of  reference  ;  but  what  does 
this  prove  ?  Only,  so  far  as  I  can  see,  that  we  should 
probably  never  have  discovered  that  all  motions  are 
subject  to  laws  if  we  had  not  had  the  fixed  stars  avail- 
able as  bodies  of  reference.  When  we  say  :  "  It  is  only 
motions  relative  to  certain  bodies  (of  which  the  fixed 
stars  are  typical)  which  obey  the  laws  of  Mechanics," 
this  is  true  in  one  sense  and  false  in  another.  It  is  true 
that  only  such  motions  obey  even  approximately  the 
simple  and  familiar  laws  of  motion  discovered  by  Galileo 
and  Newton.  It  is  not  true  that  motions  with  respect 
to  other  bodies  obey  no  laws,  or  that  the  laws  which 
they  obey  are  incompatible  with  or  independent  of 
Newton's.  The  laws  of  such  motions  must  be  just 
mathematical  transformations,  often  of  unmanageable 
complexity,  of  the  familiar  and  simple  laws  which 
govern  motions  with  respect  to  the  fixed  stars.  This 
seems  to  be  a  necessary  consequence  of  the  two  facts 
(a)  that  all  motions  with  respect  to  the  fixed  stars  are 
subject  to  Newton's  laws,  and  {b)  that  the  motions  of 
any  body  with  respect  to  any  other  can  be  compounded 
out  of  the  motions  of  both  with  respect  to  the  fixed 
stars. 

If  this  argument  be  sound,  we  can  now  give  an 
answer  to  the  present  objection  to  the  Relational  Theory, 
which  shall  accept  all  that  is  true  in  Mach's  answer 
and  shall  not  shock  our  physical  instincts  or  prejudices. 
The  objection,  I  may  once  more  remind  the  reader, 
was  this:  If  the  earth  be  flattened  and  water  in  a 
spinning  pail  depressed  only  through  rotation  with 
respect  to  the  fixed  stars,  then,  if  there  were  no  fixed 
stars,  the  earth  would  not  be  flattened  nor  the  water 
depressed.  We  can  now  see  that  this  consequence 
does  not  really  follow  from  the  Relational  Theory  of 
Motion.     If  you  twisted  the  pail  in  the  absence  of  the 


ri2  SCIENTIFIC  THOUGHT 

fixed  stars  there  would  still  be  relative  motion  between 
ii  and  other  thing's.  It  is  true  that  these  other  relative 
motions  would  not  be  connected  with  the  depression 
of  the  water  by  the  same  simple  laws  which  connect 
that  depression  with  the  rotation  of  the  pail  relative  to 
the  fixed  stars.  But  the  depression  would  be  connected 
with  these  other  relative  motions  by  laws  which  are 
mathematical  transformations  of  these  simpler  ones.  In 
that  sense  it  would  be  true  to  say  that  the  annihila- 
tion of  the  fixed  stars  would  not  necessarily  make  any 
difference  to  the  phenomena.  On  the  other  hand,  we 
can  still  admit  with  Mach  that  it  would  not  be  safe 
to  assume  that  laws  which  have  been  discovered  and 
verified  in  the  presence  of  the  fixed  stars  would  neces- 
sarily continue  to  hold  when  such  a  large  and  important 
part  of  the  material  universe  as  the  fixed  stars  had  been 
annihilated.  The  difference  between  our  answer  and 
Mach's  comes  to  this  :  Mach  accepts  it  as  a  necessary 
consequence  of  the  Relational  Theory  that  the  exist- 
ence of  the  fixed  stars  is  an  essential  condition  of  the 
phenomena  under  discussion  ;  he  then  devotes  himself 
to  showing  that  we  ought  not  to  be  surprised  at  the 
disappearance  of  these  phenomena  in  the  absence  of 
the  fixed  stars,  and  therefore  that  this  consequence 
of  the  Relational  Theory  is  no  objection  to  it.  We 
argue  that  this  is  not  a  necessary  consequence  of  the 
theory,  but  add  that  we  too  should  not  be  surprised 
if  laws  which  had  been  ascertained  in  the  presence  of 
the  fixed  stars  should  be  found  to  break  down  after  so 
hug^e  a  change  as  the  annihilation  of  those  bodies. 

The  upshot  of  the  discussion  seems  to  me  to  be 
that  there  is  no  conclusive  objection  to  the  view  that 
all  motion  is  relative,  and  that  all  arguments  which 
have  been  produced  to  show  that  we  must  recognise,  and 
can  indirectly  measure,  absolute  motion,  are  fallacious. 
This  being  so,  I  think  there  are  strong  reasons  for 
rejecting  the  Absolute  Theory.  After  all,  the  laws  of 
motion  are  empirical  laws,  discovered  by  observing  and 


THE   TRADITIONAL   KINEMATICS  113 

reflecting  upon  the  actual  movements  of  actual  bodies. 
Now,  all  that  we  can  observe  in  the  way  of  motion  is 
the  change  in  position  of  one  body  with  respect  to 
others.  It  were  strange  indeed  if  such  observations 
could  lead  to  laws  about  something  which  is,  from  its 
very  nature,  unobservable,  and  stranger  still  if  such 
laws  enabled  us  to  control  and  predict  the  movements 
of  bodies  in  nature.  Absolute  Space,  Time,  and  Motion 
have  all  the  appearance  of  being  mathematical  devices, 
and  not  substantial  constituents  of  nature,  and  a  theory 
is  to  be  preferred  which  reduces  such  mathematical 
scaffolding  to  a  minimum,  provided  of  course  that  it  is 
adequate  to  all  the  facts  with  which  it  professes  to  deal. 
I  think  that  mathematicians  and  writers  on  dynamics 
have  been  justified  in  rejecting  the  Relational  Theory  in 
the  forms  under  which  it  has  been  commonly  presented 
in  the  past  ;  but  I  think  that  this  is  because  it  has 
been  badly  and  inadequately  stated,  and  not  because 
it  is  impossible  to  make  it  fit  all  the  facts. 

This  is  about  as  far  as  we  can  go  when  we  confine 
the  discussion  to  ordinary  mechanical  phenomena.  But 
the  whole  question  arose  again  in  recent  years  over 
electro-dynamics,  and  it  has  been  found  that  reflection 
on  the  facts  of  this  region  of  phenomena  necessitates  a 
still  more  radical  overhauling  of  the  traditional  concepts 
of  kinematics.  This  leads  to  the  Theory  of  Relativity, 
which  I  shall  deal  with  in  the  next  chapter. 

The  following  additional  works  may  be  consulted 
with  advantage  : 

Leibniz,  Correspondence  with  Clarke. 

E.  Mach,  Science  of  Mechanics,  Chap.  II.,  §  vi.,  Appendix  XX. 

and  XXII. 
B.  A.  W.   Russell,  Principles  of  Mathematics,  vol.  i.,   Chap. 

LVIII. 
A.    Muller,  Das  Problem  des  absoluten  Raumes.     (Vieweg. 

Braunschweig.,  191 1.) 
P.    Painleve,    Les    Axiomes   de    la   Mecanique.       (Gauthier- 

Villars,  Paris,  1922.) 
H.  Poincare,  Science  et  Hypoth&se,  Chap.  VII.     (Flammanon, 

Paris.) 
H.  Poincare,  Science  et  Methode,  Part  II.,  Chap.  I. 


CHAPTER   IV 

"Ah!  that  accounts  for  it,"  said  the  Hatter.  "He  won't 
stand  beating.  Now,  if  you  only  kept  on  good  terms  with 
Time,  he'd  do  almost  anything  you  liked  with  the  clock.  .  .  . 
You  could  keep  it  to  half-past  one  as  long  as  you  liked." 

(Lewis  Carroll,  Alice's  Adventures  in  Wonderland.) 

Modification  of  the  Traditional  Kinematics  in  the 
Region  of  Physics  (continued).  (2)  The  Special 
Theory  of  Relativity 

The  older  controversies  between  Absolutists  and  Re- 
lationists,  which  we  have  discussed  in  the  last  chapter, 
took  place  wholly  within  the  region  of  dynamics,  i.e. 
they  dealt  with  the  movements  of  bodies  and  with  the 
changes  of  shape,  such  as  flattening  and  depression, 
which  some  of  these  movements  produce.  It  is  clear, 
however,  that  the  same  kind  of  question  could  be  raised 
over  anything  whatever  that  moves,  and  over  any  kind 
of  effects  which  movement  may  seem  to  produce.  Now 
there  is  good  evidence — some  of  which  will  be  men- 
tioned in  a  later  chapter  —  for  the  view  that  light 
travels  out  from  its  sources  with  a  very  great  but  finite 
velocity  ;  and  this  velocity  has  been  measured.  Again, 
the  motions  of  charged  bodies  produce  magnetic  effects 
which  vary  with  the  velocities  of  the  bodies. 

Thus  in  theory  the  whole  question  between  the 
Absolute  and  the  Relational  views  of  Motion  might 
be  argued  out  again  in  the  regions  of  light  and  electro- 
magnetics. A  wave  of  light  might  be  expected  to  have 
all  sorts  of  different  relative  velocities,  and  the  question 
might  be  raised  :   Which,   if  any  of  these,  is  what  the 

physicist  means  by  the  velocity  of  light?    The  Absolutist 

114 


FIRST  THEORY   OF   RELATIVITY  115 

might  here  step  in  and  say  that  by  the  velocity  of  light 
we   must  mean,    not  any   of  its   relative  velocities,   but 
its  absolute  velocity,  in  the  sense  discussed  in  the  last 
chapter.     Similarly,  we  might  ask  :  Which,   if  any,  of 
the  numerous  different  relative  velocities  of  any  charged 
piece  of  matter  produces   magnetic  effects?      And    the 
Absolutist  might  say  that  no  relative  velocity  has  this 
effect,    but  only  the  absolute   velocity  of  the  charged 
body.      I  do  not  think  that  these  additional  facts  really 
make   any    difference    in    principle   to   the    conclusions 
which  we   reached    about  the   Absolute  and   the   Rela- 
tional Theories  in  the  last  chapter.      I  will  try  to  justify 
this  statement  before  going  on  to  discuss  what  modifica- 
tions the  new  facts  do  make  in  the  traditional  kinematics. 
The  subject  is  a  little  confused  at  the  outset  through 
the    introduction    of    a    new    friend  —  the    Luminiferous 
Ether — which  did  not  enter  into  the  purely  dynamical 
arguments.      Thus  we  get  an   apparently  intermediate 
view,    put   forward   by    physicists  who  reject  Absolute 
Space,    Time,    and   Motion    with    righteous    horror    as 
metaphysical    figments,    and    tell    us    that  what   is   im- 
portant in   light  and  electro-magnetics  is   motion,   not 
with   respect  to  this  or  that  body,    but  with  respect  to 
the  Luminiferous  Ether.      It  seems  to  me  that  for  the 
present  purpose  there  is  no  important  difference  between 
the  Ether  and  Absolute  Space.     A  distinction  was  origin- 
ally drawn,   because  various  physical   properties,  such 
as  elasticity  and   density,    used   to   be  ascribed   to   the 
ether,  and  because  it  was  supposed  to  produce  various 
effects  on   ordinary  matter.     This   is  inconsistent  with 
the  traditional  view  that  Space  does  nothing,  has  no 
physical    properties,    and    is    thus    distinguished    from 
Matter.     But  there  are  two  circumstances  which  make 
the  distinction  between  the  Ether  of  the  modern  physicist 
and  the  Absolute  Space  of  the  older  Mechanics  so  slight 
as   not  to    be  worth   keeping.      On  the  one  hand,    the 
Absolutist    has    really   no    right   to   say    that   Absolute 
Space  does  nothing  to  matter.     For  it  is  of  the  essence 


Il6  SCIENTIFIC   THOUGHT 

of  his  view  that  absolute  motion  produces  flattening 
and  other  mechanical  effects  on  matter ;  and,  since 
Absolute  Space  is  involved  in  Absolute  Motion,  it  is 
clear  that  he  ought  to  hold  that  it  is  an  essential  factor 
in  the  production  of  these  effects.  On  the  other  hand, 
as  we  shall  see,  the  Ether  has  proved  to  be  a  more  and 
more  retiring  entity,  until  it  is  difficult  to  discover  that 
it  plays  any  part  in  physics  except  that  which  Absolute 
Space  played  in  the  older  Mechanics.  Thus  I  do  not 
regard  the  two  views  that  the  velocity  of  light  means 
its  absolute  velocity  and  that  it  means  its  velocity 
relative  to  the  Ether  as  genuine  alternatives.  The 
Ether  just  is  Absolute  Space  plus  some  hypothesis  as 
to  its  filling,  and  this  latter  addition  is  irrelevant  for 
our  present  purpose. 

Having  cleared  this  complication  out  of  the  way, 
we  can  see  fairly  easily  that  the  facts  about  light  and 
electro-magnetism  make  no  difference  in  principle  to 
the  question  of  Absolute  versus  purely  Relative  Motion. 
When  the  velocity  of  light  was  measured,  and  when 
the  fundamental  equations  of  the  electro-magnetic  field 
were  laid  down,  writers  did  not  as  a  rule  state  very 
clearly  what  frames  of  reference  they  were  assuming. 
But  it  is  certain  that  they  were,  in  fact,  assuming  the 
familiar  frame  of  reference  with  respect  to  which  Newton's 
laws  of  motion  hold.  If  this  be  Absolute  Space,  then 
they  were  talking  about  Absolute  Motion,  and  if  it  be 
the  fixed  stars,  then  they  were  talking  about  motions 
with  respect  to  the  fixed  stars.  Every  reason  that  there 
is  for  taking  the  latter  alternative  as  regards  ordinary 
dynamics  exists  for  doing  the  same  with  regard  to  light 
and  electro-magnetics.  The  velocity  of  light  is  some- 
thing that  has  been  experimentally  measured,  and  what 
has  been  measured  must  have  been  the  time  that  a 
wave  of  light  took  to  get  from  one  body  to  another  (or 
rather  from  one  body  to  a  second  and  then  back  again 
to  the  first).  Clearly  it  was  the  velocity  of  light  relative 
to  these  bodies  that  was   measured,   and  not  the  time 


FIRST  THEORY   OF   RELATIVITY  117 

that  it  took  to  get  from  one  point  of  Absolute  Space 
or  one  bit  of  the  Ether  to  another.  Similarly  the  laws 
of  electro-magnetics  were  discovered  and  verified  by 
experiments  on  bodies,  and  the  velocities  that  were 
observed  were  the  velocities  of  these  bodies  relative 
to  others.  Again,  all  the  arguments  that  could  be 
produced  to  show  that  in  light  and  electro-dynamics 
we  must  be  dealing  with  absolute  motions,  and  that  we 
have  the  means  of  indirectly  measuring  them,  are  pre- 
cisely parallel  to  the  arguments  to  prove  the  same  con- 
clusion from  the  phenomena  of  rotation.  And  they 
could  be  met  in  precisely  the  same  way.  Thus  the 
new  sciences  which  have  developed  since  Newton's 
time  leave  the  question  between  the  Absolutists  and  the 
Relationists  exactly  where  it  was  ;  and  that  is,  if  we 
are  right,  they  leave  the  Relationists  in  possession  of 
the  field,  provided  they  state  their  case  carefully  enough. 

I  do  not  suppose  that  any  physicist  would  deny  one 
side  of  the  above  statement,  viz.,  that  the  facts  about 
light  and  electro-magnetics  lend  no  fresh  support  to 
the  Absolute  Theory.  But  he  might  be  inclined  to 
think  that  they  do  provide  additional  grounds  for  the 
Relational  Theory.  I  do  not  think  this  is  strictly  true  ; 
but  it  is  plausible,  and  an  explanation  of  why  it  is  so 
will  carry  us  into  the  heart  of  our  present  subject. 

In  the  purely  dynamical  arguments  between  Absol- 
utists and  Relationists  the  Absolutist  staked  his  case 
on  absolute  acceleration  and  absolute  rotation.  He  did 
not  profess  to  be  able  to  produce  any  direct  empirical 
evidence  for  absolute  rectilinear  velocity ;  though,  of 
course,  if  he  could  prove  the  existence  of  absolute 
acceleration,  that  of  absolute  velocity  would  be  proved 
indirectly.  It  follows  at  once  from  the  form  of  Newton's 
laws  of  motion  that  absolute  rectilinear  velocity,  even 
if  it  exists,  will  not  show  itself  by  any  dynamical  con- 
sequences ;  for  it  is  acceleration,  and  not  velocity  in  a 
straight  line,  which  Newton's  laws  connect  with  force, 
and    therefore   with    possible    deformations    of    bodies. 


n8  SCIENTIFIC  THOUGHT 

Now,  when  we  come  to  deal  with  light  and  electro- 
magnetics,  there  is  a  real  difference  in  this  respect.  If 
what  is  called  the  velocity  of  light  be  its  absolute 
velocity  (or  its  velocity  with  respect  to  the  "stagnant 
ether,"  if  you  prefer  that  expression)  we  might  expect 
to  be  able  to  measure  the  absolute  velocity  of  a  body 
like  the  earth  by  finding  the  velocity  of  light  with 
respect  to  it  and  noticing  how  much  greater  or  less  it 
was  than  the  velocity  of  light.  The  absolute  velocity 
of  the  earth  in  its  orbit  would  presumably  be  the  differ- 
ence between  the  absolute  velocity  of  light  and  the 
velocity  of  a  wave  of  light  as  measured  from  the  moving 
earth,  given  that  the  earth  and  the  wave  of  light  were 
moviner  in  the  same  direction  when  the  measurement 
was  made.  Again,  various  observable  electro-magnetic 
effects  depend  on  the  velocities  of  charged  moving 
bodies.  If  it  be  the  absolute  velocity  of  the  charged 
body  that  is  relevant  to  these  effects,  we  ought  to  be 
able  to  discover  what  part  of  the  observed  relative 
velocity  of  a  moving  charged  body  is  due  to  its  own 
absolute  velocity  and  what  part  is  due  to  the  absolute 
velocity  of  our  axes  of  reference,  for  it  will  be  only  the 
former  that  will  be  responsible  for  the  electro-magnetic 
effects  which  we  measure. 

Now  it  is  a  fact,  and  a  very  important  one,  as  we 
shall  see  in  detail  in  a  moment,  that  all  attempts  to  find 
the  absolute  velocities  of  bodies  by  these  means  have 
failed,  although  the  experiments  were  quite  delicate 
enough  to  detect  the  effects  which  were  being  looked  for, 
if  they  had  really  happened.  We  can  now  see  what 
amount  of  truth  there  is  in  the  popular  view  that  the 
new  facts  about  light  and  electro-magnetics  have  pro- 
duced strong  additional  arguments  for  the  Relationist 
and  against  the  Absolutist  view  of  Motion.  It  is  true 
that  light  and  electro-magnetics  seemed  to  offer  for  the 
first  time  a  means  of  detecting  and  measuring  absolute 
rectilinear  velocities^  and  that  when  the  experiments  were 
done  the  results  were  always  wholly  negative.     But  the 


FIRST  THEORY   OF   RELATIVITY  119 

negative  results  of  these  experiments  are  just  as  para- 
doxical on  the  traditional  Relationist  Theory  as  on  the 
traditional  Absolutist  Theory.  They  cannot  therefore 
be  taken  as  arguing  for  the  former  and  against  the 
latter.  It  is  clear  that  neither  theory,  as  it  stands,  is 
fitted  to  deal  with  the  facts.  Of  course,  if  it  should 
be  found  that  the  Relationist  Theory  can,  and  the 
Absolutist  Theory  cannot,  be  so  modified  as  to  fit  the 
facts  of  light  and  electro-magnetics,  we  may  say  that 
ultimately  these  facts  furnish  a  conclusive  argument 
against  the  Absolute  Theory.  But  at  present  we  must 
hold  that  their  immediate  consequence  is  simply  to  show 
the  need  of  modifying  both  theories.  To  this  modifica- 
tion we  will  now  turn. 

I  shall  confine  myself  to  the  question  of  the  velocity 
of  light,  and  not  touch  on  purely  electro  -  magnetic 
experiments.  The  argument  in  the  former  case  can  be 
followed  by  any  person  who  takes  a  little  trouble  and  is 
acquainted  with  the  first  book  of  Euclid  and  with 
algebra  up  to  simple  equations  ;  whilst  the  electro- 
magnetic experiments  cannot  be  understood  without  a 
fair  knowledge  of  mathematical  physics.  And  there  is 
no  loss  of  generality  in  restricting  ourselves  to  the 
simple  case  of  light,  for  light  is  really  an  electro- 
magnetic phenomenon.  All  that  the  reader  needs  to 
remember  here  is  that  the  paradoxical  result  which  we 
are  going  to  explain  about  the  velocity  of  light  is  not  an 
isolated  phenomenon,  but  is  exactly  paralleled  by  every 
electro-magnetic  experiment  that  has  ever  been  done 
with  a  view  to  detecting  the  absolute  velocity  of  the 
earth  or  other  bodies. 

The  Michelson-Morley  Experiment.  I  shall  state  the 
argument  here  in  terms  of  the  Absolute  Theory,  because, 
with  our  scientific  traditions,  this  makes  it  more  easy 
to  follow.  But  I  shall  show  at  the  end  that  this  does 
not  mean  that  the  argument  implies  the  truth  of  the 
Absolute  Theory,  or  that  it  would  be  inconsistent  to 
use  the  conclusion  as  the  premise  of  an  argument  against 


IJO 


SCIENTIFIC   THOUGHT 


that  theory.  Suppose  we  had  a  platform  moving  through 
the  "stagnant  Ether"  (which,  as  we  have  seen,  is 
practically  the  same  thing  as  Absolute  Space)  in  a 
certain  direction  with  a  constant  velocity  v.  On  this 
platform  let  there  be  an  observer,  a  source  of  light,  and 
a  couple  of  plane  mirrors.  Draw  a  straight  line  on  the 
platform  through  the  source  of  light  and  parallel  to  the 
direction  of  motion  of  the  platform.  Draw  another 
straight  line  on  the  platform  through  the  source  and  at 
right  angles  to  the  first  line.  Measure  off  equal  distances 
from  the  source  along  the  two  lines.  At  the  points  thus 
obtained  place  the  two  mirrors,  each  one  normally  to  its 
line.     The  illustration  below  will  show  the  arrangement. 


At  a  certain  moment  let  the  source  S  give  out  a 
flash  of  light  and  let  part  of  this  go  to  the  mirror  M1, 
and  another  part  to  the  mirror  M2.  Let  us  first  consider 
the  part  that  travels  to  Mr  This  will  have  to  travel 
further  through  the  ether  than  the  marked  distance  / 
between  S  and  M1}  for  Mx  will  have  travelled  a  certain 
distance  through  the  ether  while  the  light  is  moving 
towards  it,  and  therefore  the  light  will  have  to  overtake 
it.  Now  let  the  light  be  reflected  back  along  its  old 
path  to  the  source.  It  will  now  have  to  travel  less  than 
the  marked  distance  through  the  ether,  because  the 
source  is  moving  towards  it.  Suppose  the  light  left  S 
at  time  O,  reached  Mx  at  tv  was  reflected  instantaneously, 
and  got  back  to  S  at  t%.  Let  c  be  the  absolute  velocity 
of  light,  i.e.  its  velocity  through  the  "  stagnant  ether." 
It  is  then  clear  that 


and 


FIRST   THEORY   OF   RELATIVITY 


121 


M 


/ 


M^T 


f 


\ 


whence  it  follows  that  t.z  =  2lc\(cl  —  v%).  This  then  is 
the  total  time  that  elapses  between  the  emission  of  this 
part  of  the  light  and  its  return  to  the  source  after  its 
double  journey. 

Let  us  now  deal  with  the  light  which  travels  to  the 
other  mirror  M.,  and  is  reflected  back  from  it  to  the 
source.  This  light  must  not  travel  out  in  the  direction 
SM2,  as  marked  on  the  platform, 
or  it  will  never  reach  M2.  For  M2 
will  have  moved  to  the  right  by 
the  time  such  light  had  got  to 
where  it  was  when  the  light  started. 
We  have  therefore  to  consider  light 
which  strikes  the  mirror  at  a  point 
in  the  ether  equidistant  between 
the  point  where  the  source  was  when  the  light  left  it 
and  the  point  where  the  source  will  be  when  the  light 
returns  to  it.  The  diagram  above  will  make  this 
quite  clear. 

The  actual  course  of  the  light  in  the  ether  is  the  line 
SWgS2.  If  T2  be  the  time  when  this  light  gets  back  to 
S  it  is  easy  to  see  that 

*"P  2  T  *7 

£2±2_  =  /2  +  t,2i2 


5° 


S' 


>V 


whence 


TV 


2/ 


*Jc2-v2 


Thus  the  two  parts  of  the  original  beam  of  light  do  not 
get  back  to  the  source  at  the  same  time  ;  or,  to  put 
it  in  a  different  but  equivalent  way,  light  which  gets 
back  to  the  source  at  the  same  time  from  the  two  mirrors 
must  have  started  from  the  source  at  different  times. 
Now,  under  these  conditions,  there  ought  to  be  a 
shifting  of  the  position  of  the  interference  bands  which 
always  arise  when  the  two  beams  of  light  which  have 
travelled  by  different  paths  from  the  same  source  meet 
again.  And  from  the  shift  of  the  bands  it  would  be 
possible  to  find  the  difference  between  tt  and  T2.     From 


122  SCIENTIFIC   THOUGHT 

this  we  could  calculate  v,  the  absolute  velocity  of  the 
platform,  in  terms  of  cf  the  absolute  velocity  of  light,  by 
using  the  two  formula?  just  proved. 

An  experiment  of  this  kind  was  done  with  great 
care  by  Michelson  and  Morley.  Their  moving  platform 
was  the  earth.  The  velocity  v  was  the  tangential 
velocity  of  the  earth  in  its  yearly  motion  round  the 
sun.  Their  apparatus  was  quite  delicate  enough  to 
detect  smaller  shifts  in  the  interference  bands  than  those 
which  were  expected.  Yet  not  the  slightest  trace  of 
any  shifting  at  all  was  detected.  A  great  many  other 
experiments  have  been  tried  in  which  electro-magnetic 
effects  were  looked  for  as  a  result  of  the  earth's  motion 
through  the  ether  ;  in  every  case  the  results  have  been 
nil.  This  negative  fact,  that  no  effect  due  to  the 
uniform  rectilinear  motion  of  a  body  through  the  ether 
has  ever  been  detected,  although  it  had  been  predicted, 
and  although  the  apparatus  used  was  quite  delicate 
enough  to  detect  and  measure  it  if  it  were  present,  is 
the  basis  of  the  first  Theory  of  Relativity. 

Before  going  any  further  I  want  to  impress  on  the 
reader  the  extremely  paradoxical  nature  of  this  fact, 
and  to  point  out  that  it  is  as  embarrassing  to  the 
traditional  Relational  Theory  of  Motion  as  to  the 
additional  Absolute  Theory.  If  I  travel  in  a  slow  local 
train,  and  an  express  passes  me  going  in  the  same 
direction  on  the  main  line,  I  expect  to  find  and  I  do 
find  that  the  express  moves  more  slowly  relative  to  me 
than  it  would  if  I  were  standing  on  the  platform  of  a 
station.  It  is  obvious  that  the  express  takes  longer 
to  pass  me  under  the  former  circumstances  than  under 
the  latter.  Now  we  should  certainly  expect  this  to 
happen  for  all  kinds  of  motion,  and  this  is  common 
ground  to  the  traditional  Absolutist  and  the  traditional 
Relationist.  Yet  the  negative  result  of  the  Michelson- 
Morley  and  the  electro-magnetic  experiments  might 
quite  fairly  be  summed  up  as  follows  :  The  velocity 
of  light  with  respect  to  various  bodies  is  the  same,  even 


FIRST   THEORY   OF   RELATIVITY  123 

though  these  bodies  be  moving  with  various  velocities 
in  the  same  direction  as  the  light  or  in  the  opposite 
direction  to  it.  In  the  Michelson-Morley  experiment 
the  earth  in  its  orbit  corresponds  to  a  slow  local  train, 
and  the  light  which  goes  from  S  to  Mx  corresponds  to 
a  very  fast  express  moving  in  the  same  direction  on  a 
parallel  line.  The  result  is  as  if  an  express  train  should 
appear  to  be  going  just  as  fast  to  observers  in  the  local 
train  as  to  observers  standing  on  a  station  platform. 
The  paradox  can  be  stated  just  as  well  in  terms  of  the 
Absolute  and  in  terms  of  the  Relational  Theory.  In 
terms  of  the  Absolute  Theory  we  can  say  that,  although 
the  earth  is  moving  with  an  absolute  velocity  through 
the  ether  in  the  same  direction  as  the  light,  this  does 
not  diminish  the  velocity  of  the  light  with  respect  to 
the  earth  ;  everything  goes  on  as  if  the  earth  were 
absolutely  at  rest  in  the  ether.  In  terms  of  the  Rela- 
tional Theory  we  can  say  that  the  relative  velocities  of 
a  wave  of  light,  with  respect  to  a  number  of  bodies 
which  are  moving  relatively  to  each  other  in  the  same 
direction  as  the  light,  are  nevertheless  all  the  same. 

Naturally  the  first  thing  to  do  is  to  see  whether  any 
physical  explanation  can  be  given  for  this  paradox, 
without  modifying  the  traditional  views  of  Space  and 
Time  which  are  common  to  the  older  Absolute  and 
Relational  Theories.  What  physical  assumptions  were 
made  in  the  argument  which  led  to  the  formulas  of  the 
Michelson-Morley  experiment?  We  assumed  (a)  that 
the  ether  is  not  dragged  along  by  the  moving  platform, 
as  water  would  be  by  a  stick  that  was  trailed  through 
it ;  (b)  that  the  absolute  velocity  of  light  in  the 
"  stagnant  ether"  is  the  same  in  all  directions  ;  (c)  that 
the  reflection  at  the  mirrors  takes  place  practically 
instantaneously  ;  and  (d)  that  the  fact  that  a  source, 
which  emits  light,  is  itself  in  motion  through  the  ether 
makes  no  difference  to  the  velocity  of  the  emitted  light. 
Would  it  be  reasonable  to  account  for  the  negative 
result  of  the  Michelson-Morley  experiment  by  rejecting 


124  SCIENTIFIC   THOUGHT 

or  modifying  any  of  these  physical  assumptions?  As 
regards  (a)  any  modification  will  bring  us  into  imme- 
diate conflict  with  another  set  of  well-established 
experimental  facts,  viz.,  the  aberration  of  light  from 
distant  stars,  due  to  the  yearly  movement  of  the  earth 
in  its  orbit.  We  shall  have  occasion  to  refer  again  to 
this  phenomenon  in  a  later  chapter.  For  the  present 
we  may  say  that  the  amount  of  aberration  will  vary 
according  to  the  extent  to  which  the  earth  drags  the 
ether  along  with  it.  The  actually  observed  aberration 
corresponds  to  the  hypothesis  that  there  is  no  dragging 
at  all,  which  is  what  we  assumed  in  our  argument. 

The  assumption  (/;)  seems  to  be  the  only  reasonable 
one  to  make  on  the  subject.  Nor  would  it  help  us  to 
reject  it.  For  the  earth  is  moving  in  its  orbit  in 
different  directions  at  different  times  of  year.  It  follows 
that  the  assumption  that  the  velocity  of  light  in  the 
ether  is  different  in  different  absolute  directions,  even 
if  it  be  intelligible,  could  only  account  for  the  negative 
result  of  the  Michelson-Morley  experiment  at  one  time 
of  year.  At  other  seasons  the  discrepancy  between 
prediction  and  observation  would  be  worse  than  before. 

The  assumption  (<r)  is  needlessly  sweeping  ;  all  that 
we  need  to  assume  is  that,  whatever  time  the  reflection 
may  take,  it  is  the  same  for  both  mirrors.  It  were 
surely  absolutely  arbitrary  to  suppose  that  reflection  at 
M0  always  takes  up  a  different  amount  of  time  from 
reflection  at  Mx,  and  that  this  difference  is  always  exactly 
such  as  to  neutralise  the  expected  difference  in  the  times 
of  arrival  of  the  two  beams  of  light  at  the  source. 

{d)  On  the  wave  theory  of  light  there  is  no  reason 
why  the  velocity  of  a  source  at  the  moment  of  emission 
should  have  any  effect  on  the  velocity  with  which  the 
emitted  disturbance  afterwards  travels  through  the  ether. 
If  we  held  the  corpuscular  theory  of  light,  matters  would 
be  different ;  for  a  corpuscle  shot  out  of  a  moving  source 
would  presumably  have  a  velocity  compounded  of  that 
of  the  source  and   that  due   to  the  emitting  impulse. 


FIRST   THEORY   OF   RELATIVITY  125 

But  the  cumulative  evidence  for  the  wave  theory  and 
against  the  corpuscular  theory  is  so  strong  that  it 
seems  idle  to  try  to  explain  the  negative  result  of  the 
experiment  by  a  hypothesis  which  is  only  plausible 
on  the  latter  view. 

Interpretation  of  the  Michelson-Morley  Result  in  terms 
of  the  Absolute  Theory.  It  is  clear  then  that  no  ordinary 
modification  in  our  physical  assumptions  will  explain 
the  negative  result  of  the  Michelson-Morley  experiment 
without  bringing  us  into  still  worse  collision  with  well- 
established  facts.  We  are  therefore  forced  to  consider 
the  assumptions  that  were  tacitly  made  in  our  measuring 
of  distances  and  time-lapses.  This  brings  us,  as  regards 
Space,  to  the  Lorentz  -  Fitzgerald  Contraction,  and,  as 
regards  Time,  to  the  notion  of  Local  Time. 

I  shall  still  confine  myself  in  my  exposition  to  the 
terminology  of  the  Absolute  Theory,  and  we  shall 
now  be  seeing  what  assumptions  as  to  our  measure- 
ments of  distance  and  time-lapse  have  to  be  made  in 
order  to  square  the  results  with  that  theory.  It  will 
be  remembered  that  we  measured  off  on  our  platform 
two  lines  at  right  angles  to  each  other,  each  of  which 
had  the  measured  length  /.  This  means  that  our 
measuring  rod  had  to  be  laid  down  exactly  /  times 
(if  it  was  of  unit  length)  before  we  made  our  mark 
on  each  line.  Now,  on  the  assumption  that  identity 
of  measure  means  identity  of  physical  distance,  we  saw 
that  the  times  taken  by  the  two  beams  to  get  back 
to  the  source  were  tv  for  the  one  that  travelled  parallel 
to  the  direction  of  motion  of  the  platform,  and  T2 
for  the  other.  The  physical  distances  travelled  by 
the  two,  on  the  present  assumption,  will,  of  course, 
be    ct.,   and   cT.2   respectively.      The   first    of    these    is 

and  the  second  is 


c1  T       ? 


Now  actually  the  two  get   back   at  the  same  time 
instead  of  the  two  different  times  /.,  and  T.,.      It  therefore 


m 


[26  SCIENTIFIC   THOUGHT 

is  necessary  to  suppose  that  really  they  travelled  the 
same  physical  distance  through  the  ether.  We  can 
only  explain  this  on  the  assumption  that,  although  our 
measurements  in  the  two  mutually  normal  directions 
on  the  platform  were  the  same,  the  physical  distances 
measured  were  not  the  same.  This  is  equivalent  to 
assuming  that  our  measuring  rod  does  not  remain  of 
the  same  physical  length  when  it  is  turned  in  different 
directions  on  the  moving  platform.  If  we  suppose 
that  the  physical  distance  at  right  angles  to  the  direction 
of  motion  really  is  /,  whilst  that  in  the  direction  of  the 

otion  is  only  /./  I  —  -^ ,  we  can  account  for  the  negative 

result  of  the  experiment.  For,  in  that  case,  both  beams 
will  have  traversed  the  same  physical  distance  through 

2/ 

the  ether,   viz. :       .  ;  and,  as  they  travel  with   the 

J       vL 

same  velocity  c,  they  will  get  back  at  exactly  the 
same  time.  What  we  have  to  assume  then  is  that  a 
measuring  rod,  which  is  of  unit  physical  length  when 
held  broadways  on  to  the  direction  of  motion  of  the 
platform    through    the    ether,    shrinks    to    a    physical 

/      V- 

length  v  i  —  —  when  laid  down  on  the  platform  in  the 

direction  of  its  motion.  This  is  what  is  called  the 
Lorentz  -  Fitzgerald  Contraction.  It  is  not,  of  course, 
supposed  to  be  confined  to  one  particular  rod,  but  is 
common  to  the  platform  and  everything  on  it.  The 
result  is  that  it  cannot  be  detected  by  the  use  of  another 
measuring  rod,  because  that  will  contract  in  precisely 
the  same  way  as  the  first  when  you  lay  it  alongside 
the  first. 

We  can  now  deal  with  the  question  of  Local  Time. 
We  have  supposed  that  the  velocity  of  light  in  the 
stagnant  ether  is  c  units  of  length  per  second.  Now, 
assuming  the  Lorentz-Fitzgerald  Contraction,  we  have 
seen  that  the  distance  travelled  in  the  ether  by  either 


FIRST   THEORY   OF   RELATIVITY  127 

beam  of  light  from  source  to  mirror  and  back  again  to 
2/ 


2/ 
source  is     ,  units  of  length.      It  is  clear  then  that 


c2 


a  clock  at  the  source,  which  marked  zero  when  the 
flash  started  ought  to  mark      .         .^-c  seconds  when  the 

flash  returns  to  the  source,  if  it  is  set  in  such  a  way 
that  it  accurately  measures  seconds  of  physical  time- 
lapse.  Now  the  distance  travelled  by  the  light  relatively 
to  the  platform  is  2/  units  of  length.  Therefore  the 
measured  velocity  of  the  light  relatively  to  the  platform 

will    be    2l^r      ,=  =*  or       , 9   units   of  length    per 

<?  e* 

second,  assuming  that  the  clock  at  the  source  is  going 
at  such  a  rate  that  a  second,  as  measured  by  it,  really 
does  represent  a  physical  time-lapse  of  one  second. 
The  relative  velocity  of  light  would  therefore  vary  with 
the  velocity  of  the  platform.  But  this  is  exactly  what 
we  do  not  find,  although  we  might  have  expected  to 
do  so.  We  actually  find  that  the  measured  velocity 
of  the  light  does  not  depend  on  the  velocity  of  the 
source,  the  observer,  or  his  instruments.  It  is  therefore 
evident  that  some  further  explanation  beside  the  Lorentz- 
Fitzgerald  Contraction  is  needed  to  account  for  the  facts. 
It  is  evident  that  this  further  assumption  must  be  con- 
cerned with  our  clocks,  since  we  have  already  dealt  with 
our  measuring  rods.  Suppose  that,  when  one  second 
of  physical  time  has  elapsed,  the  clock  at  the  source  only 

indicates  *  \  —  —   seconds,   i.e.  that  it   is   a   little   slow. 
cz 

2/ 
Then  when         .  seconds   have    really   elapsed    the 

2/ 
clock  at  the  source  will  only  indicate       .         2x     / j 

CsJ  ^       V  T  _  V_J 

9  9 


128  SCIENTIFIC   THOUGHT 

i.e.  2/ r  seconds.  The  measured  distance  travelled  by 
the  light  relatively  to  the  platform  is,  as  before,  2/. 
Thus  the  measured  relative  velocity  of  the  light  will 
now  be  cy  and  will  thus  be  independent  of  the  motion 
of  the  platform.  This,  as  we  saw,  is  the  result  which 
is  actually  found  by  experiment.  We  must  therefore 
accept  it  as  a  fact  that  the  clock  at  the  source  on  the 
moving  platform  goes  more  slowly  than  it  would  do  if 

the  platform  were  at  rest  in  the  ratio  ofv  1—  2    to   1. 

This  assumption  is  of  course  additional  to  the  Lorentz- 
Fitzgerald  Contraction,  and  makes  no  difference  to  it. 

But  we  are  not  yet  out  of  our  difficulties  about  the 
measurement  of  time.  So  far  we  have  dealt  only  with 
the  case  of  a  single  clock  in  a  single  place  on  the 
platform  ;  for  the  light  came  back  in  the  end  to  the 
place  whence  it  started,  and  the  time-lapse  was  measured 
wholly  by  the  clock  there.  This  of  course  does  corre- 
spond to  the  way  in  which  the  velocity  of  light  is 
measured  in  purely  terrestrial  experiments,  such  as 
that  of  Fizeau  and  Foucault.  Still,  it  is  clear  that  we 
often  want  to  compare  the  time  at  which  one  event 
happens  in  one  place  with  the  time  at  which  another 
event  happens  in  some  other  place.  In  order  to  do 
this  we  must  have  some  reason  to  believe  that  the  clocks 
in  the  two  places  are,  not  merely  going  at  the  same 
rate,  but  also  that  they  agree  in  their  zeros.  Now  the 
mere  fact  that  they  agreed  in  these  respects  when  they 
were  together  is  no  guarantee  that  they  will  continue 
to  do  so  when  one  has  been  taken  away  to  a  distance. 
In  the  case  of  a  pair  of  ordinary  clocks,  for  instance, 
the  shaking  that  one  of  them  gets  on  its  journey,  the 
possibly  different  average  temperature  of  the  region  to 
which  it  has  been  moved,  the  different  gravitational 
attraction  at  different  parts  of  the  earth,  and  many  other 
factors,  combine  to  make  it  most  unsafe  to  argue  that, 
because  the  two  agreed  when  they  were  together,  they  will 
continue  to  do  so  now  that  they  have  been  separated. 


FIRST   THEORY   OF   RELATIVITY  129 

It  is  thus  absolutely  necessary  to  have  some  criterion 
of  sameness  of  rate  and  sameness  of  zero  which  can  be 
applied  to  widely  separated  clocks  whilst  they  remain 
in  situ.  The  only  method  that  seems  possible  is  that 
of  signals  which  travel  from  one  to  the  other.  Let  a 
signal  be  sent  out  from  clock  A  when  this  marks  tA  and 
received  at  clock  B  when  this  marks  tB.  Let  another 
be  sent  out  when  the  first  clock  marks  t'A  and  received 
when  the  second  marks  f B.  If  it  is  found  that  t' A—tA  = 
t\—tm  we  say  that  the  two  clocks  are  going  at  the  same 
rate.  Again,  if  a  signal  leaves  A  at  /.,,  reaches  B  when 
the  clock  there  marks  tn,  is  immediately  reflected  back 
to  A,  and  reaches  there  when  the  local  clock  marks 
t' A,  it  seems  reasonable  to  conclude  that  the  zeros  of 
the  two  clocks  agree,  provided  that  tB  =  \(tA  +  t' A).  This 
would  obviously  be  the  right  criterion  to  adopt  on  the 
Absolute  Theory,  provided  the  platform  were  at  rest 
in  the  ether.  But,  we  have  seen,  whether  the  platform 
be  at  rest  in  the  ether  or  not,  there  is  no  observable 
phenomenon  by  which  the  observers  on  it  can  detect 
its  absolute  motion  or  rest.  Hence,  in  any  case,  they 
are  forced  to  use  this  criterion  faute  de  mieux.  More- 
over, with  this  criterion  and  with  it  alone,  the  observers 
on  the  platform  will  find  the  same  value  for  the  velocity 
of  light  relative  to  the  platform  whether  they  measure 
it  by  observations  all  made  with  a  single  clock  in  one 
place,  or  by  observations  made  with  two  different  clocks 
in  two  different  places.  We  can  easily  show  this,  as 
follows  :  We  have  seen  that  the  velocity  of  light,  as 
determined  by  observations  with  a  single  clock,  is  found 
to  have  the  same  value  c,  no  matter  what  may  be  the 
velocity  of  the  platform  through  the  ether.  Now  let 
the  clock  B  be  put  where  the  mirror  Mx  was  in  the 
Michelson-Morley  experiment.  Let  a  flash  leave  the 
source  (where  the  clock  A  is)  when  this  clock  marks  O, 
reach  the  clock  B  when  this  marks  tB,  be  immediately 
reflected  back,  and  reach  A  again  when  this  marks  t' A. 
Then,  if  the  two  clocks  have  been  set  by  our  criterion, 


130  SCIENTIFIC   THOUGHT 

tH=  i(0  +  /'.,)--=  A /'.i-     Now  we  know  that  the  velocity  of 
light   relative  to  the  platform,  as  measured  entirely  by 
observations  made  at  A  with  the  clock  there,  is  c.     And 
the    measured    distance    that    this    light    has    travelled 
relatively  to   the  platform  is  2/,  i.e.  the  measured  dis- 
tance on  the  platform  backwards  and  forwards  between 
A    and    B  (or    S  and   M1    in   the    diagram    to  illustrate 
the    Michelson-Morley    experiment).       Hence   t'A  =  2l\c. 
Hence  tin  which  is  It'  n  is  l\c.     That  is,  a  beam  of  light 
which  left  A  when    A's  clock  marked  O  and  travelled 
the  distance  /  relative  to  the  platform  to  the  point  B, 
will  reach  B  when  the  clock  there  marks  l\c.     Thus  the 
observers  at  A  and   B  on  comparing  notes  will   again 
conclude  that  the  velocity  of  light  with  respect  to  the 
platform  is  c,  which   is  exactly  the  same  conclusion  as 
experimenters  who  had  confined  themselves  to  making 
observations  at  A  with  A's  clock  had  already  reached. 
So  that  the  conventions  just  laid  down  for  standardising 
distant  clocks  are  not  only  those  which  are  practically 
forced  on  the  observers  by  their  inability  to  detect  the 
movement  of  their    platform   through    the    ether,    they 
are   also    the    only  conventions  which  will  lead  to  the 
same  measure  for  the  velocity  of  light  relative  to  the 
platform,    when    two   different    but   equally    reasonable 
methods  of  measurement  are  adopted.     (It  ought  to  be 
remarked    that   the    last  point    is  of  merely  theoretical 
interest,  since  the  only  practical  method  of  measuring 
the    velocity   of  light  by  terrestrial    experiments  is  by 
observations  made  in  a  single  place.) 

Now  these  conventions,  reasonable  and  inevitable  as 
they  seem,  lead  to  the  result  that  on  a  moving  platform 
clocks  which  are  set  by  them  do  not  "  really"  agree  in 
their  zeros.  This  means,  in  terms  of  the  Absolute 
Theory,  that  identity  of  clock-readings  in  different 
places  does  not  imply  identity  of  physical  date,  if  the 
clocks  have  been  standardised  by  these  conventions  and 
are  dotted  about  a  platform  which  is  in  absolute  motion 
through  the  ether.     This  we  will  now  show.     We  have 


FIRST  THEORY   OF   RELATIVITY  131 

just  seen  that,  with  these  conventions,  if  a  flash  leaves 
A  when  the  clock  there  reads  O,  it  will  get  to  B  when 
the  clock  there  reads  l\c.  If  there  were  nothing  wrong 
with  the  clocks  except  the  systematic  slowness  which 
we  have  already  had  to  assume,  this  clock-reading  would 

mean  a  physical  time-lapse  of  amount  -.      Now 

actually  the    light    which    left   A    and   went   to    B    has 

I       ~v% 
travelled  (a)  a  distance  /./  1  — -^(allowing  for  the  Lorentz- 

Fitzgerald  Contraction  of  the  platform  and  the  rod  with 
which  it  is  measured),  and  (b)  has  had  further  to  catch 
up  B,  which  is  itself  travelling  through  the  ether  in  the 
same  direction  with  a  velocity  v.  A  very  simple 
calculation  of  exactly  the  same  kind  as  that  given  on 
p.  120  will  show  that  the  actual  amount  of  time  that  has 

elapsed  between  leaving  A  and  reaching  B  is  ' 

Now  we  have  seen  that,  if  we  only  allow  for  the 
systematic  slowness  of  all   the    clocks   on   the   moving 

platform,    the   physical   time-lapse  would   be      ,-  — 

r  J  sj        v*1  c 


l~~   2 
cz 


These  two  quantities  are  not  equal,  and  the  one  that  we 
have  just  obtained  by  direct  calculation  is  the  right  one. 
Hence  the  clock  at  B  is  not  merely  going  somewhat  too 
slowly,  like  the  clock  at  A  ;  it  is  also  not  really  in 
agreement  with  A  as  to  its  zero,  i.e.  identity  of  readings 
between  the  two  clocks  do  not  represent  identity  of 
physical  dates.     When  the  clock  at  B  reads  l\c  the  true 

physical  time-lapse  is This  equals 


c—v 


■I     v_t 


1  —  .2\       C  —  V      / 


l~T* 


C32  SCIENTIFIC  THOUGHT 

In  general,  if  the  clock  at  B  marks  /„,  and  the  measured 
distance  of  B  from  the  source  in  the  direction  of  motion 
of  the  platform  be  denoted  by  xm  the  physical  time-lapse 
corresponding  to  the  reading  tB  is  given  by  the  equation 


sM*+?)  <■> 


i  — 

c~ 

We  see  then,  that  if  clocks  be  dotted  about  a  platform 

which  is  moving  through  the  ether  with  uniform  velocity 

in  a  straight  line,  and  if  these  clocks  be  standardised  by 

means  of  light  signals,  and  we  want  to  pass  from  the 

readings    of  any  clock    to  the    corresponding  physical 

time-lapse,  we  must   not  merely  divide  the  reading  by 

s/       v* 

i  — — .      Before  doing  this  we  must  add  to  the  reading 

a  quantity  —^,  where  xH  is  the  measured  distance  from 

the  standard  clock  to  the  given  clock,  in  the  direction  of 
motion  of  the  platform.  Not  only  are  all  the  clocks 
slow,  in  the  sense  that  they  all  take  more  than  an  hour 
of  physical  time  to  make  a  complete  rotation  ;  in  addi- 
tion to  this  the  hands  of  the  various  clocks  are  pushed 
back  from  the  very  start  by  amounts  which  increase  the 
further  they  are  away  from  the  standard  clock  in  the 
direction  of  motion  of  the  platform.  Clock-readings, 
like  tBi  are  called  Local  Times,  because  they  vary  with 
the  position  of  the  clocks  on  the  platform,  even  when 
the  absolute  time  is  the  same. 

It  is  usual,   for  convenience,   to  denote  the  fraction 

i 


I  —  ~2   by   k.      We   can    then    say   that   the    Lorentz- 

Fitzgerald  Contraction  means  that  a  measured  length 
x  in  the  direction  of  motion  of  the  platform  represents  a 
physical  length  of  only  x\k.  And  the  equation  just 
reached  tells  us  that  the  absolute  time  is  connected  with 
the  local  time  of  a  clock  on  a  moving  platform  by  the 

formula  t=k(ta  +  vxj^  (l) 


FIRST   THEORY   OF   RELATIVITY  133 

assuming-  that  the  clocks  have  been  set  by  light  signals 
according  to  the  conventions  laid  down  on  p.  129.  We 
want  one  more  equation  before  we  can  get  any  further. 
Suppose  that  when  the  standard  clock  on  the  platform 
marked  O  it  was  opposite  to  a  point  a  in  Absolute  Space. 
When  the  clock  B  marks  tB  let  that  clock  be  opposite  to 
a  point  (3  of  Absolute  Space.  The  co-ordinate  of  /3,  in 
the  direction  of  motion  of  the  platform  and  relative  to 
the  platform,  will  of  course  simply  be  x„  the  distance  as 
measured  along  the  platform  in 

this  direction  from  the  standard     a. — 5ji ,s 

clock   to  the   clock    B.      How       |     xB        \ 

will  this  be  related  to  X/3,  the       !'  " — 1       — *    /i  = 

physical   distance  in  Absolute  A g—  ^-*    fB=  fB 

Space  between  the  point  /Sand 

the  point  a,  which  the  standard  clock  was  opposite  to 
at  the  beginning?  The  diagram  above  will  illustrate 
the  problem. 

We  have  two  factors  to  consider.  (1)  Owing  to  the 
Lorentz-Fitzgerald  Contraction  the  measured  length  xB 
only  represents  a  physical  length  xB/k.  (2)  The  plat- 
form has  moved  through  the  ether  for  the  physical 
time-lapse  that  corresponds  to  the  local  time  tB.  If  this 
lapse  be  /  the  platform  has  moved  a  physical  distance  vt. 

(VX  \ 
tR-\ — 2"BJ.     Hence 

=  k\XB\   ,2 


1       v\  \ 

=  k{xB  +  vtB).  (2) 


This  is  the  other  fundamental  equation  of  the  subject, 
for  it  connects  the  physical  distance  of  two  points  in 
Absolute  Space  with  the  measured  magnitude  of  their 
co-ordinates  relative  to  a  moving  platform.     The  k  factor 


134  SCIENTIFIC   THOUGHT 

enters  through  the  Contraction  and  the  Local  Time,  the 
v  factor  through  the  ordinary  rules  of  relative  motion. 

We  can  now  sum   up  the  results  of  the  Michelson- 
Morley  experiment  in   terms  of  the   Absolute  Theory. 
To   explain    the    negative    results   of    that    experiment, 
whilst  preserving  the   Absolute  Theory,  we  have   had 
to    make    three    assumptions.      Two    of    these    involve 
action  between  Space  and   Matter  ;  the  third  is  merely 
the  explicit  recognition  of  a  convention,     (i)  We  have 
had  to  assume  that  Absolute  Motion  of  a  body  produces 
a  contraction  in  the  direction  of  motion.      (2)   We  have 
had  to  assume  that  all  clocks  on  a  platform,  which  moves 
through  the  ether,  are  thereby  made  to  go  more  slowly. 
These  are  both   definite  assertions  as  to  the  action   of 
Absolute  Space  (or  ether)  on  matter.     (3)  We  saw  that 
the  conventions  which  we   use   to  judge  of  identity  of 
zero  in  scattered  clocks  are   not  justified   if  the  clocks 
be  in   motion   through   the  ether.      This   is   not  a  new 
physical  assumption,  but  is  in  accordance  with  common- 
sense.     What  is  new  is  that  we  must  still  go  on  using 
this  convention,  because  we  can  never  tell  whether  we 
are  in  motion  or  not  through  the  ether.     It  will  be  seen 
then  that  the  results  of  the   Michelson-Morley  Experi- 
ment can  be  dealt  with  in  terms  of  the  Absolute  Theory, 
provided    we   are   prepared    to    make  suitable   physical 
assumptions  as  to  the  effect  of  absolute  motion  on  clocks 
and  measuring  rods.     Thus,  it  cannot  be  said  that  the 
newer  facts  definitely   settle  the   old   question  betweerf 
Absolutists   and    Relationists    in    favour   of  the    latter. 
Nevertheless,  I  think  that  reflection  on  the  newer  facts 
does  strengthen  the  case  of  the  Relationists  by  making 
the  Absolute  Theory  seem  more  and  more  arbitrary  and 
improbable.     Before  going  further  I  will  point  out  why 
I    think   this.       (1)    In    order   to   explain    the   fact   that 
motion   through   the  stagnant  ether  does   not  produce 
the    observable    effects    which    one    might    reasonably 
expect  it  to  do,   the   Absolutist  has  to  assume  that  it 
does  produce  two  different  effects  on  matter,  and  that 


FIRST   THEORY   OF   RELATIVITY  135 

the  combination  of  these  exactly  neutralises  the  ex- 
pected phenomena.  If  a  student,  when  taxed  with  not 
showing  up  an  essay,  were  to  reply  that  he  had  written 
it  and  then  upset  the  ink  over  it,  we  should  perhaps 
feel  a  little  doubtful,  and  ask  him  to  let  us  see  the  paper. 
If  he  then  said  that,  by  a  strange  coincidence,  as  the 
ink  dried  it  faded,  so  that  it  was  now  impossible  to 
see  anything  on  the  paper,  even  the  Charity  which 
"believeth  all  things"  would  be  severely  strained. 
Yet  this  is  about  the  position  in  which  the  Absolute 
Theory  finds  itself  when  dealing  with  the  Michelson- 
Morley  experiment.  (2)  The  alleged  physical  effects  of 
motion  through  the  ether  are  of  the  most  extraordinary 
kind.  For  instance,  the  Lorentz-Fitzgerald  Contraction, 
if  taken  as  a  physical  fact,  affects  all  kinds  of  matter 
equally.  A  rod  of  steel  contracts  as  much  as  a  bit  of 
india-rubber.  We  might  at  least  expect  that  such  a 
contraction  would  be  accompanied  by  strains,  and  that 
these  would  show  themselves  in  the  usual  way  by  lead- 
ing to  phenomena,  such  as  double  refraction,  in  other- 
wise isotropic  transparent  materials  like  glass.  Such 
effects  have  been  carefully  looked  for*  and  have  never 
been  found.  Similar  remarks  apply  to  the  systematic 
slowing  of  the  clocks.  In  fact  we  may  fairly  say  that 
the  assumptions  which  the  Absolute  Theory  has  to 
make  to  square  itself  with  the  results  of  the  Michelson- 
Morley  experiment  are  so  "  fishy  "  as  to  cast  additional 
^grave  doubt  on  that  theory.  Let  us  then  try  to  interpret 
the  Michelson-Morley  result  in  terms  of  the  Relational 
Theory. 

Interpretation  of  the  Michelson-Morley  Result  in  terms 
of  the  Relational  Theory.  The  two  transformation  equa- 
tions which  we  reached  in  the  last  section  contain 
unobservable  factors  which  we  must  now  try  to  eliminate. 
On  their  left-hand  sides  they  contain  absolute  time- 
lapses  and  absolute  distances.  On  their  right-hand 
sides  they  contain   v,    the  supposed    absolute    velocity 

*  In  particular,  by  Rayleigh  and  Brace. 


136  SCIENTIFIC   THOUGHT 

of  the  platform  through  the  ether,  which  it  is  admitted 
we  cannot  detect.  This  occurs  both  explicitly,  and  also 
implicitly  in  the  term  /'.  We  want  to  get  equations 
which  will  contain  nothing  but  relative  velocities, 
actual  clock-readings,  and  measured  distances.  This 
is  not  difficult  to  do.  First  of  all  we  must  take 
two  platforms,  px  and  pv  Let  us  still  talk  in  terms 
of  the  Absolute  Theory,  and  suppose  that  p1  has  an 
absolute  velocity  vx  and  p.,  an  absolute  velocity  v2  in  the 
same  direction.  Let  this  common  direction,  as  before, 
be  taken  as  the  ,i-axis.  The  first  thing  that  we  must  find 
is  the  measured  relative  velocity  z/a  which  the  platform  />2 
has  with  respect  to  observers  on/j,  who  measure  it  with 
their  own  clocks  and  rods.  Let  a  certain  point  on  the 
platform  p%  be  opposite  to  the  standard  clock  of  px  when 
this  reads  O.  Let  the  same  point  of  p2  be  opposite  to  B 
in  px  when  the  clock  there  reads  tB.  The  velocity  of  p2 
relative  to  px  as  measured  by  the  observers  on  px  will 
then  obviously  be  xB\tB.  This  is  v,,x.  Now  from  equations 
(i)  and  (2)  we  can  easily  derive  the  equations 

tr=k(t-vxXp/c2)  (1) 

and         x  =  k(Xp  —vxt).  (2) 

Xp-vJ 
Hence  v9,  = ^ 

21       f     ^t 

1        c2 
Now      — ' s  =  z/2,  the  absolute  velocity  of/2. 

.•.,  dividing  through  by  i,  we  get 

21      !_?!&_.  (3) 

This    formula    is  both  intrinsically  interesting,   and 
essential   for  the   next  stage  of  our  work.     Let  us  put 

h=   ,    l  2  ,      h=  /==,  and     K=  /=^=2. 

c2  c2  c2 


FIRST   THEORY   OF   RELATIVITY  137 

We  have  t  =  kx{tx  +  *f)  =  k%  (t%  +  V-f) 

and  x  =  k1(xl  +  v1t1)  =  k2(x2  +  v2t2), 

where  xx  and  tx  are  the  measured  co-ordinate  and  the 
clock-reading  on  px  which  correspond  to  physical 
distance  x  and  absolute  time-lapse  t  respectively, 
whilst  x2  and  t2  are  the  measured  co-ordinate  and  clock- 
reading  that  correspond  on  p2  to  the  same  physical 
quantities.  From  these  equations  we  can  at  once 
show  that 


fj  —  ^i^2\  I 


VlV3\   ( t >  +  *2V2-Vl 


=  ^2(i-^2)(^^2)  by  (3). 

i  —  -V2) ;  whence 

'1  =  ^2  +  ^)'  (4) 

In  the  same  way  we  can  prove  that 

x\  =  ^21(^2  +  vziQ'  (5) 

These  equations  are  absolutely  symmetrical  as  between 
tx  and  t2,  xl  and  x2.      For  it  follows  from  them  that 

t  -k  (t  -v*&\ 

and  x2  =  k2l  {xx  —  v2lt^) . 

But  k2X  =  k12  and  v2l  =  —  v12,  whence 

'2  =  M/i  +  ^)  (41) 

and  x2  =  k12(x\  +  v^tj  (51) 

which  are  of  precisely   the  same  form   as   (4)   and    (5) 
respectively. 

We  have  thus  eliminated  almost  the  last  trace  of 
anything  "  absolute  "  and  unobservable.     Our  equations 

K 


138  SCIENTIFIC"   THOUGHT 

now  contain  only  clock-readings  ;  measured  distances  ; 
relative  velocities  of  one  platform  to  another  ;  and 
the  velocity  of  light  with  respect  to  the  two  platforms, 
which  the  Michelson-Morley  experiment  shows  to  have 
the  same  value  for  all  platforms,  even  though  they  be 
in  motion  relatively  to  each  other,  provided  the  motion 
be  rectilinear  and  uniform.  The  equations  now  tell 
us  what  co-ordinates  and  dates  observers  on  one  plat- 
form will  ascribe  to  an  event,  provided  we  know  what 
co-ordinates  and  dates  the  observers  on  any  other 
platform  ascribe  to  the  same  event,  and  also  know  the 
measured  velocity  of  the  one  platform  with  respect  to 
the  other.  The  only  trace  of  "absoluteness"  that  is 
left  is  the  proviso  that  the  platforms  must  be  moving 
in  straight  lines,  and  with  uniform  velocities  in  the  ether. 
This  must  be  left  till  we  come  to  the  General  Theory 
of  Relativity  in  Chapter  VI. 

In  the  meanwhile  the  reader  may  be  inclined  to  raise 
a  purely  logical  question,  which  ought  to  be  settled 
before  we  go  anv  further.  He  may  say  :  "You  have 
just  been  deducing  certain  transformation  equations 
from  the  assumption  of  absolute  motion  through  the 
stagnant  ether,  and  in  this  connexion  you  have 
assumed  a  real  physical  contraction  in  moving  bodies 
and  a  real  physical  slowing  down  of  moving  clocks. 
It  is  true  that  you  have  at  last  deduced  a  set  of  equations 
which  are  entirely  in  terms  of  measured  distances, 
clock-readings,  and  measured  relative  velocities.  But 
even  these  were  deduced  from  the  assumption  of  two 
platforms  moving  with  different  absolute  velocities 
through  the  stagnant  ether.  Would  it  not  be  a  gross 
inconsistency  if  you  were  finally  to  make  these  equations 
the  basis  of  a  purely  Relational  Theory  of  Space,  Time, 
and  Motion?  Would  you  not  obviously  be  using  your 
conclusions  to  prove  something  which  directly  con- 
tradicts the  premises  from  which  you  derived  those 
conclusions?     And  is  this  not  plainly  inconsistent?" 

This  objection  is  invalid,  as  I  shall  now  show.     To 


FIRST  THEORY   OF   RELATIVITY  139 

some  people  this  fact  may  be  obvious,  and  they  may 
think  the  whole  objection  far  fetched.  I  can  assure 
them,  however,  that  it  is  fetched  from  no  farther  than 
the  University  of  Oxford  ;  and  respect  for  the  difficulties 
felt  by  that  learned  body  induces  me  to  make  the  logical 
position  perfectly  clear.  To  say  that  p  is  the  premise 
from  which  we  deduce  q  means  more  than  to  say  that 
p  implies  q,  though  of  course  it  involves  this.  It  means 
in  addition  that  our  belief  in  p  is  our  only  ground  for 
believing  in  q.  When  p  and  q  are  related  in  this  way 
we  cease  to  have  any  ground  for  believing  in  q  so  soon 
as  we  cease  to  believe  in  p.  But/  may  imply  q,  though 
/  is  false  and  q  is  true.  And,  provided  that  we  have 
other  grounds  for  believing  q,  there  is  not  the  least 
logical  objection  to  our  first  getting  to  know  q  as  an 
implication  of  p  and  then  using  our  belief  in  q  as  an 
argument  against  p.  A  foreigner  might  come  to  believe 
the  true  proposition  that  the  Prime  Minister  of  Great 
Britain  in  192 1  was  a  Welshman  because  he  mistakenly 
believed  that  Mr  Asquith  was  Prime  Minister  at  that 
date  and  that  Mr  Asquith  was  a  Welshman.  He  might 
then  find  other  grounds  for  believing  that  the  Prime 
Minister  was  a  Welshman  ;  he  might,  e.g.,  read  in  the 
papers  that  the  Prime  Minister  had  delivered  a  moving 
address  in  Welsh  to  the  Free  Calvinistic  Anabaptists  of 
Llanfairpwllgwyn.  ...  On  subsequently  comparing 
the  Welsh  national  characteristics  with  what  he  could 
learn  about  those  of  Mr  Asquith  he  might  begin  to 
feel  a  legitimate  doubt  as  to  his  original  belief  that 
Mr  Asquith  was  Welsh.  Yet  he  would  commit  no 
inconsistency  if  he  continued  to  believe  that  the  Prime 
Minister  in  192 1  was  Welsh.  He  would  have  been 
inconsistent  if  he  had  never  had  any  other  reason  for 
thinking  that  the  Prime  Minister  was  Welsh  except 
the  belief  that  Mr  Asquith  was  Welsh  and  was  Prime 
Minister ;  but  we  are  assuming  that  this  was  only  his 
original  ground  for  his  conclusion,  and  that  he  subse- 
quently found  other  reasons  to  support  it. 


i4o  SCIENTIFIC   THOUGHT 

Now  this  is  precisely  the  position  about  the  trans- 
formation equations.  They  do  not  begin  to  be  directly 
verifiable  till  they  are  got  in  the  purely  relational 
forms  (4)  and  (5).  Once  they  are  in  these  forms  they 
contain  nothing  but  what  is  observable,  and  the 
evidence  for  them  is  that  they,  and  they  alone,  fit  all 
the  known  facts.  They  do  indeed  follow  from  the 
Absolute  Theory,  together  with  the  physical  assumptions 
about  contractions  and  clocks.  This  is  not  surprising, 
since  those  assumptions  were  made  precisely  in  order 
to  square  the  Absolute  Theory  with  such  facts  as  the 
negative  result  of  the  Michelson-Morley  experiment. 
But,  once  they  have  been  reached,  by  whatever  means, 
the  evidence  for  or  against  them  is  direct  and  inductive. 
The  Absolute  Theory  is  not  the  premise  of  them,  and 
there  is  thus  no  inconsistency  in  using  them  to  cast 
doubt  on  the  Absolute  Theory.  We  do  this  just 
because  the  Absolute  Theory  only  leads  to  them  when 
supplemented  by  certain  physical  assumptions  which 
are  intrinsically  very  improbable.  If  q  be  known  to 
be  true,  and  p  only  leads  to  q  when  supplemented  by 
the  very  improbable  premise  p',  the  truth  of  q  reflects 
the  improbability  of  p'  back  on  to  p.  This  I  think 
settles  the  purely  logical  question.  In  future  the  trans- 
formation equations  in  the  relational  forms  (4)  and  (5) 
are  to  be  accepted  on  their  own  merits,  and  without 
regard  to  the  particular  way  in  which  it  happens  to  be 
convenient  to  introduce  them  to  the  notice  of  readers 
brought  up  (as  most  of  us  are)  on  Absolutist  traditions. 

There  is,  however,  a  real  logical  incoherence  in  a 
good  many  expositions  of  the  Theory  of  Relativity.  The 
Lorentz-Fitzgerald  Contraction  and  the  slowing  of  the 
clocks  on  a  moving  platform  are  first  introduced  as 
physical  changes  due  to  absolute  motion.  Later  on 
the  Absolute  Theory  is  rejected.  But  the  Lorentz- 
Fitzgerald  Contraction  is  still  recognised  as  a  fact,  and 
the  same  is  true  of  the  slowing  down  of  the  clocks. 
There  is  an  apparent  inconsistency  here  which  is  very 


0 


FIRST   THEORY   OF   RELATIVITY  141 

puzzling  to  the  student  of  the  subject.  It  is  clear  that, 
if  the  Contraction  and  the  slowing  of  the  clocks  are 
still  to  be  recognised,  they  must  be  reinterpreted,  and 
this  is  what  is  actually  intended  but  not  always  clearly 
brought  out.  Let  us  then  reinterpret  them  in  purely 
Relational  terms. 

We  have  two  platforms,  px  and  p.2,  of  which  the 
second  moves  in  a  straight  line  along  the  Jt-axis  of  the 
first  with  a  uniform  measured  relative  velocity  of  v.21. 
A  rod  is  lying  on  p2  along  the  A'-axis.  The  people  on 
p.2  measure  it  and  find  that  their  unit  measure  goes  into 
it  /2  times.  What  measure  will  the  people  on/j  ascribe 
to  this  rod?  They  cannot,  of  course,  measure  it  directly 
so  long  as  it  remains  on  p2,  so  they  will  have  to  adopt  the 
following  expedient.  Suppose  that  one  end  of  the  rod  is 
opposite  to  a  point  B  of  px  when  the  clock  there  marks  tiB. 
Suppose  that  the  other  end  is  opposite  to  a  point  C  of  P1 
when  the  clock  there  marks  he.  Let  tiB  —  tv:.  Then  the 
people  on  pi  will  say  that  the  distance  BC  on  their  plat- 
form, as  measured  by  themselves,  is  the  length  of  the 
rod  which  is  fixed  in  p.2.  For  it  is  the  distance  between 
the  points  in  pi  which  were  opposite  the  two  ends  of 
the  rod  at  the  same  moment,  as  judged  by  the  clocks 
on  pY.  The  length,  as  measured  by  them,  will  therefore 
be  Xic  —  x-iB'     Now,  by  equation  (5), 

xiC  =  k2i{x2c  +  v2i  t2c) 

and  x1B  =  ti21[x2ll  +  ^21*2^) 

Xlc      XiB  =  K21\{X2c.      X2ls)  +^2i('2c       Izb))' 

By  equation  (4), 

+  h     ( /      _1_  V^X'' 


and     tu,  =  k2l(t2C  +  V^) 
Now  /1B=  tlc,  by  hypothesis, 

•     •         t2c        t2B=  ZzK^-ZC        X2b). 


142  SCIENTIFIC   THOUGHT 

Hence  xx  —  x1B  =  kn{xt0— xiB)[i  -     ^ 

=  T     (.XZr       -Vj/.j 
A  21 


i.e.     /        '  h^i-Hh  (6). 

Thus  we  see  that  a  rod  whose  length  is  /.,,  as  measured 
by  observers  who  are  at  rest  relatively  to  it,  has  a 
shorter  length  as  measured  by  observers  relatively  to 
whom  it  moves  with  a  uniform  rectilinear  velocity.  If 
the  two  sets  of  observers  can  communicate  with  each 
other,  those  on  px  will  say  that  moving  bodies  are 
shortened  in  the  direction  in  which  they  are  moving, 
and  the  amount  of  shortening  is  that  given  by  the 
Lorentz-Fitzgerald  formula.  Suppose  now  that  the  rod 
were  transferred  from  p.,  to  pi,  and  the  observers  on 
pt  now  measured  it  directly,  whilst  those  on  p.,  now 
measured  it  in  the  same  indirect  way  which  the  px 
observers  had  to  use  before.  The  observers  on  px 
would  now  find  that  the  rod  had  the  measured  length  /2, 
whilst  those  on  p.2  would   ascribe   to    it   the  measured 

length   j^,    which    is   the    same   as      2-    since   kvz  =  k21. 

The  observers  on  p2  would  put  the  case  to  themselves 
as  follows  :  They  would  say  that  the  rod,  which  was 
formerly  at  rest,  has  now  acquired  the  velocity  vl2 
(which  is  equal  to  —  v21),  and  that  this  makes  it  con- 
tract in  the  proportion  given  by  the  Lorentz-Fitzgerald 
formula.  Thus  both  parties  would  agree  that  motion 
causes  contraction,  and  both  would  agree  in  the  formula 
which  connects  contraction  with  velocity.  Both  get 
the  same  measure  when  the  rod  is  at  rest  on  their  plat- 
forms and  they  can  measure  it  directly.  This  measure 
is  l%.  Both  get  the  same  measure  when  the  rod  is 
moving  relatively  to  their  platform  and  they  can  only 

measure  it  indirectly.     This  measure  is    ~,  or,  what  is 


FIRST   THEORY   OF   RELATIVITY  143 

the  same,    ~  •      The   contraction    is  thus    no   longer   a 

^2t 

physical  change  caused  by  absolute  motion  through  the 
stagnant  ether  ;  it  is  simply  a  change  in  the  measure 
of  length  of  the  same  body,  according  as  it  is  at  rest 
relatively  to  the  observers  and  can  be  measured  directly, 
or  is  in  uniform  motion  with  respect  to  the  observers 
and  can  only  be  measured  indirectly.  The  measure- 
ments of  the  two  sets  of  observers  are  perfectly  con- 
cordant with  each  other,  whenever  the  conditions  under 
which  they  are  made  are  precisely  similar.  And  there 
is  nothing  particularly  shocking  in  the  fact  that  the 
measurements  by  two  different  sets  of  observers  of  the 
same  body  are  not  concordant  when  the  conditions  under 
which  they  measure  it  are  not  precisely  similar.  It  is 
not  even  inconvenient,  since  the  transformation  equa- 
tions tell  us  how  to  pass  from  the  one  measure  to  the 
other. 

We  can  now  deal  with  the  interpretation  of  the 
facts  about  the  clocks  in  terms  of  the  Relational  Theory. 
Let  the  clock  at  the  point  B  on  p2  first  read  t2B  and 
later  on  let  it  read  T2«.  The  time-lapse  as  measured 
by  observers  on  p2  will,  of  course,  be  T2S  —  t2B.  Let 
the  clock  which  is  opposite  to  B  in  p1  on  the  first 
occasion  read  t1B,  and  the  clock  which  is  opposite 
to  B  in  pi  on  the  second  occasion  read  TlB.  Then 
we  have 


^21-^2  B 
IB"  ~ 72" 


A    «  B    /Soil        1    OB  ~T 


"^21^ZB 


and  *i*  =  &2i(*m+  — 

Whence  TlB—t1B  =  k21(T2B—t2B)  =  2(T2fl  —  t2B)       (7). 

V   I  ~  U21 


c2 


Thus  the  time-lapse,  as  measured  indirectly  from  pv 
is  greater  than  the  time-lapse  as  measured  directly  on 
p2.  The  people  on  px,  on  communicating  with  those 
on   p2,    will    therefore    say    that    the   clocks    on  p2   are 


i44  SCIENTIFIC   THOUGHT 

rendered  slow  by  the  motion  of  f>2.  If,  however,  a 
clock  from  />2  were  transferred  to  px  and  the  time-lapse 
were  measured  with  it  directly  by  people  on  pt  and 
indirectly  by  people  on  p.2,  the  latter  would  say  that 
their  old  clock  was  now  going  more  slowly,  and  would 
ascribe  this  to  its  transference  to  the  moving  body  px. 
Thus  both  parties  would  agree  that  rectilinear  motion 
slows  clocks,  and  both  would  agree  as  to  the  connexion 
between  this  slowing  and  the  relative  velocity.  But, 
once  again,  the  slowing  is  not  now  a  physical  effect, 
due  to  absolute  motion  through  the  ether.  It  is  simply 
a  change  in  the  measure  of  time-lapse,  according  as  it 
is  measured  by  the  readings  of  a  single  clock  which 
is  fixed  in  the  place  where  the  time-lapse  is  measured, 
or  by  the  readings  of  two  different  clocks  which 
successively  face  this  place  in  the  course  of  their 
motion  with  respect  to  it.  The  measurements  of  the 
two  sets  of  observers  are  again  quite  concordant, 
whenever  they  are  carried  out  under  precisely  similar 
conditions;  and  when  the  conditions  of  the  two  observa- 
tions differ  in  the  way  described  above,  we  can  always 
pass  from  the  one  measured  time-lapse  to  the  other 
by  using  the  equations. 

We  might  sum  up  these  results  as  follows:  (i) 
There  is  a  direct  and  an  indirect  way  of  measuring 
length.  The  former  can  only  be  applied  to  bodies  that 
are  at  rest  relatively  to  the  person  who  is  making  the 
measurement,  and  consists  of  the  familiar  process  of 
applying  a  measuring  rod  and  seeing  how  many  times 
it  has  to  be  laid  down  before  it  reaches  the  other  end 
of  the  body.  When  the  body  to  be  measured  is  moving 
relatively  to  the  observer  this  method  cannot  be  applied. 
What  has  to  be  done  then  is  for  two  observers  on  the 
same  platform  to  note  what  points  on  the  platform  the 
two  ends  of  the  moving  body  face  at  the  same  moment 
as  judged  by  the  clocks  on  their  platform.  They  then 
measure  this  distance  directly,  and  take  it  as  the 
measure  of  the  length   of  the   moving  body.      These 


FIRST   THEORY   OF   RELATIVITY  145 

two  methods  lead  to  the  same  measure  for  the  same 
body  (assuming  that  clocks  have  been  standardised  on 
the  two  platforms  by  the  principles  laid  down  earlier 
in  the  chapter)  if  and  only  if  the  two  platforms  be  at 
rest  relatively  to  each  other.  If  the  two  platforms  be 
in  uniform  rectilinear  relative  motion,  the  two  methods 
do  not  lead  to  the  same  measure  for  the  same  body. 
The  two  measures  are  then  connected  with  each  other 
and  with  the  measured  relative  velocity  by  the  Lorentz- 
Fitzgerald  formula.  It  will  be  noticed — and  this  is 
very  important — that  the  indirect  method  of  measuring 
length  necessarily  involves  a  reference  to  time,  since  we 
measure  the  distance  between  those  two  points  which 
the  two  ends  of  the  moving  body  are  judged  to  face 
simultaneously.  Whether  the  direct  method  of  measure- 
ment also  implicitly  involves  a  reference  to  time  we 
will  not  discuss  at  present,  though  we  shall  have  to 
do  so  later. 

(2)  There  is  a  direct  and  an  indirect  way  of 
measuring  the  time  that  elapses  between  two  successive 
events  which  happen  at  the  same  point  on  a  platform. 
The  former  can  only  be  applied  by  observers  who  are 
and  remain  at  this  place  on  the  platform,  and  it  con- 
sists of  the  familiar  process  of  noting  how  far  the 
hands  of  the  clock  there  have  turned  between  the  two 
events.  When  the  two  events  happen  on  a  body  which 
is  moving  relatively  to  the  observer  this  method  cannot 
be  used.  What  has  to  be  done  then  is  for  two  observers 
to  note  the  readings  of  their  clocks  when  the  first  event 
happens  opposite  to  one  and  the  second  event  happens 
opposite  to  the  other.  The  difference  between  the 
readings  of  these  two  separated  clocks  is  then  taken 
as  the  measure  of  the  time-lapse  between  the  two  events 
on  the  moving  body.  These  two  methods  lead  to  the 
same  measure  for  the  time-lapse  between  the  same  pair 
of  events  (assuming  that  both  sets  of  clocks  have  been 
standardised  by  the  principles  already  laid  down)  if 
and    only    if   the    two    platforms    be    at    rest   relatively 


i4<)  SCIENTIFIC   THOUGHT 

to  each  other.  If  the  two  platforms  be  in  uniform 
rectilinear  relative  motion,  the  two  methods  do  not 
lead  to  the  same  measure  of  the  time-lapse  between 
the  same  pair  of  events.  The  two  measures  are  then 
connected  with  each  other  and  with  the  measured 
relative  velocity  by  the  formula  (7).  It  is  important 
to  notice  that  the  indirect  measure  of  time-lapse  is 
essentially  bound  up  with  distance.  For  the  two  events 
which  happen  in  the  same  place  with  respect  to  the 
one  platform  happen  in  different  places  with  respect 
to  the  other.  The  greater  the  relative  velocity  of 
the  two  platforms  the  greater  the  spatial  separation 
of  the  two  events  will  be,  and  the  greater  will  be 
the  discrepancy  between  the  two  measures  of  the  time- 
lapse. 

This  connexion  between  the  spatial  and  temporal 
separations  of  a  pair  of  events  comes  out  still  more 
clearly  when  we  consider  a  more  general  case,  which 
must  anyhow  be  treated  for  the  sake  of  completeness. 
We  have  assumed  so  far  that  the  two  events  whose 
temporal  separation  was  to  be  measured  happened  at 
the  same  point  on  one  of  the  platforms.  Let  us  now 
suppose  that  a  certain  event  happens  at  B  on  p2  when 
the  clock  there  reads  iiB.  Let  a  second  event  happen 
at  C  on  p2  when  the  clock  there  marks  t2C. 

Then  the  time-lapse  as  measured  on p2  istiC.—  t2B.     But 


1  7       /  21     2.C  \ 

and  t1c  =  Ki[t2o+— -J-)- 

Whence    tlc-tVl  =  k21{(t2C-t2lj)  +  -f(x2c-x2H)}.  (8). 

Now  x2  B  =  k12  {x1H  +  vlZt1B) 

X2  c  =  A\2  [X1    +"V12txc). 

Whence      x2C-x2R  =  k12{(xlc-xlls)  +  v12(tlc-t1B)} 

—  Kn{\x\c—xlB)  —  v2k(tlC—tlB)}. 


FIRST   THEORY   OF   RELATIVITY  147 

Whence      tlc-tx  =  £21{(72  -  t2B)  +  -^r{x10-x1B) 

,-2     Vl  l\n)) 


k    2V 

Whence       k^{tx  - tllt)  =  k21(t2  -t2R)+^L^{xlc-x\B), 


V2Xt 


°r  *X     -tlB=T-{t2C-t2B)  +  -2{X10-X1B).  (9) 


k21 


Thus  the  time-lapse  between  two  remote  events  has 
a  different  measure  according  to  whether  it  is  deter- 
mined by  clocks  which  are  at  rest  relatively  to  the 
events,  or  by  clocks  which  are  in  uniform  rectilinear 
motion  relatively  to  ^em.  The  discrepancy  between 
the  two  measures  depends  on  the  spatial  separation 
between  the  two  events,  in  the  direction  of  relative 
motion  of  the  two  platforms.  Equation  (8)  expresses  the 
relation  in  terms  of  the  spatial  separation,  as  measured 
by  observers  who  are  at  rest  relatively  to  the  two  events  ; 
equation  (9)  expresses  it  in  terms  of  the  spatial  separa- 
tion as  measured  by  observers  who  are  in  uniform 
rectilinear  motion  relatively  to  the  two  events.  In  par- 
ticular, let  us  suppose  that  the  two  events  are  contem- 
porary as  judged  by  the  clocks  of  their  own  platform. 
This  means  that  tilB  =  t.1  .  Then  they  will  not  be  contem- 
porary as  judged  by  the  clocks  on  the  other  platform, 

for  txc—  tXB  will  be  equal  to  z(x\c~ x\b)-  Thus  the  tem- 
poral separation  with  respect  to  p  will  increase  with 
the  spatial  separation. 

The  upshot  of  the  whole  matter  is  to  show  how 
inextricably  our  measurements  of  distance  and  of  time- 
lapse  are  bound  up  with  each  other.  It  is  now  quite 
evident  that  any  attempt  to  measure  lengths  of  bodies 
which  are  moving  relatively  to  us  involves  judgments 
of  simultaneity.  On  the  other  hand,  a  pair  of  events 
which  are  simultaneous  with  respect  to  a  certain  plat- 
form,  and  are  separated  in  space  with  respect  to  that 


148  SCIENTIFIC   THOUGHT 

platform,  will  be  successive  with  respect  to  any  platform 
that    moves    relatively    to   the   first;   and   the  time-lapse 
between  them  with  respect  to  the  second  platform  will 
depend  on  the  spatial  separation  of  the  two  events.      It 
is    only  pairs  of  events  that  happen  both  at  the  same 
place  and  at  the  same  date  with  respect  to  some  platform 
which  will    happen  at   the   same    place   and  date  with 
respect  to  rf// platforms  that  move  with  uniform  rectilinear 
velocities  relative  to  the  first.     A  pair  of  contemporary 
events,  which  occupy  different  places  with  respect  to  the 
platform  in  which  they  are  contemporary,  will  be  succes- 
sive in  all  other  platforms  that  move  relatively  to  the 
first.     A  pair  of  successive  events,    which  occupy  the 
same  place  with  respect  to  a  certain  platform,  will  occupy 
different  places  with  respect  to  all  other  platforms  which 
move  relatively  to  the  first.     The  latter  fact  was  familiar 
enough  before  the  Theory  of  Relativity  was  developed. 
If  I  travel  to  Scotland  and  eat  my  lunch  in  the  dining- 
car,  the  two  events  of  eating  my  soup  and  drinking  my 
coffee   are   successive  ;    and    they   happen  in  the    same 
place    relatively    to   the  train,    viz.,   at   my  seat  in  the 
dining-car.     But,  with  respect  to  the  earth,  they  happen 
at  different  places,  e.g.,  at  Grantham  and  at  York.     The 
fact  which  has  only  lately  been  recognised  is  that  the 
same   applies  to    the  dates  of  events  which  happen    in 
different  places.     If  the  watches  of  the  travellers  and  the 
officials  on  the  train  had  been  set,  by  the  same  principles 
as  clocks  are  set  on  the  earth,  while  the  train  was  in 
motion,    we   should    have    the    following    result :     My 
neighbour  and  I  might  each  take  a  mouthful  of  soup  at 
the  same  time,  as  judged  by  our  watches  ;  but,  as  judged 
by  the  clocks  on  the  earth,  his  mouthful  would  happen 
a  little  later  than  mine,  if  I  were  facing  the  engine  and 
he  had  his  back  to  it.     And  the  difference  in  date  would 
be  proportional  to  the  width  of  the  table  at  which  we  were 
both  sitting.     The  reason  why  this  point  has  long  been 
obvious  about  Space  but  has  needed  very  delicate  experi- 
ments to  force  it  on  our  attention  as  regards  Time  is 


FIRST   THEORY   OF   RELATIVITY  149 

the  following  :  The  separation  between  Grantham  and 
York  is  gross  and  unmistakable.  But  the  separation 
in  time  between  my  mouthful  and  my  neighbour's,  as 
judged  by  clocks  on  the  earth,  is  proportional  to  the 
ratio  of  the  velocity  of  the  train  to  the  square  of  the 
velocity  of  light  (see  equations  S  and  9).  Now  the 
velocity  of  light  is  enormous  as  compared  with  that  of 
the  trains  on  even  so  efficient  a  railway  as  the  Great 
Northern,  and  so  the  temporal  separation  is  negligible 
and  can  only  be  detected  indirectly  through  the  negative 
results  of  such  delicate  experiments  as  the  Michelson- 
Morley. 

We  see  then  that,  in  the  long  run,  the  Theory  of 
Relativity  is  more  whole-heartedly  relational  than  the 
traditional  Relational  Theory  of  Motion  which  we 
discussed  in  the  last  chapter.  For,  according  to  it, 
not  only  is  the  spatial  separation  of  successive  events 
relative  to  the  system  of  co-ordinates  chosen,  but  also 
the  temporal  separation  of  two  events  in  different  places 
is  relative  to  the  system  of  co-ordinates  and  the  clocks 
associated  with  them. 

The  Restricted  Physical  Principle  of  Relativity.  I  will 
end  this  chapter  by  trying  to  state  this  physical  principle 
clearly,  and  then  to  explain  it.  It  may  be  stated  as 
follows  :  The  laws  of  any  physical  phenomenon  have 
the  same  mathematical  form,  whether  they  have  been 
discovered  and  verified  by  observers  who  were  at  rest 
relatively  to  this  phenomenon  or  by  observers  who 
were  moving  relatively  to  it  with  a  uniform  rectilinear 
velocity.  Let  us  now  try  to  see  exactly  what  this  means. 
The  law  of  any  phenomenon,  when  expressed  in 
mathematical  form,  is  a  differential  equation  connecting 
some  measured  quantity  which  is  observed  in  a  certain 
place  at  a  certain  time  with  some  other  measured 
quantity  which  is  observed  in  some  other  (or  it  may  be 
the  same)  place  at  some  other  (or  it  may  be  the  same) 
time.  The  law  will  also  involve  the  distance  between 
the    two   places   and   the   time-lapse   between   the   two 


150  SCIENTIFIC   THOUGHT 

dates.  Maxwell's  equations  are  a  perfect  example 
of  a  physical  law.  Now  it  is  clear  that  such  laws 
are,  in  the  end,  verifiable  only  in  so  far  as  they 
express  relations  between  actually  measured  magnitudes, 
such  as  clock-readings,  deflexions  of  galvanometers 
or  magnetometers,  number  of  weights  put  into  a  balance, 
number  of  times  that  a  certain  rod  has  to  be  laid  down 
to  get  from  one  place  to  another,  and  so  on.  We  may 
take  these  measures  to  represent  so  much  time-lapse,  so 
great  a  current  or  magnetic  force,  such  and  such  a 
gravitational  attraction,  so  much  length,  etc.  ;  and 
we  may,  if  we  like  (and  if  we  can  make  clear  what 
we  mean),  raise  the  question  whether  these  actual 
measures  which  we  read  off  our  instruments  "truly" 
represent  the  "real"  physical  magnitudes  in  question. 
But,  so  far  as  our  laws  and  their  verification  are  con- 
cerned, the  measured  magnitudes  are  the  important 
things,  and  the  question  of  what  they  stand  for  in 
the  physical  world  is  a  secondary  matter  of  theoretical 
interpretation.  E.g.,  Maxwell's  equations,  so  far  as 
they  can  be  verified,  state  relations  between  the  readings 
of  electrometers,  magnetometers  and  galvanometers  in 
various  places  ;  the  readings  of  clocks  in  these  places  ; 
and  the  number  of  times  rods  have  to  be  laid  down  to 
get  from  one  place  to  another. 

Now  it  is  not  true,  and  the  Physical  Principle  of 
Relativity  does  not  assert,  that  if  one  observer  is  at  rest 
with  his  instruments  relatively  to  a  certain  phenomenon, 
and  a  second  observer  is  in  uniform  motion  with  his 
instruments  relatively  to  the  first,  the  corresponding 
instruments  of  the  two  observers  will  give  the  same 
readings.  We  already  know  in  fact  that  they  will 
ascribe  different  time-lapses  and  different  spatial  separa- 
tions to  the  phenomena  under  observation.  And  the 
same  is  true  in  general  of  their  other  measurements. 
Suppose,  e.g.,  that  one  observer  with  a  magnetometer 
and  a  quadrant  electrometer  is  at  rest  with  respect 
to  a  charged  particle,  and  the  other  observer,  provided 


FIRST   THEORY   OF   RELATIVITY  151 

with  similar  instruments,  is  in  uniform  rectilinear 
motion  with  respect  to  the  first.  The  first  observer's 
magnetometer  will  give  a  zero  reading,  whilst  the  second 
observer's  will  give  a  finite  reading.  What  the  Physical 
Principle  of  Relativity  does  assert,  and  what  is  true,  so 
far  as  we  know,  is  the  following  proposition  :  The 
equations  which  interconnect  the  readings  of  one 
observer's  instruments  with  each  other  and  with  his 
measured  distances  and  time-lapses  are  of  precisely 
the  same  form  as  those  which  interconnect  the  read- 
ing's of  the  other  observer's  instruments  with  each 
other,  and  with  his  measured  distances  and  time- 
lapses. 

To  put  the  principle  formally,  let  us  suppose  that 
the  observers  on  px  are  at  rest  with  respect  to  the 
phenomenon  in  question.  Let  the  relevant  readings 
of  their  measuring  instruments  be  Px,  Qx,  Rr  .  .  .  Let 
the  relevant  distances  and  time-lapses,  as  measured  by 
them,  be  dt  and  tx  respectively.  The  velocity  of  the 
phenomenon  with  respect  to  them  is  o.  Suppose  they 
find  that  these  various  readings  are  connected  with  each 
other  and  with  the  measured  distances,  time-lapses, 
and  velocity,  by  the  equation  or  set  of  equations — 

<£i  (pi>  Qi>  Rr   •   •   •  ;  dx  ;  tx\  0)=  o. 

Let  the  corresponding  readings  of  the  observers  on  p2 
who  watch  the  same  phenomenon  be  P2,  Q2,  R2.  .  .  . 
Let  their  measured  distances  and  time-lapses  be  d2 
and  t2  respectively.  With  respect  to  them  of  course 
the  phenomenon  under  observation  has  the  measured 
velocity  v12.  Then  their  readings  will  be  connected 
with  each  other  by  the  equation  or  set  of  equations — 

&  (p2>  Q2>  R2.  .  .  •  ;  4  ;  4  ;  ^12)  =  0. 

Now  what  the  physical  principle  states  is  that  <£2  is  the 
same  as  <\>x.  This  may  be  briefly  summed  up  in  the 
statement  that,  according  to  the  Restricted  Physical 
Principle  of  Relativity,  the  laws  of  nature  are  co-variant 


152  SCIENTIFIC   THOUGHT 

with  respect   to  the    space-time   transformations  of  the 
Special  or  Restricted  Theory  of  Relativity. 

It  is  important  to  be  quite  clear  as  to  the  connexion 
between    this     principle    and    the     invariance    of    the 
measured  velocity  of  Light  with  respect  to  all  observers 
who  move  relatively  to  each  other  in  straight  lines  with 
uniform  velocities.     This  latter  fact  neither  implies  nor 
is   implied   by  the   physical   principle,    though   it   is   of 
course  compatible  with   it.      It    is   obvious  that  a    fact 
about  light  could  not  by  itself  logically  imply  a  principle 
about  all    natural   phenomena   whatever.      Conversely, 
the  physical  principle  only  implies  that  the  measured 
velocities  of  light  with  respect  to  all  observers  will  be 
the  same  function  of  their   respective    measurements  of 
distance  and  time-lapse.      It   does  not   imply   that  all 
these   measured   relative  velocities  will   have  the   same 
numerical  value.     That  they  do  in  fact  have  the  same 
numerical  value  is  an  uncovenanted  mercy,  revealed  to 
us   by   the    Michelson-Morley   and    other  experiments. 
This  fact  is  of  immense  practical  importance,   because 
it  enables  us  to  bring  the  Physical  Principle  down  from 
the  clouds  and  apply  it  to  get  concrete   results.     For 
the  invariance  of  the  measured  velocity  of  light  enables 
us,    in   the  way  that  we  have  described,    to  reach  the 
transformations  for  space  and  time,  i.e.,   to  express  d2 
and   t2   in   terms  of  dx  and   tx.      Having  done  this,  we 
can  see  how  P2,  Q2,  R2.   .   .   .   must  be  related  to  Px,  Qx, 
Rr   ...   in   order   that   the    form    of  the    laws  of  any 
phenomenon  may  be  the  same  for  the  observers  on  px 
as  for  those  on  p%.     The  result  is  that,  if  we  once  know 
the  readings  on  the  instruments  of  an  observer  who  is 
at  rest  with  respect  to  a  phenomenon,  we  can  calculate 
the  corresponding  readings   of  the   instruments  of  an 
observer  who  is  moving  with  uniform  rectilinear  velocity 
relatively  to  the   phenomenon.      This   is  of  course  an 
immensely  important  power  to  possess. 

If  we  accept  the  Physical  Principle  we  shall  have 
to  investigate  all  alleged  laws  of  nature  to  see  whether 


FIRST   THEORY   OF   RELATIVITY  153 

they  agree  with  it,  i.e.,  whether  they  be  co-variant  with 
respect  to  the  transformations  of  the  Special  Theory 
of  Relativity.  Some  alleged  laws  of  nature,  we  find, 
are  already  in  the  right  form  ;  Maxwell's  equations  are 
a  case  in  point.  Others  are  not,  e.g.,  the  Conservation 
of  Momentum,  on  the  traditional  view  that  mass  is 
independent  of  velocity.  Such  examples  might,  at  first 
sight,  be  taken  as  casting  doubts  on  the  principle. 
Here,  however,  there  are  two  points  to  notice:  (1)  If 
the  principle  be  true  and  the  laws  wrongly  stated,  it 
is  not  surprising  nevertheless  that  the  laws  have  seemed 
to  be  constantly  verified.  For  the  divergence  would 
only  begin  to  show  itself  when  we  deal  with  velocities 
which  are  comparable  with  that  of  light.  Now  of 
course  the  velocities  of  ordinary  bits  of  matter  are  quite 
negligible  in  comparison  with  that  of  light.  (2)  As 
soon  as  people  did  come  to  deal  with  matter  moving 
with  very  high  velocities,  as  in  the  case  of  particles 
shot  out  from  radio-active  bodies  or  from  the  poles  of 
vacuum  tubes,  it  was  found  that  the  traditional  laws 
had  to  be  modified,  and  that  the  modification  was  in 
the  same  direction  and  of  the  same  order  as  that  de- 
manded by  the  Physical  Principle.  The  strong  point 
about  the  principle  in  such  cases  is  this  :  If  you  keep 
the  traditional  form  of  the  laws  and  try  to  reconcile 
them  with  the  facts  about  particles  that  move  with 
velocities  comparable  to  that  of  light,  you  have  to 
make  special  physical  hypotheses  as  to  the  nature 
and  minute  structure  of  matter.  The  other  plan,  of 
modifying  the  laws  till  they  accord  with  the  Physical 
Principle,  has  the  advantage  that  it  accounts  for 
the  experimental  results,  and  requires  no  special 
physical  hypotheses  as  to  the  nature  and  structure  of 
matter. 

With  the  further  development  of  the  Theory  of 
Relativity,  and  the  further  modification  of  traditional 
physical  concepts  which  this  entails,  I  will  deal  in  the 
next  chapter  but  one. 


154  SCIENTIFIC  THOUGHT 

The  following  works  may  be  consulted  with 
advantage  : — 

L.  Silbkrstein,  Theory  of  Relativity. 

M.  SCHLICK,  Space  and  Time  in  Contemporary  Physics. 

E.  Cunningham,  Relativity,  Electron  Theory,  and  Gravitation. 

[The  reader  may  here  be  warned  that  most  popular 
expositions  of  the  Theory  are  either  definitely  wrong, 
or  so  loosely  expressed  as  to  be  dangerously  misleading; 
and  that  all  pamphlets  against  it — even  when  issued  by 
eminent  Oxford  tutors — are  based  on  elementary  mis- 
understandings.] 


CHAPTER   V 

"  Die  Entscheidung  dieser  Fragen  kann  nur  gefunden  werden, 
indem  man  von  der  bisherigen  durch  die  Erfahrung  bewahrten 
Auffassung  der  Erscheinungen,  wozu  Newton  den  Grund  gelegt, 
ausgeht  und  diese  durch  Tatsachen,  die  sich  aus  ihr  nicht 
erklaren  lassen,  getrieben  allmahlich  umarbeitet ;  solche  Unter- 
suchungen,  welche  ....  von  allgemeinen  Begriffen  ausgehen, 
konnen  nur  dazu  dienen,  dass  diese  Arbeit  nicht  durch  die 
Beschranktheit  der  Begriffe  gehindert  und  der  Fortschritt  im 
Erkennen  des  Zusammenhangs  der  Dinge  nicht  durch  iiber- 
lieferte  Vorurteile  gehemmt  wird." 

(Riemann,  Uber  die  Hypothesen  welche 
der  Geometrie  zu  Grunde  liegen.) 

The  Traditional  Kinetics,  and  its  Gradual  Modification 
in  the  Region  of  Physics,  (i)  Newton's  Laws  of 
Motion  and  Gravitation 

I  do  not  propose  to  pass  directly  from  the  Special 
Theory  of  Relativity,  explained  in  the  last  chapter, 
to  the  General  Theory  of  Relativity.  The  latter  is 
largely  concerned  with  the  laws  of  motion  and  the  law 
of  gravitation,  and  so  it  will  be  more  profitable  to  begin 
by  discussing  the  traditional  form  of  these.  Thus  this 
chapter  will  be  more  closely  connected  with  Chapter  III, 
and  the  next  with  Chapter  IV. 

Newton's  first  law  of  motion  states  that,  under  the 
action  of  no  forces,  a  body  continues  at  rest  or  in 
uniform  rectilinear  motion.  This  statement,  as  it  stands, 
is  meaningless,  if  we  do  not  assume  the  Absolute  Theory, 
and  is  a  mere  pious  opinion  incapable  of  verification  or 
refutation  if  we  do  assume  that  theory.  If  we  assume 
the  Relational  Theory,  it  is  an  incomplete  statement. 
If  all  motion  be  change  of  position  of  one  body  with 
respect  to  others  it  is  useless  to  talk  of  rest  or  of  motion 

155 


156  SCIENTIFIC   THOUGHT 

in  a  straight  line  until  we  have  specified  what  set  of 
bodies  we  are  using  as  our  axes  of  reference.  I  am  at 
rest  with  respect  to  my  room  and  in  motion  with  respect 
to  the  sun.  The  planet  Mars  is  describing  an  ellipse 
with  respect  to  the  sun  and  a  very  complicated  curve 
with  respect  to  the  earth.  No  doubt  the  law,  as  origin- 
ally stated,  professed  to  apply  to  motions  in  Absolute 
Space.  But,  as  these,  even  if  they  exist,  are  unobserv- 
able,  the  law  with  this  interpretation  is  as  idle  as  the 
statements  in  the  Athanasian  Creed  on  the  internal 
structure  of  the  Blessed  Trinity.  The  first  thing  needed 
then,  is  to  assign  our  axes  of  reference.  I  assume  these 
to  be  the  fixed  stars  primarily.  But  it  follows  from  the 
form  of  the  first  two  laws  that  any  set  of  axes  which 
is  in  uniform  rectilinear  motion  with  respect  to  the 
fixed  stars  will  do  equally  well,  provided  we  take  tradi- 
tional views  about  the  measurement  of  Space  and  Time, 
and  do  not  at  present  introduce  the  complications  which 
emerged  in  the  last  chapter. 

Even  when  the  spatial  axes  have  been  fixed  there 
remained  two  unexplained  terms,  viz.,  uniformity  and 
force.  Let  us  begin  with  uniformity.  Uniformity  of 
motion  is  meaningless  unless  it  refers  to  absolute 
motion  or  states  clearly  what  it  takes  as  its  standard 
measurer  of  time.  A  uniform  motion  means  one  which 
covers  equal  distances  in  equal  lapses  of  time.  If  we 
take  the  Relational  View  of  Time  a  lapse  of  time  is  a 
relation  between  two  events  ;  and,  even  if  in  theory 
we  take  the  Absolute  View,  it  is  only  lapses  between 
events  that  can  actually  be  observed  and  measured. 
It  is  therefore  assumed  that  we  have  some  process 
which  recognisably  repeats  itself,  and  that  the  time- 
lapse  between  corresponding  stages  in  each  repetition 
is  the  same.  A  uniform  motion  is  one  that  covers 
equal  distances  during  the  same  number  of  repetitions 
of  some  standard  process  which  is  itself  isochronous. 

The  question  at  once  arises :    How  are  you   to  tell 
that  your  standard  process  is  isochronous,  i.e.,  that  the 


TRADITIONAL   KINETICS  157 

time-lapse  between  corresponding  stages  in  it  is  always 
the  same  ?    If  you  determine  this  indirectly  by  mechanical 
arguments  the  first  law  of  motion  becomes  a  tautology, 
for  you  will  first   use  arguments   based  on   the  law  to 
prove  that  such  and  such  a  process  is  isochronous  and 
will  then   use  this    process   to    give  a   meaning  to  the 
uniformity   of  motion,    which    the   first    law    is   about. 
This  fallacy  is  not,  of  course,  commonly  committed  in 
so  glaring  a  form.      But,  in  a  rather  subtler  form,  some- 
thing very  like  it  is  committed.      Our  common  standard 
of  isochrony  is  the  successive  swings  of  a  pendulum. 
Suppose  then  we  define   uniform   motion   with   respect 
to  a  certain  set  of  axes,   as   motion    that  covers  equal 
distances  with  respect  to  these  axes  during  successive 
swings  of  a   pendulum.      So  far  no    fallacy  has  been 
committed.     But  if  we  verify  the  first  law  experiment- 
ally on  this  definition  of  uniformity,  and  then  later  on 
use  the  first  law  as  the  basis  of  an  argument  to  explain 
that  the  pendulum  does  not  take  quite  equal  times  for 
successive   swings,    and    to    correct   its    errors,    we    do 
commit  a  fallacy.     If  uniformity  of  motion  in  the  first 
law  just  means  uniformity  as  compared  with  a  pendulum, 
anyone  who  afterwards  says  that  pendula  do  not  move 
quite  isochronously  cannot  continue  to  use  "uniformity" 
in  the  original  sense  in  which  it  was  used  in  formulat- 
ing the  first  law.     And  then  two  difficulties  will  arise. 

(1)  We  must  ask  him  what  process  he  is  now  taking 
as  his  standard,  since  it  is  admitted  that  uniformity,  if 
it  is  to  be  observable  and  measurable,  must  involve 
a   comparison    with    some    standard    physical    process. 

(2)  We  may  remind  him  that,  if  the  first  law  has  been 
verified  when  uniformity  is  interpreted  by  reference  to 
a  pendulum,  no  argument  resting  on  the  law  can  fairly 
be  used  to  prove  that  pendulums  do  not  in  that  sense 
move  isochronously.  Whilst  (3),  if  the  law  be  not 
accurately  true,  when  uniformity  is  defined  in  this  way, 
it  ought  not  to  be  used  to  prove  anything  until  either 
(a)  it  has  been  modified  so  as  to  be  accurately  true  on 


158  SCIENTIFIC   THOUGHT 

the  old  definition  of  uniformity,  or  (/<>)  a  new  meaning 
of  uniformity  has  been  given  in  which  it  is  accurately 
true  in  its  original  form. 

There  are  in  fact  only  two  alternatives  open  to  us. 
Either  the  first  law  is  simply  a  definition  of  uniformity, 
in  which  case  it  reduces  to  the  statement  that  a  uniform 
motion  means  one  that  takes  place  under  the  action  of 
no  forces.  Or  it  is  a  substantial  statement,  in  which 
case  some  standard  process  or  set  of  processes  must  be 
judged  immediately  to  be  isochronous  and  used  after- 
wards as  the  criterion  of  uniformity.  I  think  it  is  quite 
certain  that  the  first  alternative  is  not  the  right  one.  It 
seems  quite  clear  that  the  meaning  of  uniformity  or  of 
isochronism  has  nothing  to  do  with  the  laws  of  motion. 
People  judged  certain  processes,  such  as  the  swings 
of  pendula,  the  burning  of  candles  in  the  absence  of 
draughts,  the  descent  of  sand  in  hour-glasses,  etc.,  as 
isochronous  long  before  they  had  thought  of  the 
question  whether  forces  were  present  or  absent. 

We  must  therefore  take  the  second  alternative.  This 
implies  that,  under  favourable  circumstances,  we  can 
directly  judge  equality  of  time-lapses,  just  as  we  can 
judge  equality  of  lengths.  This  seems  to  be  true.  It 
does  not  of  course  imply  that  such  judgments  are 
infallible.  And  the  question  arises  :  Can  we  ever  con- 
sistently correct  our  standard  process  by  means  of  laws 
which  are  in  terms  originally  defined  by  it?  I  think 
that  we  can  and  do,  and  that  the  logic  of  such  a  pro- 
cedure is  well  worth  considering. 

I  take  it  that  our  immediate  judgment  that  the  time- 
lapses  between  successive  swings  of  an  ordinary 
pendulum  are  equal  is  very  approximately  true,  if  we 
be  at  rest  with  respect  to  it.  Suppose  we  take  this  as 
our  original  standard  of  isochrony  and  define  uniformity 
by  means  of  it,  and  that  we  find  that,  with  this  defini- 
tion, the  first  law  is  verified  over  a  wide  range.  This 
verification  again  will  only  be  within  the  limits  of 
experimental  error.     Now,   suppose  we  apply  the  first 


TRADITIONAL   KINETICS  159 

law,  thus  stated  and  thus  approximately  verified,  to  a 
very  large  number  of  phenomena.      We  may  find,  as  we 
extend   our  observations  and  make  our  measurements 
more  accurate,  that  a  great  number  of  phenomena  are 
very  approximately,  but  not  exactly,  in  accordance  with 
the  first  law.    There  are,  we  will  suppose,  small  residual 
effects  left  unexplained  in  a  number  of  cases.     At  this 
stage  two  alternatives  are  open  to  us  :  (1)  We  may  keep 
the  first  law,  as  originally  stated,  and  hold  that  small 
disturbing  causes  are  operating  in   all  the  exceptional 
cases.     We  may  then  put  forward  physical  hypotheses 
to  account  for  these.     Or  (2)  we  may  say  that  the  first 
law,  as  originally  stated,   is  not  accurately  true.     Sup- 
pose we  find  that  a  single  slight  modification  in  it  will 
account  for  all  the  slight  inaccuracies  in  the  predictions 
based    upon    it.     Obviously    it    is    more    reasonable   to 
make  this  one  modification  than  to  put  forward  different 
supplementary  physical  hypotheses  in  each  case  which 
the  original  law  fails  accurately  to  account  for.     Now, 
this  modification  of  the  first  law  might  itself  take  place 
in   two  alternative  ways,      (a)   We   might   say:    "The 
pendulum    is   accurately    isochronous,    and    under   the 
action  of  no  forces,  bodies  move  with  very  nearly,  but 
not  quite,  uniform  rectilinear  motions  with  respect  to  the 
fixed  stars. "     Or  we  might  say  (b):  "  The  swinging  of  a 
pendulum    is   an    approximately,    but    not   exactly    iso- 
chronous   process,    and    therefore   a    body  that  moves 
'uniformly,'  as  judged   by  a  pendulum,   is   not  really 
moving  uniformly."     If  we  assume  that  the  times  taken 
by  successive   swings  differ    by   a   certain    very   small 
amount,  we  may  be  able  to  keep  the  form  of  the  first 
law  unmodified,  and  yet  accurately  explain  all  the  facts. 
So,    in    a  sense,   you    may  say  that  the  first  law  was 
formulated    in    terms    of  uniformity,    as   defined    by   a 
pendulum,    and    was    then    used    to    show    that    such 
"uniformity"    is    not    quite    uniform.       Is    there   any 
logical  objection  to  such  a  process? 

Not  if  we  clearly   understand    what  we  are  doing. 


160  SCIENTIFIC   THOUGHT 

We  did  not  start  by  defining  equality  of  time-lapses  to 
mean  the  relation  between  the  successive  swings  of  a 
pendulum.  We  simply  said  that  these  two  durations 
could  be  immediately  perceived  to  be  in  fact  very  nearly 
equal.  We  admitted  that  this  judgment  might  quite 
well  ignore  differences  too  small  to  be  immediately  per- 
ceived. Again,  we  find  that,  with  the  sense  of  uniformity 
which  is  based  on  the  assumption  that  pendula  are 
accurately  isochronous,  the  first  law  is  true  within  the 
limits  of  unaided  observation.  More  extended  and  more 
delicate  observations  forced  us  either  to  modify  the  law 
itself,  or  to  make  a  large  number  of  supplementary 
physical  hypotheses,  or  to  reject  the  view  that  pendula 
are  exactly  isochronous.  We  preferred  to  take  the  last 
of  these  alternatives.  The  result  is  that  both  the  law 
and  the  standard  of  uniformity  contain  a  small  leaven 
of  convention  and  a  large  mass  of  substantial  experi- 
mental fact.  Uniformity  is  tested  by  a  standard  physical 
process,  known  to  be  nearly  isochronous,  but  slightly 
"cooked,"  so  as  to  keep  the  form  of  the  first  law  fixed. 
The  first  law  is  known  to  be  very  nearly  true,  even  when 
uniformity  is  tested  by  the  uncorrected  process  ;  but  the 
test  for  uniformity  is  slightly  changed,  so  as  to  make  the 
law,  in  its  original  verbal  form,  quite  true  and  yet 
compatible  with  all  the  facts. 

This  mixture  of  convention  and  observation  is  a  very 
common  feature  in  scientific  laws,  and  is  unobjection- 
able on  three  conditions:  (i)  That,  even  without  it, 
the  law  is  verified  very  approximately  over  a  very  wide 
range;  (2)  that  the  amount  of  "  cooking "  needed  is 
below  the  limits  of  possible  direct  observation  ;  and 
(3)  that,  with  it,  the  law  keeps  its  original  simple  form, 
and  yet  now  accounts  accurately  for  all  the  facts  without 
supplementary  hypotheses. 

The  remaining  ambiguous  term  in  the  first  law 
is  Force.  Granted  that  the  first  law  is  not  a  definition 
of  uniformity,  it  might  still  be  held  to  be  a  definition 
of  the  absence  of  forces.      If  it  is  not  to  be  this,  but  is  to 


TRADITIONAL   KINETICS  161 

be  a  substantial  statement,  the  following  conditions 
must  be  fulfilled.  We  must,  in  certain  cases  at  least, 
be  able  to  know  whether  a  body  is  or  is  not  acted  on 
by  forces,  independently  of  knowing  whether  that  body 
is  in  fact  moving  uniformly  in  a  straight  line  in  the 
sense  defined  above.  For  the  first  law  says  that,  under 
the  action  of  no  forces,  bodies  rest  or  move  uniformly 
in  straight  lines.  If  this  be  an  experimental  fact  about 
nature  it  must  be  based  on  observing  bodies  which  were 
known  to  be  under  the  action  of  no  forces,  and  finding 
that  they  always  rested  or  moved  in  straight  lines  with 
respect  to  the  fixed  stars  with  a  velocity  which  is  uniform, 
as  judged  by  some  standard  process,  corrected,  if 
necessary,  in  the  way  discussed  above.  We  must 
therefore  ask  :  What  do  we  mean  by  force,  and  can 
we  ever  tell,  apart  from  the  laws  of  motion,  whether 
forces  are  acting  on  a  body  or  not? 

To  answer  this  question  we  shall  need  to  take  account 
of  the  second  law  of  motion  as  well  as  the  first.  Many 
eminent  men  have  held  that  the  notion  of  force  is  need- 
less and  useless  in  Mechanics.  Their  view  is  that  the 
so-called  second  law  of  motion  is  not  the  expression 
of  an  experimental  fact,  but  is  simply  a  definition  of 
force;  so  that,  wherever  the  latter  word  occurs  in 
Mechanics,  we  can  substitute  for  it  the  definition  given 
in  the  second  law.  Now,  the  second  law  may  be  put 
in  the  form  that  the  rate  of  change  of  momentum  of 
a  particle  at  any  moment  in  a  given  direction  is  equal 
to  the  force  which  is  acting  on  the  particle  at  that 
moment  in  that  direction.  "Direction"  of  course 
involves  a  tacit  reference  to  some  set  of  axes,  and 
"  rate  of  change  "  involves  a  reference  to  some  standard 
process  for  time  measurement.  These  may  be  taken  to 
be  the  same  as  those  which  have  already  been  fixed 
upon  in  discussing  the  first  law.  Now,  we  might  regard 
the  second  law  in  two  different  ways  :  (i)  We  might 
suppose  that  we  already  know  what  we  mean  by  force, 
and  already  have  a  method  of  measuring  its  magnitude 


162  SCIENTIFIC   THOUGHT 

and  direction.  On  that  view  the  second  law  is  a  sub- 
stantial statement  expressing  the  observed  connexion 
in  magnitude  and  direction  between  a  force  and  the 
rate  of  change  of  momentum  of  a  particle.  (2)  The 
other  view  is  that  the  second  law  simply  gives  a  meaning 
to  the  word  "  force,"  and  defines  the  phrase  "a  force  of 
such  and  such  a  magnitude  acting  in  such  and  such  a 
direction."  The  latter  interpretation  is,  for  some  reason 
or  other,  considered  to  be  tremendously  hard-headed  and 
"scientific,"  the  former  to  savour  of  metaphysics.  We 
shall  see  that,  although  there  is  a  certain  amount  of  truth 
underlying  the  second  view,  it  is  greatly  exaggerated 
and  has  nothing  to  do  with  any  antithesis  between 
"  science  "  and  "  metaphysics." 

It  seems  clear  to  me  that  no  one  ever  does  mean  or 
ever  has  meant  by  "  force  "  rate  of  change  of  momentum. 
It  is  certain  that  the  second  law,  as  originally  stated, 
was  not  intended  for  a  definition  of  force  but  for  a 
substantial  statement  about  it.  Unquestionably  the 
sensational  basis  of  the  scientific  concept  of  force  is 
the  feelings  of  strain  that  we  experience  when  we  drag 
a  heavy  body  along,  or  throw  a  stone,  or  bend  a  bow.  I 
do  not  understand  that  this  historical  fact  is  denied  by 
the  upholders  of  the  "descriptive"  (or  better,  "defini- 
tional ")  theory.  What  they  would  probably  say  is 
that,  in  this  sense,  force  is  purely  human  and  has  no 
relevance  to  the  laws  of  Mechanics.  We  cannot 
seriously  suppose,  e.g.,  that  the  sun  feels  a  strain  in 
keeping  the  earth  in  its  orbit,  as  we  do  when  we  whirl 
a  weight  on  a  string.  Hence  it  is  argued  that  what  we 
mean,  when  we  say  that  the  sun  exerts  a  force  on  the 
earth,  cannot  be  derived  from  the  experiences  of  strain 
which  we  feel.  I  think  there  are  two  answers  to  this  : 
(1)  We  must  distinguish  between  our  feeling  of  strain 
and  the  strains  that  we  feel,  just  as  we  must  distinguish 
between  our  feeling  of  movement  and  the  movement 
which  we  feel  ourselves  to  be  making-.  Force  is  not 
supposed    to    be   our  feelings   of  strain  ;    it    is    simply 


TRADITIONAL   KINETICS  163 

supposed  that  the  strains  which  we  feel  are  forces,  or 
are  indications  of  forces.  It  is  of  course  absurd  to 
suppose  that  the  sun  feels  a  strain  when  it  pulls  the 
earth  ;  but  this  is  absurd,  not  because  the  sun  could  not 
be  subject  to  a  strain,  but  because — having  no  mind — it 
cannot yW  a  strain  or  anything  else.  It  is  thus  perfectly 
consistent  for  a  man  to  describe  forces  as  the  sort  of 
factors  in  nature  which  reveal  themselves  to  us  directly 
in  our  feelings  of  strain,  and  to  add  that  inanimate 
bodies,  like  the  sun,  are  subject  to  forces.  (2)  The 
argument  under  discussion,  if  pressed,  would  make  it 
as  unreasonable  to  say  that  an  inanimate  body  like  the 
earth  is  round  or  rotates  as  to  say  that  it  is  acted  on  by 
forces.  For  there  is  no  kind  of  doubt  that  our  concepts 
of  roundness  and  rotation  are  founded  upon  sensations 
of  sight  and  touch.  If  I  had  not  had  sensations  of 
round  or  approximately  round  objects,  I  should  no 
more  know  what  roundness  means  than  a  colour-blind 
man  knows  what  red  means.  The  person  who  uses  the 
argument  about  the  sun  not  feeling  strains,  as  an 
objection  to  the  view  that  the  feeling  of  strain  is  the 
sensational  experience  which  gives  a  meaning  to  the 
concept  of  force,  may  be  invited  to  consider  the  follow- 
ing parallel  argument :  "  How  can  the  concept  of 
roundness  be  based  on  our  sensations  of  sight  and 
touch  when  the  earth,  which  can  neither  see  nor  feel, 
is  admitted  to  be  round?"  The  answer  of  course  is 
that  the  earth  has  the  sort  of  properties  which  we  have 
become  acquainted  with  by  seeing  and  feeling,  and  that 
it  does  not  need  to  see  or  feel  in  order  to  have  them. 
Similarly,  there  seems  to  be  no  reason  why  the  earth 
should  not  be  subject  to  forces  which  it  does  not 
feel,  whilst  forces  are  the  sort  of  natural  facts  which 
we  become  acquainted  with  through  our  feelings  of 
strain. 

I  think  then  that  we  may  quite  reasonably  hold 
that  the  strains  that  we  feel  are  the  original  sensational 
data  on  which  we  have  based  the  concept  of  physical 


i64  SCIENTIFIC   THOUGHT 

force,  just  as  coloured  and  shaped  patches  sensed  by 
us  are  the  original  sensational  data  on  which  we  have 
based  the  concepts  of  physical  shapes  and  colours.  The 
descriptive  theory  simply  puts  our  sensations  of  sight 
and  touch  into  a  quite  irrationally  privileged  position 
as  compared  with  our  sensations  of  strain.  We  shall 
see  later  on,  what  amount  of  practical  justification  there 
is  for  this  procedure. 

t  Now,  even  if  we  confine  ourselves  to  the  crude  data 
of  muscular  sensation,  we  can  distinguish  the  factors  of 
direction  and  magnitude.  We  have  to  exert  ourselves 
more  to  throw  a  heavy  hammer  than  to  throw  a  small 
stone  with  the  same  velocity.  And  to  make  a  thing 
move  in  a  given  direction  we  have  got  to  adjust  our 
bodies  so  as  to  push,  pull,  or  throw  it  in  that  direction. 
Thus  force,  as  actually  sensed  in  our  feelings  of  strain, 
is  obviously  in  rough  general  agreement  with  the  second 
law,  when  the  surface  of  the  earth  is  taken  as  our  spatial 
axes  and  any  common  rate  measurer  as  our  standard 
of  time.  The  trouble,  of  course,  is  that  felt  strains  are, 
and  remain,  vague  both  in  magnitude  and  direction. 
Moreover,  most  of  the  forces  with  which  we  have  to 
deal  in  science  are  not  felt  by  us  as  strains.  We  cannot, 
then,  base  a  satisfactory  scientific  measure  of  force  on 
felt  strains.  But  this  is  not  a  peculiarity  of  strains. 
It  is  equally  true  of  felt  temperatures.  The  meaning  of 
temperature  and  of  force  is  derived  from  felt  hotness 
and  felt  strain  respectively.  A  person  who  had  no 
such  sensations  would  not  understand  these  terms  at  all. 
Again,  both  these  felt  characteristics  have  a  perfectly 
noticeable  though  vaguely  discriminated  intensive  mag- 
nitude. We  want  to  define  methods  of  measurement 
in  each  case,  which  shall  agree  in  the  main  with  our 
rough  immediate  judgments,  but  shall  be  capable  of 
much  greater  accuracy,  and  of  application  to  cases 
where  the  sensations  cannot  be  got  at  all.  This  is  what 
a  thermometer  does  for  us,  in  the  instance  of  tempera- 
ture; but  no  one  " except  a  fool  or'an  advanced  thinker" 


TRADITIONAL   KINETICS  165 

(to  quote  Mr  Bradley)  imagines  that  what  we  mean  by 
temperature  is  the  height  of  a  column  of  mercury, 
v  In  any  case,  then,  the  second  law  is  not  a  statement 
of  what  is  meant  by  force.  But  it  might  still  be  merely 
a  statement  of  how  force  is  to  be  measured  for  scientific 
purposes.  -'  It  will  be  so  if  the  one  and  only  way  of 
measuring  force  is  by  measuring  rate  of  change  of 
momentum.  If,  however,  there  be  any  independent 
way  of  accurately  determining  the  direction  and  magni- 
tude of  a  force,  the  second  law  will  be  neither  a  defini- 
tion of  force  nor  a  mere  statement  as  to  how  it  is  to  be 
scientifically  measured.  It  will  be  a  substantial  state- 
ment about  force.  Now  I  think  it  is  quite  evident 
that,  in  favourable  cases,  we  can  measure  force  without 
reference  to  rate  of  change  of  momentum.  Suppose  a 
number  of  strings  are  attached  to  a  body  ;  that  they 
then  pass  over  pulleys  ;  and  have  weights  attached  to 
them.  Then  the  momentary  directions  of  the  strings 
give  a  clear  and  measurable  meaning  to  the  directions 
of  the  forces,  and  the  weights  give  a  clear  measure  of 
their  magnitudes.  And  these  magnitudes  and  direc- 
tions are:  (1)  in  fair  agreement  with  what  our  sensations 
of  strain  tell  us  in  all  cases  where  a  comparison  can 
be  made  ;  (2)  are  far  more  accurate  and  definite,  and 
can  be  determined  in  cases  where  we  cannot  get  sen- 
sations of  strain  ;  and  (3)  are  quite  independent  of  all 
reference  to  rate  of  change  of  momentum.  The  second 
law  is,  therefore,  neither  a  definition  nor  a  statement 
as  to  how  force  is  to  be  measured  ;  but  is  a  substantial 
proposition,  asserting  a  connexion  between  two  inde- 
pendently measurable  sets  of  facts  in  nature. '  Of  course, 
once  this  connexion  between  the  magnitude  and  direc- 
tion of  a  force  on  the  one  hand  and  the  rate  of  change  of 
momentum  of  a  body  on  the  other  has  been  established 
from  a  study  of  those  favourable  cases  where  force  can 
be  measured  independently,  we  can  use  the  law  to 
measure  indirectly  the  forces  which  are  acting  in  un- 
favourable cases,  where  direct  measurement  is  impossible, 


i66  SCIENTIFIC   THOUGHT 

If  I  want  to  find  the  pull  on  a  string  which  is  whirling 
a  weight,  my  best  plan  now  is  to  find  the  angular 
velocity  of  the  weight  and  its  mass;  to  determine  from 
these  data  its  rate  of  change  of  momentum  ;  and  to 
equate  the  magnitude  of  the  pull  to  this.  But  I  now 
use  this  method,  not  because  I  mean  rate  of  change 
of  momentum  by  "  force"  ;  nor  because  this  is  the  only 
possible  way  of  measuring  force  accurately ;  but  because, 
in  the  past  and  in  more  favourable  cases,  I  have  been 
able  to  measure  force  independently,  and  have  found  it 
to  be  proportional  to  rate  of  change  of  momentum. 

So  far  then  we  have  not  seen  anything  in  favour  of 
the  "  descriptive  "  theory  of  force.  Yet  I  believe  that  an 
important  truth  underlies  it,  and  that  it  has  been  obscured 
by  carelessness  of  statement.  The  typical  descriptionist 
generally  combines  the  two  views  that  force  just  means 
rate  of  change  of  momentum  and  that  force  is  not 
ultimately  a  very  important  conception  in  Mechanics. 
He  often  gives  the  former  as  a  reason  for  the  latter 
proposition.  We  have  seen  that  the  former  is  false. 
And  in  any  case  it  is  inconsistent  to  combine  it  with 
the  latter.  For,  if  force  just  means  rate  of  change  of 
momentum,  and  if  force  be  unimportant  in  Mechanics, 
it  follows  inevitably  that  rate  of  change  of  momentum 
is  unimportant  in  Mechanics.  And  no  one  in  his  senses 
would  maintain  this  proposition.  I  believe  the  truth  to 
be  that  force  is  not  ultimately  a  very  important  concep- 
tion in  Mechanics  ;  although  this  is  not  implied  by  the 
view  that  force  means  rate  of  change  of  momentum, 
and  although  that  view  about  the  meaning  of  force  is 
mistaken. 

I  will  now  try  to  explain  why  I  hold  this.  To  know 
what  forces  are  acting  on  a  body  you  need  to  know 
what  other  bodies,  near  and  far,  are  made  of,  what 
physical  and  chemical  states  they  are  in,  and  so  on. 
For  instance,  when  magnetic  forces  are  under  discussion, 
it  is  vital  to  know  whether  the  moving  body  and  those 
in  its  neighbourhood  are  made  of  iron  or  of  wood,  and 


TRADITIONAL   KINETICS  167 

so  on.  Again,  when  motion  is  produced  by  impact  or 
impeded  by  friction,  it  is  vital  to  know  the  elasticities 
of  the  bodies  and  the  state  of  their  surfaces.  Now, 
when  we  reflect  on  the  special  laws  of  nature  which 
involve  these  special  properties  that  vary  from  one  bit 
of  matter  to  another,  we  notice  that  force  simply  acts 
as  a  kind  of  middle  term  between  the  special  laws  of 
nature  and  the  general  laws  of  motion  ;  and  that,  except 
for  convenience  of  expression,  it  might  be  dropped. 
You  may  regard  the  laws  of  motion  as  being  expressed 
by  equations,  with  force  on  one  side  and  rate  of  change 
of  momentum  on  the  other.  You  may  regard  the  special 
laws  of  nature  as  being  expressed  by  equations,  with 
forces  on  one  side  and  the  special  configurations,  electric 
charges,  magnetic  properties,  etc.,  of  the  bodies  that  you 
are  dealing  with,  on  the  other.  Thus  you  might  just 
as  well  express  the  facts  by  a  single  set  of  equations, 
directly  connecting  the  configurations,  charges,  etc., 
with  the  rate  of  change  of  momentum,  and  drop  the 
mention  of  force  altogether.  In  practice  this  is  what  we 
generally  do  when  we  get  the  final  equations  for  solving 
any  particular  problem.  To  take  a  very  simple  case, 
the  final  set  of  differential  equations  for  the  motion  of 
a  particle  in  a  central  orbit  contains  nothing  that  stands 
for  force.  They  connect  the  rate  of  change  of  momentum 
of  the  particle  directly  with  the  mass  and  distance  of 
the  attracting  central  body,  and  with  the  gravitational 
constant. 

Why  then  do  we  trouble  to  keep  the  concept  of  force, 
and  why  were  the  laws  of  Mechanics  stated  in  terms  of 
it?  The  main  advantage  of  keeping  it  is  when  we  want 
to  make  general  statements.  We  want  to  be  able  to 
state  and  discuss  the  general  laws  of  motion,  without 
reference  to  any  particular  cause  which  produces  or 
modifies  motion.  It  is  then  convenient  to  lump  to- 
gether every  such  cause  under  the  common  name  of 
force.  Again,  we  want  to  be  able  to  state  the  special 
laws  of  nature  (e.g.,  those  of  electricity  or  magnetism), 


168  SCIENTIFIC   THOUGHT 

without  referring  to  the  particular  motion  of  some  definite 
body  in  some  definite  system  of  other  bodies.  It  is 
then  convenient  to  use  the  term  force  for  the  effect  of 
any  such  system  on  a  hypothetical  particle  of  unit  mass. 
When  we  pass  from  general  statements  to  some  definite 
problem  the  notion  of  force  becomes  useless  and  drops 
out.  Now  many,  though  by  no  means  all,  material 
systems  which  affect  the  motions  of  a  body  also  cause 
feelings  of  strain  in  our  own  bodies.  That  is  why  force 
does  not  appear  to  us  as  a  mere  mathematical  parameter, 
although  this  is  the  position  that  it  actually  comes  to 
occupy  in  the  treatment  of  concrete  problems.  Lastly, 
material  systems  which  affect  the  motions  of  bodies  do 
also  produce  other  measurable  effects,  such  as  balancing 
weights  on  strings  over  pulleys,  or  stretching  spring- 
balances.  The  first  and  second  laws  are  really  state- 
ments about  the  observed  relations  between  these  latter 
effects  of  material  systems  and  their  effects  in  modifying 
the  motions  of  bodies. 

We  have  now  cleared  up  the  notion  of  force,  so  far 
as  it  is  common  to  the  first  and  second  of  the  traditional 
laws  of  motion.  But  the  second  law  involves  another 
concept,  viz.,  that  of  mass,  and  this  we  must  now  discuss. 
The  momentum  of  a  body  is  defined  as  the  product  of 
its  velocity  by  its  mass.  All  that  we  need  say  at  present 
about  its  velocity  is  that  its  magnitude  and  direction 
must  be  determined  with  reference  to  a  suitable  set  of 
material  axes,  such  as  those  given  by  the  fixed  stars, 
and  a  suitable  physical  time-measurer,  such  as  an 
ordinary  pendulum. 

The  factor  of  mass  actually  enters  into  the  traditional 
Mechanics  in  two  quite  different  ways  ;  and  it  is  simply 
a  stransre  coincidence  that  the  two  kinds  of  mass  are 
proportional  to  each  other,  so  that,  by  a  suitable  choice 
of  units,  the  two  masses  of  a  body  have  the  same 
measure.  We  may  call  the  two  kinds  of  mass  gravita- 
tional and  inertial  respectively.  The  first  is  the  mass 
that  is  mentioned  in  the  law  of  gravitation,  the  second 


TRADITIONAL   KINETICS  169 

is  the  mass  which  is  involved  in  the  second  law  of 
motion.  At  present  we  shall  deal  with  inertial  mass, 
a  factor  which  occurs  equally  in  every  kind  of  motion, 
whether  produced  by  impact,  gravitation,  electric  or 
magnetic  attraction,  or  any  other  cause.  We  will  start, 
as  we  did  in  treating  force,  with  the  crude  data  of 
sensation,  and  consider  what  feature  it  is  in  these  which 
forms  the  basis  of  the  scientific  concept  of  inertial  mass. 
If  we  take  two  bodies  which  are  geometrically  exactly 
alike,  say  a  sphere  of  wood  and  an  equal  sphere  of 
platinum,  we  may  find  that  we  have  to  exert  ourselves 
to  a  markedly  different  extent  to  make  them  move  with 
the  same  velocity  relative  to  the  same  axes  and  the 
same  time-measurer.  We  have  already  seen  that,  with 
a  single  body,  e.g.,  the  wooden  sphere,  we  have  to  exert 
ourselves  more  the  faster  we  wish  to  make  it  move.  We 
see  then  that  the  effort  that  we  feel  ourselves  exerting 
when  we  try  to  make  a  body  move  depends  on  two 
factors.  One  of  these  is  the  velocity  which  we  give  to 
the  body.  The  other  is  a  factor  which  apparently  depends 
simply  on  the  material  of  the  body  itself.  It  is  the  latter 
which  gives  us  the  primary  meaning  of  inertial  mass. 
As  usual,  the  crude  data  of  sense  only  allow  of  a  very 
crude  measure  of  magnitude.  We  therefore  need  some 
method  of  measuring  mass  which  shall  agree  pro  tanto  in 
its  results  with  the  rough  judgments  based  on  our  ex- 
periences of  effort,  but  shall  be  capable  of  much  greater 
accuracy. 

Experiments  on  the  impact  of  bodies  give  us  a  means 
of  accurately  measuring  inertial  mass  in  favourable 
cases.  When  two  bodies  Bx  and  B2  hit  each  other,  it 
is  found  that  we  can  ascribe  a  numerical  coefficient  mvl 
to  Bx  and  a  coefficient  m21  to  B2,  such  that,  if  ux  and  u2 
be  their  respective  velocities  before  and  vA  and  v2  their 
respective  velocities  after  the  collision 

m12u1  +  m21u2  =  ?n12v1  +  in2Xv2. 

What  we  have  learnt  at  this  stage  is  that  (1)  the  two 

M 


170  SCIENTIFIC  THOUGHT 

coefficients  are  independent  of  the  velocities  ux  and 
u.y  And  (2)  that,  for  any  pair  of  bodies,  such  a  pair  of 
coefficients  can  be  found.  But,  suppose  that  we  first 
try  the  experiments  with  a  pair  of  bodies  Bj  and  B2, 
and  then  with  B.,  and  a  third  body  B8.  It  is  ante- 
cedently possible  that  mnt  the  coefficient  which  has 
to  be  ascribed  to  B.2  in  its  transactions  with  Bp  might 
differ  from  ;;/.,3,  the  coefficient  which  has  to  be  ascribed 
to  B2  in  its  transactions  with  B.,.  Further  experiments 
prove  that  this  is  not  so,  i.e.  that  the  coefficient  of  any 
given  body  is  independent,  not  only  of  its  velocity,  but 
also  of  the  other  bodies  with  which  it  is  interacting. 
We  can  thus  in  future  drop  doubly-suffixed  coefficients, 
like  w.(1,  and  write  simply  mlf  mv  etc.  We  find  then 
that  to  any  body  there  can  be  ascribed  a  certain  co- 
efficient, which  is  independent  of  its  velocity,  and 
which  it  carries  with  it  into  all  its  mechanical  trans- 
actions with  other  bodies.  This  coefficient  is  the 
scientific  measure  and  meaning  of  inertial  mass.  It 
obviously  accords  in  rough  outline  with  the  notion  of 
mass  which  we  get  from  our  sensations  of  effort,  but 
it  is  capable  of  accurate  measurement.  Having  defined 
and  measured  the  inertial  mass  of  a  body  in  this  way, 
we  find  two  further  important  facts  about  it  by  experi- 
ment. (1)  It  belongs  to  a  body,  not  only  in  the  case 
of  motions  caused  by  impact,  but  in  all  its  motions 
however  produced  or  modified.  (2)  Such  coefficients 
are  additive  scalar  magnitudes.  If  you  do  experiments 
with  a  compound  body,  made  up  of  two  smaller  ones, 
to  which  you  have  already  ascribed  the  masses  mx  and 
m2,  you  will  find  that  you  have  to  ascribe  to  this 
compound  body  the  mass  m1  +  m.2. 

We  can  now  deal  with  gravitational  mass.  All 
bodies,  no  matter  what  their  inertial  mass  may  be, 
fall  to  the  ground  with  the  same  acceleration  in  vacuo 
in  the  same  region  of  the  earth.  Now  the  rate  of 
change  of  momentum  of  a  body  of  constant  mass  is 
equal  to  the   product  of  its   mass  by   its  acceleration. 


TRADITIONAL   KINETICS  171 

Since  bodies  of  different  inertial  mass  all  fall  with  the 
same  acceleration,  it  follows  from  the  second  law  that 
they  must  be  acted  on  by  unequal  forces,  and  that 
these  forces  must  be  proportional  to  the  inertial  masses 
of  the  bodies.  Again,  if  we  do  experiments  with  a 
delicate  torsion  balance,  we  find  that  the  attraction  of 
a  body  A  on  a  body  B  is  proportional  to  the  inertial 
mass  of  A.  Combining  these  two  facts  we  see  that 
the  gravitational  attraction  between  any  two  bodies  is 
proportional  to  the  product  of  their  inertial  masses. 
It  is  evident  then  that,  even  if  we  had  never  done 
experiments  with  moving  bodies  at  all,  but  had  con- 
fined ourselves  to  statical  experiments  with  balances, 
torsion  apparatus,  etc.,  we  should  have  come  to  ascribe 
certain  coefficients  to  every  body.  We  should  also 
have  found  that  these  coefficients  were  independent  of 
the  velocity,  chemical  or  physical  state,  etc.,  of  the 
body  to  which  they  were  ascribed,  and  were  more- 
over independent  of  the  other  bodies  with  which  it  was 
interacting.  And  these  coefficients  would  have  been 
additive.  They  would,  in  fact,  be  proportional  to  the 
inertial  masses  ;  and  therefore,  with  a  suitable  choice 
of  units,  identical  with  the  latter.  Now,  the  coefficients 
required  by  the  gravitational  facts  are  what  we  mean 
by  gravitational  masses  ;  and,  on  the  traditional  theory, 
it  is  just  a  strange  coincidence  that  the  two  masses  of 
a  body  are  proportional  to  each  other.  The  theory  of 
gravitation  which  is  bound  up  with  the  General  Theory 
of  Relativity  suggests  a  reason  for  this  identity  of 
inertial  and  gravitational  mass. 

We  must  next  consider  the  third  law  of  motion, 
which  says  that  action  and  reaction  are  equal  and 
opposite.  It  involves  no  new  concepts,  but  it  makes 
a  most  important  additional  statement  about  force. 
It  says,  in  fact,  that  the  force  on  one  particle  is  only 
one  side  of  a  transaction  which,  taken  as  a  whole,  is 
a  stress  between  two  particles.  It  is  in  virtue  of  this 
principle   that  we  are   able   to   deal    with  the  motions 


172  SCIENTIFIC  THOUGHT 

of  finite  rigid  bodies,  which  rotate  as  well  as  change 
their  places,  and  therefore  cannot  be  treated  as  particles. 
The  law,  as  stated,  is  indefinite  both  as  to  direction 
and  as  to  time.  The  action  and  reaction  between  two 
particles  might  be  equal  and  opposite,  but  might  make 
any  angle  with  the  line  joining  them.  It  seems  to  be 
sometimes  assumed  that  the  law  requires  the  direction 
of  the  two  forces  to  be  the  line  joining  the  particles. 
This  is  not  so,  and  the  law  would  be  false  if  it  were. 
Two  moving  electrons  exert  equal  and  opposite  forces 
on  each  other,  but  these  are  not  in  the  line  joining 
the  two  electrons.  In  fact  the  question  of  the  direction 
of  the  two  opposite  and  equal  forces  belongs  to  the 
special  laws  of  nature,  such  as  gravitation,  electricity, 
magnetism,  etc.,  and  not  to  the  general  laws  of  motion. 
Again,  I  think  it  is  often  assumed  that  action  and 
reaction  are  always  contemporary.  If  the  law  be 
understood  to  assert  this,  it  is  certainly  false,  unless 
we  supplement  it  by  assuming  particles  of  ether  and 
a  mechanical  theory  about  stresses  among  them. 
When  a  beam  of  light  from  the  sun  strikes  upon  any 
surface  on  the  earth  it  produces  a  pressure  on  that 
surface.  If  there  be  any  reaction  from  the  earth  it 
will  be  exerted  primarily  on  the  surface  of  the  ether 
next  to  the  earth,  and  will  not  be  conveyed  back  to 
the  sun  in  less  time  than  light  takes  to  travel  between 
the  two.  Thus,  if  you  confine  yourself  to  the  earth 
and  the  sun,  action  and  reaction  are  not  contemporary 
as  regards  light-pressure. 

The  first  "two  laws  of  motion  have  been  stated  with 
respect  to  motions  relative  to  the  fixed  stars  and  to  a 
standard  time-measurer,  such  as  an  ordinary  pendulum. 
Now,  it  is  very  important  to  notice  that,  apart  from  the 
third  law,  this  restriction  to  a  particular  set  of  axes 
and  a  particular  physical  time-measure  could  be  removed, 
provided  that  we  introduced  suitable  new  forces  with 
each  new  frame  of  reference.  I  will  illustrate  what  I 
mean  by  two  examples  :  (i)  Suppose  that  a  particle  is 


TRADITIONAL   KINETICS  173 

at  rest  on  a  plane  with  respect  to  a  Newtonian  frame 
of  reference,  i.e.,  with  respect  to  such  axes  and  such  a 
time-measurer  as  we  have  hitherto  been  assuming. 
Suppose  that  in  this  plane  there  lies  a  wheel,  and  that 
we  take  two  mutually  normal  spokes  of  this  wheel  as 
our  X  and  Y  axes  respectively.  So  long  as  the  wheel 
is  at  rest,  these  two  spokes  and  the  line  through  the 
centre  of  the  wheel  perpendicular  to  the  plane  in  which 
it  lies,  constitute  a  Newtonian  set  of  axes  ;  and  the 
particle  is  at  rest  with  respect  to  them.  It  is  therefore 
under  the  action  of  no  Newtonian  forces.  Now  suppose 
that  the  wheel  is  spun  with  a  uniform  angular  velocity 
co  in  its  own  plane.  Let  us  continue  to  take  the  two 
spokes  as  our  axes,  and  the  old  clock  as  our  time- 
measurer.  The  resulting  frame  is,  of  course,  non- 
Newtonian,  for  it  is  neither  at  rest  nor  in  uniform 
rectilinear  motion  with  respect  to  the  fixed  stars. 
Relatively  to  this  new  frame  the  particle  describes  a 
circle  in  the  X-Y  plane  with  uniform  angular  velocity  <o. 
It  therefore  has  a  relative  acceleration  of  amount  m? 
towards  the  origin.  But  this  can  be  made  compatible 
with  the  first  and  second  laws  if  we  assume  a  force  of 
this  intensity  per  unit  mass  attracting  the  particle  to 
the  origin.  The  particle  is  acted  on  by  no  forces  with 
respect  to  the  Newtonian  frame  ;  it  is  acted  upon  by 
an  attraction  of  amount  mroo2  towards  the  origin  with 
respect  to  the  new  non-Newtonian  frame.  Thus  the 
first  and  second  laws  have  been  rendered  independent 
of  special  reference  to  Newtonian  frames  by  the  assump- 
tion that  force  (like  position,  velocity,  etc.)  is  relative 
to  the  spatio-temporal  frame  of  reference  which  is 
used  for  placing  and  dating  the  phenomena  under 
consideration. 

(2)  Let  us  now  take  a  slightly  more  complex  case. 
Let  us  suppose  that  the  particle  in  question  is  a  friction- 
less  ring  which  can  slide  along  the  particular  spoke 
of  the  wheel  that  is  chosen  as  the  X-axis,  and  that  the 
wheel   rotates  as  before.     Relative  to   Newtonian  axes 


174  SCIENTIFIC   THOUGHT 

the  ring  has  no  acceleration  along  the  instantaneous 
direction  of  this  spoke.  Along  the  instantaneous 
direction  of  the  normal  to  it,  it  has  an  acceleration 
2.1V0.  It  is  therefore  acted  upon  by  a  Newtonian  force 
(viz.,  the  pressure  of  the  spoke  pushing  it  from  behind) 
of  amount  P  =  2mxa>.  How  will  this  appear  to  people 
who  rotate  with  the  wheel?  Relatively  to  their  axes, 
the  particle  will  move  along  the  X-axis  with  an  accelera- 
tion .r,  whilst  it  will  have  no  velocity  or  acceleration 
along  the  Y-axis.  They  will  therefore  have  to  say  (if 
they  want  to  keep  the  form  of  the  first  two  laws  of 
motion)  that  the  ring  is  repelled  from  the  origin  with  a 
force  mx.  And  it  is  easy  to  show  that  the  intensity 
of  this  must  be  ;/mo2,  i.e.,  it  will  be  a  force  varying 
directly  with  the  distance  of  the  particle  from  the  origin. 
On  the  other  hand,  they  will  have  to  say  that  there  is 
no  resultant  force  acting  on  the  ring  in  the  direction 
of  their  Y-axis.  For  the  ring  keeps  all  the  time  to  the 
X-axis.  But,  if  they  measured,  they  might  be  expected 
actually  to  find  the  pressure  P  acting  from  the  spoke 
to  the  ring.  How  would  they  get  over  this?  They 
would  say  :  "The  spoke  attracts  the  ring  with  a  force 
equal  to  P,  and  this  just  balances  the  pressure  of  the 
spoke  on  the  ring."  Thus  by  assuming  a  repulsive 
force  from  the  origin,  varying  directly  with  the  distance, 
and  an  attractive  force  between  the  ring  and  the  spoke, 
varying  directly  with  the  velocity  along  the  spoke,  they 
could  reconcile  the  form  of  the  first  two  laws  with  their 
non-Newtonian  frame  of  reference.  This  latter  force 
would  indeed  be  of  a  curious  kind,  for  particles  would 
be  attracted  by  the  side  of  the  spoke  that  faced  the 
direction  of  rotation  and  repelled  by  the  other  face,  but 
they  could  deal  with  this  by  something  like  a  "two- 
fluid  theory." 

In  these  two  examples  we  have  only  partially  departed 
from  a  Newtonian  frame  of  reference.  We  have  taken 
non-Newtonian  axes  but  have  kept  to  a  Newtonian  clock. 
It  is  obvious  that,  if  we  kept  Newtonian  axes  but  took  a 


TRADITIONAL   KINETICS  175 

non-Newtonian  clock,  we  could  equally  preserve  the 
form  of  the  first  two  laws  by  introducing  suitable  non- 
Newtonian  forces.  Suppose  a  particle  were  moving 
with  a  uniform  rectilinear  velocity  with  respect  to  a 
Newtonian  frame.  Suppose  that  we  then  substituted 
for  a  pendulum  clock  a  water-tank  with  a  hole  in  it  as 
our  time-measurer,  and  judged  equal  times  as  those  in 
which  equal  masses  of  water  flowed  from  the  tank.  Let 
us  keep  the  Newtonian  spatial  axes  this  time.  As  the 
head  of  water  in  the  tank  decreases  the  water  flows  out 
more  slowly,  as  judged  by  a  Newtonian  clock.  It  follows 
that,  at  the  latter  part  of  the  experiment,  the  particle  will 
move  further  while  a  pound  of  water  flows  out  of  the 
tank  than  it  did  at  the  beginning.  Hence,  with  respect 
to  our  new  non-Newtonian  clock,  the  particle  will  be 
moving  with  an  accelerated  rectilinear  motion.  If  we 
want  to  keep  the  form  of  the  first  two  laws  we  shall 
therefore  have  to  introduce  a  non-Newtonian  force,  acting 
in  the  direction  of  motion  of  the  particle. 

It  should  now  be  evident  that,  so  far  as  concerns  the 
first  two  laws  of  motion,  their  form  can  be  kept,  irre- 
spective of  the  frame  of  reference  chosen,  provided  we 
admit  the  (at  any  rate  partial)  relativity  of  forces  to 
frames  of  reference.  It  remains  to  consider  more  care- 
fully the  nature  of  the  non-Newtonian  forces  that  would 
have  to  be  introduced  with  non-Newtonian  frames  of 
reference.  In  particular  we  want  to  know  whether  the 
third  law  can  be  kept  too  when  we  give  up  the  restriction 
to  Newtonian  frames.  One  thing  we  notice  at  once. 
That  is  that  the  non-Newtonian  attractionsand  repulsions, 
which  were  introduced  by  the  adoption  of  non-Newtonian 
frames  of  reference,  are  all  proportional  to  the  inertial 
masses  of  the  particles  on  which  they  act.  Again,  they 
act  on  every  particle  under  consideration,  regardless  of 
its  physical  or  chemical  peculiarities,  of  the  medium  in 
which  it  may  happen  to  be,  and  so  on.  Now  this  reminds 
us  irresistibly  of  gravitational  attractions  ;  and  suggests, 
as  it  did  to  Einstein,  that  the  law  of  gravitation    may 


176  SCIENTIFIC  THOUGHT 

have  some  connexion  with  these  non-Newtonian  forces 
which  are  bound  up  with  non-Newtonian  frames  of 
reference.  Compare  e.g.,  the  two  cases  of  a  heavy  body 
resting  on  a  weighing  machine,  and  the  ring  in  the 
second  example.  The  heavy  body  rests  in  a  Newtonian 
frame,  and  yet  the  spring  of  the  machine  is  compressed, 
thus  indicating  that  an  upward  thrust  is  being  exerted 
by  the  spring  on  the  heavy  body.  We  say  that  this 
thrust  must  be  balanced  by  a  pull  downwards  on  the 
body,  and  we  ascribe  this  pull  to  the  gravitational 
attraction  of  the  earth.  In  exactly  the  same  way  we 
found  that  the  observers  who  used  the  rotating  wheel 
as  their  spatial  axes  would  have  to  assume  an  attraction 
between  the  ring  and  one  side  of  the  spoke,  to  account 
for  the  fact  that  the  ring  did  not  move  at  right  angles  to 
the  spoke  in  spite  of  the  observable  pressure  of  the  latter 
on  the  former.  Lastly,  consider  the  repulsive  force 
from  the  origin  which  the  observers  on  the  moving 
wheel  would  have  to  suppose  to  be  acting  on  the  ring. 
The  peculiarity  of  this  is  that  to  all  appearance  it  does 
not  obey  the  third  law.  There  is  a  field  of  force,  to 
which  every  particle  is  subjected  when  referred  to  the 
axes  in  question  ;  but  it  cannot  be  said  that  the  force 
on  one  particle  is  balanced  by  an  equal  and  opposite 
force  on  another  particle.  Some  non-Newtonian  forces 
then,  it  would  seem,  do  not  obey  the  third  law.  Thus 
it  seems  that  the  first  two  laws  are  more  general  than 
the  third,  since  they  can  be  reconciled  with  any  frame 
of  reference  by  the  introduction  of  suitable  forces,  whilst 
it  is  only  for  Newtonian  forces  that  the  third  law  holds 
universally.  This  conclusion  could  however,  in  theory, 
be  avoided  by  the  introduction  of  hypothetical  concealed 
masses  ;  so  that  the  non-Newtonian  forces  on  observable 
masses  might  be  regarded,  as  the  third  law  requires, 
as  one  side  of  stresses  between  these  observable  masses 
and  the  hypothetical  concealed  ones.  Thus  all  the  laws 
of  motion  can  be  formally  preserved  relative  to  any 
frame  of  reference,    provided   it    is  assumed    that    new 


TRADITIONAL   KINETICS  177 

frames  imply  new  forces,  and  provided  that  we  are 
allowed  to  assume  such  concealed  masses  as  we  need. 

I  will  end  this  chapter  by  trying  to  make  clear  the 
difference  between  the  laws  of  motion  and  the  special 
laws  of  nature,  such  as  those  of  electricity  or  magnetism 
or  heat.  We  shall  then  see  that,  on  the  traditional 
view,  the  law  of  gravitation  occupies  a  curious  position, 
intermediate  between  the  two  sets  of  laws. 

The  laws  of  motion  do  not  profess  to  tell  us  in  detail 
how  motions  are  caused  or  modified.  What  they  do  is 
to  tell  us  the  general  conditions  which  all  motions,  how- 
ever produced,  must  conform  to.  They  take  no  account 
of  the  kind  of  matter  which  is  moved,  or  of  its  physical 
or  chemical  state  at  the  time  ;  the  one  property  of 
matter,  other  than  purely  geometrical  properties,  which 
appears  in  the  laws  of  motion  is  inertial  mass.  The 
special  laws  of  nature,  on  the  other  hand,  tell  us  about 
the  various  causes  of  motion.  They  have  to  take  into 
account  all  sorts  of  properties  of  bodies  beside  their 
inertial  masses.  They  have  to  consider  whether  they 
be  electrically  charged  or  not,  whether  they  be  hot 
or  cold,  magnetised  or  unmagnetised,  and  what  sort 
of  medium  surrounds  them.  Now,  the  law  of  gravi- 
tation, on  the  traditional  view,  is  in  one  way  like  a 
special  law  of  nature,  and,  in  another  way,  more  like 
the  general  laws  of  motion.  It  professes  to  tell  us  one 
of  the  causes  which  start  and  modify  motions.  So  far 
it  resembles  a  special  law  of  nature.  But  the  only 
property  of  matter  that  it  has  to  consider  is  common 
to  all  matter,  viz.  gravitational  mass.  And  this  proves 
to  be  identical  with  the  one  property  which  is  considered 
in  the  laws  of  motion,  viz.  inertial  mass.  Thus  there 
seems  to  be  a  very  much  closer  connexion  between  the 
laws  of  motion  and  the  law  of  gravitation  than  between 
any  of  the  special  laws  of  nature  and  the  laws  of  motion. 
Again,  if  we  are  in  earnest  with  the  Relational  Theory 
of  Motion,  we  must  suppose  that  all  the  motions  with 
which    Mechanics    deals    take    place    with    respect    to 


i78  SCIENTIFIC   THOUGHT 

material  axes.  And,  since  all  matter  attracts  all  other 
matter  gravitationally,  on  the  traditional  view,  all  bodies 
will  be  attracted  more  or  less  by  the  axes  to  which  their 
motions  are  referred.  It  thus  seems  not  unlikely  ante- 
cedently that  there  should  be  a  very  close  connexion 
between  the  laws  of  motion  and  the  law  of  gravitation, 
and  that  a  completely  Relational  system  of  Mechanics 
should  contain  a  theory  of  gravitation.  The  details  of 
this  are  reserved  for  the  next  chapter,  but  it  is  hoped 
that  the  foregoing  discussion  of  the  traditional  laws  of 
motion  and  gravitation  may  have  brought  the  reader 
into  a  proper  frame  of  mind  for  understanding  and 
criticising  the  General  Theory  of  Relativity. 

The  following  additional   works   may  be  consulted 
with  advantage  : 

B.  A.  W.  Russell,  Principles  of  Mathematics,  vol.  i,  Part  VII. 

E.  Mach,  Scie?ice  of  Mechanics. 

H.  Poincare,  La  Science  et  VHypothese. 

„  Scie?ice  et  Methode. 

,,  Le  Vaieur  de  la  Science. 

P.  Painleve,  Les  Axiomes  de  la  Mecaniq ue.    (Paris.    Gauthier- 
Villars.) 


CHAPTER   VI 

"What's  the  use  of  Mercator's  North  Poles  and  Equators, 
Tropics,  Zones,  and  Meridian  Lines  ?" 
So  the  Bellman  would  cry  ;  and  the  crew  would  reply  ; 
"  They  are  merely  conventional  signs  !  " 

"  Other  maps  are  such  shapes,  with  their  islands  and  capes  ! 
But  we've  got  our  brave  Captain  to  thank," 
(So  the  crew  would  protest),  "  that  he's  bought  us  the  best — 
A  perfect  and  absolute  blank  !  " 

(Lewis  Carroll,  The  Hunting  of  the  Snark.) 

Modification  of  the  Traditional  Kinetics  (continued). 
(2)  The  General  Theory  of  Relativity.  Summary 
of  Part  I 

In  the  last  chapter  we  treated  the  traditional  laws  of 
motion  without  reference  to  the  kinematic  results  of  the 
Special  Theory  of  Relativity,  outlined  in  Chapter  IV. 
That  is  to  say,  we  combined  the  traditional  Kinetics 
with  the  traditional  Kinematics.  We  must  now  take 
a  step  forward,  and  show  that  the  traditional  laws  of 
motion  are  not  compatible  with  the  modified  kinematics 
of  even  the  Special  Theory  of  Relativity.  We  shall 
then  be  able  to  advance  to  the  General  Theory. 

There  is  no  need  for  me  to  treat  the  kinetics  of 
the  Special  Theory  in  any  detail,  because  it  is  only  a 
half-way  house  to  the  General  Theory.  I  will  therefore 
content  myself  with  a  single  example  to  show  that 
the  traditional  laws  of  motion  cannot  be  reconciled, 
without  modification,  with  the  kinematics  of  the  Special 
Theory  and  with  the  Restricted  Physical  Principle  of 
Relativity. 

Let  us  suppose  that  two  sets  of  observers  were  doing 

179 


i8o  SCIENTIFIC   THOUGHT 

experiments  to  determine  inertial  mass  by  the  impact 
of  bodies,  as  described  in  the  last  chapter.  One  shall 
be  on  the  platform/,  and  the  other  on  the  platform />2  of 
Chapter  IV.  These  platforms  are  in  uniform  rectilinear 
relative  motion  in  a  Newtonian  frame.  The  velocity 
of  the  first  with  respect  to  the  second,  as  measured  by 
observers  on  the  second,  is  v12.  Let  two  bodies  be 
moving  along  />,  in  the  direction  in  which  px  is  itself 
moving  relatively  to  p2.  Let  their  velocities  relative 
to  />,,  as  measured  by  observers  on  it,  be  Uj  and  ut 
respectively,  before  they  hit  each  other.  After  they 
have  hit,  let  their  velocities  with  respect  to  px  be  W, 
and  w1  respectively.  Let  the  observers  on  px  ascribe 
to  these  bodies  the  inertial  masses  M1  and  mx  respec- 
tively.    As  we  saw  in  the  last  chapter, 

M1Ul  +  m1u1=M1W1  +  mlw1.  (i) 

Each  body  has  its  own  coefficient,  which  it  keeps  when 
its  velocity  is  altered  by  the  collision,  and  which  is 
independent  of  its  initial  velocity.  There  is  no  doubt 
that  this  is  very  approximately  true  under  ordinary 
conditions  of  experiment  ;  the  question  is  whether  it 
can  be  exactly  true,  consistently  with  the  Physical 
Principle  of  Relativity  and  the  kinematics  of  the 
Special  Theory. 

Let  the  whole  experiment  be  also  watched  by  the 
observers  on  p2.  Let  the  velocities  which  they  ascribe 
to  the  bodies  relatively  to  p2  be  U2,  u2,  W2  and  w2 
respectively.  The  Physical  Principle  of  Relativity  tells 
us  that  if  equation  (i)  expresses  a  genuine  law  of  nature 
in  terms  of  the  observations  of  people  on/j,  the  people 
on  p2  must  be  able  to  find  an  equation  of  precisely  the 
same  form  in  terms  of  their  observations  on  the  same 
phenomena.  That  is,  they  ought  to  find  that  their 
observed  relative  velocities  are  connected  by  an  equation 

M2U2  +  m2u2=M2W2  +  m2w2.  (2) 

In  this  equation  M2  and  m2  will  have  to  be  independent 
of  the  velocities  of  the  bodies  ;    for  it   is  obvious  that 


GENERAL   THEORY   OF    RELATIVITY      181 

the  form  of  the  law  would  not  be  the  same  for  both  sets 
of  observers,  if,  in  the  one  case,  the  coefficients  were 
constants,  and,  in  the  other,  were  functions  of  the 
velocity  of  the  body. 

Now  it  is  easy  to  see  that  anything  of  the  kind  is 
inconsistent  with  the  kinematics  of  the  Special  Theory 
of  Relativity.  If  the  reader  will  look  back  to  equa- 
tion (3)  in  Chapter  IV  he  will  see  that 


U.= 


2—  TT  „.    : 

I  — ■ 


C8 

with  similar  equations,  mutatis  mutandis,  for  u2,  W,  and 
zv2.  It  is  quite  obvious  that,  if  these  values  be  substi- 
tuted in  equation  (2),  we  shall  reach  a  result  which  is 
inconsistent  with  equation  (1),  on  the  assumption  that 
the  masses  are  independent  of  the  velocities.  It  follows 
that  the  traditional  view  that  mass  is  independent  of 
velocity  cannot  be  reconciled  with  the  Physical  Principle 
that  genuine  laws  of  nature  have  the  same  form  for 
all  observers  who  are  in  uniform  rectilinear  relative 
motion,  and  with  the  kinematics  of  the  Special  Theory 
of  Relativity.  It  is  not  difficult  to  see  what  modification 
is  needed.  Let  us  denote  by  MliTJ  the  mass  which  has 
to  be  assigned  to  a  body  moving  with  a  measured 
velocity  \J1  relatively  to  the  Newtonian  frame  px.  Let 
us  put 

M  M 

M      —  Q—    —  K      M        M      — °        —  K      M  • 

ml.  u—      -. FT~2—       l-u       01        mi,w—      ,— tTt~2—       i-w       o> 


l—*  l 


and 


mo         _u     _  m  mo 


J    III  \/,_z^l 


c* 


where  M0  and  m0  are  independent  of  the  velocity.     Let 
us  then  see  whether  the  equation 


M1,uU1  +  *«1,1(K1=M1,wW1  +  7//1,wze/1  (4 


182  SCIENTIFIC   THOUGHT 

expresses  a  possible  law  of  nature,  consistent  with  the 
Physical  Principle  of  Relativity  and  the  kinematics  of 
the  Special  Theory.  If  it  does,  we  ought  to  find  that 
the  measured  velocities  U2,  etc.,  which  the  observers  on 
/\,  ascribe  to  the  bodies  under  experiment,  are  inter- 
connected by  the  equation 

MvvU%+mvjta=  M2,wWz+m2,„w2.  (5) 

By  using  the  transformation  equation  for  relative 
velocities,  and  doing  a  little  tedious  but  quite  straight- 
forward algebra,  the  reader  will  be  able  to  see  for  him- 
self that  this  is  so,  on  one  condition.  The  condition  is 
that  the  total  mass  of  the  system  in  the  direction  of 
motion  is  unaltered  by  the  collision,  i.e. ,  that 

M1,u  +  w1„/=M1,w  +  /«1,,„.  (6) 

On  the  traditional  view  this  is  of  course  a  merely 
analytical  proposition,  since  it  is  part  of  that  view  that 
the  mass  of  each  body  is  an  absolute  constant.  On  the 
present  view  of  mass,  it  is  an  additional  assumption. 
The  law,  obtained  by  combining  (4)  and  (6)  with  the 
definitions  embodied  in  (3),  is  then  a  permissible  law 
of  nature,  whilst  the  traditional  law  embodied  in  (1)  is 
not.  The  assumption  (6)  is,  to  a  very  high  degree  of 
approximation,  equivalent  to  the  assumption  that  the 
total  kinetic  energy  of  the  system  is  unaltered  by  the 
collision.      For 

M 
0  1  M  U  2 

M1,u  =  N/I_Ui2=M0  +  2  -^  very  nearly. 

c2 
Whence  (6)  practically  reduces  to 

1  MoU,2  +  Imp*  =  iMoW,2  +  l-m^w*.  (7) 

2  22  2 

Thus  the  attempt  to  express  the  laws  of  Mechanics  in 
a  form  which  is  consistent  with  the  kinematics  of  the 
Special  Theory  of  Relativity  leads  to  a  connexion 
between    the   three   principles   of  the    Conservation    of 


GENERAL   THEORY   OF   RELATIVITY      183 

Momentum,    of  Mass,   and  of  Energy,  which  was  not 
obvious  on  the  traditional  view. 

The  modified  conception  of  mass,  which  the  Special 
Theory  of  Relativity  requires,  differs  so  little  in 
magnitude  from  that  of  the  traditional  view,  for  all 
ordinary  velocities,  that  it  is  reasonable  to  suppose 
that  the  modified  laws  are  not  merely  admissible  in 
form  but  also  true  in  substance.  Moreover,  the  modified 
laws  agree  with  observations  on  the  motions  of  electrons, 
shot  out  with  enormous  velocities  in  vacuum  tubes ; 
whereas  the  traditional  form  of  the  law  cannot  be 
brought  into  accordance  with  these  results,  except  by 
the  help  of  supplementary  physical  hypotheses  about 
the  charges,  shapes,  etc.,  of  the  particles. 

The  General  Theory  of  Relativity.  Enough  has  now 
been  said  to  show  that  the  traditional  kinetics  needs 
modification  as  soon  as  the  traditional  kinematics  is 
dropped  and  that  of  the  Special  Theory  of  Relativity 
is  substituted  for  it.  And,  as  I  have  tried  to  show  in 
Chapter  IV,  the  negative  results  of  the  Michelson- 
Morley  and  other  experiments  leave  us  no  option  about 
making  at  least  this  substitution.  The  question  now  is, 
not  whether  we  shall  go  so  far,  but  whether  we  ought 
not  to  go  further  still.  Let  us  open  the  subject  by 
asking :  In  what  way  is  the  Special  Theory  of 
Relativity  special? 

The  answer  to  this  question  is  obvious.  In  discuss- 
ing the  Special  Theory  of  Relativity  we  explicitly 
confined  ourselves  to  Newtonian  frames.  In  the  first 
place,  our  kinematic  transformations  assumed  that  the 
two  platforms  px  a.ndp2  were  in  uniform  rectilinear  relative 
motion.  We  did  not  deal  at  all  with  the  case  of  pt 
rotating  with  respect  to  pt  or  moving  with  a  rectilinear 
but  accelerated  motion  with  respect  to  px.  But  this  is 
not  all.  If  one  frame  be  Newtonian  and  another  moves 
with  a  uniform  rectilinear  motion  relatively  to  it,  the 
second  is  also  Newtonian.  But  the  converse  of  this  is 
not  true.    Two  platforms  might  be  in  uniform  rectilinear 


184  SCIENTIFIC   THOUGHT 

relative  motion,  but  neither  of  them  need,  for  that  reason, 
be  Newtonian.  E.g.,  if  their  clocks  were  non-Newtonian 
(e.g.,  were  water-tanks,  as  in  a  previous  example)  both 
these  platforms  would  have  accelerated  rectilinear 
motions  in  a  Newtonian  frame,  and  therefore  neither 
of  them  would  be  a  Newtonian  set  of  axes.  Again, 
suppose  that  px  and  pa  were  attached  at  different 
distances  from  the  centre  to  the  same  spoke  of  a  wheel 
which  rotated  uniformly  in  a  Newtonian  frame.  There 
would  be  no  relative  motion  between  them,  but  neither 
of  them  would  be  Newtonian  axes.  So  the  "speciality" 
of  the  Special  Theory  is  that  it  is  wholly  concerned 
with  Newtonian  frames ;  and  this  not  only  restricts 
the  transformations  to  uniform  rectilinear  relative 
motion,  but  imposes  a  further  condition,  in  virtue 
of  which  one  at  least  of  the  set  is  known  to  be 
Newtonian. 

How  does  this  limitation  show  itself?  The  funda- 
mental fact  on  which  the  kinematic  transformations 
of  the  Special  Theory  was  based  was  that  light  was 
found  to  travel  with  the  same  velocity,  and  in  a 
straight  line,  relative  to  all  the  observers,  although 
they  were  in  motion  relatively  to  each  other.  It  is 
quite  obvious  that,  if  observers  had  chosen  the  spokes 
of  a  rotating  wheel  as  their  axes,  they  would  not  have 
found  that  light  travelled  in  straight,  lines  with  respect 
to  them.  And,  if  they  had  taken  as  their  time-measurer 
some  process  which  was  not  isochronous  as  compared 
with  a  Newtonian  clock,  they  would  not  have  found 
the  velocity  of  light  to  be  uniform,  even  though  they/ 
had  used  the  fixed  stars  as  their  axes.  A  Newtonian 
frame  may  then  be  defined  in  one  of  two  alternative 
ways :  (i)  It  is  a  set  of  axes  and  a  physical  time- 
measurer  with  respect  to  which  light  in  a  homogeneous 
medium  travels  with  a  uniform  rectilinear  velocity. 
Or  (2)  it  is  a  set  of  axes  and  a  time-measurer  with 
respect  to  which  a  particle,  under  the  action  of  no 
resultant  force,  rests  or  moves  uniformly  in  a  straight 


GENERAL  THEORY   OF   RELATIVITY      185 

line.  Owing  to  the  universality  of  gravitation  the 
second  criterion  cannot  literally  be  applied.  We  shall 
also  see,  later  on,  that  the  same  reason  renders  the 
first  criterion  not  strictly  true  of  any  natural  frame. 
Thus  a  Newtonian  frame  is  an  ideal  limit  rather  than 
an  actual  fact.  Still,  the  frame  in  which  the  fixed  stars 
form  the  axes  and  a  properly  constructed  and  regulated 
clock  forms  the  time-measurer  is  very  nearly  Newtonian 
for  all  experiments  that  we  can  do.  The  transformation 
equations  of  the  Special  Theory  enable  us  to  pass  from 
the  place  and  date  of  any  event  in  any  one  such  frame 
to  its  place  and  date  in  any  other  such  frame.  But 
they  tell  us  nothing  about  its  place  or  date  in  any 
frame  which  is  not  Newtonian  ;  and  no  frame  is 
Newtonian  unless  its  axes  either  rest  or  move  with 
a  uniform  rectilinear  velocity,  as  judged  by  a  New- 
tonian clock,  relatively  to  Newtonian  axes.  Again,  the 
Restricted  Physical  Principle  of  Relativity  only  says 
that  observers  on  different  Newtonian  frames  will  all 
find  laws  of  identical  form  for  the  same  natural 
phenomena.  It  does  not  assert  that  an  observer  on 
a  non-Newtonian  frame  will  find  no  difference  in  the 
form  of  the  laws  which  interconnect  the  magnitudes 
that  he  measures,  when  watching  a  certain  natural 
phenomenon. 

The  question  is  whether,  and  to  what  extent,  this 
restriction  to  a  certain  set  of  frames  of  reference  can 
be  removed.  It  is  easy  to  state  in  general  terms  the 
kind  of  problem  with  which  we  are  faced.  On  the 
one  hand,  we  can  get  at  the  laws  of  nature  only  by 
measuring  various  observable  magnitudes  and  finding 
out  the  functional  correlations  that  hold  between  them. 
And  we  can  do  this  only  by  referring  all  events 
in  nature  to  a  spatio-temporal  frame  of  reference  of 
some  kind,  in  which  each  event  has  a  certain  place 
and  date.  Innumerable  different  frames  of  reference 
could  be  taken  for  dating  and  placing  the  events  of 
nature.     On  the  other  hand,  presumably  there  are  laws 

N 


i86  SCIENTIFIC   THOUGHT 

of  nature  which  are  absolute,  and  independent  of  any- 
particular  frame  of  reference.  The  laws  discovered  by 
observers  who  use  a  certain  frame  of  reference  wrill 
be  transcriptions  of  these  absolute  relations,  in  terms 
of  that  particular  frame.  Thus,  we  may  suppose  that 
they  will  depend  partly  on  the  absolute  relations  of 
events  in  nature  and  partly  on  the  particular  frame 
used  by  these  observers.  It  would  thus  be  reasonable 
to  suppose  that,  on  comparing  the  laws  discovered  by 
observers  who  observe  the  same  phenomenon  and  use 
all  kinds  of  different  frames  of  reference,  we  might  be 
able  to  extract  a  kind  of  "kernel,"  which  should  be 
neutral  as  between  them  all.  This  kernel  would  be  the 
absolute  law  of  the  phenomenon  in  question,  and  it 
is  this  which  the  General  Theory  of  Relativity  seeks 
to  extract. 

It  may  be  worth  while  to  give  a  few  illustrations 
from  other  regions,  in  order  to  make  the  idea  familiar 
to  the  reader.  (i)  Suppose  the  League  of  Nations 
were  to  lay  down  certain  general  rules  about  naviga- 
tion, which  were  binding  on  all  members  of  the 
League.  They  would  have  to  be  translated  into 
English,  French,  Italian  (and  soon,  one  hopes,  German 
and  Russian).  These  various  translations  would  look 
extremely  different.  And  it  would  be  impossible  to 
express  the  rules  without  some  symbolism  or  other 
until  telepathy  becomes  commoner  than  it  now  is. 
Yet  there  would  be  something,  viz.,  the  content  of  the 
rules,  which  would  be  independent  of  any  particular 
language  or  other  system  of  symbols  in  which  they 
happened  to  be  expressed. 

(2)  Another  example  may  be  helpful  to  persons  with 
an  elementary  knowledge  of  mathematics.  It  is  a  very 
simple  intrinsic  property  of  the  triangle  that  the  bisectors 
of  its  three  angles  all  meet  at  one  point.  If  you  try 
to  prove  this  by  analytical  geometry  you  will  have  to 
choose  some  set  of  co-ordinates  ;  they  may  be  rect- 
angular Cartesians,    or   oblique   Cartesians,   or  polars. 


GENERAL  THEORY   OF   RELATIVITY      187 

In  any  case  you  will  get  very  complicated  equations 
in  terms  of  the  co-ordinates  which  you  assign  to  the 
three  corners  of  the  triangle.  And  these  equations 
will  be  very  different  according  to  the  system  of  co- 
ordinates that  you  have  chosen  for  reference.  Yet  they 
all  express  the  same  simple  fact,  which  is  intrinsic  to 
the  triangle  as  such,  and  quite  independent  of  any  set 
of  co-ordinates. 

Now,  on  the  traditional  view,  the  distance  between 
two  events  and  the  time-lapse  between  them  are  two 
distinct  facts.  It  is  true  that,  on  the  traditional  view, 
the  measured  distances  between  non-contemporary  events 
will  be  different  for  observers  who  are  in  uniform  recti- 
linear motion  with  respect  to  each  other.  But  it  is 
supposed  that  their  dates  will  be  the  same  for  all 
Newtonian  frames,  and  that  it  will  be  independent  of 
the  distance  between  the  events.  Now,  the  Special 
Theory  shows  that  this  is  not  true  even  when  we 
confine  ourselves  to  Newtonian  frames.  We  saw  that 
observers  on  platforms  which  are  in  relative  recti- 
linear uniform  motion  will  not  ascribe  the  same  time- 
lapse  to  the  same  pair  of  events  ;  and  that,  if  these 
events  be  separated  in  space,  the  amount  of  time-lapse 
ascribed  to  them  by  observers  who  move  relatively 
to  them  will  depend  on  their  distance  apart.  Thus, 
measured  distance  between  events  and  measured  time- 
lapse  between  events  are  mixed  up  with  each  other, 
and  are  partly  dependent  on  the  frame  of  reference, 
even  when  we  confine  ourselves  to  Newtonian  frames. 
Is  there  anything  connected  with  spatial  and  temporal 
separation  which  has  the  same  measure  for  all  Newtonian 
frames?  There  is,  as  can  easily  be  seen.  Suppose  that 
two  adjacent  events  have  respectively  the  co-ordinates 
and  dates  xly  yx,  z1}  /,,  andxx  +  dxx,  yx  +  dyx,  sx  +  dzx,  and 
tlJrdt1  with  respect  to  the  Newtonian  frame  px.  Let 
them  have  the  corresponding  letters,  with  2  suffixed 
instead  of  1,  with  respect  to  the  frame  p^,  which  moves 
relatively   to  px   in    the   ^-direction    with    the    uniform 


iSS  SCIENTIFIC  THOUGHT 

velocity  v21.     It  follows  immediately  from  the  transfor- 
mation equations  of  Chapter  IV  that 

dx2  =  kn(dx1  —  v^dtj) 
a n d  dtt  =  kAd^  —  " dxx )  • 

Whence 

since  kol--=  —==.  by  definition. 

c2 

Now  d^2  =  d[y22  and  dz*  =  ^2a,  since  there  is  no  relative 
motion  in  these  directions.     Therefore  finally, 

dx2  +  dy2  +  dz2  —  c2dt2  =  dx2  +  dy2  +  dz2  —  c2dt2.     (8) 

Here  then  we  have  a  magnitude,  connected  with  a 
pair  of  events,  which  has  the  same  numerical  measure 
with  respect  to  all  Newtonian  frames.  We  will  take 
this  magnitude  with  its  sign  reversed,  for  reasons  which 
will  appear  later.  We  will  call  it  the  square  of  the 
Spatio-Temporal  Separation  of  the  two  events,  and  will 
denote  it  by  dcr.  The  square  of  the  spatial  separation 
is,  of  course,  dx^  +  dy^  +  dz^  in  the  one  system  and 
dx£-\-dy£-\-dz£  in  the  other.  The  temporal  separation 
is  dtx  in  one  system  and  dt2  in  the  other.  It  is  clear 
that  the  spatio-temporal  separation  has  a  claim  to 
represent  something  intrinsic  to  the  pair  of  events, 
and  neutral  as  between  different  frames  of  reference, 
which  claim  cannot  be  made  for  either  the  spatial  or 
the  temporal  separation.  It  is,  at  any  rate,  invariant 
and  neutral  as  between  all  Newtonian  frames,  whilst 
the  other  two  are  not  invariant  or  neutral,  even  with 
this  restriction. 

It  will  be  noticed  that,  if  the  two  events  be  the 
successive  occupations  of  two  adjacent  places  by  some- 
thing that  travels  with  velocity  ux  with  respect  to  one 


GENERAL   THEORY   OF   RELATIVITY      189 

frame  and  u2  with  respect  to  the  other,  the  spatio- 
temporal  separation  takes  the  form 

do*  =  {<*-  u*)dt*  =  (c-2  -  tt*)dt2\ 

If  what  is  travelling  be  light,  or  any  other  electro- 
magnetic disturbance,  ?/x  =  u2  —  c.  Whence  da*  =  o. 
That  is,  the  spatio-temporal  separation  between  two 
events  which  are  the  successive  arrivals  of  a  wave  of 
light  at  two  adjacent  positions  is  o,  although  of  course 
both  the  spatial  and  the  temporal  separations  of  the 
two  events  are  finite.  This  explains  why  we  took  the 
expression  with  its  sign  reversed.  We  want  the  square 
of  the  separation  to  be  always  positive  for  the  successive 
events  that  constitute  any  real  motion.  With  the  present 
choice  of  sign  this  will  be  so,  unless  the  moving  thing 
travels  faster  than  light.  With  the  other  choice  of 
sign  the  square  of  the  separation  would  always  be 
negative  for  anything  that  travelled  more  slowly  than 
light.  Now  we  know  nothing  that  travels  faster  and 
innumerable  things  that  travel  more  slowly  than  light. 
Hence  our  convention  as  to  sign  is  justified. 

This  concept  of  spatio-temporal  separation  is  funda- 
mental to  the  General  Theory  of  Relativity.  We  take 
it  as  a  hypothesis  that  this  separation  is  an  intrinsic 
relation  between  a  pair  of  events,  which  has  nothing  to 
do  with  frames  of  reference,  though,  of  course,  we  shall 
always  meet  with  it  and  measure  it  in  terms  of  the 
particular  frame  that  we  happen  to  use  in  order  to  place 
and  date  the  events  of  nature.  If  it  be  asked  what 
ground  there  is  for  this  hypothesis,  I  think  we  must 
begin  by  distinguishing  between  what  suggests  it  and 
what  justifies  it.  What  suggests  it  is  the  in  variance  of 
this  measured  magnitude  as  between  all  Newtonian 
frames.  But,  if  it  is  to  be  justified,  this  must  be  done 
in  the  usual  way  by  working  out  the  consequences  of 
the  hypothesis  and  seeing  whether  they  accord  with 
experimental  facts. 

We  have  seen  what  form  the  spatio-temporal  separa- 


190  SCIENTIFIC   THOUGHT 

tion  takes  when  expressed  in  terms  of  Newtonian  co- 
ordinates and  clock- readings.  It  will  be  worth  while, 
however,  explicitly  to  mention  the  important  character- 
istics of  this  expression  before  going  further,  (i)  It 
is  homogeneous  and  of  the  second  degree  in  the  four 
variables  which  it  involves.  (2)  The  coefficients  of  the 
variables  are  all  constants.  In  fact,  by  a  suitable  choice 
of  units,  they  could  all  be  reduced  to  unity.  When 
distance  is  measured  in  centimetres  and  time-lapse  in 
seconds,  light  has  the  velocity  c,  and  the  time-factor 
has  to  be  multiplied  by  this  constant.      But,  if  the  unit 

of  time  were  taken  to  be,   not  the  second,   but  -  of  a 

c 

second,  the  velocity  of  light  would  be  unity.  We  chose 
our  units  of  space  and  our  units  of  time  quite  inde- 
pendently, when  it  was  not  suspected  that  there  was  a 
fundamental  connexion  between  these  two  factors  in 
nature.  It  so  happens  that  we  have  chosen  a  very 
large  unit  of  time  as  compared  with  the  unit  of  space  ; 
and  that  is  the  only  reason  why  the  large  constant  c 
appears  in  the  expression  for  the  spatio-temporal  separa- 
tion. (3)  The  last  important  point  to  notice  in  this 
connexion  is  that  the  coefficient  of  the  time-variable  is 
of  opposite  sign  to  that  of  the  space-variables  in  the 
expression  for  the  spatio-temporal  separation.  This 
betrays  the  fact  that  there  is  ultimately  a  radical  dis- 
tinction between  the  space  factor  and  the  time  factor 
in  nature,  in  spite  of  their  intimate  interconnexion,  and 
in  spite  of  the  fact  that  the  two  are,  within  certain  limits, 
interchangeable. 

Now  we  can  quite  well  understand  that  the  expres- 
sion for  the  spatio-temporal  separation,  in  terms  of  the 
co-ordinates  and  time  -  readings  of  a  non-Newtonian 
frame,  may  be  very  different  from  the  expression  for  the 
same  fundamental  fact  in  terms  of  a  Newtonian  frame. 
Let  us  first  illustrate  this  by  a  very  simple  example 
from  ordinary  geometry.  If  we  take  the  traditional 
view  of  Space  and  Time  the  distance  between  two  points 


GENERAL   THEORY   OF   RELATIVITY      191 

is  an  intrinsic  relation  between  them,  and  is  wholly 
independent  of  the  system  of  co-ordinates  to  which  we 
refer  the  points.  Let  us  first  suppose  that  they  are 
referred  to  a  set  of  rectangular  Cartesian  co-ordinates 
Cx.  Let  their  ;r-co-ordi nates  in  this  system  be  x\  and 
.r1  +  dx\  respectively,  with  similar  expressions  for  their 
y-  and  ^-co-ordinates.  Then  the  expression  for  the 
square  of  their  distance  apart  is 

dx\2  4-  dyf  +  dz*. 
Now  refer  them  to  another  set  of  rectangular  Cartesians 
C2.  This  might  consist  of  the  original  ones  twisted  as 
a  rigid  body  about  their  origin.  The  three  edges  of  a 
biscuit  box  with  one  corner  fixed  would  be  an  example. 
Let  the  co-ordinates  of  the  points  with  respect  to  this 
system  be  x\  and  x2  +  dx'2,  etc.,  respectively.  The  ex- 
pression for  the  square  of  the  distance  apart  of  the  two 
points  in  the  new  co-ordinates  is 

dx22  +  dy22  +  dz?. 
It  is  of  the  same  form   and    the    same    magnitude    as 
before.     This  is  exactly  analogous  to  the  invariance  of 
the  expression  for  the  spatio-temporal  separation  of  two 
events  with  respect  to  two  Newtonian  frames. 

Suppose  now  that,  instead  of  referring  the  two  points 
to  Cartesian  co-ordinates,  we  were  to  refer  them  to  polars. 
Call  this  system  P3.  Let  the  co-ordinates  of  the  two 
points  be  respectively  r3,#3,c£3  and  r3  +  dr3,93  +  d63,<f>3  +  d<i>3, 
in  this  system.  The  distance  apart  will  now  be  ex- 
pressed by  the  formula 

dr./  +  r32d032  +  r32sin%d<f>3*. 

It  will  be  noticed  that  this  expression  has  one  important 
analogy  to,  and  one  important  difference  from,  the  ex- 
pression in  terms  of  Cartesians.  It  resembles  the  latter 
in  that  it  is  still  a  homogeneous  function  of  the  second 
degree  in  terms  of  the  three  differentials.  It  differs  in 
that  these  differentials  no  longer  all  have  constant  co- 
efficients. Their  coefficients  now  contain  functions 
of  the  co-ordinates  themselves. 


K)j  SCIENTIFIC   THOUGHT 

Now,  just  as  the  passage  from  Cartesian  to  Polar 
co-ordinates  makes  this  difference  in  the  expression  for 
the  distance  between  two  points  on  the  ordinary  geo- 
metrical view,  so  we  may  expect  that  the  passage  from 
a  Newtonian  to  a  non-Newtonian  frame  of  reference 
will  make  a  similar  difference  to  the  expression  for  the 
spatio-temporal  separation  between  two  events.  We 
may  expect  that  the  expression  will  still  be  homo- 
geneous and  of  the  second  degree  in  terms  of  the 
differentials  of  the  non-Newtonian  co-ordinates  and 
dates,  but  that  these  differentials  will  no  longer  have 
constant  coefficients. 

In  order  to  make  the  next  step,  let  us  again  revert 
to  a  simple  example  in  ordinary  geometry.  Let  us 
confine  ourselves  to  points  on  a  surface,  and  let  us 
suppose,  to  begin  with,  that  this  surface  is  a  sphere. 
We  will  suppose  that  persons  confined  to  the  surface 
of  the  sphere  are  trying  to  find  an  expression  for  the 
distance  apart  of  two  adjacent  points,  as  measured  on 
the  surface  of  the  sphere.  This  will  of  course  be  that 
part  of  the  great  circle  passing  through  the  two 
points,  which  is  included  between  them.  Now  the 
surface  of  the  sphere  could  be  mapped  out  into  a 
network  of  co-ordinates  in  innumerable  different  ways. 
We  might  fix  the  position  of  a  point  by  parallels 
of  latitude  and  meridians  of  longitude,  as  ordinary 
Atlases  do.  Or  we  might  fix  it  by  taking  an  origin 
on  the  equator  and  drawing  a  great  circle  from  here  to 
the  point  in  question,  and  noticing  the  length  of  this 
arc  and  the  angle  that  it  makes  with  the  equator. 
Again  we  might  take  the  equator  and  some  meridian 
of  longitude  as  a  pair  of  mutually  normal  axes  and 
define  the  position  of  a  point  by  the  arcs  of  the  two 
great  circles  which  pass  through  it  and  are  normal  to 
the  equator  and  the  meridian  respectively.  The  last- 
mentioned  set  of  co-ordinates  would  be  analogous  to 
Cartesians  in  a  plane,  and  the  set  mentioned  before 
would  be  analogous  to  plane  Polars.     We  should  find 


GENERAL   THEORY   OF   RELATIVITY      193 

that  two  independent  variables  were  always  necessary 
to  fix  the  position  of  a  point.  And  we  should  find  that 
the  distance  between  any  pair  of  adjacent  points  on  the 
sphere,  as  measured  along  the  sphere's  surface,  was 
always  a  homogeneous  quadratic  function  of  the  small 
differences  between  their  corresponding  co-ordinates  in 
any  system.  So  far  there  is  complete  analogy  with  a 
plane.  But  we  should  find  the  following  very  important 
difference.  In  the  plane,  or  in  ordinary  three  dimen- 
sional Space,  as  we  saw,  we  always  can  find  a  system 
of  co-ordinates,  viz.,  Cartesians,  in  terms  of  which  the 
expression  for  the  distance  involves  no  coefficients 
other  than  constants  (which  can  of  course  always  be 
reduced  to  unity  by  a  suitable  choice  of  our  units). 
On  the  sphere  we  should  find  that  it  was  impossible  to 
choose  any  set  of  co-ordinates  for  the  whole  surface,  in 
terms  of  which  the  expression  for  the  distance  between 
two  points  involves  nothing  but  constant  coefficients. 
Always  we  shall  find  that  one  or  both  of  the  differentials 
is  multiplied  by  a  function  of  the  co-ordinates. 

This  then  is  an  intrinsic  difference  between  spheres 
and  planes.  It  is  connected  with  the  fact  that  a  sphere 
cannot  be  unfolded  into  a  plane  without  stretching,  as,  for 
instance,  a  cone  can.  We  see  then  that  there  are  at  least 
two  intrinsically  different  kinds  of  surface.  With  both 
of  them  the  expression  for  the  distance  of  two  points 
measured  along  the  surface  will  involve  non-constant 
coefficients,  when  expressed  in  terms  of  some  set  of  co- 
ordinates upon  the  surface.  But  with  the  one  kind  of 
surface  this  will  be  so,  not  merely  for  some,  but  for  all 
possible  sets  of  co-ordinates  upon  the  surface.  And, 
with  the  other  kind,  it  will  be  possible  to  find  a  set  of 
co-ordinates  on  the  surface,  in  terms  of  which  the  ex- 
pression for  the  distance  of  two  adjacent  points  involves 
no  coefficients  but  constants. 

Let  us  now  leave  the  points  and  surfaces  of  pure 
geometry,  and  apply  our  results  to  the  events  of  nature 
and  their  spatio-temporal  separations.     Just  as  surfaces 


194  SCIENTIFIC   THOUGHT 

mav  be  of  two  intrinsically  different  kinds,  so  nature, 
as  a  sum  total  of  events,  might  theoretically  be  of  one 
kind  or  another.  It  might  have  such  an  intrinsic 
structure  that  it  was  always  possible  to  find  a  frame, 
viz.,  a  Newtonian  one,  with  respect  to  which  the  spatio- 
temporal  separation  of  any  pair  of  events  takes  the  form 

<*d?-cb?-df-d&. 

On  the  other  hand  nature  might,  like  the  sphere 
in  geometry,  have  such  an  intrinsic  structure  that  no 
possible  frame  could  be  found  with  respect  to  which 
the  spatio-temporal  separation  involved  only  constant  co- 
efficients. Now  the  most  general  homogeneous  quadratic 
expression  for  the  spatio-temporal  separation  of  a  pair 
of  adjacent  events  in  terms  of  any  frame  is  obviously  of 
the  form 

+  gudOidt + g2Zdd2d63  +  gtide2dt  +  gZidOzdt,  (9) 

where  6V  02,  and  $3  are  the  spatial  parameters,  and  t  is 
the  temporal  parameter,  which  one  of  the  events  has  in 
respect  to  the  spatial  axes  and  the  clocks  of  this  frame. 
The    g's    are    any    functions   whatever    of    these    four 
variables.      Now,  if  it  is  to  be  possible  to  find  a  frame 
with    respect  to    which    the  spatio-temporal   separation 
takes  the  Newtonian  form,  these  g's  cannot  be  just  any 
functions.      The    reducibility    to    the    Newtonian    form 
imposes   certain    very    general    conditions    on    the  g's. 
It  can   be  shown   that   it  is    possible    to   find   a  frame, 
with    respect   to   which    the  spatio-temporal   separation 
assumes  the  form  with  constant  coefficients,  if  and  only 
if  the  g's  are  of  such  a  kind  that  a  certain  very  com- 
plicated function  of  them,  called  the  Riemann-Christoffel 
Tensor',  vanishes.     To  say  that  the  Riemann-Christoffel 
Tensor  vanishes  would  therefore  be  equivalent  to  saying 
that  nature,  as  a  system  of  interconnected  events,    has 
a  certain  kind  of  intrinsic  structure,  which  is  formally 
analogous  to  that  of  the  plane  in  Euclidean  space  and 


GENERAL   THEORY   OF   RELATIVITY      195 

formally   unlike    that   of  the   surface    of    a    sphere    in 
Euclidean  space. 

The  next  thing  that  we  have  to  consider  is  the 
dynamical  meanings  of  the  various  conceptions  which 
we  have  been  introducing  and  discussing.  There  are 
now  two  problems  to  be  considered.  The  first  is 
independent  of  the  view  that  we  take  as  to  the  two 
alternative  possible  intrinsic  structures  of  nature.  This 
leads  to  a  generalisation  of  the  first  law  of  motion,  so 
that  it  becomes  independent  of  any  particular  frame  of 
reference.  The  second  depends  on  which  alternative 
the  facts  force  us  to  choose  as  to  the  intrinsic  structure 
of  nature.  This  leads  to  a  generalisation  of  the  law  of 
gravitation.     We  will  now  consider  them  in  order. 

(1)  According  to  Newton's  first  law  of  motion  a 
particle  which  is  under  the  action  of  no  resultant  force 
in  a  Newtonian  frame  either  rests  or  moves  with  uniform 
rectilinear  velocity  in  that  frame.  Consider  two  events 
in  the  history  of  this  particle  as  it  moves.  One  is 
its  presence  at  the  point  xM  jr,,  zA  in  the  axes  of  the 
frame  at  the  date  tA  as  measured  by  the  A-clock  of 
the  frame.  The  other  is  its  presence  at  the  point  xB,  yEy 
zB,  in  the  same  axes  when  the  B-clock  reads  ta.  Since 
the  particle  is  under  the  action  of  no  Newtonian  forces 
it  will  have  moved  in  a  straight  line  between  these 
two  points  with  a  uniform  velocity.  Let  us  consider 
the  total  spatio-temporal  separation  between  these  two 
events.  By  this  we  are  going  to  mean  the  sum  of 
all  the  infinitesimal  spatio-temporal  separations  between 
successive  closely  adjacent  events  in  the  history  of  the 
particle,  which  are  intermediate  between  the  first  and  the 
last  event  under  consideration.  It  is  easy  to  show  that, 
when  the  particle  moves  uniformly  in  a  straight  line, 
this  total  separation  has  a  stationary  value.  This 
means  that  it  would  either  be  greater  for  all  alternative 
ways  of  moving  from  the  one  place  to  the  other  in 
the  given  time,  or  that  it  would  be  less  for  all  alternative 
ways.     As  a  matter  of  fact  the  actual  path  is  that  which 


196  SCIENTIFIC   THOUGHT 

makes  the  total  spatio-temporal  separation  a  maximum. 
If  the  particle  moved  in  any  other  course,  or  with  a 
non-uniform  velocity,  the  total  spatio-temporal  separa- 
tion would  be  less  than  it  is  when  it  moves  uniformly 
in  a  straight  line. 

Now  the  fact  that  the  total  separation  between  remote 
events  in  the  history  of  this  particle  is  a  maximum  is 
an  intrinsic  fact  about  the  history  of  the  particle.  It 
depends  in  no  way  on  the  frame  of  reference  which  is 
chosen  for  placing  and  dating  the  events.  We  have 
thus  got  to  something  about  the  motion  of  the  particle 
which  is  independent  of  frames  of  reference.  Now 
refer  the  particle  to  any  other  frame  you  like.  The 
characteristics  of  the  new  frame  are  completely  summed 
up  in  the  ten  g's  which  appear  in  the  expression  for 
the  spatio-temporal  separation  of  two  adjacent  events 
in  terms  of  the  spatial  and  temporal  parameters  of  this 
frame.  We  have  therefore  simply  to  express  the  fact 
that  the  integral  of  the  expression  (9)  has  a  stationary 
value  for  the  course  which  the  particle  actually  takes 
with  respect  to  this  frame.  This  can  easily  be  done 
by  the  Calculus  of  Variations.  As  a  result  a  set  of 
four  second-order  differential  equations  emerges.  These 
are  the  equations  of  motion  in  any  frame  whatever  for 
a  particle  which  is  under  the  action  of  no  forces  in  a 
Newtonian  frame. 

Now,  as  we  saw  in  last  chapter,  the  change  from  a 
Newtonian  to  a  non-Newtonian  frame  of  reference  in- 
volves the  introduction  of  non-Newtonian  forces.  These 
forces  are  completely  determined  by  the  nature  of  the 
non-Newtonian  frame  chosen.  Again,  as  we  have  seen, 
the  nature  of  the  frame  is  completely  determined  by 
the  ten  gs  which  appear  in  the  expression  for  the 
spatio-temporal  separation  in  terms  of  the  parameters 
of  the  frame.  Thus  there  is  complete  correlation  between 
the  g's  which  characterise  the  frame,  and  the  non- 
Newtonian  forces  which  people  who  used  this  frame 
would  observe  to  act  on  particles.     Thus,   if  all  forces 


GENERAL   THEORY   OF   RELATIVITY      197 

be  of  this  type,  the  four  differential  equations  which 
express  the  fact  that  the  total  spatio-temporal  separation 
for  the  actual  course  of  the  particle  is  to  be  stationary 
will  be  the  laws  of  motion.  For  they  will  sum  up  the 
relations  between  the  motion  of  any  particle  with  respect 
to  any  frame  and  the  observable  forces  which  people 
who  use  that  frame  find  to  be  acting  on  the  particle. 
To  observers  on  a  Newtonian  frame  it  will  appear  that 
the  other  observers  are  using  very  foolish  axes  and 
very  wild  clocks  {e.g.,  a  rotating  wheel  and  a  water- 
tank).  For  the  Newtonian  observers  then,  theg's  will  not 
seem  to  have  anything  to  do  with  forces,  but  only  to 
characterise  the  particular  kind  of  axes  and  clocks  which 
the  other  observers  are  using.  But,  for  the  observers 
who  use  the  frame  characterised  by  the  gs,  these  g's 
will  appear  as  the  potentials  of  forces  which  are  functions 
of  position  and  time  with  respect  to  their  frame.  (I 
say  as  potentials  of  forces,  and  not  as  forces,  because  the 
g's  do  not  appear  as  such  in  the  equations  of  motion, 
but  appear  in  the  form  of  first-order  differential  co- 
efficients with  respect  to  the  co-ordinates  and  dates 
which  events  have  in  the  frame.)  The  four  differential 
equations  of  motion,  thus  deduced  for  any  frame  what- 
ever, degenerate,  in  the  special  case  of  a  Newtonian 
frame,  to  the  three  ordinary  equations  which  express 
the  fact  that  the  acceleration  of  the  particle  vanishes 
in  three  mutually  rectangular  directions,  and  to  the 
platitude  0  =  0. 

I  will  illustrate  the  connexion  between  the  g's  and 
the  potentials  of  the  non-Newtonian  forces  which  are 
introduced  along  with  a  non-Newtonian  frame,  by 
working  out  a  little  further  a  simple  example  which 
was  used  in  the  last  chapter.  It  will  be  remembered 
that  we  there  took  a  particle  at  rest  on  a  plane  in  a 
Newtonian  frame  and  referred  it  to  a  non-Newtonian 
frame,  consisting  of  the  same  clock  as  before  for  the 
time-measurer  and  two  mutually  rectangular  spokes 
of  a  rotating  wheel,  that  lay  in  this  plane,  as  the  spatial 


igS  SCIENTIFIC   THOUGHT 

axes.  We  saw  that  the  observers  who  use  this  frame 
will  ascribe  a  non-Newtonian  attraction  from  the  particle 
to  the  origin  of  amount  mrao2.  The  non-Newtonian 
potential  required  to  produce  this  force  is  £////"V,  since 

Fr=  —  -3—  by  definition,  and   F,.  =  —  mrw    in    this  case. 

Ov 

Now  let  us  consider  what  will  be  the  expression  for 
the  separation  of  two  adjacent  events  in  terms  of  the 
new  frame.  In  terms  of  the  original  Newtonian  frame 
it  is,  of  course,  c*dtz  —  dx2  —  dy2.  It  is  easy  to  show  that 
it  will  be  {c"-i^)df-de-dif+2^rid^dt-2i,4dndt  in 
terms  of  the  new  frame.  Thus  the  new  frame  is 
characterised  by  the  following  values  for  the  six  g's 
which  are  needed  when  we  confine  ourselves  to  a  two 
dimensional  space,  as  we  are  doing  in  this  example  : — 

gtt  =  <*-  o)V  ;  g^  =  gvv  =  -  1  ;    g$=  2a)>7  ;    g¥ 2<  ; 

gt„  =  o.  If  we  ascribe  to  the  non-Newtonian  force  a 
potential    —  hngtt^   we  shall  account  for  the  observable 

facts,    since    —  ^-(  —  \mg  )=  —  ?WV,    and    the    observed 

dr  tt 

non-Newtonian  force  is  —mw2r.  Thus  we  see  that  gto 
which,  from  the  point  of  view  of  observers  on  the 
Newtonian  frame,  is  merely  one  of  the  coefficients 
that  characterise  the  special  non-Newtonian  frame  used 
by  the  other  observers,  is,  from  the  point  of  view  of 
the  non-Newtonian  observers  themselves,  the  potential 
of  a  force  which  acts  on  all  particles  with  respect  to  their 
frame. 

So  far  we  have  confined  ourselves  to  the  case  of  a 
particle  which  is  under  the  action  of  no  Newtonian 
force,  and  we  have  derived  the  equations  of  motion  for 
such  a  particle  under  the  action  of  the  non-Newtonian 
forces  to  which  it  will  be  subjected  when  referred  to  a 
non-Newtonian  frame.  But  of  course  most  particles, 
if  not  all,  are,  at  some  time  at  least  in  their  history, 
under  the  action  of  Newtonian  forces,  and  do  not  move 
uniformly  or  in  straight  lines  with  respect  to  Newtonian 


GENERAL  THEORY   OF   RELATIVITY      199 

frames.     What  are  we  to  say  of  the  equations  of  motion 
of  such  particles? 

We  have  said  that  a  particle  under  the  action  of  no 
Newtonian  force  moves  in  such  a  way  that  the  total 
separation  between  two  remote  events  in  its  history  is 
greater  than  it  would  be  for  any  other  possible  way  of 
moving.  We  also  said  that  this  property  of  the  actual 
history  of  the  moving  particle  is  independent  of  the 
particular  frame  of  reference  to  which  it  may  be  referred. 
Before  we  can  get  any  further  we  must  clear  up  these 
two  statements  a  little  further.  We  will  begin  with  a 
geometrical  analogy. 

Suppose  there  were  two  remote  points  and  we  were 
told  to  find  the  shortest  possible  path  from  one  to  the 
other.  The  problem  would  not  yet  be  perfectly  deter- 
minate. Possibility  is  always  relative  to  a  set  of 
conditions  implied  or  asserted.  What  would  be  the 
shortest  possible  path,  relative  to  one  set  of  conditions, 
would  not  be  so,  relative  to  another  set.  If  we  were 
allowed  to  move  from  one  point  to  the  other  on  the 
Euclidean  plane  on  which  they  both  lie,  the  shortest 
possible  path  would  of  course  be  the  Euclidean  straight 
line  joining  them.  But  if  we  were  told  that  we  must 
keep  to  the  surface  of  a  certain  sphere  on  which  both 
points  are  situated,  the  shortest  possible  path  would  be 
along  the  great  circle  on  this  sphere  which  joins  them. 
And  a  great  circle  is  an  intrinsically  different  kind  of 
curve  from  a  Euclidean  straight  line.  Thus  the  curve 
which  is  the  shortest  path  between  two  points  depends  on 
the  intrinsic  structure  of  the  region  in  which  the  points 
are  situated,  and  to  which  all  paths  between  them  are  to 
be  confined.  Once  this  intrinsic  structure  is  given,  the 
property  of  being  the  shortest  path  between  the  two 
points  is  independent  of  all  possible  sets  of  axes  which 
might  be  used  for  mapping  out  the  region.  But,  of 
course,  the  intrinsic  character  of  the  region  will  impose 
certain  restrictions  on  the  kind  of  axes  that  are  possible 
for  mapping  it  out.     Similarly,  the  nature  of  the  move- 


200  SCIENTIFIC   THOUGHT 

ment  which  gives  the  maximum  possible  spatio-temporal 
separation  for  two  remote  events  in  the  history  of  a 
moving  particle  will  depend  on  the  structure  of  that 
part  of  the  history  of  Nature  in  which  the  events  happen, 
and  within  which  all  courses  from  one  to  the  other  are 
to  be  confined.  Given  the  structure  of  this  part  of  the 
history  of  Nature,  the  course  with  the  maximum  possible 
total  spatio-temporal  separation  is  independent  of  all 
frames  of  reference  which  can  be  used  for  placing  and 
dating  events  within  this  region.  But  the  intrinsic 
structure  of  this  part  of  the  history  of  Nature  will 
impose  certain  restrictions  on  the  kind  of  frames  that 
are  possible  for  mapping  it  out. 

We  can  now  deal  with  the  case  of  a  particle  subject 
to  Newtonian  forces.  We  assume  (a)  that  it  is  a  general 
fact  about  all  moving  particles  (and  not  merely  about 
those  which  are  under  the  action  of  non-Newtonian 
forces)  that  they  move  in  such  a  way  that  the  total 
spatio-temporal  separation  for  two  remote  events  in 
their  history  is  greater  than  it  would  be  for  any  other 
way  of  moving  which  the  intrinsic  structure  of  the 
part  of  the  history  of  Nature  in  which  the  two  events 
fall  would  allow,  {b)  That,  in  those  parts  of  the  history 
of  Nature  in  which  Newtonian  forces  show  themselves, 
the  intrinsic  structure  is  not  such  that  the  expression 
for  the  spatio-temporal  separation  for  two  adjacent 
events  can  be  reduced  to  the  form  with  constant 
coefficients.  This  is  equivalent  to  assuming  that 
Newtonian  frames  are  strictly  applicable  only  to  those 
parts  of  the  history  of  Nature  (if  such  there  be)  in  which 
no  Newtonian  forces  are  acting. 

On  these  assumptions  the  general  equations  of 
motion,  which  have  just  been  deduced  for  ?ton- 
Newtonian  forces,  will  hold  for  all  forces.  These 
four  equations  are  simply  the  analytical  conditions 
which  must  be  fulfilled  if  the  actual  course  of  a  particle 
is  to  be  such  that  the  total  spatio-temporal  separation 
between  two    remote  events  in    its  history  shall  be   a 


GENERAL  THEORY   OF   RELATIVITY      201 

maximum  or  minimum.  And  they  were  deduced  from 
the  most  general  expression  possible  for  the  spatio- 
temporal  separation  of  a  pair  of  adjacent  events.  For, 
although  we  were  in  fact  dealing  with  cases  where  the 
expression  for  the  separation  can  be  reduced  to  the 
Newtonian  form  with  constant  coefficients,  no  use  was 
made  of  this  special  assumption  in  deducing  the  con- 
ditions that  the  total  separation  for  the  actual  course 
shall  be  stationary.  We  may  say  then  that,  if  the 
above  assumptions  be  true,  we  have  got  the  general 
equations  of  motion  in  a  form  which  is  (a)  independent 
of  any  special  frame  of  reference,  and  (b)  applies  equally 
to  Newtonian  and  non-Newtonian  forces.  If  the  forces 
be  all  non-Newtonian  there  will  in  addition  be  a  set  of 
equations  between  the  g's  of  all  possible  frames,  ex- 
pressing the  fact  that  the  structure  of  the  region  under 
discussion  is  such  that  the  separation  can  be  reduced 
to  the  form  with  constant  coefficients.  If  some  of  the 
forces  be  Newtonian  this  extra  set  of  conditions  will 
not  of  course  hold,  though  it  will  still  be  possible  that 
the  g's  of  all  possible  frames  are  subject  to  some  less 
rigid  set  of  conditions. 

On  this  view  the  one  fundamental  mechanical  fact, 
which  is  absolute  and  independent  of  all  frames  of 
reference,  is  the  stationary  character  of  the  actual  history 
of  a  moving  particle,  i.e.,  the  fact  that  it  moves  with 
such  a  velocity  and  in  such  a  path  that  the  total 
separation  between  remote  events  in  its  history  is  a 
maximum  or  minimum.  This  is  independent  of  whether 
it  be  under  the  action  of  Newtonian  forces  or  not.  But 
the  course  which  in  fact  has  the  greatest  or  least  possible 
separation  will  differ  intrinsically,  according  to  the 
intrinsic  structure  of  the  history  of  Nature  in  the  spatio- 
temporal  region  under  discussion.  If  this  region  be 
such  that  the  separation  between  two  adjacent  events 
in  it  can  be  expressed  in  the  form  with  constant  co- 
efficients, the  course  which  has  the  stationary  property 
is  a  Euclidean  straight  line  traversed  with  a  uniform 

o 


202  SCIENTIFIC  THOUGHT 

velocity  as  judged  by  a  Newtonian  clock.  If  the  region 
be  such  that  the  separation  cannot,  by  any  choice  of 
frame,  be  reduced  to  this  specially  simple  form,  the 
stationary  course  will  be  some  intrinsically  different 
kind  of  curve  traversed  with  a  non-uniform  velocity. 
It  is  assumed  that  the  presence  of  Newtonian  forces  in 
a  region  of  the  history  of  Nature  is  a  sign  that  the 
intrinsic  structure  of  that  region  is  such  that  no  frame 
can  be  found,  with  respect  to  which  the  separation  of 
two  adjacent  events  takes  the  form  with  constant 
coefficients. 

How  are  we  to  verify  or  refute  these  assumptions? 
Obviously  the  only  way  is  to  see  whether  (a)  they 
agree  with  known  facts  as  well  as  the  traditional 
theory,  and  (b)  account  for  and  predict  facts  which  were 
not  predicted  or  accounted  for  by  the  traditional  theory. 
We  have  seen  that,  when  the  forces  are  purely  non- 
Newtonian,  the  g's  of  any  frame  of  reference  appear 
to  the  observers  who  use  that  frame  as  the  potentials 
of  the  non-Newtonian  forces.  Reversing  this  analogy, 
it  is  reasonable  to  suppose  that  the  potentials  of 
the  Newtonian  forces  that  are  observed  with  respect 
to  any  frame  will  be  the  g's  which  characterise  the 
spatio-temporal  separation  of  two  adjacent  events  in 
that  part  of  the  history  of  Nature  in  which  these 
Newtonian  forces  act.  In  dealing  with  any  particular 
field  of  Newtonian  force  we  must  therefore  find  a  set 
of  g1  s  which  (a)  satisfy  the  general  equations  of  motion, 
and  {b)  differ  numerically  from  the  potentials  which 
the  traditional  theory  would  ascribe  to  this  field  by 
amounts  which  fall  below  the  limits  of  experimental 
error  in  the  experiments  that  have  already  been  done 
with  such  fields.  If  this  can  be  done,  the  resulting 
equations  will  have  at  least  as  good  a  claim  to  represent 
the  facts  of  motion  in  this  field  as  the  traditional 
equations.  And  if,  in  addition,  they  enable  us  to 
predict  small  residual  effects,  which  are  not  accountable 
for  on  the  traditional  theory  but  can  be  observed  when 


GENERAL  THEORY   OF   RELATIVITY      203 

looked  for,  they  will  have  better  claims  to  truth  than 
the  traditional  equations.  It  must  be  admitted,  how- 
ever, that  this  would  not  amount  to  a  knock-down 
proof  of  the  truth  of  the  assumptions,  since  the 
modified  equations  could  no  doubt  be  deduced  on 
traditional  views  of  space  and  time,  provided  suitable 
modifications  were  made  in  the  expressions  for  the 
potentials. 

Evidently  then  we  can  only  hope  to  find  evidence 
for  or  against  the  present  theory  by  considering  definite 
fields  of  force  and  the  observable  phenomena  that 
happen  in  them.  And,  even  so,  as  it  seems  to  me, 
no  absolutely  conclusive  proof  of  the  theory  will  ever 
be  found,  since  alternative  explanations  which  involve 
the  traditional  views  of  space,  time,  and  force  could 
always  be  constructed  to  fit  the  facts.  If,  however, 
these  should  prove  to  be  very  complicated  and  artificial, 
as  compared  with  the  explanation  offered  by  the  new 
theory,  we  shall  have  the  same  sort  of  grounds  for 
preferring  the  latter  as  we  had  for  preferring  the 
Relational  Theory  of  Motion,  in  spite  of  the  fact  that 
no  downright  refutation  of  the  Absolute  Theory  is 
possible. 

(2)  We  have  now  to  raise  the  question  whether 
Nature,  as  a  sum  total  of  events,  has  any  one  type  of 
intrinsic  structure  always  and  everywhere,  and,  if  so, 
of  what  type  the  intrinsic  structure  is.  It  is  admitted 
that  not  all  forces  are.  non-Newtonian,  i.e.,  that,  if  we 
insist  on  trying  to  refer  all  the  events  in  Nature  to 
a  Newtonian  frame,  many  particles  will  at  some  time 
in  their  history  be  subject  to  observable  forces  with 
respect  to  it.  And  there  is  no  frame  that  we  can  take 
which  will  transform  away  all  forces  always  and  every- 
where, though  it  is  always  possible  to  find  a  sufficiently 
wild  frame  which  will  transform  away  Newtonian  forces 
over  a  small  enough  region  of  space  for  a  short  enough 
lapse  of  time.  Now  we  might  deal  with  this  fact  in  one 
of  two  alternative  ways  :    (a)  We  might  hold  that  the 


204 


SCIENTIFIC   THOUGHT 


intrinsic  structure  of  Nature   is  such   that   the  spatio- 
temporal   separation   of  a   pair  of  adjacent  events  can 
take  the  Newtonian  form  always  and  everywhere.     We 
shall  then  have  to  hold  that  this  fact  is  disguised  from 
us  by  the  presence  of  forces  in   Nature,  which  appear 
in  every  frame  we  choose.     This  is  a  little  like  Swift's 
view  that  the  English  Government  always  chose  admir- 
able bishops  for  Ireland,    but  unfortunately  they  were 
always  stopped  on   Hounslow  Heath  by  highwaymen, 
who  exchanged  clothes  with  them  and  travelled  on  in 
their  coaches.      Or  (b)  we  might  hold  that  Nature  is  so 
constituted  that   no  frame   can   be  found    with    respect 
to  which   the  separation  takes  this  simple   form.     We 
might  then  try  to  explain  the  forces,  which  are  found 
in  all  frames,  by  reference  to  the  intrinsic  peculiarity 
of  structure   in    Nature,  which   prevents  the  separation 
from   being  expressed  in  this  simple  way. 

Before    attempting    to    decide    between    these    two 
alternatives  for  the  dynamical   case,    I    will,  as  usual, 

illustrate  their  precise  meaning  by 
a  geometrical  example.  Suppose 
people  were  confined  to  the  sur- 
face of  a  sphere,  and  that  they 
took  as  axes  a  pair  of  mutually 
normal  great  circles.  The  co- 
ordinates of  any  point  P  on  the 
sphere  are  to  be  the  arcs  of  the 
two  great  c.ircles  through  it  which 
are  normal  to  these  two  axes  respectively.  The  figure 
above  will  illustrate  the  arrangement. 

If  they  measured  the  arcs  OP,  P;«  and  Pn,  and 
found  their  lengths  to  be  r,  x  and  y  respectively  they 
would  find  that  r2  is  not  equal  to  x*+y*,  as  it  would  be 
if  the  square  of  the  spatial  separation  for  adjacent  points 
on  a  sphere  were  of  the  form  dxt  +  dy*.  But,  if  they  were 
specially  wedded  to  the  view  that  the  spatial  separation 
must  take  this  form,  they  could  get  over  the  difficulty 
by  assuming  that  there  are  forces  of  suitable  magni- 


GENERAL  THEORY   OF   RELATIVITY      205 

tudes  and  directions  at  different  points  on  the  sphere 
which  distort  their  measuring  rods.  Conversely,  they 
might  just  recognise  that  they  were  "up  against"  an 
intrinsic  peculiarity  of  spherical  surfaces,  and  avoid  the 
supposition  of  distorting  forces.  Similarly,  when  you 
find  that  there  are  untransformable  forces  with  respect 
to  Newtonian  frames,  you  can  either  leave  it  at  that, 
or  take  up  the  suggestion  that  Nature  has  such  an 
intrinsic  structure  that  the  spatio-temporal  separation 
of  two  adjacent  events  is  not  accurately  expressible  in 
the  Newtonian  form. 

The  actual  relation  between  r,  the  total  separation, 
and  x  and  y,  the  co-ordinates  in  this  system  is 

•   2  r      •   2 x  ,     •   2  y 
sin2T  =  sin2-7  +sin  ^ 

where  k  is  the  radius  of  the  sphere.  If  the  observers 
confined  themselves  to  a  very  small  region,  the  sines 
could  be  replaced  by  the  angles  themselves,  and  the 
relation 

r2  =  x2+y\ 

which  is  characteristic  of  the  Euclidean  plane,  would 
approximately  hold.  This  is  analogous  to  the  fact, 
already  mentioned,  that  it  is  always  possible  to  find 
a  frame,  in  terms  of  which  particles  move  with  uniform 
rectilinear  velocities  for  a  sufficiently  small  region  of 
Space  and  for  a  sufficiently  small  lapse  of  time,  though 
not  for  all  places  and  all  time. 

We  can  now  return  from  the  geometrical  analogy 
to  the  dynamical  problem.  If  we  consider  the  various 
kinds  of  Newtonian  forces  we  find  that  they  divide 
sharply  into  two  classes,  viz.,  gravitational  attractions 
and  the  rest.  We  have  already  pointed  out  the 
peculiarities  of  gravitation.  It  acts  always  and  every- 
where, it  is  independent  of  all  properties  of  matter 
except  its  inertial  mass,  it  is  indifferent  to  the  sur- 
rounding medium,  and  so  on.  We  saw  that  these 
peculiarities  make  gravitation  closely  analogous  to  the 


206  SCIENTIFIC   THOUGHT 

non-Newtonian  forces  to  which  a  particle,  at  rest  or  in 
uniform  motion  in  a  Newtonian  frame,  is  subjected 
when  referred  to  a  non-Newtonian  frame.  Again,  we 
saw  that,  in  no  frame  composed  of  material  axes  and 
clocks,  could  a  particle  literally  be  under  the  action  of 
no  forces,  since  there  would  always  be  gravitational 
attractions  between  it  and  the  axes  themselves,  though 
these  might  be  negligible  if  it  were  a  solitary  particle 
referred  to  the  fixed  stars  as  axes.  For  these  reasons 
it  seems  plausible  to  suppose  that  gravitation,  at  least, 
is  something  connected  with  the  intrinsic  structure  of 
Nature  as  a  sum  total  of  events.  This  structure  is  such 
that  no  frame,  in  which  the  spatio-temporal  separation 
takes  the  simple  form  with  constant  coefficients,  accu- 
rately fits  the  whole  of  Nature  ;  and  the  gravitational 
forces,  which  we  find  when  we  use  a  Newtonian  frame, 
are  an  expression  of  the  "misfit"  of  that  frame  to  the 
structure  of  Nature.  This  is  exactly  analogous  to  the 
fact  that  the  contracting  and  expanding  forces,  which 
observers  on  the  sphere  would  have  to  assume  to  be 
acting  on  their  measuring  rods  in  the  last  example, 
would  simply  be  an  expression  of  the  "  misfit"  between 
the  intrinsic  character  of  the  surface  of  a  sphere  and 
the  plane  system  of  co-ordinates  which  they  insisted 
on  applying  to  it. 

As  regards  other  kinds  of  Newtonian  forces,  which 
depend  on  the  special  properties  of  bodies  and  of  the 
medium,  and  do  not  show  themselves  always  and 
everywhere,  as  gravitation  does,  we  can  hardly  expect 
a  similar  explanation  to  work.  We  may  illustrate  this 
difference  again  from  the  example  of  people  living  on 
the  surface  of  a  sphere  and  trying  to  measure  it,  on 
the  assumption  that  the  expression  for  the  square  of  the 
spatial  separation  of  two  adjacent  points  must  be  reduc- 
ible to  the  simple  form  dx2 '  +  dy2 '.  Let  us  suppose  that 
there  were  big  fires  burning  at  some  parts  of  the  surface 
of  the  sphere.  The  measurements  of  the  observers 
would    then    be    inconsistent    with    their    fundamental 


GENERAL  THEORY   OF   RELATIVITY      207 

assumption   and  would  have   to  be   "  cooked"   in   two 
different    ways  :      (a)    They    would    be    systematically 
wrong-   on    account   of  the   fact  that  no   system   of  co- 
ordinates on   the  surface  of  a  sphere  can   really    give 
an   expression   for  the  separation,  which  shall   involve 
only  constant  coefficients.     This  systematic  error  they 
will  have  to  correct  by  ascribing  contracting  and  ex- 
panding forces  on  their  rods  to  the  sphere  itself,      (fr) 
Apart  from  these  systematic  errors,  there  will  be  special 
discrepancies  when  they  measure  near  one  of  the  fires, 
owing  to  the  physical  expansion  of  their  rods  in  such 
a    neighbourhood.     Now    we    should    say   that   it    was 
not  unreasonable  of  the  observers  to  ascribe  the  special 
discrepancies  in  their  measurements   near  the  fires   to 
forces  acting  there  on  their  rods,  for  there  is  something 
visible  and  tangible  there  (viz.,  the  fire)  to  account  for 
these  assumed   forces.      But  we  should   think    it   very 
foolish    of  them    to   ascribe  the   systematic  discrepancy 
between    measurement    and    theory,    which    they    find 
everywhere   on    the    sphere,    to    forces    bound    up   with 
the  sphere  and  varying  in  a  systematic  way  from  place 
to    place    on    its    surface.       We    should    advise    them, 
instead  of  sticking  obstinately  to   their   view   that   the 
separation  of  adjacent  points  on   the  sphere  must  take 
the  form  with  constant  coefficients,  and  then  invoking1 
forces  to  account  for  the  discrepancies  between  this  fact 
and  their  observations,  to  see  whether  they  could  not 
account  much  more  simply  for  the  facts  by  supposing 
that  the  surface  on  which   they  live  is   intrinsically  of 
such  a  character  that  no  set  of  axes,  in  which  the  ex- 
pression for  the  separation  of  two  adjacent  points  takes 
this  specially  simple  form,  can  exist  upon  it.      In   the 
same  way,  when  you  find  that  there  is  a  certain  kind 
of  force,  viz.,  gravitation,  which  acts  always  and  every- 
where   on    all    particles,    when    referred   to    Newtonian 
frames,    it   becomes    reasonable    to    suppose    that    this 
"force"  is  merely  an  expression  of  the  inappropriate- 
ness   of  a  Newtonian   frame  to  the    intrinsic   structure 


208  SCIENTIFIC   THOUGHT 

of  Nature,  as  a  sum  total  of  events.  Other  Newtonian 
forces,  which  act  in  one  place  and  not  in  others,  or 
at  one  time  and  not  at  another,  or  on  one  kind  of 
matter  and  not  on  another,  are  in  a  different  situation, 
and  may  be  compared  to  the  fires  at  various  places 
on  the  sphere  in  our  geometrical  example. 

We  are  going  to  see  then,  whether  we  can  account 
for  the  gravitational  forces,  which  are  present  in  all 
Newtonian  frames,  by  the  assumption  that  the  events 
of  Nature  form  an  interconnected  manifold  of  such  an 
intrinsic  structure  that  no  frame  of  reference  can  be 
found,  in  respect  to  which  the  expression  for  the  spatio- 
temporal  separation  of  two  adjacent  events  accurately 
takes  the  form  (8)  with  constant  coefficients. 

Now  we  have  so  far  distinguished  two  kinds  of 
surfaces  in  ordinary  space.  With  one  of  them  (such 
as  the  plane;  the  cone,  the  cylinder,  etc.)  it  was 
possible  to  find  a  system  of  co-ordinates  on  the  surface, 
in  terms  of  which  the  expression  for  the  spatial  separa- 
tion of  two  adjacent  points,  as  measured  along  the 
surface,  contains  only  constant  coefficients.  The  sign 
of  this  was  the  vanishing  of  the  Riemann-Christoffel 
Tensor.  The  more  familiar  criterion  is  that  such 
surfaces  are  either  planes  or  can  be  unfolded  without 
distortion  or  stretching  into  planes.  In  the  other  kind 
of  surface  this  condition  is  not  fulfilled.  We  gave 
the  sphere  as  an  example.  We  agree  then  that  the 
universality  and  other  peculiarities  of  gravitation  suggest 
that  the  structure  of  Nature,  as  a  sum  total  of  events, 
is  not  formally  analogous  to  that  of  surfaces  of  the 
first  kind,  i.e.,  we  shall  henceforth  [reject  the  view  that 
the  intrinsic  structure  of  Nature  is  such  that  the 
Riemann-Christoffel  Tensor  vanishes  for  all  frames  of 
reference  within  Nature.  Does  Nature  then  impose 
no  general  condition  on  possible  frames  of  reference 
except  this  negative  one? 

If  we  return  once  more  to  elementary  geometry  we 
shall  see  that  the  surfaces  for  which  the  expression  for 


GENERAL  THEORY   OF   RELATIVITY      209 

the  spatial  separation  cannot  take  the  form  with  constant 
coefficients  can  be  further  subdivided.  We  took  the 
sphere  as  an  example  of  such  a  surface.  The  outside 
of  an  egg  would  be  another  example.  Now  these  two 
surfaces  have  an  important  intrinsic  difference.  A 
sphere  is  a  much  more  special  type  of  surface  than 
an  egg-shell,  just  as  a  plane  or  a  cone  is  of  a  much 
more  special  type  than  a  sphere.  The  sphere  agrees 
with  the  plane  and  differs  from  the  egg-shell  in  the 
following  respect :  A  triangle  bounded  by  arcs  of 
great  circles  on  the  sphere  could  be  slid  about  all 
over  the  surface,  remaining  everywhere  in  complete 
contact  with  it,  and  needing  no  stretching  or  distortion. 
In  fact  any  figure  that  fits  on  to  the  sphere  in  one  part 
will  do  so  in  all  parts.  The  same  is  obviously  true 
of  figures  in  a  plane.  It  is  not  true  of  figures  on 
the  surface  of  an  egg-shell.  A  cap,  which  fitted  the 
blunt  end  of  the  egg-shell,  could  not  be  made  to  fit 
exactly  on  to  the  sharp  end  without  stretching  some 
parts  of  it  and  folding  others.  Thus,  granted  that 
the  Riemann-Christoffel  Tensor  does  not  vanish  for 
Nature,  and  that  the  intrinsic  interconnexions  of  events 
in  Nature  are  therefore  not  formally  analogous  to  those 
of  points  on  a  plane,  the  question  can  still  be  raised  : 
Are  the  intrinsic  relations  of  events  in  Nature  formally 
analogous  to  those  of  points  on  a  sphere  or  to  those  of 
points  on  an  egg-shell?  If  the  former  alternative  be 
fulfilled  a  function  of  the  g's,  derived  from  the  Riemann- 
Christoffel  Tensor,  and  called  the  Modified  Riemann- 
Christoffel  Tensor,  will  have  to  vanish.  This  imposes 
a  limitation  upon  possible  gs,  and  therefore  upon 
possible  natural  frames  of  reference,  but  the  restriction 
is  less  rigid  than  it  would  be  if  the  unmodified  Tensor 
were  to  vanish. 

If  then  gravitation  be  the  way  in  which  a  certain 
intrinsic  peculiarity  in  the  structure  of  Nature  exhibits 
itself,  we  might  suppose  that  the  equating  of  the 
Modified  Tensor  to  O  would  be  the  generalised  expres- 


210  SCIENTIFIC   THOUGHT 

sion  for  the  law  of  gravitation,  with  respect  to  any 
admissible  frame  of  reference.  So  far,  however,  this  is 
merely  a  conjecture.  It  might  be  that  gravitation  is 
not  the  expression  of  a  general  intrinsic  peculiarity  in 
the  structure  of  Nature,  as  a  sum  total  of  interconnected 
events.  And  it  might  be  that,  even  if  this  were  true, 
the  structure  is  not  of  the  particular  kind  which  is 
expressed  by  the  vanishing  of  the  Modified  Tensor. 
Here,  as  elsewhere,  we  must  carefully  distinguish 
between  what  suggests  the  theory  and  what  verifies  it. 
What  suggests  that  gravitation  is  an  expression  of  the 
general  intrinsic  structure  of  Nature  is  its  universality 
and  its  peculiarities  as  compared  with  other  forces. 
What  suggests  taking  the  vanishing  of  the  Modified 
Tensor  as  the  expression  of  this  structure  is  that  it  is 
the  next  simplest  assumption  to  make,  after  the  facts 
have  proved  to  be  inconsistent  with  the  still  more 
special  structure  which  would  be  indicated  by  the 
vanishing  of  the  unmodified  Tensor.  We  have  now 
to  see  what  verifies  the  theory  thus  suggested. 

We  know  the  traditional  form  of  the  law  of  gravita- 
tion, with  respect  to  the  nearest  approach  that  we  can 
get  to  Newtonian  frames.  For  a  region  free  from 
matter  (approximately  for  the  inside  of  an  exhausted 
bulb)  it  takes  the  form  of  Laplace's  Equation 

92V     92V     92V_ 

dx*     dy2     dz2  ~  °' 

where  V  stands  for  the  gravitational  potential  at  a  point 
in  the  region,  and  x,  j>,  and  z  are  the  Cartesian  co- 
ordinates of  this  point  with  respect  to  a  Newtonian 
frame.  There  is  no  doubt  that  this  equation  is  true 
to  a  very  high  degree  of  approximation.  It  follows 
that  any  candidate  for  the  position  of  the  true  law  of 
gravitation  must  reduce  to  something  which  differs 
very  slightly  indeed  from  Laplace's  equation,  when 
expressed  in  terms  of  the  nearest  approach  to  a 
Newtonian  frame  that  we  can  get. 


GENERAL  THEORY   OF   RELATIVITY      211 

Now  the  Modified  Riemann-Christoffel  Tensor  is 
an  expression  involving  second  order  differential  co- 
efficients of  the  g's  for  a  frame,  with  respect  to  the  co- 
ordinates and  dates  of  an  event  as  referred  to  this  frame. 
So  far  there  is  a  formal  analogy  between  it  and  the 
left-hand  side  of  Laplace's  Equation,  if  the  g's  be  re- 
garded as  analogous  to  Laplace's  V.  The  right-hand 
side  is  o  in  both  cases.  Now  Laplace's  V  is  a  potential, 
and  we  have  already  seen  the  close  analogy  between 
the  g's  of  a  frame  and  the  potentials  of  the  forces  which 
act  on  particles  when  referred  to  that  frame.  The 
only  question  that  remains  then,  is  the  following:  Can 
we  find  a  set  of  ten  functions  g^v  of  the  Newtonian 
co-ordinates  and  clock-readings,  which  (a)  when  sub- 
stituted in  the  expression  for  the  Modified  Tensor 
make  it  equal  to  o,  and  {b)  differ  so  little  from  the 
gravitational  potentials  of  the  ordinary  Newtonian 
theory  that  the  difference  could  only  have  been  detected 
by  very  special  methods,  and  when  there  was  a  very 
special  reason  for  looking  for  it?  If  so,  we  may 
reasonably  suppose  that  gravitation  is  an  expression 
of  the  fact  that  Nature  has  a  kind  of  intrinsic  structure 
formally  analogous  to  that  of  the  sphere,  and  that 
the  formula  obtained  by  equating  the  Modified  Tensor 
to  o  is  the  true  form  of  the  law  of  gravitation.  The 
answer  to  this  question  is  in  the  affirmative  ;  and  so 
we  may  take  it  that  the  vanishing  of  the  Modified 
Tensor  is  the  true  form  of  the  law  of  gravitation  for 
a  region  empty  of  matter. 

There  is  one  point  which  must  be  mentioned  here. 
We  are  accustomed  to  think  of  the  traditional  law  of 
gravitation  in  the  form  that  two  particles  attract  each 
other  with  a  force  proportional  to  their  masses  and 
inversely  proportional  to  the  square  of  the  distance 
between  them.  And  we  are  wont  to  regard  Laplace's 
differential  equation  as  a  rather  recondite  mathematical 
deduction  from  this.  In  the  Relativity  theory  of  gravi- 
tation   the    order    is    reversed.     The    law    obtained    by 


212  SCIENTIFIC   THOUGHT 

equating  the  Modified  Tensor  to  o  is  directly  analogous 
to  Laplace's  Equation.  The  notion  of  remote  particles 
attracting  each  other  is  here  a  rather  recondite  mathe- 
matical deduction  from  the  differential  equations.  In 
fact,  material  particles  turn  up  now  only  as  points  of 
singularity  in  a  gravitational  field  ;  the  field  itself  is 
the  fundamental  thing.  And,  when  you  do  make  this 
deduction,  it  is  found  that  the  force  between  two 
particles  is  not  wholly  in  the  line  joining  them,  if  I 
may  put  it  rather  crudely.  The  remaining  term, 
which  the  new  form  of  the  law  involves,  accounts  for 
the  slow  rotation  of  the  orbits  of  the  planets  as  wholes 
in  their  own  planes.  This  had  been  noticed  for  the 
planet  Mercury,  and  was  unintelligible  on  the  tradi- 
tional law  of  gravitation.  It  is  accounted  for  both 
qualitatively  and  quantitatively  by  the  Relativity 
theory. 

The  last  point  to  be  noticed  is  that,  on  the  present 
theory,  gravitation  modifies  the  movements,  not  merely 
of  ordinary  material  particles,  as  on  the  traditional  view, 
but  also  of  any  form  of  energy,  such  as  light,  radiant 
heat,  etc.,  which  travels  through  space.  We  must 
now  see  how  this  comes  about.  In  the  first  place  some 
such  consequence  is  suggested  at  once  by  the  modifica- 
tions which  the  Special  Theory  of  Relativity  entails  in 
the  traditional  conception  of  mass.  We  saw  at  the 
beginning  of  this  chapter  that,  if  a  body  moves  with 
velocity  v  in  a  straight  line  with  respect  to  a  Newtonian 

..  M0     . 

frame,  it  is  necessary  to  ascribe  to  it  a  mass  8  in 

l-V-2. 

r 
order    to    get    the    Principle    of    the    Conservation    of 
Momentum  into  a  form  consistent  with  the  Restricted 
Physical   Principle   of   Relativity.     We   also   saw  that 

this    is   approximately  equal    to    M0  +  | — |— .     Now  the 

second  term  in  this  is  the  kinetic  energy  of  the  particle 
divided  by  the   square  of  the  velocity  of  light.      It  is 


GENERAL  THEORY   OF   RELATIVITY      213 

thus   certain    that   the   kinetic   energy   of  a   particle   of 
matter  appears  as  an   increase  in  its  inertial  mass.     It 
is  therefore  plausible  to  suppose  that  any  region  filled 
with  any  form  of  energy,  such  as  light  or  radiant  heat, 
would    thereby  acquire  an    inertial  mass  equal    to   the 
total  energy  contained  in  it  divided   by  the  square  of 
the  velocity  of  light.      It  by  no  means  follows,  on  the 
traditional   theory    of  gravitation,   that   such   a    region 
would  contain  any  gravitational  mass.     It  is  true  that 
for   any   particle    of  matter   the    gravitational    and    the 
inertial  masses  are  proportional,  to  an  extremely  high 
degree   of  approximation.     Still,   this    would    be   com- 
patible   with    the    view   that    the    gravitational    effect 
depends   wholly   on    the    factor    M0 ;    seeing    that   the 
second  factor  in  the  inertial  mass  contains  the  square 
of  the  velocity  of  light  in  its  denominator,  and  is  there- 
fore excessively  small  unless  the  energy  of  the  body  be 
excessively  great.     On  this  view  we  should  not  expect 
a  beam  of  light  to  have  gravitational  mass,  in  spite  of 
its  having  inertial  mass.     On   the  other  hand,  it  is  of 
course  possible  that  the  gravitational  and  the  inertial 
masses   are   always   exactly,   and    not  merely  approxi- 
mately,  proportional.     In  that  case  we  should  expect 
the  course  of  a  beam  of  light  to  be  modified  when  it 
passes  through  a  gravitational  field,  just  as  the  path 
of  a  material  particle   is   known  to  be   modified   under 
like    conditions.       Now    experiments   with    pendulums 
had  already  suggested  very  strongly  that  the  gravita- 
tional mass  of  a  piece  of  matter  is  accurately,  and  not 
merely  approximately,  proportional  to  its  whole  inertial 
mass,  and  not  only  to  the  first  factor  in  this.     Thus, 
the  Special  Theory  of  Relativity  had  already  made  it 
extremely  likely  that  the  course  of  a  beam  of  light  or 
any  other  kind   of  radiant  energy  would   be  modified 
when  it  passed  through  a  gravitational  field. 

Now  what  is  thus  merely  a  plausible  suggestion  on 
the  traditional  theory  of  gravitation,  combined  with  the 
modified  dynamics  of  the  Special  Theory  of  Relativity, 


214  SCIENTIFIC   THOUGHT 

is  a  necessary  consequence  of  the  General  Theory  of 
Relativity.  We  know  that  light  would  not  travel 
uniformly  or  in  a  straight  line  with  respect  to  non- 
Newtonian  frames.  The  people,  e.g.,  who  used  the 
spokes  of  the  rotating  wheel  as  their  axes  would  not 
find  that  light  travelled  in  a  straight  line  with  respect 
to  their  axes,  or  with  a  uniform  velocity  with  respect 
to  their  clocks.  And  the  actual  course  that  a  beam  of 
light  would  follow  in  their  system  would  be  determined 
by  the^-V  which  characterise  that  system.  Now  it  is  a 
fundamental  assumption  of  the  General  Theory  that 
the  analogy  between  the  g's  of  a  non-Newtonian  frame 
and  the  potentials  of  the  non-Newtonian  forces  which 
act  on  particles  with  respect  to  that  frame  is  to  be 
extended  to  the  potentials  of  Newtonian  forces. 

Suppose  then  that  we  have  found  the  equations  for 
the  path  of  a  beam  of  light  with  respect  to  any  frame, 
in  terms  of  the  gs  of  that  frame,  on  the  assumption 
that  it  would  move  accurately  in  a  straight  line  with  a 
uniform  velocity  relative  to  a  Newtonian  frame  in  the 
absence  of  gravitation.  To  find  its  actual  path  with 
respect  to  a  Newtonian  frame  in  a  gravitational  field  we 
must  just  substitute  in  these  equations  those  values  of 
the  g's  which  (a)  satisfy  the  condition  that  they  make 
the  Modified  Riemann-Christoffel  Tensor  vanish,  and 
{b)  account  for  the  observed  strength  and  distribution 
of  the  field.  These  equations  will  not  in  general 
represent  a  motion  with  a  uniform  velocity  in  a 
straight  line  with  respect  to  the  axes  defined  by  the 
fixed  stars.  The  divergence,  which  is  excessively  small 
even  in  the  intense  gravitational  field  which  surrounds 
a  huge  body  like  the  sun,  can  be  calculated  and  has 
been  experimentally  detected. 

I  have  now  sketched  to  the  best  of  my  ability  the 
gradual  modifications  which  experimental  facts  and 
reflection  upon  them  have  forced  upon  physicists. 
There  are  two  dangers  to  be  avoided  here  by  plain 
men.     One  is  to  think  that  the  Theory  of  Relativity  is 


GENERAL  THEORY   OF   RELATIVITY      215 

essentially  unintelligible  to  all  but  profound  mathe- 
maticians, and  that  therefore  it  is  useless  to  try  to 
understand  it.  The  other,  and  much  more  serious 
danger,  is  to  suppose  that  it  can  be  made  intelligible 
in  popular  expositions  of  a  few  pages  to  men  who  have 
never  had  occasion  to  consider  the  subjects  with  which 
it  deals.  Like  every  other  conceptual  scheme  it  grew 
up,  by  a  kind  of  inner  necessity,  against  a  whole 
background,  of  interconnected  concepts,  principles,  and 
experimental  facts.  Presented  in  the  absence  of  this 
background  it  is  and  must  be  as  unintelligible  as  the 
orthodox  doctrine  of  the  Trinity  is  to  persons  who  know 
nothing  of  the  theological  controversies  which  preceded 
the  formulation  of  the  Athanasian  Creed.  In  the  course 
of  my  exposition  I  have  constantly  enlivened  the  dis- 
cussion by  geometrical  anecdotes  about  men  living  on 
spheres,  and  dynamical  parables  about  persons  with  an 
unintelligible  fondness  for  rotating  wheels  as  axes  of 
reference.  I  think  this  course  was  inevitable,  in  order 
to  illustrate  the  conceptions  which  I  was  expounding. 
But  it  has  the  grave  disadvantage  of  breaking  the  train 
of  argument  and  obscuring  that  distinction  between 
inference  and  illustration  which  it  is  so  important  to 
keep  clear.  I  shall  therefore  end  by  summarising  the 
whole  matter  in  a  connected  form. 

Summary  of  Arguments  and  Conclusions  of  Part  I. 
(1)  Nature  is  a  sum  total  of  interconnected  events; 
and  every  actual  event  lasts  for  some  time,  has  some 
extension,  and  is  in  spatio-temporal  relations  to  the 
other  events  in  Nature.  (2)  But  the  extensions, 
durations,  and  spatio-temporal  relations  of  events  are 
of  such  a  kind  that  we  can  apply  the  Principle  of 
Extensive  Abstraction  to  them,  and  thus  define 
"instantaneous  point-events"  and  their  exact  spatio- 
temporal  relations.  We  can  then  give  a  clear  meaning 
to  the  statement  that  the  actual  extended  and  enduring 
events  of  Nature  are  "composed  of"  instantaneous 
point-events,  and  that  the  crude  relations  of  such  actual 


216  SCIENTIFIC   THOUGHT 

events  are  "  compounded  out  of "  the  exact  relations  of 
the  instantaneous  point-events  which  compose  them. 
(3)  This  being  so,  we  can  henceforth  safely  state  our 
theory  in  terms  of  instantaneous  point-events  and  their 
exact  relations,  which  are  notiora  nobis,  though  not 
notiora  Natunc.  For  we  know  how  to  translate  pro- 
positions about  instantaneous  point-events  and  their 
merely  conceivable  relations  into  propositions  about 
actual  extended  and  enduring  events  and  their  per- 
ceptible relations. 

(4)  It  is  impossible  to  state  general  laws  about  the 
events  in  Nature  till  we  have  fixed  on  some  way  of 
assigning  a  date  and  a  position  to  every  instantaneous 
point-event  in  Nature.  For  the  laws  of  Nature  express 
universal  types  of  connexion  between  events  of  one 
kind  happening  in  one  place  at  one  date  and  events 
of  the  same  (or  some  other)  kind  happening  at  the 
same  (or  some  other)  place  at  the  same  (or  some  other) 
date.  If  the  places  and  dates  be  different,  the  laws  of 
Nature  will  in  general  involve  the  difference  between 
the  spatial  co-ordinates  and  the  difference  between  the 
dates  of  the  events.  (5)  There  are  infinitely  many 
different  ways  of  assigning  places  and  dates  to  all  the 
instantaneous  point-events  in  Nature ;  but  each  will 
involve  the  choice  of  certain  observable  events  and 
processes  in  Nature  as  spatial  axes  and  time-measurer. 
All  other  events  will  be  placed  and  dated  by  their 
spatio-temporal  relations  to  these  chosen  ones.  Any 
such  chosen  set  of  events  may  be  called  a  Frame  of 
Reference.  (6)  It  is  reasonable  to  suppose  that  the 
expression  for  the  laws  of  Nature  in  terms  of  any 
frame  will  depend  partly  on  the  particular  frame  chosen 
for  placing  and  dating  the  events  of  Nature  and  partly 
on  the  intrinsic  structure  of  Nature.  The  aim  of  science 
should  be  to  find  general  formulas  for  the  laws  of 
Nature,  which  will  immediately  give  the  special  ex- 
pression of  the  law  in  terms  of  any  particular  frame,  as 
soon  as  the  defining  characteristics   of  the  frame   are 


GENERAL   THEORY   OF   RELATIVITY      217 

known.  This  is  as  near  as  anyone  but  God  can  get 
to  the  absolute  laws  of  Nature.  (7)  There  are  two 
intrinsic  peculiarities  of  Nature  which  reveal  them- 
selves at  once,  (a)  No  matter  what  frame  we  choose, 
we  shall  need  four  independent  pieces  of  information 
to  place  and  date  any  instantaneous  point-event.  This 
fact  is  expressed  by  saying  that  Nature  is  a  four- 
dimensional  manifold  ;  and  nothing  further  is  expressed 
thereby,  (h)  In  whatever  frame  we  choose  we  shall 
find  that  our  four  pieces  of  information  divide  into 
two  groups  ;  three  of  them  are  spatial  and  one  is  tem- 
poral. Thus  we  must  be  careful  not  to  talk,  or  listen 
to,  nonsense  about  "Time  being  a  fourth  dimension 
of  Space." 

(8)  There  is  one  frame  which  has  been  tacitly  used 
in  the  past  for  placing  and  dating  the  events  of  Nature 
for  scientific  purposes,  and  therefore  the  laws  of  Nature 
have  been  expressed  in  terms  of  this  frame.  The  axes 
of  it  are  defined  by  the  fixed  stars,  the  dating  is  done 
by  pendulum  clocks  set  in  agreement  with  each  other 
by  means  of  light  signals.  (9)  The  choice  of  this  frame 
is  not  altogether  arbitrary.  With  it,  the  supposed  laws 
of  Nature  can  be  expressed  in  a  comparatively  simple 
form,  and  yet  are  verified  to  a  high  degree  of  approxi- 
mation. With  it,  again,  distances  and  time -lapses 
which  we  should  immediately  judge  to  be  unequal, 
.  when  we  are  favourably  situated  for  making  such 
comparisons,  are  unequal,  whilst  those  that  we  should 
immediately  judge  to  be  equal,  under  similar  condi- 
tions, are  either  exactly  or  approximately  so.  In  many 
frames  this  approximate  agreement  with  our  immediate 
judgments  of  equality  and  inequality  would  not  hold. 
(10)  With  respect  to  such  a  frame,  light  in  vacuo 
travels,  to  an  extremely  high  degree  of  approximation, 
in  straight  lines  and  with  a  constant  velocity  ;  and  the 
laws  of  motion,  in  the  traditional  Newtonian  form,  are 
very  approximately  true.  Until  quite  recent  years  there 
was  no  motive  for  adding  these  qualifying  phrases. 

p 


218  SCIENTIFIC   THOUGHT 

(i  i)  Suppose  now  that  we  take  a  set  of  frames,  whose 
clocks  are  set  in  the  same  way  as  those  of  the  funda- 
mental frame  just  described,  and  which  only  differ  from 
it  and  from  each  other  in  that  they  move  with  various 
uniform  velocities  in  the  same  straight  line  with  respect 
to  the  fundamental  frame.  On  traditional  views  about 
the  measurement  of  space  and  time  the  measured  time- 
lapse  between  any  pair  of  events  should  be  the  same 
with  respect  to  all  these  frames,  and  should  be  inde- 
pendent of  their  spatial  separation  and  of  the  relative 
velocities  of  the  two  frames.  The  spatial  separations 
should  have  different  measured  values  in  terms  of  any 
two  frames  of  the  set,  and  they  should  depend  on  the 
time-lapse  and  the  relative  velocities  ;  but  they  should 
depend  on  nothing  else,  and  the  connexion  between 
them  should  be  of  a  very  simple  form.  If  this  be 
so,  the  measured  velocity  of  anything  that  moves  with 
respect  to  the  various  frames  should  be  different  for 
each  frame.  (12)  But  very  accurate  experiments,  which 
would  be  quite  capable  of  detecting  these  expected 
differences  in  the  measured  velocity  of  light  with 
respect  to  a  pair  of  such  frames,  fail  to  show  any 
sign  of  difference.  Hence  the  traditional  views  about 
the  measurement  of  time  and  space  must  be  revised, 
or  some  purely  physical  explanation  must  be  found 
for  this  discrepancy  between  theory  and  observation. 
(13)  No  plausible  physical  explanation  can  be  found,  , 
which  does  not  conflict  with  other  well-established 
physical  results.  Hence  the  traditional  views  about  the 
measurement  of  space  and  time  must  be  revised.  (14) 
The  transformation  equations  of  the  Special  Theory 
of  Relativity  express  the  relations  which  must  hold 
between  the  measured  distances  and  the  measured  time- 
lapses  of  a  pair  of  events  with  respect  to  any  two  frames 
of  this  set,  if  the  measured  velocity  of  light  with  respect 
to  all  these  frames  is  to  be  the  same.  They  must 
therefore  be  accepted.  (15)  According  to  these  trans- 
formation equations  the  measured  time-lapses  between 


GENERAL  THEORY   OF   RELATIVITY      219 

the  same  pair  of  events  will  not  be  the  same  with 
respect  to  all  frames  of  the  set.  They  will  depend  on 
the  measured  distances  of  the  events  and  on  the  relative 
velocities  of  the  frames.  And  the  measured  distances 
will  not  be  connected  with  the  measured  time-lapses 
in  the  simple  way  in  which  they  are  connected  on 
the  traditional  theory.  The  differences  between  the 
traditional  transformation  equations  and  those  of  the 
Special  Theory  of  Relativity  are,  however,  so  extremely 
small,  when  the  relative  velocities  of  the  frames  are 
small  as  compared  with  that  of  light,  that  it  is  not 
surprising  that  the  defects  of  the  traditional  view  should 
have  remained  unnoticed  until  recent  years.  (16)  It 
follows  that,  although  (as  stated  in  (7))  the  distinction 
between  time  and  space  will  appear  in  every  frame,  time- 
separation  and  space-separation  are  not  independent  facts 
in  Nature.  Events  that  are  separated  in  time  but  co- 
incident in  space  for  one  of  these  frames  will  always 
be  separated  in  space  for  another  of  them.  And  events 
which  are  separated  in  space  but  coincident  in  time  for 
one  frame  will  be  separated  in  time  for  another.  But,  if 
a  pair  of  events  be  coincident  both  in  time  and  in  space 
for  one  frame,  they  will  be  so  for  all. 

(17)  Newton's  laws  of  motion  are  in  such  a  form  that 
they  are  co-variant  with  respect  to  this  set  of  frames  for 
the  traditional  transformation-equations,  but  are  not 
co-variant  for  the  transformations  of  the  Special  Theory 
of  Relativity.  On  the  other  hand,  Maxwell's  equations 
for  the  electro-magnetic  field  are  co-variant  for  the  latter 
and  not  for  the  former.  This  means  that  Maxwell's 
equations  are  already  in  a  form  which  remains  un- 
changed with  change  of  frame,  so  long  as  we  confine 
ourselves  to  the  particular  group  of  frames  at  present 
under  discussion  and  use  the  transformation  equations 
which  the  facts  about  light  have  shown  to  be  necessary. 
Since  this  is  not  true  for  Newton's  laws,  unless  we  use 
a  set  of  transformation  equations  which  the  facts  about 
light    have    proved    to    be    slightly     inaccurate    (viz., 


220  SCIENTIFIC  THOUGHT 

those  of  the  traditional  kinematics),  we  must  con- 
clude that  Maxwell's  equations  are  a  nearer  approach 
to  "absolute"  laws  of  Nature  than  the  laws  of  motion 
in  their  traditional  form.  (18)  It  is,  however,  easy  to 
make  quantitatively  small  modifications  in  the  traditional 
laws  of  motion,  which  will  render  them  co-variant  for  all 
frames  of  the  present  set  when  the  true  transformation 
equations  are  used.  The  modified  laws  will  then  be 
as  near  an  approximation  to  absolute  laws  of  Nature 
as  Maxwell's  equations.  (19)  The  necessary  modifica- 
tions require  us  to  drop  the  notion  that  inertial  mass  is 
an  absolute  constant.  The  measured  inertial  mass  of 
a  particle  with  respect  to  a  frame  of  the  set  depends 
on  its  velocity  in  that  frame,  and  very  approximately 
splits  up  into  two  factors,  one  of  which  is  a  constant 
and  the  other  is  its  traditional  kinetic  energy  divided 
by  the  square  of  the  velocity  of  light.  (20)  Delicate 
experiments  with  pendula  strongly  suggest  that  the 
gravitational  mass  of  a  body  is  accurately  proportional 
to  its  total  inertial  mass,  and  not  merely  to  the  part  of 
this  which  is  independent  of  the  energy.  (21)  The 
frame  whose  axes  are  determined  by  the  fixed  stars 
and  whose  clocks  are  regulated  by  light-signals,  and 
all  other  frames  whose  clocks  are  regulated  in  the 
same  way  and  whose  axes  move  with  a  uniform  recti- 
linear velocity  with  respect  to  the  former,  together 
make  up  the  set  of  empirically  Newtonian  frames.  With 
respect  to  all  frames  of  this  set  it  is  certain  that  light 
travels  very  approximately  in  straight  lines  with  the 
same  constant  velocity,  and  it  is  certain  that  Newton's 
laws  of  motion — as  modified  by  the  Special  Theory  of 
Relativity — very  approximately  hold.  So  close  is  the 
approximation  in  both  cases  that  nothing  but  theo- 
retical considerations  would  induce  us  to  look  for  any 
exception  to  it.  We  have  now  to  remove  our  previous 
restriction  to  Newtonian  frames,  and  to  try  to  generalise 
the  laws  of  Nature  for  frames  that  are  not  Newtonian. 
(22)  It  is  possible  to  keep  the  form  of  Newton's  first 


GENERAL   THEORY   OF   RELATIVITY      221 

two  laws  of  motion  for  non-Newtonian  frames,  provided 
we  will  introduce  appropriate  non-Newtonian  forces 
with  each  non-Newtonian  frame.  These  forces  will  be 
peculiar  in  that  (a)  they  act  on  all  particles  referred  to 
the  frame,  and  are  in  general  functions  of  the  position 
and  date  of  an  event  in  the  frame  ;  (If)  they  depend  on 
no  property  of  the  particle  except  its  inertial  mass  ;  and 
(c)  they  do  not  in  general  obey  Newton's  third  law, 
unless  concealed  particles  be  assumed  ad  hoc  to  carry 
the  reaction.  In  the  first  two  of  these  respects  they 
resemble  the  Newtonian  force  of  gravitation.  (23) 
According  to  Newton's  first  law  a  particle  under  the 
action  of  no  force  rests  or  moves  uniformly  in  a 
straight  line  with  respect  to  a  Newtonian  frame.  This 
is  equivalent  to  saying  that  the  total  spatio-temporal 
separation  between  any  two  remote  events  in  its  history 
is  either  greater  or  less  than  it  would  be  for  all  other 
possible  ways  in  which  the  history  of  the  particle  might 
unfold  itself  between  these  two  events.  (24)  The  spatio- 
temporal  separation  between  two  adjacent  events  (unlike 
the  spatial  and  the  temporal  separations)  is  independent 
of  the  frame  of  reference,  though  it  depends  on  the 
intrinsic  structure  of  the  region  in  which  the  events 
happen,  and  this  in  turn  determines  the  set  of  frames 
which  can  be  used  for  mapping  out  this  part  of  the 
history  of  Nature.  Its  particular  expression,  in  terms  of 
co-ordinates  and  dates,  of  course  varies  with  the  particular 
member  of  the  whole  set  of  admissible  frames  which 
is  used.  Thus,  the  fact  that  the  total  spatio-temporal 
separation  between  a  pair  of  remote  events  is  a  maxi- 
mum or  minimum  is  independent  of  frames,  though  the 
particular  course  for  which  the  total  separation  is  in  fact 
stationary  differs  according  to  the  intrinsic  structure  of 
the  region  in  which  the  events  are  contained.  (25)  The 
particular  conditions  which  must  hold  if  the  total  spatio- 
temporal  separation  is  to  be  a  maximum  or  minimum 
can  be  stated  in  a  form  which  applies  equally  to  all  struc- 
tures and  all  frames.     The  four  equations  which  sum 


222  SCIENTIFIC   THOUGHT 

up  these  conditions  constitute  the  equations  of  motion  of 
a  particle,  at  least  under  the  action  of  non-Newtonian 
forces.  On  comparing  them  with  the  traditional 
Newtonian  equations,  we  see  that  the  g*s  which 
characterise  any  non  -  Newtonian  frame  are  of  the 
nature  of  potentials  of  the  non-Newtonian  forces  intro- 
duced by  that  frame.  (26)  We  now  make  two  assump- 
tions, which  are  only  justified  in  so  far  as  they  work. 
(«)  We  assume  that  it  is  a  universal  law  of  Nature 
that  a  particle  moves  in  such  a  way  that  the  total 
separation  of  remote  events  in  its  history  is  stationary, 
as  compared  with  that  of  all  other  possible  ways  of 
moving.  This  is  to  hold  equally  whether  it  be  subject 
only  to  non-Newtonian  or  also  to  Newtonian  forces. 
In  that  case  the  equations  deduced  for  the  non- 
Newtonian  case  become  the  equations  of  motion,  (b) 
We  assume  that  in  those  regions  of  Nature,  regarded 
as  a  sum  total  of  events,  in  which  Newtonian  forces 
show  themselves,  the  structure  of  Nature  is  not  such 
that  the  separation  can  be  reduced  to  the  form  with 
constant  coefficients.  If  that  be  so,  the  course  with 
the  maximum  total  spatio-temporal  separation  is  not 
a  Euclidean  straight  line  traversed  with  a  constant 
velocity,  as  judged  by  a  Newtonian  clock.  We  treat 
the  traditional  potentials  of  the  Newtonian  forces  in 
any  field  as  first  approximations  to  a  set  of  g's,  which 
satisfy  the  general  equations  of  motion  thus  deduced. 
And  we  treat  the  result  as  the  true  law  of  the  field. 

(27)  Continuous  manifolds  of  several  dimensions, 
such  as  Nature  has  proved  itself  to  be,  can  be  of  various 
intrinsically  different  kinds.  As  we  might  put  it,  they 
can  be  "plane-like,"  "sphere-like,"  "egg-like,"  and 
so  on.  Whatever  intrinsic  spatio-temporal  structure 
Nature  may  have,  there  will  be  an  infinite  number  of 
different  possible  frames  to  be  found  for  placing  and 
dating  the  events  of  Nature.  Nevertheless,  the  intrinsic 
structure  of  Nature  will  impose  certain  conditions  on 
all    possible    natural    frames   of   reference.      These    re- 


GENERAL  THEORY   OF   RELATIVITY       223 

strictions  will  take  the  form  of  certain  very  general 
equations  connecting  the  g's  of  any  possible  natural 
frame.  If  the  structure  of  Nature  be  plane-like,  the 
condition  is  that  the  unmodified  Riemann-Christoffel 
Tensor  shall  vanish  for  the  g's  of  all  possible  natural 
frames.  If  its  structure  be  sphere-like,  the  condition 
is  that  the  Modified  Riemann-Christoffel  Tensor 
shall  vanish  for  the  gs  of  all  possible  frames.  The 
latter  is  a  less  rigid  condition  than  the  former.  (28) 
If  the  intrinsic  structure  of  Nature  be  plane-like,  an 
accurately  Newtonian  frame  will  be  fitted  for  dating 
and  placing  all  the  events  of  Nature  ;  otherwise  it 
will  not.  (29)  If  we  try  to  map  out  a  manifold  by  a 
frame  which  is  unsuited  to  its  intrinsic  structure,  we 
shall  only  be  able  to  square  our  measurements  with 
our  theory  by  the  assumption  of  forces  which  distort 
our  measuring  instruments  and  upset  their  readings. 

(30)  We  cannot  find  any  frame  that  will  transform 
away  gravitational  forces  always  and  everywhere, 
though  we  can  find  non-Newtonian  frames  which  will 
transform  them  away  over  sufficiently  small  regions 
of  space  and  time.  With  respect  to  Newtonian  frames 
all  particles  are  always  acted  on  by  gravitational  forces, 
though  these  may  sometimes  be  negligibly  small  for 
practical  purposes.  It  is  therefore  plausible  to  suppose 
that  the  universality  of  gravitation  with  respect  to 
Newtonian  frames  is  a  mark  of  the  misfit  between  this 
type  of  frame  and  the  intrinsic  structure  of  Nature. 
(31)  On  the  other  hand  (a)  gravitation  has  many 
analogies  to  non-Newtonian  forces  ;  (b)  the  traditional 
law  of  gravitation,  which  is  certainly  very  nearly  true, 
can  be  expressed  as  a  differential  equation  of  the 
second  order,  involving  the  gravitational  potential  at 
a  place  and  the  co-ordinates  of  the  place  with  respect 
to  Newtonian  axes  ;  and  (c)  we  have  already  assumed 
that  potentials  and  the  g's  of  frames  are  mutually 
equivalent.  (32)  The  facts  mentioned  in  (31)  strongly 
suggest   that   the    law    of    gravitation    must    be    some 


224  SCIENTIFIC   THOUGHT 

general  condition  imposed  on  the  g's  of  all  possible 
natural  frames,  and  expressed  as  a  differential  equation 
of  the  second  order  involving  these  g's.  The  facts 
mentioned  in  (30)  suggest  that  this  condition  is  not 
that  the  unmodified  Tensor  vanishes.  For,  if  this 
were  so,  the  intrinsic  structure  of  Nature  would  be 
such  that  a  Newtonian  frame  is  suited  to  it,  and  the 
necessity  of  assuming  gravitational  forces  always  and 
everywhere  with  Newtonian  frames  strongly  suggests 
that  this  is  not  so.  (33)  It  is  obvious  that  the 
next  suggestion  to  try  is  to  suppose  that  the  law  of 
gravitation  is  expressed  by  the  vanishing  of  the 
Modified  Tensor,  i.e.,  that  gravitation  is  the  sign  of 
an  intrinsically  sphere-like  structure  in  Nature.  (34) 
It  is  found  that,  if  this  be  the  true  law  of  gravitation, 
the  observable  effects  will  in  most  cases  differ  so  little 
from  those  predicted  by  the  traditional  law  that  the 
difference  could  not  be  detected.  Hence  the  very  full 
verification  which  the  traditional  law  has  received  is 
no  obstacle  to  accepting  the  amended  law.  (35)  On 
the  other  hand,  there  are  certain  very  special  cases 
in  which  a  small  observable  effect  might  be  expected 
on  the  new  form  of  the  law  and  not  on  the  old.  In 
such  cases  (notably  the  movement  of  the  perihelion  of 
Mercury  and  the  bending  of  a  ray  of  light  in  passing 
near  a  very  massive  body  like  the  sun)  the  predicted 
effects  have  been  verified  both  qualitatively  and 
quantitatively. 

The  following  additional  works   may    be   consulted 
with  advantage  : 

A.  S.     Eddington,    Report    on    the    Relativity    Theory    of 

Gravitation. 
„  ,,  Space,  Time,  and  Gravitation. 

E.  Cunningham,  Relativity,  Electron  Theory,  and  Gravitation. 

B.  Riemann,    Uber  die  Hypothese?i  welche  der  Geometrie zu 

Grunde  liegen  .     (Julius  Springer.      Berlin.) 
H.  Weyl,  Space,  Time,  and  Matter. 


PART   II 

THE  SENSATIONAL  AND  PERCEPTUAL  BASIS 
OF  OUR  SCIENTIFIC  CONCEPTS 


Contents  of  Part  II 

CHAPTER 

VII.  Matter  and  its  Appearances  ;  Preliminary  Definitions 

VIII.  The  Theory  of  Sensa,  and  the  Critical  Scientific  Theory 

IX.  The  Positions  and  Shapes  of  Sensa  and  of  Physical  Objects 

X.  The  Dates  and  Durations  of  Sensa  and  of  Physical  Objects 
and  Events 

XL  Sensible  and  Physical  Motion 

XII.  Sensible  and  Physical  Space-Time 

XIII.  The  Physiological  Conditions  of  Sensations,  and  the  Onto- 
logical  Status  of  Sensa 


CHAPTER   VII 

"  Fallunt  nos  oculi,  vagique  sensus 
Oppressa  ratione  mentiuntur. 
Nam  turris,  prope  quae  quadrata  surgit, 
Detritis  procul  angulis  rotatur." 

(Petronius  Arbiter.) 

Matter  and  its  Appearances  ;  Preliminary  Definitions 

In  the  First  Part  we  have  been  dealing  with  the 
gradual  development  and  modification  of  the  traditional 
scientific  concepts  of  Space,  Time,  and  Motion,  within 
the  region  of  Physics.  These  concepts  were  taken  over 
by  science  from  educated  common-sense,  and  we  have 
been  tracing  the  process  of  clarification  and  definition 
which  they  have  undergone  at  the  hands  of  scientists 
in  pursuit  of  their  own  business.  At  two  places  only 
have  we  deliberately  gone  outside  the  range  of  ordinary 
scientific  reflection.  The  first  was  where  we  explained 
the  Principle  of  Extensive  Abstraction,  and  tried  to 
justify  by  its  means  what  mathematical  physicists  take 
for  granted,  viz.,  the  application  of  geometry  and 
mechanics,  stated  in  terms  of  points,  instants,  and 
particles,  to  a  world  of  extended  objects  and  non-instan- 
taneous events.  The  second  was  where  we  dealt  with 
the  general  problem  of  Time  and  Change,  and  tried 
to  defend  their  reality  against  the  very  plausible  ob- 
jections which  have  been  made  to  them  by  certain 
philosophers. 

Now  the  careful  reader  will  have  been  struck  by 
two  points  in  Part  I.  (i)  He  will  have  noticed  that  the 
"  raw  material,"  which  science  took  over  from  common- 
sense  and  elaborated,  was  really  anything  but  "raw." 

227 


>2$  SCIENTIFIC   THOUGHT 

It  was  already  highly  complex  and  sophisticated.  The 
common-sense  notions  of  a  single  Space,  a  single  Time, 
and  persistent  bits  of  Matter  which  exist,  move,  and 
change  within  them,  are  by  no  means  primitive.  They 
must  be  the  results  of  a  long  and  complex  process  of 
reflection  and  synthesis,  carried  out  by  countless  genera- 
tions of  men  on  the  crude  deliveries  of  their  senses, 
embodied  in  everyday  speech,  and  thus  handed  down 
from  father  to  son  for  further  elaboration.  The  main 
outlines  of  this  conceptual  scheme  have  been  accepted 
without  question  by  scientists,  and  we  have  so  far 
merely  been  tracing  those  modifications  of  detail  within 
the  scheme,  which  a  more  accurate  knowledge  of  the  facts 
of  nature  has  shown  to  be  necessary.  In  Part  II,  I 
want  to  dig  below  the  foundations  of  Part  I,  and  to 
try  to  connect  the  concepts  of  science  and  common- 
sense  with  their  roots  in  crude  sensation  and  perception. 
If  we  should  find,  as  I  think  we  shall,  that  recent 
modifications  in  the  traditional  concepts,  which  have 
been  made  on  purely  scientific  grounds,  bring  the 
general  scheme  into  closer  connexion  with  its  sensible 
and  perceptual  basis,  this  will  be  an  additional  argument 
in  favour  of  such  modifications,  and  should  tend  to 
neutralise  the  impression  of  paradox  which  these  later 
developments  produce  on  men  who  have  been  brought 
up  on  the  traditional  scheme. 

(2)  The  second  point  which  will  have  struck  the 
reader  is  that  practically  nothing  has  been  said  so  far 
about  the  concept  of  Matter.  This  is  true.  There  is 
a  much  wider  divergence  between  the  common-sense 
and  the  scientific  concepts  of  Matter  than  between  the 
two  concepts  of  Space  or  of  Time.  The  scientific  con- 
cepts of  Space  and  Time  are  fairly  straightforward  de- 
velopments and  clarifications  of  the  concepts  of  common- 
sense.  But  common-sense  thinks  of  Matter  as  having 
many  intrinsic  qualities,  such  as  colour,  temperature, 
etc.,  besides  its  merely  spatio-temporal  characteristics. 
Science,  on  the  other  hand,  tends   to  think  of  Matter 


MATTER   AND   ITS   APPEARANCES         229 

as  being  simply  "the  movable  in  space,"  and  to  ascribe 
to  it  no  intrinsic  non-spatio-temporal  qualities  except 
mass.  Now  the  treatment  of  Matter  and  our  knowledge 
of  it  will  bring  us  in  the  most  direct  way  to  the  heart 
of  the  problem  of  Part  II.  Matter  is  admitted  to  be, 
or  to  be  specially  closely  connected  with,  what  we 
perceive  with  our  senses.  And  again,  it  would  be 
admitted  by  most  people  that  we  should  never  have 
known  of  spatial  attributes,  like  shape,  size,  and  posi- 
tion, if  we  had  not  perceived  bits  of  matter  of  various 
shapes  and  sizes  in  various  places.  Lastly,  we  learn 
about  Motion  by  watching  bits  of  Matter  moving  about, 
and  by  moving  about  ourselves.  Thus,  in  trying  to 
clear  up  the  relations  between  Matter,  as  conceived  by 
science,  and  what  we  perceive  with  our  senses,  we 
shall  at  the  same  time  be  dealing  with  the  sensible  and 
perceptual  bases  of  the  concepts  of  Space,  Time,  and 
Motion.  So,  in  one  sense,  this  Part  will  be  wholly 
about  the  concept  of  Matter.  But  this  will  involve  a 
reconsideration  of  the  concepts  of  Space,  Time,  and 
Motion.  I  shall  begin  by  stating  the  problem  in  its 
most  general  form,  and  shall  gradually  go  into  greater 
detail. 

The  Traditional  Notion  of  a  bit  of  Matter. — When  we 
ask  what  is  meant  by  a  bit  of  Matter  the  question  is 
itself  ambiguous.  In  one  sense  a  complete  answer  to 
it  would  be  a  complete  theory  of  Matter,  and  this 
could  only  be  made,  if  at  all,  at  the  very  end  of  our 
discussion.  This,  however,  is  not  the  sense  in  which 
I  am  asking  the  question  here.  All  that  I  am  asking 
is:  "What  is  the  irreducible  minimum  of  properties 
which  practically  everybody  would  agree  that  an  object 
must  possess  if  it  is  to  be  called  a  bit  of  Matter?"  I 
think  that  science  and  common-sense  would  agree  that 
at  least  the  following  conditions  must  be  fulfilled  : 
(i)  Its  existence  and  properties  must  be  independent 
of  the  minds  that  happen  to  observe  it,  and  it  must 
be  capable  of  being  observed  by  many  minds.     This 


230  SCIENTIFIC  THOUGHT 

characteristic  may  be  summed  up  by  saying  that  Matter 
is  neutral  as  between  various  observers,  or  is  "public" 
— to  use  a  convenient  word  of  Mr  Russell's.  This  dis- 
tinguishes Matter  sharply  from  any  ordinary  conscious 
state  of  mind.  The  latter  is  in  a  unique  way  private 
to  the  person  whose  state  it  is.  My  belief  that  2  +  2  =4 
is  different  from  yours,  though  the  two  beliefs  refer  to 
the  same  fact.  My  belief  cannot  literally  wander  out 
of  my  mind  and  turn  up  in  yours.  It  is  true  that  I 
may  convert  you  from  your  erroneous  belief  that 
2  +  2  =  5,  and  replace  it  by  my  true  belief  that  2  +  2=4. 
This  does  not,  however,  mean  that  my  belief  has 
become  yours,  in  the  sense  that  it  has  left  my  mind 
and  taken  up  its  abode  in  yours.  Were  this  so,  I 
could  never  persuade  you  of  anything  without  losing 
my  own  belief  in  it,  and  schoolmasters  would  pre- 
sumably be  distinguished  from  other  men  by  an  ultra- 
Humian  scepticism  as  to  all  the  subjects  that  they 
teach.  This  is  not,  in  fact,  found  to  be  the  case.  All 
that  really  happens  when  A  converts  B  to  his  own 
belief  is  that  A's  arguments,  or  the  amount  of  A's 
bank  balance,  produce  in  B's  mind  a  state  of  belief 
which  refers  to  the  same  fact  as  B's  belief,  and  has 
the  same  relation  of  concordance  or  discordance  to  this 
fact.  My  belief  and  yours  are  only  called  the  same 
belief  in  the  derivative  sense  that  they  are  two  different 
acts  of  believing  which  are  related  in  the  same  way 
to  the  same  fact. 

Exactly  the  same  is  true  of  desires.  We  do  some- 
times say  that  you  and  I  have  the  same  desire  ;  but 
what  we  mean  is  that  your  desire  and  mine,  though 
two  states  of  mind,  have  a  single  object.  Now,  if 
there  be  such  things  as  bits  of  Matter  at  all,  they  are 
not  private  in  this  way  to  each  mind,  but  are  common 
to  all  the  minds  that  observe  them.  We  talk  of  my 
beliefs  and  your  wishes  ;  we  do  not  talk  of  my  hydrogen 
atom  or  of  your  electron.  We  just  speak  of  the  or  this 
atom  or  electron.     It  is,  of  course,  true  that  a  hat  or 


MATTER   AND   ITS   APPEARANCES         231 

an  umbrella  is  regarded  as  a  bit  of  Matter,  and  that 
we  do  talk  of  my  hat  and  of  your  umbrella.  But  this, 
which  at  first  sight  seems  an  objection,  is  seen  on 
further  reflection  to  support  what  we  have  been  saying. 
The  sense  in  which  my  umbrella  is  mine  is  different 
from  that  in  which  my  beliefs  are  mine.  My  umbrella 
is  mine  only  in  the  sense  that  it  is  legally  my  property  ; 
my  beliefs  are  mine  in  the  sense  that  they  could  not 
exist  out  of  my  mind  or  pass  into  yours.  You  cannot 
take  my  beliefs  ;  it  is  only  too  fatally  easy  for  you  to 
take  my  umbrella.  So  that  even  those  bits  of  Matter 
to  which  we  apply  possessive  adjectives  are  public  in 
a  way  in  which  no  state  of  mind  is  public. 

(ii)  A  bit  of  Matter  is  supposed  to  be  neutral,  not 
only  between  different  observers,  but  also  to  be  in  a 
certain  way  neutral  as  between  several  senses  of  the 
same  observer.  We  are  said  to  see,  hear,  and  feel  a 
bell.  This  sort  of  neutrality  is  not  supposed  to  be 
complete.  The  shape  and  size  of  the  bell  are  indeed 
supposed  to  be  in  some  way  common  to  sight  and 
touch.  As  regards  its  sensible  qualities  the  view  of 
common-sense  is  that  any  bit  of  Matter  combines  a 
number  of  these,  and  that  different  senses  are  needed 
to  reveal  different  sensible  qualities.  Thus  sight,  and 
it  alone,  makes  us  aware  of  the  colours  of  bodies ; 
touch,  and  it  alone,  makes  us  aware  of  their  temper- 
atures ;  and  so  on.  But  it  is  part  of  the  ordinary  view 
of  a  piece  of  Matter  that  all  these  various  sensible 
qualities  co-exist  in  it,  whether  the  requisite  senses 
be  in  action  to  reveal  them  all  or  not.  If  we  first 
only  look  at  a  body,  and  then  shut  our  eyes  and  go 
up  to  it  and  feel  it,  it  is  not  supposed  that  it  had  no 
temperature  on  the  first  occasion  and  no  colour  on 
the  second. 

(iii)  These  two  properties  of  publicity,  as  between 
different  observers,  and  neutrality,  as  between  the 
various  senses  of  a  single  observer,  are  closely  con- 
nected   with    a    third    feature    which     is    held    to    be 


232  SCIENTIFIC   THOUGHT 

characteristic  of  Matter.  Bits  of  Matter  are  supposed 
to  persist  with  very  little  change,  whether  anyone 
happens  to  observe  them  or  not,  and  to  pursue  their 
own  affairs  and  interact  with  each  other,  regardless  of 
our  presence  and  absence. 

(iv)  This  brings  us  to  the  fourth  characteristic  of 
Matter.  It  is  commonly  held  to  be  part  of  what  we 
mean  by  a  bit  of  Matter  that  it  shall  have  a  more  or 
less  permanent  shape  and  size,  and  that  it  shall  have 
a  position  in  Space,  and  be  capable  of  moving  from 
one  position  to  another.  It  is  admitted  that  bits  of 
Matter  are  constantly  changing  their  shapes,  sizes, 
and  positions  ;  but  it  is  held  that  they  do  this  through 
their  interactions  with  each  other  and  not  through  any 
change  in  our  acts  of  observation,  and  that  in  all  their 
changes  they  continue  to  have  some  shape,  size  and 
position.  If  it  could  be  shown  that  nothing  in  the 
world  actually  has  such  properties  as  these,  it  would 
commonly  be  held  that  the  existence  of  Matter  had 
been  disproved,  even  though  there  were  public,  inde- 
pendent, and  persistent  objects. 

Berkeley,  e.g.,  is  commonly  held  to  have  denied 
the  existence  of  Matter,  and  he  certainly  thought 
himself  that  he  had  done  so.  Yet  Berkeley's  theory 
undoubtedly  involves  the  existence  of  certain  entities, 
viz.,  the  volitions  (and  perhaps  the  sensations)  of  God, 
which  are  independent  of  the  mind  of  any  finite  observer 
and  are  neutral  as  between  my  mind  and  yours.  The 
reason  why  we  say  that,  if  Berkeley  be  right,  there  is 
no  Matter,  is  because  the  volitions  of  God,  though 
neutral  and  independent  of  us  observers,  have  nothing 
corresponding  to  shape,  size,  and  position  ;  whilst  the 
only  entities  which  Berkeley  allows  to  have  these 
attributes,  viz.,  our  sensations,  are  private  to  each  of 
us,  and  exist  only  so  long  as  we  have  them.  Very 
few  philosophers  have  denied  that  there  are  entities 
answering  to  the  first  three  conditions,  but  a  great 
many  have  denied  that  there  are  any  answering  both 


MATTER   AND   ITS   APPEARANCES         233 

to  these  and  to  the  fourth  condition.  Such  philosophers 
are  held  by  themselves  and  by  common-sense  to  have 
denied  the  existence  of  Matter.  Now  we  shall  have 
plenty  of  opportunity  for  seeing  that  there  is  a  real 
difficulty  in  holding  that  the  entities  which  have  shapes, 
sizes,  and  positions  are  neutral  and  independent,  and 
that  those  which  are  neutral  and  independent  have 
shapes,  sizes,  and  positions. 

Before  we  consider  these  points  in  detail  at  all  we 
must  mention  an  additional  complication  which,  though 
partly  verbal,  is  sure  to  puzzle  us  if  we  do  not  resolutely 
drag  it  into  the  light.  No  doubt  it  is  part  of  what  we 
mean  by  a  bit  of  Matter  that  it  shall,  in  some  sense,  have 
shape,  size,  and  position.  But  in  how  literal  a  sense 
must  this  be  true?  We  have  already  seen  that,  in  some 
sense,  an  extension  or  a  duration  is  composed  of  points 
or  of  instants  respectively.  But  this  sense  is  highly 
complicated  and  sophisticated,  or,  to  use  a  happy 
phrase  of  Dr  G.  E.  Moore's,  "Pickwickian."  Now 
we  shall  doubtless  be  able  to  find  Pickwickian  senses 
in  which  there  are  entities  that  are  at  once  public  and 
extended.  The  question  is  :  How  Pickwickian  may 
the  terms  in  our  statement  become  before  it  ceases  to 
be  useful,  and  becomes  merely  misleading,  to  say  that 
we  accept  the  existence  of  matter?  Our  theological 
friends  have  much  the  same  difficulties  in  their  inter- 
pretations of  the  terms  that  are  used  in  the  Creeds.  It 
could  obviously  only  be  true  in  a  highly  Pickwickian 
sense  that  the  Second  Person  of  the  Trinity  is  the  son 
of  the  First.  No  one  supposes  it  to  be  true  in  the 
literal  sense  in  which  George  V  is  the  son  of  Edward 
VII  ;  and  the  only  substantial  point  at  issue  is  whether 
the  sense  in  which  it  might  be  true  (assuming,  for  the 
sake  of  argument,  that  the  Persons  exist)  is  not  so 
extremely  Pickwickian  that  the  statement  is  more  likely 
to  mislead  than  to  enlighten.  Fortunately  for  us  the 
terminology  of  our  problem  is  not  surrounded  with  the 
same  emotional  fringe  as  surrounds  the  terms  used  in 

Q 


234  SCIENTIFIC   THOUGHT 

Theology.  It  is  no  part  of  our  duty  to  pay  compliments 
to  Matter,  and  so  long  as  we  state  clearly  what  we  do 
mean,  it  is  of  little  importance  whether  our  terms  be 
used  in  a  literal  or  in  a  highly  Pickwickian  sense.  It 
will  be  a  question  of  taste  whether  it  shall  be  said  that 
the  theory  that  we  finally  adopt  amounts  to  the  accept- 
ance or  the  denial  of  Matter.  If  we  should  be  accused 
of  saying  that  "  Matter  is  not  Matter,"  we  shall  at  least 
be  better  off  than  *Dr  F.  R.  Tennant,  who  labours  under 
the  dreadful  imputation  of  teaching  that  "Sin  is  not 
Sin." 

The  Notion  of  Sensible  Appearance. — I  have  now  tried  to 
point  out  what  is  the  irreducible  minimum  of  properties 
which  ordinary  people  consider  must  be  possessed  by 
anything  if  it  is  to  count  as  a  piece  of  Matter.  I  have 
also  pointed  out,  by  anticipation,  that  the  history  of 
philosophy  shows  there  to  be  a  great  difficulty  in 
holding  that  there  are  any  entities  which  fulfil  all  these 
conditions  in  a  literal  sense.  Lastly,  we  have  noticed 
that  the  question  of  the  reality  or  unreality  of  Matter, 
thus  defined,  is  not  perfectly  clear-cut,  because  of  the 
practical  certainty  that  many  of  our  terms  will  have  to  be 
interpreted  in  a  more  or  less  Pickwickian  manner,  and 
the  doubt  whether  it  is  worth  while  to  go  on  using 
familiar  phrases  after  their  literal  meaning  has  been 
departed  from  beyond  a  certain  point.  We  must  now 
consider  what  facts  make  it  hard  to  believe  that  anything 
obeys  all  four  conditions  in  at  all  a  literal  sense. 

The  difficulty  arises  because  of  the  group  of  facts 
which  we  sum  up  by  saying  that  it  is  necessary  to 
distinguish  between  things  as  they  are  and  things  as 
they  seem  to  us,  or  between  physical  reality  and  sensible 
appearance.  Difficulties  always  arise  when  two  sets  of 
properties  apparently  belong  to  the  same  object,  and 
yet  are  apparently  incompatible  with  each  other.  Now 
the  difficulty  here  is  to  reconcile  the  supposed  neutrality, 
persistence,  and  independence  of  a  physical  object  with 

*  See  his  Origin  of  Sin. 


MATTER   AND   ITS   APPEARANCES         235 

the  obvious  differences  between  its  various  sensible 
appearances  to  different  observers  at  the  same  moment, 
and  to  the  same  observer  at  different  moments  between 
which  it  is  held  not  to  have  undergone  any  physical 
change.  We  know,  e.g.,  that  when  we  lay  a  penny 
down  on  a  table  and  view  it  from  different  positions  it 
generally  looks  more  or  less  elliptical  in  shape.  The 
eccentricity  of  these  various  appearances  varies  as  we 
move  about,  and  so  does  the  direction  of  their  major 
axes.  Now  we  hold  that  the  penny,  at  which  we  say 
that  we  were  looking  all  the  time,  has  not  changed  ; 
and  that  it  is  round,  and  not  elliptical,  in  shape.  This 
is,  of  course,  only  one  example  out  of  millions.  It  would 
be  easy  to  offer  much  wilder  ones ;  but  it  is  simple  and 
obvious,  and  involves  no  complications  about  a  trans- 
mitting medium  ;  so  we  will  start  with  it  as  a  typical 
case  to  discuss. 

Now  there  is  nothing  in  the  mere  ellipticity  or  the 
mere  variation,  taken  by  itself,  to  worry  us.  The 
difficulty  arises  because  of  the  incompatibility  between 
the  apparent  shapes  and  the  supposed  real  shape,  and 
between  the  change  in  the  appearances  and  the  supposed 
constancy  of  the  physical  object.  We  need  not  at 
present  ask  why  we  believe  that  there  is  a  single 
physical  object  with  these  characteristics,  which  appears 
to  us  in  all  these  different  ways.  It  is  a  fact  that 
we  do  believe  it.  It  is  an  equally  certain  fact  that 
the  penny  does  look  different  as  we  move  about. 
The  difficulty  is  to  reconcile  the  different  appearances 
with  the  supposed  constancy  of  the  penny,  and  the 
ellipticity  of  most  of  the  appearances  with  the  supposed 
roundness  of  the  penny.  It  is  probable  that  at  first 
sight  the  reader  will  not  see  much  difficulty  in  this. 
He  will  be  inclined  to  say  that  we  can  explain  these 
various  visual  appearances  by  the  laws  of  perspective, 
and  so  on.  This  is  not  a  relevant  answer.  It  is  quite 
true  that  we  can  predict  what  particular  appearance  an 
object  will  present  to  an  observer,  when  we  know  the 


236  SCIENTIFIC   THOUGHT 

shape  of  the  object  and  its  position  with  respect  to 
the  observer.  But  this  is  not  the  question  that  is 
troubling'  us  at  present.  Our  question  is  as  to  the 
compatibility  of  these  changing  elliptical  appearances, 
however  they  may  be  correlated  with  other  facts  in 
the  world,  with  the  supposed  constancy  and  roundness 
of  the  physical  object. 

Now  what  I  call  Sensible  Appearance  is  just  a  general 
name  for  such  facts  as  I  have  been  describing.  It  is 
important,  here  as  always,  to  state  the  facts  in  a  form 
to  which  everyone  will  agree,  before  attempting  any 
particular  analysis  of  them,  with  which  it  is  certain 
that  many  people  will  violently  disagree.  The  funda- 
mental fact  is  that  we  constantly  make  such  judgments 
as:  "  This  seems  to  me  elliptical,  or  red,  or  hot,"  as  the 
case  may  be,  and  that  about  the  truth  of  these  judgments 
we  do  not  feel  the  least  doubt.  We  may,  however,  at 
the  same  time  doubt  or  positively  disbelieve  that  this 
is  elliptical,  or  red,  or  hot.  I  may  be  perfectly  certain 
at  one  and  the  same  time  that  I  have  the  peculiar 
experience  expressed  by  the  judgment:  "This  looks 
elliptical  to  me,"  and  that  in  fact  the  object  is  not 
elliptical  but  is  round. 

I  do  not  suppose  that  anyone,  on  reflection,  will 
quarrel  with  this  statement  of  fact.  The  next  question 
is  as  to  the  right  way  to  analyse  such  facts  ;  and  it  is 
most  important  not  to  confuse  the  facts  themselves 
with  any  particular  theory  as  to  how  they  ought  to 
be  analysed.  We  may  start  with  a  negative  remark, 
which  seems  to  me  to  be  true,  and  is  certainly  of  the 
utmost  importance  if  it  be  true.  Appearance  is  not 
merely  mistaken  judgment  about  physical  objects.  When 
I  judge  that  a  penny  looks  elliptical  I  am  not  mistakenly 
ascribing  elliptical  shape  to  what  is  in  fact  round. 
Sensible  appearances  may  lead  me  to  make  a  mistaken 
judgment  about  physical  objects,  but  they  need  not,  and, 
so  far  as  we  know,  commonly  do  not.  My  certainty 
that  the  penny  looks  elliptical  exists  comfortably  along- 


MATTER   AND   ITS   APPEARANCES         237 

side  of  my  conviction  that  it  is  round.  But  a  mistaken 
judgment  that  the  penny  is  elliptical  would  not  continue 
to  exist  after  I  knew  that  the  penny  was  really  round. 
The  plain  fact  is  then  that  "looking  elliptical  to  me" 
stands  for  a  peculiar  expedience,  which,  whatever  the  -* 
right  analysis  of  it  may  be,  is  not  just  a  mistaken 
judgment  about  the  shape  of  the  penny. 

Appearance  then  cannot  be  described  as  mistaken 
judgment  about  the  properties  of  some  physical  object. 
How  are  we  to  describe  it,  and  can  we  analyse  it?  Two 
different  types  of  theory  seem  to  be  possible,  which  I 
will  call  respectively  the  Multiple  Relation  Theory,  and 
the  Object  Theory  of  sensible  appearance.  The  Multiple 
Relation  Theory  takes  the  view  that  "  appearing  to  be 
so  and  so"  is  a  unique  kind  of  relation  between  an 
object,  a  mind,  and  a  characteristic.  (This  is  a  rough 
statement,  but  it  will  suffice  for  the  present.)  On  this 
type  of  theory  to  say  that  the  penny  looks  elliptical  to 
me  is  to  say  that  a  unique  and  not  further  analysable 
relation  of  "appearing"  holds  between  the  penny,  my 
mind,  and  the  general  characteristic  of  ellipticity.  The 
essential  point  for  us  to  notice  at  present  about  theories 
of  this  kind  is  that  they  do  not  imply  that  we  are  aware 
of  anything  that  really  is  elliptical  when  we  have  the 
experience  which  we  express  by  saying  that  the  penny 
looks  elliptical  to  us.  Theories  of  this  type  have  been 
suggested  lately  by  Professor  Dawes  Hicks  and  by 
Dr  G.  E.  Moore.  So  far,  they  have  not  been  worked 
out  in  any  great  detail,  but  they  undoubtedly  deserve 
careful  attention. 

Theories  of  the  Object  type  are  quite  different. 
They  do  not  involve  a  unique  and  unanalysable 
multiple  relation  of  "  appean;/^","  but  a  peculiar  kind 
of  object — an  "appear«/z^."  Such  objects,  it  is  held, 
actually  do  have  the  characteristics  which  the  physical 
object  seems  to  have.  Thus  the  Object  Theory  analyses 
the  statement  that  the  penny  looks  to  me  elliptical  into 
a  statement  which  involves  the  actual  existence  of  an 


238  SCIENTIFIC  THOUGHT 

elliptical  object,  which  stands  in  a  certain  cognitive 
relation  to  me  on  the  one  hand,  and  in  another  relation, 
yet  to  be  determined,  to  the  round  penny.  This  type 
of  theory,  though  it  has  been  much  mixed  up  with 
irrelevant  matter,  and  has  never  been  clearly  stated  and 
worked  out  till  our  own  day,  is  of  respectable  antiquity. 
The  doctrine  of  "representative  ideas"  is  the  tradi- 
tional and  highly  muddled  form  of  it.  It  lies  at  the 
basis  of  such  works  as  Russell's  Lowell  Lectures  on  the 
External  World.  In  this  book  I  shall  deliberately  con- 
fine myself  to  this  type  of  theory,  and  shall  try  to  state 
it  clearly,  and  work  it  out  in  detail. 

The    following"  additional   works   may  be  consulted 
with  advantage  : 

G.  E.  Moork,  Philosophical  Studies,  V.  and  VII. 
G.  D.  HlCKS,  Proceedings  of  the  Aristotelian  Society,  1913,  1916. 
G.  F.  Stout,  Manual  of  Psychology,  Bk.  III.,  Part  II.  Cap.  I. 
,,  „       Proceedings  of  the  Aristotelian  Society,  19 13. 


CHAPTER    VIII 

"  Jack. — That,  my  dear  Algy,  is  the  whole  truth,  pure  and 
simple. 

"  Algernon. — The  truth  is  rarely  pure  and  never  simple. 
Modern  life  would  be  very  tedious  if  it  were  either,  and  modern 
literature  a  complete  impossibility." 

(Wilde,  Importance  of  being  Earnest.) 

The  Theory  of  Sensa,  and  the  Critical 
Scientific  Theory 

I  propose  now  to  state  more  fully  the  theory  that 
appearances  are  a  peculiar  kind  of  objects,  and  to  con- 
sider what  sort  of  objects  they  must  be.  The  reader 
will  bear  in  mind  throughout  the  whole  of  the  long 
story  which  follows  that  there  is  a  totally  different  view 
of  sensible  appearance,  viz.,  the  Multiple  Relation 
Theory,  and  that  this  may  quite  possibly  be  true. 
In  this  book  I  shall  leave  it  wholly  aside.  On  the 
theory  that  we  are  now  going  to  discuss,  whenever 
a  penny  looks  to  me  elliptical,  what  really  happens 
is  that  I  am  aware  of  an  object  which  is,  in  fact 
elliptical.  This  object  is  connected  in  some  specially 
intimate  way  with  the  round  physical  penny,  and  for 
this  reason  is  called  an  appearance  of  the  penny.  It 
really  is  elliptical,  and  for  this  reason  the  penny  is  said 
to  look  elliptical.  We  may  generalise  this  theory  of 
sensible  appearance  as  follows :  Whenever  I  truly 
judge  that  x  appears  to  me  to  have  the  sensible  quality 
q,  what  happens  is  that  I  am  directly  aware  of  a  certain 
object  y,  which  (a)  really  does  have  the  quality  q,  and 
(a)  stands  in  some  peculiarly  intimate  relation,  yet  to 
be  determined,  to  x.  (At  the  present  stage,  for  all  that 
we  know,  y  might  sometimes  be    identical  with  x,   or 

239 


240  SCIENTIFIC    THOUGHT 

might  be  literally  a  part  of  x.)  Such  objects  as  y  I 
am  going  to  call  Sensa.  Thus,  when  I  look  at  a  penny 
from  the  side,  what  happens,  on  the  present  theory, 
is  at  least  this  :  I  have  a  sensation,  whose  object  is  an 
elliptical,  brown  sensum  ;  and  this  sensum  is  related 
in  some  specially  intimate  way  to  a  certain  round 
physical  object,  viz.,  the  penny. 

Now  1  think  it  must  at  least  be  admitted  that  the 
sensum  theory  is  highly  plausible.  When  I  look  at  a 
penny  from  the  side  I  am  certainly  aware  of  something ; 
and  it  is  certainly  plausible  to  hold  that  this  something 
is  elliptical  in  the  same  plain  sense  in  which  a  suitably 
bent  piece  of  wire,  looked_at  from  straight  above,  is 
elliptical.  If,  in  fact,  nothing  elliptical  is  before  my 
mind,  it  is  very  hard  to  understand  why  the  penny 
should  seem  elliptical  rather  than  of  any  other  shape. 
I  do  not  now  regard  this  argument  as  absolutely  con- 
clusive, because  I  am  inclined  to  think  that  the  Multiple 
Relation  theory  can  explain  these  facts  also.  But  it  is 
at  least  a  good  enough  argument  to  make  the  sensum 
theory  well  worth  further  consideration. 

Assuming  that  when  I  look  at  a  penny  from  the  side  I 
am  directly  aware  of  something  which  is  in  fact  elliptical, 
it  is  clear  that  this  something  cannot  be  identified  with 
the  penny,  if  the  latter  really  has  the  characteristics  that 
it  is  commonly  supposed  to  have.  The  penny  is  sup- 
posed to  be  round,  whilst  the  sensum  is  elliptical.  Again, 
the  penny  is  supposed  to  keep  the  same  shape  and  size 
as  we  move  about,  whilst  the  sensa  alter  in  shape  and 
size.  Now  one  and  the  same  thing  cannot,  at  the  same 
time  and  in  the  same  sense,  be  round  and  elliptical.  Nor 
can  one  and  the  same  thing  at  once  change  its  shape 
and  keep  its  shape  unaltered,  if  "shape"  be  used  in  the 
same  sense  in  both  statements.  Thus  it  is  certain  that, 
if  there  be  sensa,  they  cannot  in  general  be  identified 
with  the  physical  objects  of  which  they  are  the  appear- 
ances, if  these  literally  have  the  properties  commonly 
assigned  to  them.     On  the  other  hand,  all  that  I  ever 


THEORY   OF   SENSA  241 

come  to  know  about  physical  objects  and  their  qualities 
seems  to  be  based  upon  the  qualities  of  the  sensa  that 
I  become  aware  of  in  sense-perception.  If  the  visual 
sensa  were  not  elliptical  and  did  not  vary  in  certain 
ways  as  I  move  about,  I  should  not  judge  that  I  was 
seeing  a  round  penny.  t 

The  distinction  between  sensum  and  physical  object 
can  perhaps  be  made  still  clearer  by  taking  some  wilder 
examples.  Consider,  e.g.,  the  case  of  looking  at  a  stick 
which  is  half  in  water  and  half  in  air.  We  say  that  it 
looks  bent.  And  we  certainly  do  not  mean  by  this  that 
we  mistakenly  judge  it  to  be  bent;  we  generally  make 
no  such  mistake.  We  are  aware  of  an  object  which  is 
very  much  like  what  we  should  be  aware  of  if  we  were 
looking  at  a  stick  with  a  physical  kink  in  it,  immersed 
wholly  in  air.  The  most  obvious  analysis  of  the  facts 
is  that,  when  we  judge  that  a  straight  stick  looks  bent, 
we  are  aware  of  an  object  which  really  is  bent,  and 
which  is  related  in  a  peculiarly  intimate  way  to  the 
physically  straight  stick.  The  relation  cannot  be  that 
of  identity  ;  since  the  same  thing  cannot  at  once  be  bent 
and  straight,  in  the  same  sense  of  these  words.  If  there 
be  nothing  with  a  kink  in  it  before  our  minds  at  the 
moment,  why  should  we  think  then  of  kinks  at  all,  as 
we  do  when  we  say  that  the  stick  looks  bent?  No  doubt 
we  can  quite  well  mistakenly  believe  a  property  to  be 
present  which  is  really  absent,  when  we  are  dealing 
with  something  that  is  only  known  to  us  indirectly,  like 
Julius  Cagsar  or  the  North  Pole.  But  in  our  example 
we  are  dealing  with  a  concrete  visible  object,  which  is 
bodily  present  to  our  senses  ;  and  it  is  very  hard  to 
understand  how  we  could  seem  to  ourselves  to  see  the 
property  of  bentness  exhibited  in  a  concrete  instance, 
if  in  fact  nothing  was  present  to  our  minds  that  possessed 
that  property. 

As  I  want  to  make  the  grounds  for  the  sensum  theory 
as  clear  as  possible,  I  will  take  one  more  example. 
Scientists   often    assert    that    physical    objects    are    not 


242  SCIENTIFIC  THOUGHT 

"  reallv  "  red  or  hot.  We  are  not  at  present  concerned 
with  the  truth  or  falsehood  of  this  strange  opinion,  but 
only  with  its  application  to  our  present  problem.  Let 
us  suppose  then,  for  the  sake  of  argument,  that  it  is 
true.  When  a  scientist  looks  at  a  penny  stamp  or 
burns  his  mouth  with  a  potato  he  has  exactly  the  same 
sort  of  experience  as  men  of  baser  clay,  who  know 
nothing  of  the  scientific  theories  of  light  and  heat. 
The  visual  experience  seems  to  be  adequately  described 
by  saying  that  each  of  them  is  aware  of  a  red  patch 
of  approximately  square  shape.  If  such  patches  be 
not  in  fact  red,  and  if  people  be  not  in  fact  aware  of 
such  patches,  where  could  the  notion  of  red  or  of  any 
other  colour  have  come  from  ?  The  scientific  theory 
of  colour  would  have  nothing  to  explain,  unless  people 
really  are  aware  of  patches  under  various  circumstances 
which  really  do  have  different  colours.  The  scientists 
would  be  in  the  position  of  Mr  Munro's  duchess,  who 
congratulated  herself  that  unbelief  had  become  impos- 
sible, as  the  Liberal  Theologians  had  left  us  nothing 
to  disbelieve  in.  Thus  we  seem  forced  to  the  view 
that  there  are  at  least  hot  and  coloured  sensa  ;  and,  if 
we  accept  the  scientific  view  that  physical  objects  are 
neither  hot  nor  coloured,  it  will  follow  that  sensa  cannot 
be  identified  with  physical  objects. 

The  reader  may  be  inclined  to  say,  "  After  all,  these 
sensa  are  not  real  ;  they  are  mere  appearances,  so  why 
trouble  about  them  ?  "  The  answer  is  that  you  do  not 
get  rid  of  anything  by  labelling  it  "appearance." 
Appearances  are  as  real  in  their,  own  way  as  anything 
else.  If  an  appearance  were  nothing  at  all,  nothing 
would  appear,  and  if  nothing  appeared,  there  would  be 
nothing  for  scientific  theories  to  account  for.  To  put 
the  matter  in  another  way:  Words  like  real  and  reality 
are  ambiguous.  A  round  penny  and  an  elliptical  visual 
sensum  are  not  real  in  precisely  the  same  sense.  But 
both  are  real  in  the  most  general  sense  that  a  complete 
inventory    of   the    universe    must    mention    the   one  as 


THEORY   OF   SENSA  243 

much  as  the  other.  No  doubt  the  kind  of  reality  which 
is  to  be  ascribed  to  appearances  will  vary  with  the 
particular  type  of  theory  as  to  the  nature  of  sensible 
appearance  that  we  adopt.  On  the  present  theory  an 
appearance  is  a  sensum,  and  a  sensum  is  a  particular 
existent,  though  it  may  be  a  short-lived  one.  On  the 
Multiple  Relation  theory  appearances  have  a  very 
different  type  of  reality.  But  all  possible  theories  have 
to  admit  the  reality,  in  some  sense,  of  appearances  ;  and 
therefore  it  is  no  objection  to  any  particular  theory 
that  it  ascribes  a  sort  of  reality  to  appearances. 

I  hope  that  I  have  now  made  fairly  clear  the  grounds 
on  which  the  sensum  theory  of  sensible  appearance 
has  been  put  forward.  Closely  connected  with  it  is  a 
theory  about  the  perception  of  physical  objects,  and 
we  may  sum  up  the  whole  view  under  discussion  as 
follows  :  Under  certain  conditions  I  have  states  of 
mind  called  sensations.  These  sensations  have  objects, 
which  are  always  concrete  particular  existents,  like 
coloured  or  hot  patches,  noises,  smells,  etc.  Such 
objects  are  called  sensa.  Sensa  have  properties,  such 
as  shape,  size,  hardness,  colour,  loudness,  coldness, 
and  so  on.  The  existence  of  such  sensa,  and  their 
presence  to  our  minds  in  sensation,  lead  us  to  judge 
that  a  physical  object  exists  and  is  present  to  our 
senses.  To  this  physical  object  we  ascribe  various 
properties.  These  properties  are  not  in  general  identical 
with  those  of  the  sensum  which  is  before  our  minds 
at  the  moment.  For  instance,  the  elliptical  sensum 
makes  us  believe  in  the  existence  of  a  round  physical 
penny.  Nevertheless,  all  the  properties  that  we  do 
ascribe  to  physical  objects  are  based  upon  and  correlated 
with  the  properties  that  actually  characterise  our  sensa. 
The  sensa  that  are  connected  with  a  physical  object 
1  in  a  certain  specially  intimate  way  are  called  the 
appearances  of  that  object  to  those  observers  who  sense 
these  sensa.  The  properties  which  x  is  said  to  appear 
to  have  are  the  properties   which  those  sensa  that  are 


244  SCIENTIFIC   THOUGHT 

.vs  appearances  really  do  have.  Of  course,  the  two 
properties  may  happen  to  be  the  same,  e.g.,  when  I  look 
straight  down  on  a  penny,  both  the  physical  object  and 
the  visual  appearance  are  round.  Generally,  however, 
there  is  only  a  correlation  between  the  two. 

It  follows  from  this  theory  that  sensa  cannot  appear 
to  have  properties  which  they  do  not  really  have,  though 
there  is  no  reason  why  they  should  not  have  more 
properties  than  we  do  or  can  notice  in  them.  This  point 
perhaps  needs  a  little  more  elaboration,  since  a  good 
deal  of  nonsense  has  been  talked  by  opponents  of  the 
sensum  theory  in  this  connexion.  We  must  distinguish 
between  failing  to  notice  what  is  present  in  an  object 
and  "  noticing  "  what  is  not  present  in  an  object.  The 
former  presents  no  special  difficulty.  There  may  well 
be  in  any  object  much  which  is  too  minute  and  obscure 
for  us  to  recognise  distinctly.  Again,  it  is  obvious 
that  we  may  sense  an  object  without  necessarily  being 
aware  of  all  its  relations  even  to  another  object  that 
we  sense  at  the  same  time.  Still  more  certain  is  it 
that  we  may  sense  an  object  without  being  aware  of 
all  its  relations  to  some  other  object  which  we  are  not 
sensing  at  the  time.  Consequently,  there  is  no  difficulty 
whatever  in  supposing  that  sensa  may  be  much  more 
differentiated  than  we  think  them  to  be,  and  that  two 
sensa  may  really  differ  in  quality  when  we  think  that 
they  are  exactly  alike.  Arguments  such  as  Stumpfs 
render  it  practically  certain  that  the  latter  possibility 
is  in  fact  realised. 

The  real  difficulty  is  when  we  seem  to  be  directly 
aware  of  some  property  in  an  object,  and  this  property 
is  not  really  present  and  is  perhaps  incompatible  with 
others  which  are  present.  This  is  the  kind  of  difficulty 
that  the  sensum  theory  is  put  forward  to  meet.  We 
seem  to  recognise  elliptical  shape  in  the  penny,  when 
the  penny  really  has  the  incompatible  quality  of  round- 
ness. The  solution  which  the  sensum  theory  offers  is  to 
"  change  the  subject."    Something,  it  admits,  is  elliptical, 


THEORY   OF  SENSA  245 

and  something  is  round  ;  but  they  are  not  the  same 
something.  What  is  round  is  the  penny,  what  is  ellip- 
tical is  the  sensum.  Now  clearly,  this  would  be  no 
solution,  if  the  same  sort  of  difficulty  were  to  break 
out  in  sensa  themselves.  In  that  case  we  should  need 
to  postulate  appearances  of  appearances,  and  so  on 
indefinitely. 

We  must  hold,  as  regards  positive  sensible  qualities 
which  characterise  a  sensum  as  a  whole  and  do  not 
involve  relations  to  other  sensa,  that  a  sensum  is  at 
least  all  that  it  appears  to  be.  Now,  so  far  as  I  know, 
there  is  no  evidence  to  the  contrary.  Some  people  have 
thought  that  arguments  like  Stumpf's  raised  this  diffi- 
culty ;  but  that  is  simply  a  mistake.  Stumpf's  argu- 
ment deals  merely  with  the  relation  of  qualitative 
likeness  and  difference  between  different  sensa,  and 
shows  that  we  may  think  that  two  of  them  are  exactly 
alike  when  there  is  really  a  slight  qualitative  or  quanti- 
tative difference  between  them.  This  has  no  tendency  to 
prove  that  we  ever  find  a  positive  non-relational  quality 
in  a  sensum,  which  is  not  really  there. 

Next,  we  must  remember  that  attributes  which  in- 
volve a  negative  factor  often  have  positive  names.  A 
man  might  quite  well  think,  on  inspecting  one  of  his 
sensa,  that  it  was  exactly  round  and  uniformly  red. 
And  he  might  well  be  mistaken.  But  then,  "exactly 
round"  means  "with  no  variation  of  curvature,"  and 
"uniformly  red"  means  "with  no  variation  of  shade 
from  one  part  to  another."  Now  universal  negative 
judgments  like  these  can  never  be  guaranteed  by  mere- 
inspection  ;  and  so,  in  such  cases,  the  man  is  not  "see- 
ing properties  that  are  not  there  "  in  the  sense  in  which 
he  would  be  doing  so  if  a  round  sensum  appeared  to 
him  to  be  elliptical.  To  sum  up,  it  is  no  objection  to 
the  sensum  theory  that  a  sensum  may  seem  to  be  less 
differentiated  than  it  is  ;  it  would  be  a  fatal  objection 
if  a  sensum  ever  seemed  more  differentiated  than  it  is  ; 
but  we  have  no  evidence  that  the  latter  ever  happens. 


246  SCIENTIFIC  THOUGHT 

Before  going  further  we  must  remove  a  baseless 
prejudice  which  is  sometimes  felt  against  the  sensum 
theory.  It  is  often  objected  that  we  are  not  aware  of 
sensa  and  their  properties,  as  a  rule,  unless  we  specially 
look  for  them.  It  is  a  fact  that  it  often  needs  a  good 
deal  of  persuasion  to  make  a  man  believe  that,  when 
he  looks  at  a  penny  from  the  side,  it  seems  elliptical 
to  him.  And  I  am  afraid  that  very  often,  when  he  is 
persuaded,  it  is  not  by  his  own  direct  inspection  (which 
is  the  only  relevant  evidence  in  such  a  matter),  but  by 
some  absurd  and  irrelevant  argument  that  the  area  of 
his  retina  affected  by  the  light  from  the  penny,  is  an 
oblique  projection  of  a  circle,  and  is  therefore  an  ellipse. 
Accordingly,  it  is  argued  that  we  have  no  right  to 
believe  that  such  a  man  is  directly  sensing  an  object 
which  is,  in  fact,  elliptical.  To  this  objection  a  partial 
answer  has  already  been  given,  by  implication.  It  is 
only  when  we  are  looking  at  a  penny  almost  normally 
that  any  doubt  is  felt  of  the  ellipticity  of  the  sensum  ; 
and,  in  that  case,  the  sensum  is,  in  fact,  very  nearly 
round.  Now  we  have  seen  that  it  is  no  objection  to 
our  theory  that  a  sensum  which  is  not  quite  round 
should  be  thought  to  be  exactly  round,  though  it  would 
be  an  objection  if  an  exactly  round  sensum  seemed  to 
be  elliptical.  The  reason,  of  course,  is  that  an  ellipse, 
with  its  variable  curvature,  is  a  more  differentiated  figure 
than  a  circle,  with  its  uniform  curvature.  There  is  no 
difficulty  in  the  fact  that  we  overlook  minute  differentia- 
tions that  are  really  present  in  our  sensa  ;  difficulties 
would  only  arise  if  we  seemed  to  notice  distinctions  that 
are  not  really  present. 

Apart,  however,  from  this  special  answer,  a  more 
general  reply  can  be  made  to  the  type  of  objection  under 
discussion.  The  whole  argument  rests  on  a  misunder- 
standing of  the  view  about  perception  which  the  sensum 
theory  holds.  If  the  theory  were  that,  in  perceiving  a 
penny,  a  man  first  becomes  aware  of  a  sensum,  then 
notices  that  it   is  elliptical,   and  then    infers  from   this 


THEORY   OF   SENSA  247 

fact  and  the  laws  of  perspective  that  he  is  looking  at 
a  round  physical  object,  the  argument  would  be  fatal 
to  the  theory.  But  this  is  quite  obviously  not  what 
happens.  Perceptual  judgments  are  indeed  based  upon 
sensa  and  their  properties  to  this  extent,  that  if  we  were 
not  aware  of  a  sensum  we  should  not  now  judge  that 
any  physical  object  is  present  to  our  senses,  and  that 
if  this  sensum  had  different  properties  we  should  ascribe 
different  properties  to  the  physical  object.  But  the 
relation  between  the  sensum  and  its  properties,  on  the 
one  hand,  and  the  perceptual  judgment  about  the  physical 
object,  on  the  other,  is  not  that  of  inference.  The  best 
analogy  that  we  can  offer  to  the  relation  between  our 
sensing  of  a  sensum  and  our  perceiving  a  physical 
object,  is  to  be  found  in  the  case  of  reading  a  book  in 
a  familiar  language.  What  interests  us  as  a  rule  is  the 
meaning  of  the  printed  words,  and  not  the  peculiarities 
of  the  print.  We  do  not  explicitly  notice  the  latter, 
unless  there  be  something  markedly  wrong  with  it, 
such  as  a  letter  upside  down.  Nevertheless,  if  there 
were  no  print  we  should  cognise  no  meaning,  and  if  the 
print  were  different  in  certain  specific  ways  we  should 
cognise  a  different  meaning.  We  can  attend  to  the 
print  itself  if  we  choose,  as  in  proof-reading.  In  exactly 
the  same  way,  we  are  not  as  a  rule  interested  in  sensa, 
as  such,  but  only  in  what  we  think  they  can  tell  us 
about  physical  objects,  which  alone  can  help  or  hurt 
us.  Sensa  themselves  "cut  no  ice."  We  therefore 
pass  automatically  from  the  sensum  and  its  properties 
to  judgments  about  the  physical  object  and  its  properties. 
If  it  should  happen  that  the  sensum  is  queer,  as  when 
we  see  double,  we  notice  the  sensum,  as  we  notice  an 
inverted  letter.  And,  even  in  normal  cases,  we  generally 
can  detect  the  properties  of  sensa,  and  contrast  them 
with  those  which  they  are  leading  us  to  ascribe  to  the 
physical  object,  provided  that  we  make  a  special  effort 
of  attention. 

From   what  has  just   been   said,  it  will  not  appear 


248  SCIENTIFIC   THOUGHT 

strange  that,  even  though  there  be  sensa,  they  should 
have  been  overlooked  by  most  plain  men  and  by  many 
philosophers.  Of  course,  everyone  is  constantly  sensing 
them,  and,  in  specially  abnormal  cases,  has  noted  the 
difference  between  them  and  physical  objects.  But 
sensa  have  never  been  objects  of  special  interest,  and 
therefore  have  never  been  given  a  name  in  common 
speech.  A  result  of  this  is  that  all  words  like  "seeing," 
"  hearing,"  etc.,  are  ambiguous.  They  stand  sometimes 
for  acts  of  sensing,  whose  objects  are  of  course  sensa, 
and  sometimes  for  acts  of  perceiving,  whose  objects  are 
supposed  to  be  bits  of  matter  and  their  sensible  qualities. 
This  is  especially  clear  about  hearing.  We  talk  of 
"hearing  a  noise"  and  of  "hearing  a  bell."  In  the 
first  case  we  mean  that  we  are  sensing  an  auditory 
sensum,  with  certain  attributes  of  pitch,  loudness, 
quality,  etc.  In  the  second  case  we  mean  that,  in 
consequence  of  sensing  such  a  sensum,  we  judge  that 
a  certain  physical  object  exists  and  is  present  to  our 
senses.  Here  the  word  "hearing"  stands  for  an  act 
of  perceiving.  Exactly  the  same  remarks  apply  to 
sight.  In  one  sense  we  see  a  penny  ;  in  a  somewhat 
stricter  sense  we  see  only  one  side  of  the  penny  ;  in 
another  sense  we  see  only  a  brown  elliptical  sensum. 
The  first  two  uses  refer  to  acts  of  perceiving,  the  last 
to  an  act  of  sensing.  It  is  best  on  the  whole  to  confine 
words  like  "seeing"  and  "hearing"  to  acts  of  per- 
ceiving. This  is,  of  course,  their  ordinary  use.  I  shall 
therefore  talk  of  seeing  a  penny,  but  not  of  seeing  a 
brown  elliptical  sensum.  I  shall  speak  of  the  latter 
kind  of  cognition  as  "visually  sensing,"  or  merely  as 
"sensing,"  when  no  misunderstanding  is  to  be  feared 
by  dropping  the  adjective.  This  distinction  will  be 
found  important  when  we  come  to  deal  with  illusory 
perceptions. 

I  have  now  tried  to  clear  up  certain  ambiguities  in 
the  sensum  theory,  and  to  remove  certain  mistaken 
objections  which   many   folk    feel    against  it.     If  it    be 


THEORY   OF   SENSA  249 

admitted  that  there  may  be  such  things  as  sensa,  and 
that  the  sensum  theory  at  least  provides  a  possible  and 
even  plausible  way  of  analysing  sensible  appearance, 
we  can  pass  to  the  question  of  the  nature  of  sensa  and 
their  status  in  the  universe.  This  splits  into  two 
questions,  viz.,  (i)  the  relation  of  sensa  to  minds  ;  and 
(ii)  their  relation  to  physical  objects.  Neither  of  these 
can  be  completely  answered  at  the  present  stage,  but 
we  can  say  a  good  deal  here  that  is  relevant,  and  will  be 
useful,  about  them. 

(i)  Are  Sensa  in  any  way  Mental  ? — Sensa  have  been 
supposed  by  many  philosophers  to  be  in  some  way 
mental.  This  opinion  is  based  partly  on  sheer  verbal 
confusions,  and  partly  on  genuine  facts.  The  verbal 
confusion  is  that  the  word  "sensation"  has  often  been 
used  ambiguously,  and  that,  in  one  of  its  meanings,  it 
does  undoubtedly  stand  for  something  that  is  mental. 
When  a  man  talks  of  a  "sensation  of  red,"  he  is  some- 
times referring  to  a  red  patch  which  he  senses,  some- 
times to  his  act  of  sensing  the  patch,  and  sometimes  to 
the  whole  complex  state  of  affairs  which,  on  the  sensum 
theory,  is  analysable  into  (act  of  sensing) — directed  on 
to — (red  patch).  In  the  second  meaning,  "sensation" 
is  obviously  mental  ;  in  the  third  it  is  undoubtedly  a 
complex  whole  which  involves  a  mental  factor.  In  the 
first  meaning  it  is  by  no  means  obvious  or  even  plausible 
to  say  that  a  sensation  is  mental.  I  shall  always  use 
"sensation"  in  the  third  meaning.  Now,  as  the  same 
name  is  thus  often  used,  both  for  the  patch  and  for 
something  which  undoubtedly  is  mental,  or  is  a  complex, 
involving  a  mental  factor,  it  is  not  surprising  that  some 
people  should  have  been  inclined  to  think  that  the  red 
patch  is  itself  mental.  For  is  it  not  a  "sensation"? 
And  is  not  a  sensation  a  mental  state?  This  is,  of 
course,  mere  verbal  confusion,  and  need  not  trouble 
us  further.  But  philosophers  who  have  not  fallen  into 
this   confusion   between   sensum,   sensation,  and  act  of 

R 


250  SCIENTIFIC    THOUGHT 

sensing,  have  yet  held  that  sensa  are  mental.  The  most 
important  living  holder  of  this  view  is  Professor  Stout 
(at  any  rate  he  held  it  at  the  time  when  he  wrote  the 
last  edition  of  his  Manual  of  Psychology. 

Before  we  can  profitably  carry  the  discussion  of  this 
point  further,  we   must  clear  up  the  various  meanings 
which  can  be  attached  to  the  statement  " x  is  mental." 
(i)  The  first  distinction  that  we  must  draw  is  between 
being  "  a  state  of  mind  "  and  being  "  mind-dependent." 
It  is  commonly   held    (and    I   do   not   here    propose   to 
question  it)  that  whatever  is  a  state  of  mind  is  mind- 
dependent,  i.e.,  that  it  could  not  exist  except  as  a  con- 
stituent of  a  mind,  and,  in  fact,  that  it  could  only  exist 
as  a  constituent  of  that  particular  mind,  whose  state  it 
is  said   to   be.     An   example  would   be  my   belief  that 
2  +  2  =  4  or  mv  desire  for  my  tea.     But  it  seems  perfectly 
possible  that  a  term  might  be  mind-dependent  without 
being   a   state   of  anyone's    mind.      What   would    this 
mean?     I    think   it  would  mean   that  such  a  term  can 
only  exist  as  a  constituent  of  a  state  of  mind,  but  that 
it  is   not  itself  a   constituent   of  a   mind.     Take   some 
admitted  state  of  mind,  such  as  my  perception   of  my 
table.     There  is  clearly  an  important  sense   which   we 
can  all  recognise,  even  though  none  of  us  can  define  it, 
in   which    it    is    true    to   say   that  this    perception    is   a 
constituent   of   my    mind,    whilst   the   table    is    not.     I 
should  say  that  there   was  also  an   important   (though 
<very  different)  sense  in  which  it  is  true  to  say  that  the 
table  is  a  constituent  of  my  perception  of  it,  so  long  as 
that  perception  lasts.      It  is  thus  quite  common   for  a 
term  to  be  a  constituent  of  one  of  my  states  of  mind 
without  being  a  constituent  (and  therefore  without  being 
a  state)  of  my  mind.      Now,  if  chairs  are  anything  like 
what  they  are  commonly  supposed  to  be,  they  do  not 
only  exist  as  constituents  of  states  of  mind,  since  it  is 
commonly   believed   that   such    things   go   on    existing 
with  little  or   no  change  of  quality  when  we  cease  to 
perceive  them.     But,  just  as  states  of  mind  can   only 


THEORY   OF   SENSA  251 

exist  as  constituents  of  minds,  so  there  might  be  terms 
which  can  only  exist  as  constituents  of  states  of  mind. 
Such  terms  would  be  mind-dependent  without  being 
states  of  mind.  If  Berkeley's  famous  saying  that  "the 
essence  of  a  sensible  object  is  to  be  perceived  "  be  taken 
quite  literally,  it  implies  that  such  objects  are  mind- 
dependent,  whilst  it  does  not  imply  (though  it  is,  of 
course,  consistent  with)  the  view  that  they  are  states 
of  mind. 

(2)  Even  when  this  distinction  has  been  drawn,  there 
is  a  possibility  of  confusion.  We  must  distinguish  a 
more  and  a  less  radical  sense  of  "mind-dependence." 
The  sense  just  discussed  is  the  more  radical,  and  may 
be  termed  "existential  mind-dependence."  A  term  that 
is  existentially  mind-dependent,  though  not  a  state  of 
mind,  can  only  exist  as  a  constituent  of  a  certain  state 
of  mind.  But  a  term  which  was  not  existentially  mind- 
dependent,  might  be  to  a  certain  extent  "qualitatively 
mind-dependent."  By  this  I  mean  that,  although  it 
can  exist  and  have  qualities  when  it  is  not  a  constituent 
of  any  state  of  mind,  it  might  acquire  some  new  qualities 
or  alter  some  of  its  old  qualities  on  becoming  a  con- 
stituent of  a  state  of  mind.  It  is  certain  that  everything 
that  at  some  period  in  its  history  becomes  a  constituent 
of  any  state  of  mind  thereby  acquires  at  least  one  new 
quality,  viz.,  that  it  is  now  cognised,  or  desired,  or 
shunned,  or  so  on,  by  that  mind.  And  I  do  not  see 
any  reason  in  principle  why  these  changes  of  relation 
should  not  produce  changes  in  the  non-relational 
qualities  of  the  object.  If  wax  melts  when  brought 
into  the  relation  of  proximity  to  a  fire,  I  know  no  reason 
why  some  qualities  of  an  object  should  not  be  added 
or  modified  when  it  comes  into  the  relation  of  being 
sensed  by  a  mind. 

(3)  Some  psychologists,  of  whom  Stout  is  one,  draw 
a  fundamental  distinction  between  two  sorts  of  states  of 
mind.  They  divide  them  into  acts  and  non-acts.  And  a 
state  of  mind  which  is  not  an  act  they  call  a  presentation. 


252  SCIENTIFIC   THOUGHT 

1  propose  to  state  this  distinction  in  a  different  way, 
for  reasons  which  I  will  now  explain.  A  little  while 
ago  I  took  my  perception  of  my  table  as  an  undoubted 
example  of  a  state  of  mind.  And  I  said  that  there  was 
no  doubt  that  the  table  is  a  constituent  of  it.  That  is, 
I  took  the  whole  complex  situation  (my  perceiving) — of 
—(table)  as  a  state  of  mind.  What  Stout  calls  an 
"act"  is  "  my  perceiving."  He  calls  this  a  "state  of 
mind,"  1  call  it  a  "constituent  of  a  state  of  mind." 
The  table  is  not  a  constituent  of  the  state  of  mind,  in 
Stout's  sense  of  the  word,  whilst  it  is  a  constituent 
of  the  state  of  mind,  in  my  sense  of  the  word.  In 
my  terminology  the  act  may  be  described  as  the  non- 
objective  constituent  in  a  state  of  mind  whose  other 
constituent  is  its  object.  An  act  is  something  which 
cannot  exist  by  itself,  but  can  only  exist  as  a  constituent 
in  a  complex,  whose  other  constituent  is  its  object. 
And  it  is,  of  course,  the  characteristically  mental  factor 
in  such  a  complex,  since  the  other  constituent  may 
(though  it  need  not)  be  non-mental.  My  reason  for 
calling  the  whole  complex  fact,  and  not  the  act  itself, 
a  state  of  mind,  is  the  following  :  Practically  everyone 
agrees  that  there  are  such  things  as  states  of  mind. 
And  practically  everyone  agrees  that  the  phrase  "my 
perception  of  the  table "  describes  something  real. 
But  people  differ  greatly  as  to  the  right  analysis  of 
this  fact,  and  the  notion  of  "act"  is  connected  with 
one  special  mode  of  analysis  which  would  not  be 
accepted  by  everyone.  It  therefore  seems  better  to  give 
the  name  "state  of  mind"  to  the  fact  which  everyone 
admits  to  exist,  and  not  to  a  supposed  constituent, 
which  some  people  deny  to  be  present  in  it. 

It  is  quite  easy  to  restate  the  distinction  which  Stout 
has  in  mind  in  terms  of  my  phraseology.  Some  mental 
states  can  be  analysed  into  an  act  directed  on  an  object. 
These  are  non-presentational  states  of  mind.  Others 
cannot  be  analysed  into  act  and  object.  These  are  pre- 
sentations.    A  non-presentational   state  may  contain  a 


THEORY   OF   SENSA  253 

presentation  as  object.  For  instance,  a  feeling  of  tooth- 
ache would  be  a  presentation  on  Stout's  view.  For, 
according  to  him,  it  is  mental  and  is  not  analysable  into 
an  act  of  sensing  and  a  "  toothachy  "  object  ;  it  is  just 
a  "toothachy"  state  of  mind.  Now,  if  I  were  to  intro- 
spect my  toothache,  in  order  to  describe  it  to  my 
dentist,  my  introspection  would  be  a  non-presentational 
mental  state  whose  object  is  a  presentation  ;  for  it  is  a 
complex  containing  an  act  of  introspecting  directed  on 
to  a  toothachy  feeling.  The  perception  of  a  chair  would 
be  an  example  of  a  non-presentational  mental  state, 
whose  object  is  not  a  presentation,  because  not  mental. 

We  are  now  in  a  better  position  to  deal  with  the 
question:  "  Are  sensa  mental?  "  This  might  mean  (1) 
Are  they  acts?  (2)  Are  they  states  of  mind  analysable 
into  act  and  object?  (3)  Are  they  presentations?  (4)  Are 
they  existentially  mind-dependent,  though  not  states  of 
mind?  (5)  Are  they  to  some  extent  qualitatively  mind- 
dependent,  though  not  existentially  mind-dependent? 

No  one  has  ever  suggested  that  sensa  are  acts  or 
that  they  are  states  of  mind  analysable  into  act  and 
object.  A  red  patch  sensed  by  me  when  I  look  at  a 
pillar-box  is  an  example  of  a  sensum.  It  is  plausible 
to  hold  that  the  whole  fact  known  as  "  mv  sensation  of 
the  red  patch  "  is  a  state  of  mind,  analysable  into  act  of 
sensing  and  red  patch  sensed.  But  there  would  be  no 
plausibility  in  holding  that  the  red  patch  itself  was  an 
act,  or  that  it  was  itself  divisible  into  act  and  object. 
Thus,  if  sensa  be  states  of  mind  at  all,  they  must  be 
presentations.  Now,  there  are  two  very  different  views 
included  under  the  statement  that  sensa  are  presenta- 
tions. The  first  would  deny  the  analysis  of  "  my 
sensation  of  red  patch "  into  act  of  sensing  and  red 
sensum.  It  would  treat  the  whole  thing-  as  an  un- 
analysable  state  of  mind,  and  therefore  as  a  presentation. 
This  view  would  hold  that  there  is  no  real  distinction 
between  sensa  and  sensations.  It  would  say  that 
"sensation  of  red    patch  "  =  "  red   patch    sensed,"  and 


254  SCIENTIFIC  THOUGHT 

is  a  presentation.*  The  second  view  would  admit  that 
in  mv  sensation  of  red  we  can  distinguish  my  act  of 
sensing  and  the  red  patch  sensed  ;  but  it  would  hold 
that  the  red  patch  is  itself  a  state  of  mind,  and,  being 
indivisible  into  act  and  object, .is  a  presentation.  I  do 
not  think  that  most  philosophers  have  very  clearly 
distinguished  these  two  varieties  of  the  presentational 
theory  of  sensa.  Moreover,  those  philosophers  who 
have  accepted  the  analysis  of  sensations  into  acts  of 
sensing  and  sensa,  and  have  asserted  that  sensa  are 
mental,  have  seldom  clearly  distinguished  the  alterna- 
tives that  sensa  are  presentations  and  that  sensa  are 
mind-dependent  without  being  states  of  mind.  And 
lastly,  the  distinction  between  existential  and  qualitative 
mind-dependence  has  not  always  been  clearly  seen.  So  ,\ 
that  there  is  a  very  pretty  mess  for  us  to  wipe  up  as 
well  as  we  can.  • 

(i)  Are  Sensations  analy sable  into  Act  of  Sensing  and 
Sensum  ?  The  most  plausible  argument  against  this 
analysis  would  seem  'to  be  the  following:  If  we 
consider  the  various  experiences  called  "sensations," 
we  seem  to  be  able  to  arrange  them  in  an  order, 
starting  with  those  of  sight,  passing  through  those  of 
taste  and  smell,  and  ending  with  bodily  sensations,  like 
headache.  Now,  as  regards  the  top  members  of  the 
series,  the  analysis  into  act  of  sensing  and  object  sensed 
seems  pretty  clear.  A  sensation  of  red  seems  clearly  to 
mean  a  state  of  mind  with  a  red  object,  and  not  to  mean 
a  red  state  of  mind. 

If  we  now  pass  to  the  other  end  of  the  series  the 
opposite  seems  to  be  true.  It  is  by  no  means  obvious 
that  a  sensation  of  headache  involves  an  act  of  sensing 
and  a  "headachy"  object;  on  the  contrary,  it  seems 
on  the  whole  more  plausible  to  describe  the  whole 
experience  as  a  "headachy"  state  of  mind.  In  fact 
the  distinction   of  act  and  object   seems  here  to  have 

*  This  seems  to  be  Stout's  view  in  the  Manual  of  Psychology,  but  I  may 
be  misinterpreting  him. 


THEORY   OF   SENSA  255 

vanished  ;  and,  as  there  is  clearly  something  mental  in 
feeling  a  headache,  just  as  there  is  in  sensing"  a  red 
patch,  it  seems  plausible  to  hold  that  a  sensation  of 
headache  is  an  unanalysable  mental  fact,  within  which 
no  distinction  of  act  and  object  can  be  found. 

Now  this  contrast  between  the  top  and  the  bottom 
members  of  the  series  would  not  greatly  matter,  were 
it  not  for  the  fact  that  the  two  kinds  of  sensation  seem 
to  melt  insensibly  into  each  other  at  the  middle  of  the 
series.  It  is  about  equally  plausible  to  analyse  a 
sensation  of  a  sweet  taste  into  an  act  of  sensing  and  a 
sweet  sensum,  or  to  treat  it  as  an  unanalysable  mental 
fact,  having  no  object,  but  possessing  the  property  of 
sweetness.  Common  speech  recognises  these  distinc- 
tions. We  talk  of  a  sensation  of  red,  but  never  of  a 
feeling  of  red  or  of  a  red  feeling.  On  the  other  hand, 
we  talk  indifferently  of  a  sensation'of  headache,  a  feeling 
of  headache,  a  headachy  sensation,  and  a  headachy 
feeling.  The  English  talk  of  a  sensation  of  smell, 
whereas  the  Scots  more  usually  speak  of  "feeling"  a 
smell.  Now  sensations  of  smell  are  just  on  the  border- 
line between  the  two  kinds  of  sensation.  The  rule  is 
that,  when  a  sensuous  experience  seems  clearly  to 
involve  act  and  object,  it  is  called  a  sensation  and  never 
a  feeling  ;  when  it  is  doubtful  whether  any  such  analysis 
can  be  applied,  it  is  called  indifferently  a  feeling  or  a 
sensation. 

Now  the  fact  that  all  these  experiences  are  classed 
together  as  sensations,  and  that  the  two  kinds  melt  into 
each  other  at  the  middle  of  the  series,  naturally  tempts 
men  to  treat  them  all  alike.  If  we  do  this,  we  must 
hold  either  (a)  that  it  is  a  mistake  to  think  that  a 
sensation  of  red  can  be  analysed  into  an  act  of  sensing 
and  a  red  sensum  ;  or  (f3)  that  it  is  a  mistake  to  think 
that  a  sensation  of  headache  cannot  be  analysed  into  an 
act  of  sensing  and  a  headachy  sensum.  The  former 
alternative  makes  sensation  and  sensum  fall  together 
into  a  single  peculiar  state,  even  in  the  case  of  sight ; 


256  SCIENTIFIC   THOUGHT 

and,  since  the  experience  as  a  whole  certainly  is  mental, 
we  have  to  say  that  a  sensation  of  red  =  a  red  sensum  = 
a  feeling  or  presentation  which  is  red.  The  second 
alternative  is  that  which  is  taken  by  Realists,  like 
Professors  Laird  and  Alexander. 

Now  it  is  evident  that,  if  you  insist  on  treating  all 
experiences  which  are  called  "sensations"  in  the  same 
way,  it  is  antecedently  as  reasonable  to  take  the  Laird- 
Alexander  alternative  as  the  Presentationist  alternative. 
You  might  argue  :  "  It  is  obvious  that  a  sensation  of 
red  involves  an  act  of  sensing  and  a  red  sensum,  so  a 
sensation  of  headache  must  involve  an  act  of  sensing 
and  a  headachy  sensum."  Thus  the  mere  fact  that 
sensations  can  be  arranged  in  a  series,  such  as  I  have 
described,  does  not  specially  favour  the  presentationist 
view  ;  since  exactly  the  same  type  of  argument,  starting 
from  the  other  end  of  the  series,  would  lead  to  exactly 
the  opposite  conclusion.  There  are  just  two  remarks  that 
seem  to  me  worth  making  at  this  point. 

(a)  I  do  not  find  either  the  realist  or  the  presentationist 
view  very  satisfactory  as  a  complete  account  of  all  the 
experiences  which  are  called  "sensations."  But,  if  I 
were  forced  to  take  one  alternative  or  the  other,  I  should 
prefer  the  former.  It  seems  to  me  much  more  certain 
that,  in  a  sensation  of  red,  I  can  distinguish  the  red 
patch  and  the  act  of  sensing  it,  than  that,  in  a  sensation 
of  headache,  I  cannot  distinguish  a  headachy  object  and 
an  act  of  sensing  it.  {b)  I  think,  however,  that  there  is 
no  need  to  insist  on  the  realist  analysis  of  bodily  feelings 
in  order  to  deal  with  the  question  whether  sensations 
be  analysable  into  act  of  sensing  and  sensum.  It  seems 
to  me  that  the  simplest  and  least  doubtful  way  of  treating 
the  whole  question  raised  by  the  series  of  sensations  is 
the  following:  The  word  "sensation,"  as  commonly 
used,  is  defined,  not  by  direct  inspection,  but  by  causa- 
tion. We  say  that  we  are  having  a  sensation,  if  our 
state  of  mind  is  the  immediate  response  to  the  stimula- 
tion of  a  nerve.     Now,  since  sensations  are  not  defined 


THEORY   OF   SENSA  257 

psychologically  through  their  intrinsic  properties,  but 
physiologically  through  their  bodily  antecedents,  it  is 
surely  very  likely  that  they  may  include  two  very 
different  kinds  of  experience,  one  of  which  can  and  the 
other  cannot  be  analysed  into  act  of  sensing  and  sensum. 
These  might  be  called  respectively  "true  sensations" 
and  "bodily  feelings."  The  mere  fact  that  both  are 
often  called  "sensations"  is  surely  a  very  poor  reason 
for  insisting  that  thestructure  of  both  must  be  the  same.^j, 
It  is  true  indeed  that  there  are  marginal  cases  of  which 
it  is  very  difficult  to  say  into  which  class  they  fall.  But 
this  ought  not  to  make  us  slur  over  the  plain  intro- 
spective difference  between  the  top  and  the  bottom 
members  of  the  series.  The  top  ones  at  least  do  seem 
quite  clearly  to  involve  acts  of  sensing  and  sensa  on 
which  these  acts  are  directed.  It  does  seem  clear  that, 
when  I  have  a  sensation  of  a  red  triangular  patch,  some 
things  are  true  of  the  patch  itself  {e.g.,  that  it  is  red  and 
triangular)  which  it  is  very  difficult  to  believe  to  be  true 
of  my  sensation  of  the  red  patch.  If  so,  it  seems  neces- 
sary to  hold  that  the  sensation  and  the  sensum  are  not 
identical  ;  that  the  sensum  is  an  objective  constituent 
of  the  sensation  ;  and  that  there  is  another  constituent 
which  is  not  objective  and  may  be  called  "the  act  of 
sensing."  Into  the  question  whether  this  latter  factor 
is  capable  of  further  analysis,  and,  if  so,  what  the  right 
analysis  of  it  may  be,  it  is  fortunately  not  necessary  to 
go  for  our  present  purposes. 

I  conclude,  then,  that  some  sensations  at  least  are 
analysable  into  act  of  sensing  and  sensum,  and  there- 
fore that  we  cannot  argue  that  sensum  =  sensation  = 
a  presentation. 

(2)  Are  Sensa,  though  distinct  from  Sensations,  them- 
selves Presentations  ?  Though  sensations  are  not  pre- 
sentations but  contain  objects,  which  are  sensa,  it  is 
perfectly  possible  that  these  objects  might  themselves 
be  presentations.  To  prove  that  sensa  are  presentations, 
it  would  be  necessary  to  prove  that  they  are  states  of 


258  SCIENTIFIC   THOUGHT 

mind.       And    this    involves   proving  (a)  that  they  are 
existentially    mind-dependent,    and    (/>)    that    they    are 
constituents  of  minds  and   not  merely  of  certain  states 
of  mind.     Obviously  it  might  be  possible  to  prove  the 
first,  even  if  it  were  not  possible  to  prove  the  second,  of 
these  propositions.      I  do  not  know  of  any  reasonably 
plausible  argument  to  prove  that  sensa  are  not  merely 
mind-dependent,  but  are  also  states  of  mind,  once  you 
accept  the  view  that  sensa  must  be  distinguished  from 
sensations.       Indeed,   the  assertion    would    be   open  to 
the  same  kind  of  objection  which  we  made  to  the  view 
that  sensa  and  sensations  can  be  identified.     On  either 
view  something  is  said  to  be  a  state  of  mind,  though  it 
possesses  properties  which  it  is  very  difficult  to  ascribe 
to  states  of  mind.     If  a  sensum  be  a  state  of  mind,  then 
there  are  states  of  mind  which  are  literally  red  or  round 
or  hot  or  loud  or  triangular,  and  so  on.      I  have  no 
difficulty  in  believing  that  many  states  of  mind  contain 
such  terms  as  objects,  but  I  do  find  it  very  difficult  to 
believe  that  any  state  of  mind  actually  is  a  term  of  this 
sort.      Yet  the  latter  is  implied  by  the  statement  that 
sensa  are  presentations,  just  as  much  as  by  the  state- 
ment that  sensations   are    presentations.       In  fact,  the 
reasons  which  forced  us  to  distinguish  sensations  from 
sensa,  and  to  regard  the  latter  as  objects  contained  in 
the  former,  equally  forbid  us  to  treat  sensa  themselves 
as  states  of  mind.     This  objection  may,  of  course,  be  a 
mere  prejudice  ;   but  it  is  worth  while  to  point  out  that 
the    view    that   sensa   are    presentations    does  logically 
imply  the  very  paradoxical  propositions  that  some  states 
of   mind    are    literally  hot   or    red    or   round,    for   most 
philosophers  who  have  held  the  view  under  discussion 
have  successfully  concealed  this  consequence  from  them- 
selves and  their   readers.       I   shall  therefore  reject  the 
view  that  sensa  are  states  of  mind,  until  someone  pro- 
duces  much    better  reasons  than  anyone  has  yet  done 
for  believing  such  an  extremely  par^oxical  proposition. 
There   are,    however,  quite   plausible   arguments  to 


THEORY   OF   SENSA  259 

prove  that  sensa  are  existentially  mind-dependent,  though 
not  states  of  mind.  That  is  to  say,  that,  although  sensa- 
tions are  analysable  into  act  and  sensum,  and  the  sensum 
must  therefore  be  distinguished  both  from  the  sensation 
and  from  the  act  of  sensing,  which  is  the  other  factor  in 
the  sensation,  yet  these  two  factors  are  not  capable  of 
existing  separately  from  each  other.  No  act  of  sensing 
without  some  sensum  on  which  it  is  directed,  and  no 
sensum  without  an  act  of  sensing  directed  upon  it.  The 
arguments  for  this  view  are  three  :  (a)  The  privacy  and 
variability  of  sensa  ;  {b)  the  analogy  between  sensa  and 
bodily  feelings  ;  and  (c)  the  analogy  between  sensa  and 
so-called  "mental  images." 

(a)  We  notice  at  once  that  sensa  have  some  of  the 
characteristics  of  physical  objects  and  some  of  those  of 
mental  states.  On  the  one  hand,  they  are  extended,  and 
have  shapes,  sizes,  colours,  temperatures,  etc.  On  the 
other  hand,  they  do  seem  to  be  private  to  each  observer  ; 
and  this,  it  will  be  remembered,  is  one  of  the  chief  marks 
of  the  mental  as  distinct  from  the  physical.  It  is  at 
least  doubtful  whether  two  people,  who  say  that  they  are 
perceiving  the  same  object,  are  ever  sensing  the  same 
sensum  or  even  two  precisely  similar  sensa.  This  does 
suggest  that  sensa  are  mental — at  any  rate  in  the  sense 
of  being  mind-dependent. 

If,  however,  we  look  more  closely,  we  see  that  this 
conclusion  does  not  necessarily  follow.  The  facts  are 
on  the  whole  much  better  explained  by  supposing  that 
the  sensa  which  a  man  senses  are  partly  dependent  on 
the  position,  internal  states,  and  structure  of  his  body. 
Since  no  two  men's  bodies  can  be  in  precisely  the  same 
place  at  precisely  the  same  time,  it  is  not  surprising  that 
the  sensa  of  the  two  men  should  differ.  And,  since  the 
internal  states  and  the  minute  structure  of  no  two  living 
bodies  are  exactly  alike,  it  is  still  less  surprising.  Now 
this  explanation  not  only  accounts  as  well  for  most  of 
the  facts  as  the  view  that  sensa  are  mind-dependent  ;  it 
accounts  a  great  deal  better  for  some  of  the  most  striking 


260  SCIENTIFIC   THOUGHT 

of  the  facts.  The  orderly  variation  in  the  shapes  of 
visual  sensa,  as  we  move  about,  is  intelligible  if  we 
suppose  that  the  sensa  which  we  sense  are  partly  con- 
ditioned by  the  positions  of  our  bodies.  The  assumption 
that  they  depend  on  our  minds  gives  no  explanation 
whatever  of  such  facts. 

There  is,  however,  a  better  form  of  this  argument, 
which  has,  I  think,  been  somewhat  neglected  by  people 
who  want  to  hold  that  sensa  are  never  mind-dependent 
to  any  degree.  It  does  seem  to  me  undeniable  that  in 
certain  cases,  and  to  a  certain  extent,  our  past  experi- 
ences and  our  present  expectations  affect  the  actual 
properties  of  the  sensa  that  we  sense,  and  do  not  merely 
affect  the  judgments  about  physical  objects  which  we 
base  upon  sensa.  We  shall  go  into  this  point  in  some 
detail  in  a  later  chapter;  at  present  I  will  just  illustrate 
my  meaning  by  two  examples. 

When  I  look  at  the  "staircase  figure,"  which  is 
given  in  most  psychology  text-books  as  an  instance  of 
ambiguous  figures,  it  seems  to  me  that  it  actually  looks 
sensibly  different  from  time  to  time.  Its  sensible 
appearance  changes  "  with  a  click,"  as  I  look  at  it,  from 
that  of  a  staircase  to  that  of  an  overhanging  cornice. 
This  change  tends  to  take  place  as  I  concentrate  my  mind 
on  the  idea  of  the  one  or  on  that  of  the  other.  Now, 
on  the  present  analysis  of  sensible  appearance,  such 
a  change  as  this  involves  an  actual  qualitative  change 
in  the  sensum.  So  far  is  it  from  being  a  mere  change 
in  the  judgments  which  I  happen  to  base  on  one  and 
the  same  sensum,  that  the  direction  of  my  thoughts 
changes  first  and  is  the  condition  of  the  change  in  the 
sensible  appearance. 

Again,  when  I  turn  my  head,  the  visual  sensa  are  not 
as  a  rule  affected  with  any  sensible  movement.  If, 
however,  I  put  my  glasses  a  little  out  of  focus  or  look- 
through  a  window  made  of  irregularly  thick  glass, 
and  then  turn  my  head,  the  sensa  do  sensibly  move. 
Whether  they   move  or  keep  still  seems  to  depend  on 


THEORY   OF   SENSA  261 

my  past  experiences  and  my  present  expectations  about 
physical  objects.  The  whole  psychology  of  vision  is 
full  of  such  cases,  some  of  them  of  a  highly  complex 
kind. 

Now,  of  course,  these  examples  do  not  suggest  for  a 
moment  that  sensa  are  existentially  mind  -  dependent, 
but  they  do  strongly  suggest  that  they  are  to  some 
extent  qualitatively  mind-dependent.  And  it  cannot  be 
said  here,  as  in  the  previous  examples,  that  reference 
to  the  mind  gives  no  help  in  explaining  the  facts.  Here 
the  boot  is  rather  on  the  other  foot.  No  doubt  the  facts 
just  mentioned  could  in  theory  be  accounted  for  by 
referring  to  the  past  history  of  the  body,  in  addition 
to  its  present  state  and  position.  I.e.,  we  could  talk 
learnedly  about  the  traces  left  on  our  brains  and  nervous 
systems  by  the  past  experiences,  and  could  say  that 
they  are  among  the  conditions  of  our  sensa.  But  this 
would  not  help  us  to  explain  any  concrete  characteristic 
of  our  sensa  in  any  particular  case.  For  the  plain  fact 
is,  that  we  do  often  know  what  relevant  experiences  we 
or  others  have  had,  whilst  we  know  nothing  whatever 
in  detail  about  traces  in  the  brain  and  nervous  system. 
So  here  a  reference  to  mental  conditions  really  does 
explain  concrete  facts,  whilst  a  reference  to  bodily  con- 
ditions does  not.  We  shall  have  to  return  to  this  point 
at  a  much  later  stage. 

(b)  We  have  already  noticed  the  arrangement  of 
"sensations"  in  a  scale  from  sensations  of  colour  and 
sound  to  bodily  feelings.  We  saw  that  this  might  be 
used  as  an  argument  to  prove  that  even  sensations  of 
colour  and  sound  are  presentations,  or  equally  as  an 
argument  to  prove  that  even  sensations  of  headache 
are  divisible  into  act  and  object.  Suppose  we  take  the 
latter  alternative,  which,  as  I  have  .said,  seems  to  me 
to  be  the  more  plausible  of  the  two,  though  I  do  not 
think  that  the  facts  compel  us  to  adopt  either.  It  is 
then  possible  to  produce  a  fairly  plausible  argument  for 
the   view  that  sensa  are  existentially   mind-dependent. 


262  SCIENTIFIC   THOUGHT 

The  arerument  would  run  as  follows:  "Granted  that 
a  sensation  of  headache  can  be  analysed  into  act  of 
sensing  and  headachy  sensum,  it  is  surely  obvious  that 
the  latter,  from  its  very  nature,  could  not  exist  without 
the  former.  An  unfelt  headache  is  surely  a  mere  Uniting. 
Now,  if  this  be  true  of  headachy  sensa,  does  not  the 
very  continuity  of  the  series  of  sensations  on  which  you 
have  been  insisting  make  it  likely  to  be  true  of  red 
sensa,  and  indeed  of  all  sensa?  If  so,  sensa  will  be 
from  their  very  nature  existentially  mind -dependent 
and  incapable  of  existing  save  as  objective  constituents 
of  sensations." 

1  think  that  this  is  quite  a  plausible  argument,  but 
I  do  not  think  it  conclusive.  Two  questions  could  be 
asked  about  it.  (a)  Supposing  it  to  be  true  that  an 
unfelt  headache  is  inconceivable,  does  the  continuity  of 
the  series  of  experiences  called  "  sensations,"  justify  us 
in  extending  this  conclusion  to  all  sensa,  and,  in  par- 
ticular, to  those  of  sight  and  hearing?  Secondly  (/3), 
is  it  really  true  that  an  unfelt  headache  is  inconceivable? 
(a)  To  the  first  question  I  answer  that,  as  a  matter  of 
fact,  I  do  not  find  the  slightest  intrinsic  difficulty  in 
conceiving  the  existence  of  unsensed  red  patches  or 
unsensed  noises,  whilst  I  do  find  a  considerable  difficulty 
in  conceiving  the  existence  of  unfelt  headaches.  I  do 
not  think  that  it  is  safe  to  reject  this  plain  difference  on 
the  grounds  of  a  mere  argument  from  continuity. 

(/3)  Moreover,  I  think  I  can  see  why  it  seems  so 
difficult  to  conceive  of  the  existence  of  unfelt  headaches, 
and  can  see  that  this  difficulty  is  not  really  conclusive. 
Our  main  interest  in  bodily  feelings  is  that  they  are 
pleasant  or  painful  ;  sensations  of  sight  are,  as  a  rule, 
intrinsically  neutral,  or  nearly  so.  Now  I  am  quite 
prepared  to  believe  that  an  object  has  to  be  cognised 
by  us  in  order  to  be  pleasant  or  painful  to  us.  For  it 
seems  to  me  that  the  pleasantness  or  painfulness  of 
anything  is  (or,  at  any  rate,  depends  upon)  my  recog- 
nising it  and  taking  up  a  certain  attitude  of  liking  or 


THEORY   OF   SENSA  263 

disliking  to  it.  It  might,  therefore,  be  perfectly  true 
that  an  unfelt  headache  would  not  be  a  pain,  just  as  an 
unmarried  woman  is  not  a  wife.  Since  we  are  mainly 
interested  in  headaches  as  pains,  we  are  inclined  to 
think  that  an  unfelt  headache  would  be  nothing,  when 
the  truth  merely  is  that  it  would  not  be  a.  pain.  This 
would  be  comparable  to  the  mistake  which  a  fanatical 
admirer  of  matrimony  would  make  if  he  ignored  the 
existence  of  all  spinsters  because  they  were  not  wives. 
I,  therefore,  am  not  convinced  that,  if  a  feeling  of  head- 
ache be  a  genuine  sensation  and  not  a  mere  presentation, 
the  headachy  sensum  which  it  contains  could  not  exist 
unsensed.  Still  less  could  I  extend  this  view  to  sight 
and  sound  sensa. 

(c)  The  third  argument  for  thinking  that  sensa  are 
incapable  of  existing  unsensed  is  founded  on  their 
resemblance  to  "mental  images,"  whose  very  name 
implies  that  they  are  commonly  supposed  to  be  existen- 
tially  mind-dependent,  if  not  actually  states  of  mind. 
The  resemblances  must  be  admitted,  though  in  favourable 
cases  there  seems  to  be  some  intrinsic  difference  which 
it  is  easy  to  recognise  but  hard  to  describe.  But  it 
seems  to  me  doubtful  whether  images  are  existentially 
mind-dependent.  I  do  not  see  any  very  obvious  reason 
why  there  should  not  be  "  unimaged  "  images.  It  is, 
of  course,  perfectly  true  that  images  are  to  a  much 
greater  extent  qualitatively  mind-dependent  than  are 
sensa.  Most,  if  not  all,  of  them  depend  on  our  past 
experiences  ;  and  many  of  them  depend  in  part  on  our 
present  volitions.  Voluntary  images  do,  no  doubt, 
depend  on  our  minds,  in  the  sense  that  they  would  not 
be  imaged  here  and  now,  if  we  did  not  will  them.  But 
exactly  the  same  is  true  of  many  things,  which  no  one 
would  think  of  calling  existentially  mind-dependent. 
Most  chemical  reactions  that  take  place  in  a  laboratory 
would  never  have  happened  if  someone  had  not  deliber- 
ately mixed  the  reagents  in  a  flask  and  heated  the 
latter  over  a  flame.      No  one  supposes  that  this  renders 


264  SCIENTIFIC   THOUGHT 

such  reactions  in  any  important  sense  mind-dependent. 
Thus  the  fact  that  some  images  are  voluntary  seems 
irrelevant  to  the  present  subject. 

The  other  point,  that  all  images  that  we  can  now 
image  are  in  part  determined  in  their  characteristics  by 
our  past  experiences,  is  more  important.  It  must  be 
counted  along  with  the  fact,  already  admitted,  that  many 
sensa  are  to  some  extent  qualitatively  mind-dependent. 
Here,  as  before,  we  can,  if  we  like,  substitute  a  reference 
to  traces  in  our  brains  and  nervous  systems.  But  here, 
too,  the  doubt  remains  whether  this  kind  of  explanation 
is  ultimately  of  much  philosophic  importance,  in  view 
of  the  fact  that  we  often  know  directly  what  our  relevant 
past  experiences  are,  whilst  the  traces,  etc.,  of  the 
physiologist  are  purely  hypothetical  bodily  correlates 
of  these.  Further  treatment  of  this  subject  must  be 
deferred  till  we  face  the  problem  of  the  part  played 
by  our  own  bodies  in  sensation  and  imagination. 

I  will  now  try  to  sum  up  the  results  of  this  rather 
long  and  complex  discussion  on  the  relation  of  sensa 
to  minds  and  their  states.  The  sensum  theory  is 
bound  up  with  a  special  view  as  to  the  right  analysis 
of  the  kind  of  fact  which  is  described  by  such  phrases 
as  u  my  sensation  of  .r."  It  holds  that  this  is  complex, 
and  that  within  it  there  can  be  distinguished  two  factors 
— x  itself,  which  is  the  sensum  and  is  an  object,  and 
a  subjective  factor,  which  is  called  the  "act  of  sensing." 
The  latter  may,  of  course,  be  capable  of  further  analysis, 
such,  e.g.,  as  Russell  attempts  in  his  Analysis  of  Mind ; 
or  it  may  be  (or  contain)  a  peculiar  unanalysable 
relation.  Now,  there  is  also  a  theory  which  refuses  to 
analyse  "my  sensation  of  x"  in  this  way.  It  holds 
that  the  whole  thing  is  unanalysable  into  act  and  object. 
On  such  a  view  the  distinction  between  sensum  and 
sensation  vanishes  ;  and  the  experience,  which  may  be 
called  indifferently  by  either  name,  is  a  mental  state  of 
the  kind  called  presentations.  This  view  is  supported 
by  reference  to   bodily   feelings,  and   by  an   argument 


THEORY   OF   SENSA  265 

from  the  continuity  between  them  and  the  higher 
sensations.  As  against  this  we  pointed  out  (a)  that 
there  is  just  as  good  reason  to  use  the  argument  from 
continuity  in  the  opposite  direction  ;  and  (b)  that  very 
possibly,  in  spite  of  the  continuity,  there  is  a  real 
difference  in  nature  between  genuine  sensations  and 
bodily  feelings.  In  favour  of  the  view  that  genuine 
sensations  are  analysable  into  act  and  object,  we  pointed 
out  that  there  seems  to  be  a  plain  difference  between  a 
red  patch  sensed  by  me  and  the  total  fact  described  as 
"  my  sensation  of  a  red  patch."  And  we  suggested  that 
those  who  refuse  to  make  this  analysis  are  forced  to 
the  very  paradoxical  conclusion  that  there  are  states  of 
mind  which  are  literally  red,  round,  hot,  loud,  etc. 

The  next  point  was  this.  Assuming  that  sensations 
are  analysable  into  act  of  sensing  and  sensum,  we 
raised  the  question  whether  sensa  are  states  of  mind, 
or,  if  not,  whether  they  are  existentially  mind-dependent. 
We  agreed  that,  if  they  are  states  of  mind  at  all,  they 
must  be  presentations.  But  we  found  no  positive  reason 
for  thinking  that  they  are  states  of  mind,  and  much  the 
same  reasons  against  that  view  as  led  us  to  hold  that 
sensations  are  analysable  into  act  and  sensum. 

We  then  discussed  three  more  or  less  plausible 
arguments  to  show  that  sensa  are  existentially  mind- 
dependent,  i.e.,  that  they  cannot  exist  except  as  objective 
constituents  of  sensations.  We  saw  no  intrinsic  reason 
why  coloured  patches  or  noises  should  not  be  capable 
of  existing  unsensed.  And  we  refused  to  be  moved 
from  this  view  by  an  argument  from  continuity  with 
bodily  feelings.  For  we  were  far  from  sure  whether 
bodily  feelings  really  are  analysable  into  act  of  sensing 
and  sensum  ;  and  we  suggested  that,  even  if  they  be, 
it  is  by  no  means  certain  that  their  sensa  could  not 
exist  unsensed.  We  tried  to  show  why  this  was  thought 
to  be  obvious,  and  to  show  that  it  is  not  really  so. 

The  two  remaining  arguments  seemed  to  us  to  show 
that  sensa  are   partly  dependent   on  the  position,  etc., 

s 


266  SCIENTIFIC   THOUGHT 

of  the  />0(/v,  but  they  did  not  have  any  tendency  to  show 
that  they  are  existentialist  dependent  on  the  wind.  Still, 
some  of  the  facts  adduced  did  rather  strongly  suggest 
that  sensa  and,  a  fortiori,  images,  are  to  some  extent 
qualitatively  mind-dependent.  We  thought  that  this 
reference  to  the  mind  might  be  removed  by  extending 
the  bodily  conditions,  so  as  to  include  physiological 
traces  and  dispositions.  But,  in  view  of  the  wholly 
hypothetical  character  of  these,  we  were  not  prepared 
at  this  stage  to  deny  that  sensa  and  images  might  be 
to  some  extent  qualitatively  mind-dependent.  And 
there  we  leave  the  matter,  till  we  deal  more  fully  with 
the  part  played  by  the  human  body  in  sense-perception. 
We  have  seen  that  the  whole  question  is  highly 
complex,  and  that  the  arguments  for  the  view  that  sensa 
are  mental  are  by  no  means  lacking  in  plausibility.  We 
shall  not  therefore  be  tempted  to  think  that  everyone 
who  has  been  persuaded  by  them  must  be  either  a 
knave  or  a  fool.  Some  of  those  who  call  themselves 
New  Realists  have  been  too  much  inclined  to  take  this 
attitude  ;  and,  on  one  reader  at  least,  they  have  produced 
the  impression  of  being  rather  offensively  "at  ease  in 
Zion." 

(ii)  How  are  Sensa  related  to  Physical  Objects  ? — 
We  can  now  turn  to  the  second  question  which  we 
raised  about  sensa.  The  plain  man  does  not  clearly 
distinguish  between  physical  objects  and  sensa,  and 
therefore  feels  no  particular  difficulty  about  their  mutual 
relations.  We  first  come  to  recognise  sensa  as  distinct 
from  physical  objects  by  reflecting  on  the  fact  of 
sensible  appearance,  and  the  contrast  between  it  and 
the  supposed  properties  of  physical  reality.  But  once 
the  existence  of  sensa  has  been  clearly  recognised,  the 
problem  of  their  relation  to  the  physical  world  becomes 
pressing.  We  all  believe  in  a  world  of  physical  objects, 
and  profess  to  have  a  great  deal  of  detailed  knowledge 
about  it.     Now  this  world  of  physical   objects   makes 


THEORY  OF  SENSA  267 

its  existence  and  its  detailed  nature  known  to  us  by 
the  sensible  appearances  which  it  presents  to  us.  And, 
on  the  sensum  theory,  these  appearances  are  sensa. 
Sensa  are  therefore  in  some  way  the  ratio  cognoscendi 
of  the  physical  world,  whilst  the  physical  world  is  in 
some  way  the  ratio  essendi  of  sensa.  Our  problem 
therefore  divides  into  an  epistemological  and  an  onto- 
logical  one.  The  two  problems  are  not  ultimately 
independent,  but  it  is  useful  to  state  them  separately. 

(1)  How  far  is  it  true  that  our  beliefs  about  the 
physical  world  depend  on  our  sensa?  Before  we  can 
answer  this,  we  must  draw  some  distinctions  among 
our  beliefs.  First,  there  is  our  belief  that  there  is  a 
physical  world  of  some  kind.  This,  as  we  have  seen, 
involves  at  least  the  belief  that  there  are  things  which 
are  relatively  permanent,  which  combine  many  qualities, 
and  which  persist  and  interact  at  times  when  they  are 
not  appearing  to  our  senses.  These  we  may  call 
constitutive  properties  of  the  physical  world,  since  they 
are  part  of  what  we  mean  by  "physical."  Then  there 
is  the  belief  that  these  objects  have  spatial  or  quasi- 
spatial  characteristics.  This  may  almost  be  called 
constitutive,  but  it  is  a  shade  less  fundamental  than 
the  first  set  of  properties.  Lastly,  there  are  what  might 
be  called  empirical  beliefs  about  the  physical  world. 
These  are  beliefs  about  points  of  detail,  e.g.,  that  some 
things  are  red,  and  that  there  is  now  a  red  fluted  lamp- 
shade in  my  rooms. 

Now  I  have  already  asserted  that  it  is  false  psycho- 
logically to  say  that  we,  in  fact,  reach  our  perceptual 
judgments  about  the  existence  and  properties  of  physical 
objects  by  a  process  of  inference  from  our  sensa  and 
their  properties.  Further,  it  is  false  logically  to  suppose 
that  the  existence  of  a  physical  world  in  general  could 
be  inferred  from  the  existence  of  our  sensa,  or  from 
anything  that  we  know  about  their  intrinsic  properties 
or  their  mutual  relations.  I  suppose  that  the  existence 
of  sensa  is  a  necessary  condition,  but  it  is  certainly  not 


4 

268  SCIENTIFIC  THOUGHT 

a  sufficient  condition,  of  my  belief  in  the  existence  of 
the  physical  world.  If  there  were  no  sensible  appear- 
ances to  me,  I  suppose  that  I  should  not  judge  there  to 
be  any  physical  reality.  But,  on  the  other  hand,  there 
is  nothing  in  my  sensa  to  force  me  logically  to  the 
conclusion  that  there  must  be  something  beyond  them, 
having  the  constitutive  properties  of  physical  objects. 
The  belief  that  our  sensa  are  appearances  of  something 
more  permanent  and  complex  than  themselves  seems 
to  be  primitive,  and  to  arise  inevitably  in  us  with  the 
sensing  of  the  sensa.  It  is  not  reached  by  inference, 
and  could  not  logically  be  justified  by  inference.  On 
the  other  hand,  there  is  no  possibility  of  either  refuting 
it  logically,  or  of  getting  rid  of  it,  or — so  far  as  I  can 
see — of  co-ordinating  the  facts  without  it. 

There  are  groupings  among  my  own  sensa  and 
correlations  between  my  sensa  and  those  of  others 
which  fit  in  extremely  well  with  the  belief  in  a  physical 
world  of  which  all  the  sensa  are  so  many  appearances. 
It  might  be  held  that  this  at  least  forms  the  basis  of 
a  logical  argument  in  inverse  probability,  to  show  that 
the  belief  in  the  physical  world  is  highly  probable. 
But  the  snag  here  is  that  all  such  arguments  only 
serve  to  multiply  the  antecedent  probability  of  a  pro- 
position, and,  unless  we  have  reason  to  suppose  that 
this  probability  starts  with  a  finite  magnitude,  they  lead 
us  nowhere.  Now,  although  I  do  not  know  of  any 
reason  antecedently  against  the  existence  of  a  physical 
world,  I  also  know  of  no  antecedent  reason  for  it.  So 
its  antecedent  probability  seems  quite  indeterminate, 
unless  we  are  prepared  to  hold  that  the  fact  that 
everybody  does  in  practice  believe  it,  is  a  ground  for 
ascribing  a  finite  antecedent  probability  to  it.  It  seems 
to  me  that  the  belief  that  there  is  a  physical  world  is 
logically  in  much  the  same  position  as  those  assump- 
tions about  the  constitution  of  the  existent  on  which  all 
inductive  proofs  of  special  laws  of  nature  rest.  If  these 
assumptions  start  with  a  finite  antecedent  probability, 


THEORY   OF   SENSA  269 

their  success  justifies  us  in  ascribing  a  high  final  prob- 
ability to  them.  But  do  they  have  a  finite  antecedent 
probability?  We  can  say  of  them,  as  of  the  belief  in  a 
physical  world,  that  we  all  do  believe  them  in  practice, 
that  there  is  no  positive  reason  against  them,  and  that 
we  cannot  get  on  without  assuming  them.  But,  having 
said  so  much,  we  shall  do  wisely  to  change  the  subject 
and  talk  about  the  weather. 

We  shall  not  then  attempt  to  prove  the  existence  of 
a  world  of  entities  having  the  constitutive  properties  of 
physical  objects  ;  for,  if  this  can  be  done,  I  at  any  rate 
do  not  know  how  to  do  it.  But  we  shall  point  out  those 
facts  about  our  sensa  and  their  groupings  which  specially 
fit  in  with  the  view  that  sensa  are  various  partial  and 
fleeting  appearances  of  relatively  permanent  and  inde- 
pendent things.  That  is,  we  shall  try  to  indicate  those 
facts  about  our  sensa  which  would  give  a  high  final 
probability  to  the  belief  in  a  physical  world,  provided  it 
had  a  finite  antecedent  probability.  This  will  be  our 
main  task  in  the  next  two  chapters,  which  deal  with 
the  spatial  and  temporal  characteristics  of  sensa  and  of 
physical  objects  and  events.  The  first  of  these  chapters 
will  be  concerned  with  the  facts  about  our  sensa  which 
fit  in  with  the  view  that  they  are  appearances  of  objects 
which  combine  many  properties,  and  which  can  be  per- 
ceived by  many  different  observers  at  the  same  time. 
The  second  will  be  concerned  with  the  facts  about  our 
sensa  which  fit  in  with  the  view  that  they  are  relatively 
fleeting  appearances  of  more  permanent  things  and 
processes. 

Now,  assuming  that  there  is  a  world  of  enduring 
and  independent  things,  there  is  still  room  for  wide 
differences  of  opinion  as  to  the  kind  of  whole  that  it 
forms,  the  way  in  which  it  is  divided  into  parts,  and  the 
various  empirical  qualities  which  these  parts  possess. 
Common-sense  and  science  are  agreed  that  it  is  in  some 
sense  a  spatial  whole,  whose  parts  have  various  shapes, 
sizes  and  positions,  and  are  capable  of  moving  about 


270  SCIENTIFIC  THOUGHT 

within  the  whole.  This  alleged  spatial  character  of  the 
physical  world  may  be  called  "semi-constitutive";  for, 
as  1  have  said,  we  hardly  admit  that  a  world  of  non- 
spatial  entities  would  deserve  to  be  called  "physical," 
even  though  it  were  persistent,  independent  of  us,  and 
many-qualitied.  Now,  it  is  clear  that  all  the  spatial 
characteristics  which  we  ascribe  to  the  physical  world 
are  based,  both  in  general  outline  and  in  detail,  on  the 
spatial  characteristics  of  our  sensa.  Moreover,  I  think 
it  can  be  rendered  highly  probable  that,  if  there  be  a 
physical  world  at  all,  and  our  sensa  be  appearances  of  it, 
then  that  world  is  quasi-spatial.  The  importance  and 
complexity  of  this  subject  seem  to  justify  the  length 
of  the  next  chapter,  in  which  I  have  treated  it  to  the 
best  of  my  ability. 

When  we  come  to  the  purely  empirical  qualities  of 
the  physical  world  there  is  a  sharp  difference  of  opinion 
between  science  and  common-sense.  The  latter  ascribes 
qualities,  like  colour,  temperature,  etc.,  to  physical 
objects,  whilst  the  former  refuses  to  do  so.  In  dis- 
cussing this  matter  the  partial  dependence  of  sensa  on 
what  goes  on  inside  the  body  of  the  observer  becomes 
of  great  importance,  and  the  concluding  chapter  has 
been  devoted  to  this  problem. 

(2)  This  last  question  leads  in  the  most  natural  way 
to  the  ontological  problem  as  to  the  status  of  sensa  in 
the  existent  world.  There  is  a  world  of  physical  objects 
and  a  world  of  sensa.  In  some  way  the  latter  seems  to 
be  dependent  on  the  former.  But  both  are  parts  of  the 
whole  of  existent  reality.  How  are  the  two  related? 
This  is  a  problem  which  common-sense  ignores,  because 
it  does  not  definitely  distinguish  between  sensa  and 
physical  objects.  Science  also  ignores  it,  because, 
although  in  theory  it  makes  an  equivalent  distinction, 
it  uses  it  simply  as  an  excuse  for  ignoring  sensa  and 
concentrating  on  physical  objects  and  processes.  This 
is  a  perfectly  legitimate  procedure  for  the  special 
purpose  which  natural  science  has  in  view,  but  it  is  not 


THEORY   OF   SENSA  271 

permissible  to  the  philosopher.  His  whole  business  is 
to  drag  such  skeletons  from  the  cupboards  in  which  it 
has  been  found  convenient  to  shelve  them,  and  to  give 
them  their  right  place  in  the  whole  scheme  of  things. 

Now  the  epistemological  and  the  ontological  problems 
about  sensa  and  their  relations  to  physical  objects  are 
connected  in  the  following  way.  Our  primitive  belief 
in  the  existence  of  a  world  of  relatively  permanent, 
independent  things  is  extremely  vague.  It  is  little 
more  than  a  general  scheme,  in  terms  of  which  the  actual 
groupings  which  we  find  among  our  sensa  are  stated. 
Even  when  we  go  a  step  further,  and  say  that  the  spatial 
character  and  the  special  groupings  of  sensa  practically 
force  us  to  think  of  the  physical  world  as  a  quasi-spatial 
whole,  containing  parts  with  fairly  definite  shapes,  sizes, 
and  positions,  we  still  have  only  a  very  general,  though 
much  more  definite  scheme.  Within  this  general  quasi- 
spatial  scheme  all  kinds  of  alternative  specifications  are 
possible.  We  are  not  tied  down  to  any  special  view 
as  to  the  number  of  its  dimensions.  Again,  we  are  not 
tied  down  to  any  special  view  as  to  the  "  geometry"  of 
it,  when  the  number  of  its  dimensions  is  settled.  Lastly, 
we  might  put  forward  dozens  of  different  theories  as  to 
the  nature  of  physical  objects,  all  compatible  with  the 
general  scheme  and  with  the  special  facts  about  our 
sensa  and  their  groupings.  It  is  this  extreme  variety 
of  alternative  theories,  left  open  to  us  by  the  general 
concept  of  a  physical  world  and  the  special  facts  about 
our  sensa,  which  gives  a  legitimate  hope  for  indefinite 
progress  with  the  problem  under  discussion,  provided 
the  scientists  and  the  patriots  between  them  do  not 
destroy  civilisation,  and  with  it  all  disinterested  thinking. 
With  traditional  views  about  the  nature  of  Space,  Time, 
and  Matter,  it  is  extremely  difficult  to  fit  the  world  of 
sensa  and  the  world  of  physical  objects  together  into 
a  coherent  whole.  But,  once  the  immense  number  of 
possible  alternatives  within  the  scheme  is  grasped,  the 
devising  of  theories  of  the  physical  object  which  shall 


272  SCIENTIFIC  THOUGHT 

give  sensa  a  locus  standi  in  the  physical  world  will  be  a 
winter  evening's  pastime  for  symbolic  logicians.  This 
task  we  shall  leave  to  those  better  fitted  than  ourselves 
to  accomplish  it  ;  we  shall  be  concerned  rather  with 
those  facts  about  our  sensa  with  which  any  theory  of 
physical  objects  must  deal. 

The  Critical  Scientific  Theory. — 1  propose  now  to 
try  to  state  clearly,  in  terms  of  the  Sensum  theory, 
what  appears  to  be  involved  in  the  common  scientific 
view  of  physical  objects  and  their  sensible  appearances. 
As  scientists  never  state  their  own  position  on  this 
point  clearly,  it  is  necessary  for  us  to  do  so  for  them. 
We  can  then  see  how  far  the  view  can  be  accepted, 
and  how  far  its  plausibility  has  depended  on  its  modest 
obscurity. 

Let  us  take  the  old  example  of  a  boy  looking  at  a 
penny.  He  believes  that  it  is  quite  literally  round  and 
just  as  literally  brown.  He  believes  that  the  brown 
(and,  as  he  thinks,  round)  patch  which  he  is  sensing 
is  quite  literally  a  part  (viz.,  the  upper  side)  of  the 
penny.  And  he  believes  that  this,  which  he  now  sees, 
is  the  same  as  what  he  can  feel  if  he  puts  out  his 
hand.  As  he  grows  up  he  is  probably  told,  on  the 
authority  of  "science,"  that  the  penny  is  not  "really" 
brown,  though  it  is  "really"  round.  The  sort  of 
reason  which  he  is  given  for  this  startling  statement 
is  (so  far  as  I  can  remember)  that  things  appear  to 
have  different  colours  in  different  lights.  If  he  should 
study  heat  and  light,  he  will  be  told  that  the  colour 
which  he  sees  depends  on  vibrations  which  strike  his 
eye,  and  that  the  temperature  that  he  feels  depends  on 
molecular  movements  which  are  going  on  in  the  penny. 
He  still  thinks  of  the  penny  as  literally  round,  and 
thinks  now  of  all  sorts  of  movements  going  on  within 
its  contour,  and  sending  disturbances  to  his  eye  and 
his  hand.  But  he  no  longer  thinks  of  the  penny  as 
literally  brown  or  cold.     The  brownness  and  coldness 


THEORY   OF   SENSA  273 

are  thought  to  be  effects  which  the  processes  in  the 
penny  produce  by  transmission.  The  round  shape  is 
"in"  the  penny;  the  brownness  and  coldness  are  not. 
They  are  effects  which  the  penny  produces  "in"  his 
eye  or  his  hand  or  his  brain  or  his  mind.  He  still 
thinks  that  he  literally  senses  the  same  round  upper 
side  of  the  penny,  both  with  his  eyes  and  with  his 
hand,  but  he  no  longer  thinks  that  there  is  a  brown 
colour  or  a  cold  temperature  literally  spread  over  this 
round  surface. 

This,  I  think,  is  a  fair  account  of  what  the  average 
person  with  a  scientific  training  believes  on  these 
matters  ;  so  far  as  anything  so  incoherent  can  be  said 
to  be  believed  by  anyone.  It  is  perfectly  obvious 
that  such  a  view  as  this  cannot  stand  criticism.  It  is 
an  inconsistent  mixture  of  two  utterly  different  theories 
of  perception.  As  regards  spatial  attributes,  it  keeps 
to  the  naively  realistic  view  of  unsophisticated  common- 
sense.  According  to  it,  the  seen  and  felt  shape  is  not 
an  effect  produced  in  us  by  something  else.  It  is  out 
there,  whether  we  see  it  or  feel  it  or  not.  Processes  in 
it  simply  make  us  see  it  or  feel  it  under  suitable  cir- 
cumstances. But,  as  regards  colour  and  temperature, 
the  scientific  theory  takes  quite  a  different  view.  It  is 
a  causal  theory.  The  processes  in  the  penny  do  not 
make  us  see  a  colour  or  feel  a  temperature  which  is 
already  there  to  be  seen  or  felt.  They  produce  the 
colour  or  temperature  "  in  us,"  to  use  a  discretely 
vague  phrase,  which  may  cover  our  minds,  our  brains, 
and  our  special  sense-organs. 

Now  this  muddled  mixture  of  theories  is  not  con- 
sistent with  itself  or  with  the  facts.  It  is  inconsistent 
with  itself  for  the  following  reason.  When  I  look  at 
a  penny,  the  brown  colour  that  I  see  is  seen  spread  out 
over  the  round  contour.  Similarly  with  the  cold  tem- 
perature that  I  feel.  We  are  asked  to  believe  that 
there  is  brownness  without  shape  "in  me,"  and  round 
shape   without   colour   out  there   where   the    penny    is. 


274  SCIENTIFIC   THOUGHT 

and  yet  that  in  some  mysterious  way,  the  shapeless 
brownness  "in  me"  is  projected  into  the  round  con- 
tour of  the  penny  "out  there."  If  this  be  not  nonsense 
I  do  not  know  what  nonsense  is.  We  can  all  sav  this 
kind  of  thing,  but  can  we  attach  any  clear  meaning 
to  what  we  are  saying? 

Moreover,  as  Berkeley  long  ago  pointed  out,  the 
theory  only  takes  account  of  half  the  facts.  Certainly 
colours  vary  with  the  illumination,  the  state  of  our 
eyes,  and  so  on.  But  it  only  needs  a  little  careful  in- 
spection to  see  that  visible  shapes  also  vary  with  changes 
in  the  medium,  and  with  the  position  of  the  observer. 
If  the  former  fact  proves  that  colours  and  temperatures 
are  not  "in  the  object"  but  "in  us,"  the  latter  should 
t  prove  the  same  thing  for  visible  shapes.  It  is  impos- 
sible to  reconcile  the  view  that  the  penny  is  round,  in 
the  literal  straightforward  sense,  with  the  view  that, 
when  we  look  at  it,  we  literally  sense  visually  the  upper 
surface  of  it.  For  we  sense  all  sorts  of  elliptical  patches 
from  various  positions.  It  is  clear  that  none  of  these 
can  be  identical  with  the  round  upper  surface  of  the 
penny,  and  it  is  equally  clear  that  they  are  not  parts 
of  it  in  the  literal  sense  in  which  the  King's  head  is  a 
part  of  it. 

If  we  want  to  be  consistent  then,  we  must  treat  visual 
shape  in  the  same  way  as  colour  and  temperature. 
What  we  sense  visually  is  a  sensum,  and  the  shape 
and  the  brownness  both  belong  to  it.  If  anything  be 
produced  "in  us"  by  an  external  object  when  we  look 
at  it,  it  is  not  just  the  colour,  but  is  the  whole  patch 
with  its  colour  and  its  shape.  And,  as  we  have  seen, 
this  patch  cannot  be  regarded  as  being  the  upper 
surface  of  the  external  object,  or  as  being  literally  a 
part  of  that  surface.  Nor  can  we  any  longer  hold  that 
what  we  sense  by  touch  is  literally  identical  with  what 
we  sense  by  sight,  and  that  sight  and  touch  merely 
reveal  two  different  qualities  of  this  one  object.  For 
what  we  sense  tactually  is   round  and  of  constant  size. 


THEORY   OF   SENSA  275 

What  we  sense  visually  is  not  round,  except  when  we 
are  in  that  very  special  set  of  positions  from  which 
we  are  said  to  be  "looking  straight  down  on"  the 
penny.  And,  even  if  we  confine  ourselves  to  this  series 
of  positions,  the  sizes  of  the  various  round  patches 
which  we  sense  are  not  the  same  for  different  positions 
in  the  series.  It  is  therefore  clear  that  the  scientific 
view  needs  to  be  completely  restated  in  terms  of  the 
sensum  theory.  And  this  is  not  easy,  because  the 
scientific  theory  assumed  that  we  really  were  sensing  the 
contour  of  the  actual  physical  object  out  in  space,  and 
that  our  sensations  were  due  to  what  was  going  on 
within  that  contour. 

As  we  move  about  and  continue,  as  we  say,  to  "  look 
at  the  same  object,"  we  are  aware  of  a  series  of  sensa, 
each  having  shape  and  colour,  and  all  very  much  alike 
in  these  respects.  But  there  are  certain  variations 
which  we  commonly  overlook.  These  strike  us  in 
exaggerated  cases,  and  can  be  noticed  by  careful 
inspection  in  all  cases.  Moreover,  they  are  as  a  rule 
reversed  when  we  retrace  our  steps.  If  we  are  going 
to  attempt  a  causal  theory  of  perception  we  must  try 
to  explain  this  conjunction  of  predominant  agreement 
throughout  the  series  with  slight,  regular,  and  reversible 
variations  between  its  different  members.  The  explana- 
tion that  naturally  strikes  us  is  that  the  series  of  sensa 
depends  on  two  sets  of  conditions.  One  of  these  is 
relatively  permanent,  and  accounts  for  the  predominant 
agreement  of  the  members  of  the  series.  The  other  is 
variable,  and  accounts  for  their  minor  variations. 

Again,  if  we  feel  an  object,  such  as  a  penny,  and 
meanwhile  look  at  it  from  various  points  of  view,  the 
series  of  predominantly  similar,  but  slightly  variant, 
visual  sensa  is  correlated  with  an  invariant  tactual  sensum. 
The  shape  of  the  latter  is  very  much,  but  not  exactly, 
like  those  of  most  of  the  former.  It  is  exactly  like  that 
of  the  visual  sensa  which  are  sensed  from  a  certain 
series  of  positions.     As   regards  other  qualities,  there 


276  SCIENTIFIC   THOUGHT 

is  complete  difference  between  the  visual  and  the  tactual 
sensa.  The  former  have  colour,  but  no  temperature  or 
hardness  ;  the  latter  have  coldness  and  hardness,  but  no 
colour.  Now  we  have  to  explain  this  predominant 
agreement,  combined  with  minor  differences,  between 
the  shapes  of  the  many  visual  sensa  and  the  shape  of 
the  one  tactual  sensum.  And  we  have  to  remember 
that,  as  regards  other  sensible  qualities,  the  difference  is 
complete.  Here,  again,  it  seems  natural  to  suppose  that 
there  is  something  common  and  relatively  permanent, 
which  accounts  for  the  predominant  agreement  in  shape 
between  the  visual  and  the  tactual  sensa,  and  something 
variable  that  accounts  for  their  minor  differences  in 
shape.  This  other  factor  seems  clearly  to  be  connected 
with  the  position  of  the  sense-organ.  As  the  eye  moves 
about,  the  shape  of  the  visual  sensa  varies.  The  shape 
of  the  tactual  sensum  does  not  change  :  but  then  we 
cannot  move  the  hand  to  a  distance  and  continue  to  sense 
the  tactual  sensum  at  all,  as  we  can  change  the  place 
of  the  eye  and  still  continue  to  see.  We  may  further 
suppose  that  different  factors  are  needed  to  determine 
such  very  different  sensible  qualities  as  colour  and  tem- 
perature ;  but  it  is  reasonable  to  suppose  that,  whatever 
these  factors  may  be,  they  are  subject  to  some  common 
condition  which  determines  the  very  similar  shape  of 
both  visual  and  tactual  sensa. 

Lastly,  when  we  compare  notes  with  other  people  who 
say  that  they  are  looking  at  the  same  thing  as  we  are, 
we  find  again  a  predominant  agreement  between  their 
sensa  and  ours,  combined  with  minor  variations.  It  seems 
reasonable  to  suppose  that  there  is  a  set  of  conditions, 
common  to  their  sensa  and  ours,  which  accounts  for  the 
predominant  agreement  between  the  two.  In  addition, 
there  must  be  variable  factors,  one  specially  connected 
with  one  observer  and  another  with  another  observer. 
These  are  responsible  for  the  minor  variations.  It 
seems,  then,  that  we  have  good  grounds  for  supposing 
that  there  are  physical  objects  in  the  sense  of  conditions 


THEORY   OF   SENSA  277 

which  (a)  are  common  to  us  and  to  others  ;  (#)  are 
relatively  permanent,  and,  at  any  rate,  do  not  ipso  facto 
change  when  we  move  about ;  and  (c)  determine  in 
some  way  the  attributes  of  our  sensa,  in  conjunction 
with  other  conditions  which  do  vary  from  person  to 
person  at  the  same  time  and  for  the  same  person  at 
different  times. 

It  might  be  asked  at  this  point  by  a  sceptical  reader, 
"Why  go  outside  the  series  of  correlated  sensa  at  all? 
Why  not  be  content  to  take  them  as  a  fact?  Why 
make  them  all  depend  on  conditions  outside  the  series 
of  sensa  itself?"  As  I  have  said,  this  is  a  step  which 
everyone  does  take,  but  which  no  one  can  be  logically 
compelled  to  take.  At  present  we  may  say  that  what 
induces  us  to  do  this  is  the  fact  that  we  have  reason 
to  think  that  physical  objects  change  and  act  on  each 
other  when  we  do  not  happen  to  be  sensing  any  sensa 
from  them.  We  can  drop  such  series  of  sensa  as  I 
have  been  describing  (e.g.,  by  turning  our  heads  or 
going  out  of  the  room),  and  then  by  making  suitable 
movements  we  can  pick  it  up  again  either  where  we  left 
it,  or  in  a  form  that  is  obviously  a  later  development  of  a 
course  of  change  whose  earlier  stages  we  noticed  before 
we  turned  away.  It  is  facts  of  this  kind  which  (rightly 
or  wrongly)  make  us  look  beyond  such  series  of  correlated 
sensa  to  relatively  permanent  conditions,  which  lie  out- 
side the  series  and  can  develop  on  their  own  account 
when  the  series  is  interrupted. 

Now  these  common  and  relatively  permanent  con- 
ditions might,  for  all  that  we  have  seen  up  to  the 
present,  be  so  utterly  unlike  the  sensa  that  they 
condition  that  it  would  be  misleading  to  call  them 
physical  objects.  The  question  therefore  at  once  arises  : 
"Can  we  determine  anything  further  about  their 
properties,  either  with  certainty  or  with  reasonably 
high  probability?"  I  do  not  think  that  we  could 
determine  anything  further  with  certainty,  but  I  do 
think  that  we  might  determine  something  further  with 


278  SCIENTIFIC  THOUGHT 

high  probability.  It  is,  of  course,  perfectly  true  that  a 
set  of  conditions — and,  moreover,  a  set  which  is  only 
one  part  of  the  total  conditions — of  a  sensum,  must  not 
be  assumed  to  resemble  in  its  properties  the  sensum 
which  it  partially  determines.  On  the  other  hand,  it 
were  equally  unreasonable  to  assume  that  the  two  cannot 
resemble  each  other.  There  can  be  no  inner  contra- 
diction in  the  qualities  of  shape  and  size,  since  sensa, 
at  least,  certainly  have  shape  and  size  and  certainly 
exist.  If  such  qualities  involved  any  kind  of  internal 
contradiction,  no  existent  whatever  could  possess  them. 
Hence  it  is  perfectly  legitimate  to  postulate  hypothetic- 
ally  any  amount  of  resemblance  that  we  choose  between 
sensa  and  the  permanent  part  of  their  total  conditions. 
If  now  we  find  that,  by  postulating  certain  qualities  in 
these  permanent  conditions,  we  can  account  for  the 
most  striking  facts  about  our  sensa,  and  that  without 
making  this  hypothesis  we  cannot  do  so,  the  hypo- 
thesis in  question  may  reach  a  very  high  degree  of 
probability. 

Now  we  find  that  the  visual  sensa  of  a  group  which 
we  ascribe  to  a  single  physical  object  are  related  pro- 
jectively  to  each  other  and  to  the  tactual  sensum  which 
we  ascribe  to  the  same  object.  If  we  regard  their 
common  permanent  condition  as  having  something 
analogous  to  shape,  we  can  explain  the  shapes  of  the 
various  sensa  in  the  group  as  projections  of  the  shape 
of  their  common  permanent  condition.  If  we  refuse 
to  attribute  anything  like  shape  to  the  permanent 
conditions,  we  cannot  explain  the  variations  in  shape 
of  the  visual  sensa  as  the  observer  moves  into  different 
positions.  This  does  not,  of  course,  prove  that  the 
common  and  relatively  permanent  conditions  of  a 
group  of  sensa  do  have  shape,  but  it  does  render  the 
hypothesis  highly  plausible.  We  have  already  seen 
that  it  is  a  legitimate  one,  that  there  is  no  reason  why 
these  common  conditions  should  not  have  shape  ;  we 
now  see  that  it  is  also  a  plausible  one,  since  with  it  we 


THEORY   OF  SENSA  279 

can,  and  without  it  we  cannot,  account  for  the  variations 
in  the  shapes  of  the  sensa  of  the  group. 

What  about  the  so-called  "secondary  qualities," 
like  colour  and  temperature?  We  know  that  Descartes, 
Locke,  and  the  orthodox  natural  scientists,  hold  that  we 
have  no  right  to  ascribe  them  literally  to  physical 
objects,  whilst  Berkeley  and  many  other  philosophers 
have  argued  that  primaries  and  secondaries  must  stand 
or  fall  (and  that  they,  in  fact,  fall)  together.  What  is 
the  truth  about  this  matter?  The  first  need  is  to  state 
the  doctrine  of  primary  and  secondary  qualities  in  a 
clear  and  intelligible  form.  Unquestionably,  colour 
and  temperature  belong  to  our  sensa,  at  any  rate,  in 
the  same  literal  way  in  which  shape  and  size  belong 
to  them.  What  I  am  immediately  aware  of  when  I 
look  at  a  penny  stamp  is  as  indubitably  red  as  it  is 
indubitably  more  or  less  square.  Similarly,  when  I 
hold  a  round  piece  of  ice  in  my  hand,  what  I  am  aware 
of  is  as  certainly  cold  as  it  is  certainly  round.  Thus, 
to  say  that  colours  and  temperatures  are  "unreal,"  or 
"do  not  really  exist,"  is  patently  false,  if  this  means 
that  there  is  nothing  in  the  Universe  of  which  it  is  true 
to  say:  "This  is  literally  red,"  or  "This  is  literally 
cold."  Such  statements  are  true  of  many  sensa,  at 
any  rate,  and  sensa  are  parts  of  the  existing  Universe.  -"' 

The  only  substantial  question  is  :  "  Do  colours  and 
temperatures  ever  literally  belong  to  physical  objects, 
or  do  they  belong  literally  only  to  sensa?"  What  the 
scientist  is  trying  in  an  extremely  muddled  way  to 
do  is  to  assert  the  physical  reality  of  shapes  and  sizes, 
and  to  deny  the  physical  reality  of  colours,  temperatures, 
noises,  etc.  Now  this  view,  when  clearly  stated,  comes 
to  the  following  :  "  Shapes  and  sizes  belong  to  physical 
objects  in  the  same  literal  way  in  which  they  belong 
to  sensa,  and  from  the  shapes  and  sizes  of  sensa  we  can 
generally  infer  with  reasonable  certainty  those  of  that 
physical  object  of  which  these  sensa  are  appearances. 
Colours,    temperatures,  etc.,   belong  literally  to  sensa, 


y 


28o  SCIENTIFIC   THOUGHT 

but  they  belong  to  physical  objects  only  in  a  derivative 
and  Pickwickian  sense.  There  must,  of  course,  be  some- 
thing  in  the  permanent  conditions  of  a  group  of  sensa 
which  wholly  or  partly  determines  the  colour  or  tem- 
perature of  the  latter.  But  this  something  is  not  colour 
or  temperature."  We  have  seen  what  sort  of  ground 
there  is  for  the  positive  part  of  this  view  :  is  there  any 
good  reason  to  believe  the  negative  part  of  it? 

It  is  sometimes  thought  that  the  physical  theories 
of  light  and  heat  positively  disprove  the  common-sense 
view  that  physical  objects  are  literally  coloured  or  hot. 
This  is  a  sheer  logical  blunder.  The  physical  theory 
of  light,  e.g.,  asserts  that,  whenever  we  sense  a  red 
sensum,  vibrations  of  a  certain  period  are  striking  our 
retina.  This  does  not  prove  that  bodies  which  emit 
vibrations  of  that  period  are  not  literally  red,  for  it 
might  well  be  that  only  bodies  which  are  literally  red 
can  emit  just  these  vibrations.  The  vibrations  might 
simply  be  the  means  of  stimulating  us  to  sense  the 
red  colour,  which  is  literally  in  the  body,  whether  we 
happen  to  sense  it  or  not.  (I  am  quite  certain  that 
this  simple-minded  theory  cannot  be  made  to  fit  the 
extremely  complicated  facts  ;  but  it  is  compatible  with 
the  fact  that  we  only  become  aware  of  colours  when 
vibrations  of  a  certain  kind  affect  our  eyes  ;  and  there- 
fore this  fact  does  not,  as  is  often  supposed,  refute  the 
common-sense  view  that  bodies  are  literally  coloured 
and  that  we  actually  sense  the  colours  which  are  on 
their  surfaces.) 

I  think  that  the  negative  part  of  the  scientific  view 
does  express  an  important  fact,  but  that  it  needs  to  be 
stated  in  a  much  more  guarded  way.  (i)  It  is  certain 
that,  if  physical  objects  possess  shape  and  size  at  all, 
they  must  have  some  other  quality,  related  to  shape  and 
size  in  the  same  general  kind  of  way  in  which  colour 
and  temperature  are  related  to  the  shape  and  size  of 
sensa.  You  cannot  have  extension  et  praterea  nihil ; 
you  must  have  something  that  can  be  spread  out  and 


THEORY   OF   SENSA  281 

cover  an  area  or  fill  a  volume.  (2)  There  is  no  reason 
why  these  "extensible"  qualities,  which  must  be 
present  in  physical  objects,  if  they  be  extended  at  all, 
should  not  actually  be  colour  and  temperature.  Since 
sensa  certainly  exist,  and  are  certainly  coloured,  there 
can  be  no  internal  contradiction  in  the  notion  of  an 
existent  colour.  (3)  On  the  other  hand,  of  course,  the 
extensible  qualities  of  physical  objects  need  not  be 
colour  or  temperature.  So  long  as  they  are  qualities 
that  can  cover  areas  and  fill  volumes,  as  colour  and 
temperature  do,  they  might  differ  from  any  quality 
that  is  ever  present  in  our  sensa.  (4)  Whilst  we  found 
that  the  assumption  that  the  permanent  conditions  of 
groups  of  sensa  have  shape,  and  that  they  and  our 
bodies  have  position,  does  help  us  to  predict  the  shapes 
of  various  sensa  in  the  group,  we  do  not  find  that  the 
ascription  of  colours  or  temperatures  to  these  permanent 
conditions  helps  us  to  predict  the  colours  or  tempera- 
tures of  the  sensa  in  the  group.  It  is  found  more 
profitable  to  correlate  the  colours  and  temperatures  of 
sensa  with  the  hypothetical  movements  of  hypothetical 
parts  of  their  permanent  conditions.  This  does  not 
prove,  as  has  often  been  thought,  that  physical  objects 
cannot  literally  have  colours  or  temperatures.  Of  course, 
if  the  sensa  that  we  sense  cannot  literally  be  parts  of 
the  surfaces  of  physical  objects,  it  follows  that  the 
colours  and  temperatures  of  these  sensa  cannot  literally 
be  identical  with  the  colours  and  temperatures  of 
physical  objects,  even  if  the  latter  have  such  qualities. 
The  facts  under  discussion  do  show  that  the  hypothesis 
that  physical  objects  literally  have  colours  and  tempera- 
tures, though  legitimate  enough,  is  not  capable  of 
empirical  verification,  and  therefore  cannot  be  asserted 
with  any  high  probability. 

The  view  which  I  have  been  trying  to  state  may 
be  called  the  Critical  Scientific  Theory.  It  is  simply  an 
attempt  to  formulate  clearly,  in  terms  of  the  Sensum 
Theory  of  sensible  appearance,  the  view  about  the  ex- 

T 


282  SCIENTIFIC   THOUGHT 

ternal  world  which  has  been  at  the  back  of  the  scientific 
mind  since  the  time  of  Descartes  and  Locke.  In  its 
original  form  this  view  was  a  mass  of  inconsistencies,  since 
it  was  naively  realistic  for  our  perception  of  shape,  size, 
and  position,  and  held  a  causal  theory  for  our  perception 
of  colour,  temperature,  etc.  This  combination  of  theories 
proved  to  be  inconsistent  with  the  inextricable  entangle- 
ment of  the  two  kinds  of  qualities,  which  we  actually  find. 
Moreover,  the  naively  realistic  part  of  it  proved  unten- 
able in  face  of  the  variations  of  visual  shape  and  size, 
which  are  obvious  when  we  view  what  is  regarded  as  a 
single  unchanged  physical  object  from  various  positions. 

Thus  the  only  hope  for  the  scientific  view  was  to 
restate  it  in  a  completely  causal  form.  A  serious  diffi- 
culty at  once  arose.  The  causal  part  of  the  old  view 
presupposed  the  naively  realistic  part.  When  we  were 
told  that  motions  within  a  circular  contour  at  a  certain 
place  in  space  caused  sensations  of  colour  and  tempera- 
ture "in  us,"  we  understood  this,  because  we  thought 
that  we  literally  saw  and  felt  this  contour  in  this  place. 
But,  as  soon  as  the  theory  is  made  completely  causal, 
both  spatial  and  non-spatial  attributes  belong  primarily 
to  the  effect  produced  "in  us"  by  something  else.  It 
then  becomes  difficult  to  see  that  we  have  any  better 
right  to  regard  this  cause  as  literally  endowed  with 
shape,  size,  and  position,  than  as  literally  endowed  with 
colour  and  temperature.  Yet  the  scientific  theories 
about  the  causation  of  our  sensations  of  colour,  tem- 
perature, etc.,  are  stated  in  terms  which  seem  to  lose  all 
meaning  unless  the  causes  of  these  sensations  literally 
have  shapes,  sizes,  and  positions.  The  Critical  Scientific 
Theory,  as  stated  by  us,  has  been  an  attempt  to  meet 
these  difficulties,  to  reformulate  the  distinction  between 
primary  and  secondary  qualities,  and  to  estimate  the 
amount  of  value  which  this  distinction  can  justly  claim. 

I  think  that  the  Critical  Scientific  Theory  is  internally 
consistent,  so  far  as  it  goes  ;  but  I  certainly  do  not 
believe   that  it  is  ultimately  satisfactory.     In   the  first 


THEORY   OF   SENSA  283 

place,  it  continues  to  use  a  number  of  phrases  whose 
meanings  are  no  longer  obvious  when  we  have  given 
up  the  notion  that  we  literally  sense  parts  of  the  surfaces 
of  physical  objects.  It  still  talks  of  pennies  being 
"  round,"  of  a  number  of  different  people  at  "  the  same 
time"  and  the  same  person  at  "different  times"  all 
perceiving  "  the  same  penny  "  from  "different  places." 
We  must  reinterpret  all  these  phrases  in  terms  of  our 
sensa  and  their  relations  before  we  can  hope  to  get  a 
consistent  theory.  I  shall  try  my  hand  at  this  very 
difficult  job  in  the  next  three  chapters. 

Secondly,  our  theory  uses  the  phrase  that  processes 
in  external  physical  objects  and  our  bodies  "jointly 
produce  in  us"  the  sensa  by  which  we  become  aware 
of  them.  The  phrase  in  inverted  commas  covers  a 
multitude  of  problems.  Do  physical  processes  create 
sensa  out  of  nothing?  Or  do  they  just  cause  us  to  sense 
now  one  and  now  another  selection  out  of  a  mass  of 
already  existing  sensa?  And,  on  either  alternative, 
what  is  the  status  of  sensa  once  they  have  come  into 
existence?  Do  they  just  exist  alongside  of  physical 
objects?  Do  they  ever  interact  with  each  other  or  pro- 
duce effects  on  the  physical  world  ?  Or  are  they,  in  some 
Pickwickian  sense,  parts  of  physical  objects?  With  some 
of  these  problems  I  shall  try  to  deal  in  my  last  chapter. 

The    following  additional    works    may  be  consulted 
with  advantage  : 

B.  A.  \V.  Russell,  Lectures  on  the  External  World,  Lects. 

III.  and  IV. 
M  ,,        A nalysis  of  Mind,  Lects.  V.  and  VII. 

G.  F.  Stout,  Manual  of  Psychology,  Bk.  III.  Part  II.  Cap. 

I.,  and  Bk.  II.  Cap.  I. 
,,  ,,         Proceedings  of  the  Aristotelian  Society,  191 3. 

J.  Laird,  Problems  of  the  Self,.  Cap.  III. 
S.  Alexander,  Space,    Time,  and  Deity,  Vol.   II.   p.   124, 

et  seq.  ;  p.  170,  et  seq. 
G.  E.  Moore,  Philosophical  Studies. 
Berkeley,  Principles  of  Human  Knowledge. 
Descartes,  Meditations. 


r 


CHAPTER    IX 

"  Nam  si  colorcs  et  soni  in  ipso  Objecto  csscnt,  separari  ab 
illis  non  posscnt.  Separantur  autcm,  ut  manifestum  in  reflexioni- 
bus  visibilium  per  specula,  et  audibilium  per  loca  montana. 
Scimus  autem  corpus  quod  videmus  in  uno  tantum  loco  esse, 
sed  apparentias  in  plurimis." 

(Hobbes,  Leviathan,  Part  I.  Cap.  I.) 

The  Positions  and  Shapes  of  Sensa  and  of 
Physical  Objects 

We  have  now  to  dig  beneath  the  assumptions  that  are 
tacitly  made  by  the  Critical  Scientific  Theory,  and  to 
discover  their  precise  meaning  and  value.  In  expound- 
ing it  we  talked  of  a  number  of  people  all  "  looking  at 
the  same  penny."  We  assumed  that  there  is  a  certain 
place  "seen"  by  all  the  observers,  and  that  in  this 
place  there  is  a  round  physical  object.  We  have  now 
to  ask  what  is  meant  by  a  common  place ;  what  is 
meant  by  a  physical  object  occupying  that  place  ;  and 
what  is  meant  by  calling  that  object  round.  We  shall 
find  that  all  these  questions,  which  seem  so  childishly 
simple,  present  great  difficulties,  and  can  only  be 
answered  in  highly  Pickwickian  senses.  They  seem 
easy,  because  we  habitually  confine  ourselves  to  cases, 
which  are  indeed  of  frequent  occurrence,  and  are  of 
practical  interest,  but  which  really  owe  their  simplicity 
to  the  existence  of  specially  simple  conditions.  These 
conditions  are  not  always  fulfilled,  and  then  difficulties 
arise.  This  happens,  for  instance,  with  mirror  images 
which  turn  up  in  places  where  nothing  relevant  is 
going  on.  As  a  rule,  we  simply  ignore  these  "wild" 
isensa  ;  but  we  shall  find  that  the  only  way  to  deal  fairly 
Nwjth  all  the  facts  is  to  base  our  theory  on  them,  and  to 

284 


POSITIONS   AND   SHAPES   OF   SENSA         285 

regard  "tame"  sensa  as  owing  their  tameness  to  the 
fulfilment  of  certain  special  simplifying  conditions. 

In  dealing  with  our  present  problem  we  shall  not 
only  be  learning  something  more  about  the  concept  of 
Matter  and  its  appearances  ;  we  shall  also  be  carrying 
the  theory  of  Space  a  step  further.  In  Chapter  I  we 
simply  took  the  common-sense  notion  of  a  single  all- 
containing  Space  for  granted  ;  we  have  now  to  consider 
the  exact  cash  value  of  that  conception. 

If  we  want  to  discover  the  meaning  of  the  statement 
that  we  all  see  a  certain  physical  object  in  a  certain 
place,  we  must  start  from  the  spatial  characteristics  of 
our  visual  sensa.  Unfortunately,  there  is  a  good  deal 
of  disagreement  as  to  what  these  actually  are.  Thus 
we  are  often  told  that  we  do  not  "see"  distance  or 
solidity  ;  and  this  is  undoubtedly  meant  to  mean  that 
distance  and  solidity  are  not  characteristics  of  visual 
sensa,  as  shape  and  size  are.  This  seems  to  me  to  be 
a  mistake,  and  the  whole  matter  has  become  so  much 
confused  that  our  first  duty  is  to  try  to  clear  it  up. 
This  will  be  rather  a  long  process. 

Spatial  Characteristics  of  the  Visual  Field. — When- 
ever I  open  my  eyes  I  am  aware  of  a  coloured  field  of 
view,  which  I  will  call  a  "visual  field."  It  is  admitted 
that  this  is  spread  out  and  internally  differentiated  into 
patches  of  various  shapes  and  colours.  These  are  at 
once  joined  and  separated  by  a  background,  which  also 
has  colour.  The  middle  part  of  this  field  is  the  most 
distinct.  If  I  turn  my  head  a  little,  the  field  changes 
slightly.  What  is  now  in  the  middle  and  most  distinct 
differs  from  what  was  in  the  middle  of  my  former  field. 
But  it  is  extremely  like  something  that  was  slightly  to 
one  side  of  the  former  field  and  was  slightly  indistinct. 
Conversely,  what  is  slightly  to  one  side  of  the  present 
field  is  very  much  like  what  was  in  the  middle  of  the 
former  field  and  had  there  maximum  distinctness.  The 
process  of  turning  one's  head   is,  of  course,  associated 


jS()  scientific  thought 

with  certain  kinesthetic  sensations,  which  last  longer 
and  ijTow  more  intense  the  more  the  head  is  turned. 

(d)  Usual  Motion. — So  much,  I  suppose,  is  admitted 
by  everyone.  I  now  want  to  call  attention  to  certain 
facts  that  have  an  important  bearing  on  our  present 
problem,  and  are  not  so  commonly  noticed.  As  a  rule, 
we  see  objects  through  a  practically  homogeneous 
medium,  viz.,  air,  in  which  they  and  we  are  immersed. 
Under  these  conditions  the  slight  turning  of  the  head 
only  produces  those  changes  in  centrality  and  distinct- 
ness that  we  have  noticed,  combined,  of  course,  with  the 
loss  of  certain  features  which  were  on  the  extreme  edge 
of  the  first  field  and  the  gain  of  others  on  the  opposite 
extreme  edge  of  the  second.  So  long  as  the  medium 
is  homogeneous,  the  turning  of  the  head  does  not  affect 
the  visual  sensa  with  sensible  movement.  If,  on  the 
other  hand,  we  are  looking  through  a  bad  bit  of  window 
glass,  or  through  any  optical  instrument  imperfectly 
focused,  the  sensa  in  the  field  do  visibly  move  as  we 
turn  our  heads.  What  I  call  "sensible  movement"  is 
as  distinct  and  irreducible  a  character  of  certain  sensa 
at  certain  times  as  colour  or  shape.  We  notice  then 
that,  under  normal  conditions  of  sight,  the  sensa  in  our 
visual  field  may  be  unaffected  with  sensible  movement, 
though  we  turn  our  heads  ;  but,  as  soon  as  the  condi- 
tions become  unusual,  a  turn  of  the  head  affects  all  the 
sensa  of  the  field  with  sensible  movement. 

Again,  some  of  the  sensa  in  a  field  may  be  affected 
with  sensible  movement  though  I  keep  my  head  still. 
As  I  write,  I  am  sitting  at  an  open  window  in  Trinity, 
and  looking  out  at  the  opposite  side  of  Nevile's  Court. 
All  the  points  that  I  have  mentioned  are  illustrated  in 
my  present  visual  field.  I  can  turn  my  head  without 
the  visual  appearances  of  the  opposite  windows  being 
affected  with  sensible  movement.  If  I  look  through  the 
shut  window,  which  is  at  the  side  of  my  open  one,  and 
is  made  of  rather  irregular  glass,  I  find  that  I  cannot 
turn    my    head    without   the    visual    appearance   of  the 


POSITIONS  AND   SHAPES   OF   SENSA        287 

opposite  side  of  the  Court  jumping  about.  Lastly,  there 
are  certain  features  in  the  field,  viz. ,  the  visual  appearances 
of  bedmakers  and  washerwomen — for  it  is  a  Saturday — 
which  sensibly  move,  even  though  I  keep  my  head  still. 
To  these  cases  we  must  add  one  more,  which  is  the 
least  common  in  ordinary  experience.  Sometimes  we 
find  the  whole  field  affected  with  sensible  movement, 
though  we  keep  our  heads  still.  This  happens  if  my 
open  window  swings  to  in  the  breeze. 

The  position,  then,  is  this:  There  is  no  doubt  that 
sensible  motion  and  rest  are  genuine  unanalysable 
properties   of  visual    sensa.     I    am   aware   of  them    as 


v- 


directly  as  I  am  aware  of  the  redness  of  a  red  patch, 
and  I  could  no  more  describe  them  to  anyone  who  had 
never  sensed  them  than  I  could  describe  the  colour  of 
a  pillar-box  to  a  man  born  blind.  Now,  there  are  three 
entirely  distinct,  but  constantly  confused,  questions  that 
can  be  asked  about  a  quality  of  a  sensum.  (1)  Do  sensa 
really  have  this  quality?  (2)  What  conditions  must  be 
fulfilled  in  order  that  sensa  with  this  quality  may  occur? 
and  (3)  What  right  have  I  to  base  on  this  quality  of 
my  sensa  those  judgments  about  physical  objects  and 
their  properties  which  I  do  in  fact  base  on  it?  The  first 
question  is  absolutely  independent  of  the  other  two. 
The  only  way  to  find  out  whether  a  sensum  does  or 
does  not  have  a  certain  quality  is  to  inspect  the  sensum 
itself  as  carefully  as  possible.  The  second  question 
belongs  partly  to  physics,  partly  to  physiology,  and 
partly  perhaps  to  psychology  (if  sensa  be  to  any  extent 
mind-dependent).  The  third  is  a  question  for  Critical 
Philosophy.  Naturally,  the  answer  to  it  will  determine 
the  interpretation  which  we  put  on  the  answers  given 
by  scientists  to  (2).  Conversely,  the  answer  to  (3)  will 
have  to  be  such  as  to  allow  for  any  well-established  facts 
that  the  scientists  have  discovered  in  answering  (2). 

Now  it  is  a  very  common  mistake  to  suppose  that  if 
(2)  has  to  be  answered  in  a  certain  way  it  follows  that 
sensa  cannot  have  the  quality  in  question.     This  fallacy 


288  SCIENTIFIC   THOUGHT 

seems  to  me  to  have  been  committed  by  those  persons 
who  deny  that  visual  sensa  have  sensible  solidity  and 
position.  They  argue  that  those  qualities  could  only 
have  been  acquired  through  certain  past  experiences, 
and  conclude  from  this  that  the  qualities  in  question 
cannot  now  belong  to  visual  sensa.  This  is,  of  course, 
a  sheer  fallacy  ;  but  before  discussing  it  in  detail  for 
position  and  solidity,  I  propose  to  deal  with  the  case  of 
sensible  motion.  For  exactly  similar  arguments  could 
be  used  to  prove  that  visual  sensa  do  not  have  sensible 
motion  ;  and  it  must  surely  be  obvious,  even  to  the  most 
advanced  thinker,  that  some  visual  sensa  do  have  this 
quality. 

When  I  look  through  a  homogeneous  medium  and 
turn  my  head,  the  stimulus  of  light  from  various  objects 
moves  over  my  retina  ;  nevertheless,  my  sensa  are  not 
affected  with  sensible  motion.  When  I  look  through 
a  non-homogeneous  medium,  and  turn  my  head,  the 
stimulus  moves  across  my  retina  ;  and  this  time  my 
sensa  are  affected  with  sensible  motion.  Thus  the 
movement  of  the  stimulus  over  the  retina  may  be  a 
necessary,  but  is  certainly  not  a  sufficient,  condition 
of  the  sensible  movement  of  my  visual  sensa.  When 
I  believe  that  the  object  that  I  am  looking  at  is  the  sort 
of  object  that  will  not  move  {e.g.,  the  opposite  side  of 
the  Court),  and  when  I  am  seeing  it  under  normal 
conditions  {i.e.,  through  a  homogeneous  medium)  the 
sensa  keep  still,  in  spite  of  the  movement  of  the  stimulus, 
provided  this  movement  is  caused  by  the  voluntary 
turning  of  my  head.  Thus  it  seems  to  me  to  be  clear 
that  one  condition  which  partly  determines  the  present 
motion  or  rest  of  my  visual  sensa  is  my  beliefs  as  to  the 
motion  and  rest  of  the  objects  of  which  these  sensa  are 
appearances.  These  beliefs  must  be  due  to  past  experi- 
ences, not  wholly  visual,  in  connexion  with  similar 
sensa.  They  are  presumably  present  in  the  -  form 
of  traces.  Under  normal  circumstances  these  traces 
neutralise  the  sensible  movement  which  the  motion  of 


POSITIONS   AND   SHAPES   OF   SENSA       289 

the  stimulus  over  the  retina  would  itself  produce.  But, 
as  soon  as  the  conditions  become  abnormal,  this  neutral- 
isation (which  is  merely  associative  and  instinctive,  not 
deliberate  and  rational)  fails  to  fit  the  unusual  conditions, 
and  the  sensa  visibly  move. 

If  the  above  theory  be  true,  the  present  motion  or 
rest  of  a  sensum  is  not  entirely  determined  by  anything 
in  the  nature  of  the  present  stimulus.  The  traces  left 
by  past  experiences,  some  of  which  were  not  wholly 
visual,  also  co-operate  ;  and  we  have  what  Mr  Russell 
calls  a  case  of  "  mnemic  causation."  Yet  it  is  clear 
that  this  makes  no  difference  to  the  fact  that  here  and 
now  visual  motion  and  rest  are  properties  of  visual  sensa, 
which  are  "seen,"  as  truly  as  shapes  and  colours,  and 
which  would  be  inexplicable  to  a  blind  man. 

These  facts  are  typical  of  visual  perception,  and 
render  the  situation  with  which  we  have  to  deal  highly 
complex  and  confusing.  On  the  one  hand,  we  now 
pass  from  the  visible  motion  or  rest  of  our  sensa  to 
perceptual  judgments  about  the  behaviour  of  our  bodies, 
of  the  medium,  and  of  the  object  at  which  we  say 
that  we  are  looking.  We  could  not  get  so  much  out 
of  so  little  if  it  were  not  that  many  past  experiences 
of  ourselves  and  others  co-operate  with  the  present 
visual  sensum  to  form  the  basis  of  our  perceptual  judg- 
ments. But  they  do  not  only  co-operate  to  form  judg- 
ments. The  actual  present  qualities  and  movements  of  .  / 
ourfsensalare  modified  by  the  traces  left  by  these  past  [ji.»s 
experiences.  We  have  thus  to  deal  with  a  double 
process.  The  experiences  of  many  people  (conveyed 
to  us  from  our  earliest  years  by  speech  and  corporate 
action)  and  many  past  experiences  of  our  own,  have 
helped  to  produce  our  present  beliefs  in  the  places, 
shapes,  movements,  etc.,  of  physical  objects,  and  have 
helped  to  produce  our  present  classification  of  these 
into  medium,  observer's  body,  object  looked  at,  etc. 
Pari  passu  with  this,  the  traces  left  by  these  past  experi- 
ences  (which    express  themselves   in   consciousness,    if 


2Q0  SCIENTIFIC  THOUGHT 

they  do  so  at  all,  as  expectations  and  beliefs  about 
physical  objects)  co-operate  with  present  stimuli,  and 
modify  the  qualities  of  our  sensa.  And  our  present 
judgments  about  physical  objects  are,  of  course,  based 
on  our  sensa  as  thus  modified. 

(/>)    Visual  Solidity. — Let  us  now  apply  these  general 
principles    to   the   debated  case   of  visual   solidity  and 
distance  ;  and  let  us  begin  with  solidity.      It  seems  to 
me  perfectly  clear  that,  whatever   may  have  been  true 
of  my  infancy  or  of  my  remote  ancestors,  solidity  is  now 
as  genuine  a  quality  of  some  of  my  visual  sensa  as  flat 
shape    or    red    colour.       A    sphere    does   look  different 
from  a  circle,  just  as  a  circle   looks  different  from  an 
ellipse.     That  this  is  due  to  past  experiences  of  touch 
and    past    kinesthetic   sensations    may    very    well    be 
true  in  one  sense,   though    I  think  that  it  is  certainly 
false    in    another.       We    must   distinguish    between    a 
general  quality,  capable  of  various  specific  modifications, 
and    the    particular  form   of  it  possessed   by  a  certain 
particular  sensum.     Thus  visual  solidity,  on  my  view, 
is  a  general  quality  of  visual  sensa,  whilst  sphericity  is 
a  particular  form  of  it,  which  belongs  to  some  sensa  and 
not  to  others.     Now  I  can  quite  well  believe  that  the 
particular  form  of  solidity  possessed  by  a  certain  sensum 
may   be   in   part  due  to  traces   of  past  experiences  of 
touch  and  movement.     I  can  believe,  for  instance,  that 
the  particular  distribution  of  light  and  shade  over  my 
present  sensum  resembles  that  of  a  past  sensum  which 
was  associated  with  the  experience  of  passing  my  hand 
over  a  spherical  surface.     And  I   can   believe  that  the 
resemblance  of  the  stimulus  excites  the  traces  left  by 
that   experience,,   and    that    these   co-operate   with    the 
present   stimulus   on    my   retina  to   produce  a  sensum 
which  is  visibly  spherical.     But  I  find  it  very  hard  to 
believe  that  experiences  of  touch   or    movement  could 
create  a  third  dimension  in  visual  sensa  which  originally 
had  only  two. 

Now  it  does  seem  to  me  clear  that  visual  solidity  is  in 


POSITIONS   AND   SHAPES   OF   SENSA       291 

itself  as  purely  visual  as  visual  shape  and  size.  It  does 
not  consist  of  visual  flatness,  together  with  judgments 
about  past  or  future  tactual  sensations.  Nor  does  it 
consist  of  visual  flatness,  together  with  associated 
images  of  past  or  future  tactual  sensa.  It  is  a  matter 
of  plain  inspection  that  the  experience  of  visual  solidity 
is  as  unitary  an  experience  as  that  of  visual  shape  in 
two  dimensions,  and  that  it  is  impossible  to  distinguish 
it  into  a  visual  and  a  tactual  part.  We  are  therefore 
forced  to  suppose,  either  that  the  experiences  of  one 
sense  can  create  an  additional  dimension  in  the  sensa 
of  another  sense,  or  that  visual  sensa  are  of  their  own 
nature  three  dimensional.  I  should  not  be  prepared 
to  accept  the  former  alternative  unless  very  strong 
arguments  could  be  produced  against  the  second.  We 
shall  see  in  a  moment  that  the  arguments  are  feeble 
in  the  extreme.  I  shall  therefore  suppose  that  visual 
solidity  is  a  primitive  characteristic  of  visual  sensa,  and 
that  the  traces  left  by  past  visual  and  tactual  experiences 
merely  help  to  determine  what  particular  form  of  visual 
solidity  a  particular  sensum  shall  have. 

If  this  be  the  genuine  result  of  careful  inspection, 
no  argument  from  the  physical  and  physiological  con- 
ditions of  visual  sensation  can  possibly  have  anything 
to  say  against  it.  On  the  contrary,  it  will  be  one  of 
the  facts  with  which  any  theory  as  to  the  conditions  of 
visual  sensation  will  have  to  reckon.  All  arguments 
which  attempt  to  prove  that  solidity  is  not  a  primitive 
property  of  visual  sensa  are  of  the  following  type. 
Whenever  we  see  an  object,  a  certain  area  of  the  retina 
is  stimulated  by  the  light  from  this  object.  This  area 
is  a  projection  of  the  object  on  to  the  surface  of  the 
retina,  and  such  an  area  could  equally  well  be  the 
projection  of  a  solid  or  of  a  plane  figure  of  suitable 
shape.  Consequently,  it  is  argued,  there  is  nothing 
in  the  retinal  stimulus  to  distinguish  between  light  from 
a  solid  and  light  from  a  plane  figure  of  suitable  contour. 
Therefore  sight  cannot  give  us  an  awareness  of  solidity. 


292  SCIENTIFIC   THOUGHT 

This  may  be  illustrated  in  the  following  way  :  Take 
a  sphere,  and  suppose  that  we  are  looking  at  it  with 
one  eye.  The  light  from  it  affects  a  circle  on  the  retina, 
of  diameter,  era'. 


If  we  were  to  cut  away  all  the  sphere  in  front  of  SS'  and 
all  the  sphere  behind  it,  leaving  merely  the  circular 
disc  of  diameter  SS',  the  area  of  the  retina  affected  by 
the  light  from  this  disc  would  be  exactly  the  same  as 
that  affected  by  the  light  from  the  whole  sphere,  viz., 
the  circular  area  of  diameter  ar<r' .  Hence,  it  is  argued, 
the  visual  sensum  must  be  the  same  in  both  cases.  No 
doubt  there  will  be  a  difference  in  light  and  shade  in 
the  sensum  connected  with  the  sphere,  but  this  is  the 
only  difference.  And  this  effect  could  be  reproduced 
by  using  a  suitably  shaded  fiat  disc  instead  of  an 
uniformly  illuminated  one,  as  is  in  fact  done  when 
painters  want  to  represent  spheres  on  flat  canvases. 
Conversely,  arrangements  of  lines  which  are  really  in 
one  plane  may  "look  solid."  It  is  concluded  (a)  that 
solidity  is  not  a  primitive  property  of  visual  sensa ; 
and  (d)  that,  even  now,  "to  look  solid,"  means  simply 
to  evoke  certain  images,  memories,  or  expectations  of 
tactual  and  kinesthetic  experiences. 

This  argument,  which  must  be  mistaken  if  it  is  a 
fact  that  visual  solidity  is  a  unitary  and  unanalysable 
property  of  sensa,  does  rest  on  tacit  assumptions  ;  and, 
when  these  are  laid  bare,  it  loses  its  plausibility.  It 
assumes  (a)  that,  because  the  retinal  stimulus  for  visual 
sensation  is  two-dimensional,  therefore,  the  corre- 
sponding visual  sensum  cannot  have  more  than  two 
dimensions.  It  is  this  assumption  that  makes  it  so 
plausible  to  hold  that  the  visual  sensum  must  itself  be 
a  mere  surface,  and  therefore  that  visual  solidity  needs 


POSITIONS   AND   SHAPES   OF   SENSA       293 

to  be  explained.  But  there  is  not  the  least  reason  to 
accept  the  assumption.  There  is  no  reason,  whatever, 
why  a  sensum  should  not  have  a  greater  number  of 
dimensions  than  the  physiological  stimulus  on  which 
it  depends.  Hence,  even  if  it  be  true  that  the  necessary 
and  sufficient  condition  of  a  visual  sensation  is  an 
excited  area  on  the  retina,  this  is  no  reason  why  some* 
or  all  visual  sensa  should  not  be  voluminous,  {b)  The 
argument  in  question  does  make  the  further  assumption 
that  the  complete  conditions  of  a  visual  sensum  must 
be  present  in  the  retinal  stimulus  with  which  it  is 
connected.  If  anything  else,  such  as  the  trace  of  a 
past  tactual  or  kinesthetic  experience,  co-operates,  it 
is  assumed  that  it  can  only  produce  associated  tactual 
images  and  not  modifications  of  visual  sensa.  This 
again  is  a  sheer  assumption,  and  one  that  is  not  even 
antecedently  probable.  In  any  case,  the  visual  sensation 
does  not  arise  till  the  stimulus  has  passed  from  the 
retina,  through  the  optic  nerve,  to  the  brain.  It  is  the 
wildest  dogmatism  to  assert  that  what  happens  in  the 
brain  corresponds  point  for  point  to  what  happened 
on  the  retina,  and  that  no  additional  factors  come  into 
operation  there,  which  may  be  constant  when  the 
retinal  stimuli  vary,  or  variable  when  the  retinal  stimuli 
are  the  same.  Now  if  every  visual  sensation  is  partly 
dependent  on  what  happens  in  the  brain  as  well  as  on 
what  has  happened  on  the  retina,  it  is  surely  mere 
pedantry  to  assert  that  the  solid  shape  of  a  certain  visual 
sensum  cannot  be  a  genuine  property  of  it,  because  one 
of  its  conditions  was  a  trace  left  on  the  brain  by  a  past 
tactual  experience.  We  must  judge  sensa,  like  O.B.E.'s, 
by  their  present  properties  and  not  by  their  ancestry. 

The  truth  seems  to  me  to  be  as  follows  :  (1)  Visual 
sensa,  as  such,  are  capable  of  being  solid.  There  is 
such  a  quality  as  visual  solidity,  and  it  belongs  to  some 
sensa  as  much  as  the  shape  of  a  flat  sensum  belongs  to 
it.  (2)  The  complete  conditions  of  any  visual  sensum 
include   (a)  a   stimulated   area    of   the    retina    (or  what 


204  SCIENTIFIC   THOUGHT 

corresponds  point  to  point  with  this  in  the  brain  by 
transmission  through  the  optic  nerve);  and  (/>)  certain 
conditions  in  the  brain  which  are  independent  of  the 
present  stimulus  on  the  retina.  (3)  Among  these 
independent  conditions  are  traces  left  on  the  brain  by 
past  experiences  of  sight,  touch,  and  movement.  These 
do  not  generally  show  themselves  in  consciousness  at 
all.  If  they  happen  to  do  so,  they  express  themselves 
as  memories  and  expectations  about  physical  objects. 
(4)  Generally  these  traces  merely  co-operate  with  the 
brain  states  which  are  due  to  the  retinal  stimulus,  to 
produce  a  visual  sensation  whose  sensum  is  of  such  and 
such  a  kind.  It  is,  therefore,  reasonable  to  expect  that 
the  visual  solidity  of  two  sensa  may  be  different,  though 
the  stimulated  retinal  area  is  the  same.  Let  us  illustrate 
this  by  the  case  of  the  disc  and  the  sphere.  In  both 
cases  the  same  circular  area  of  the  retina  is  stimulated 
and  the  disturbance  is  transmitted  from  it  to  a  correlated 
part  of  the  brain.  In  neither  case  is  this  sufficient  to 
determine  completely  the  nature  of  the  visual  sensum 
which  shall  be  sensed  at  the  moment.  The  other 
necessary  conditions  include  factors  in  the  brain  which 
are  independent  of  the  present  stimulus  and  existed 
before  it  took  place.  Among  these  are  traces  left  by 
past  experiences.  Now  the  distribution  of  the  light  in 
the  case  of  the  sphere  excites  certain  traces,  ts,  whilst 
the  different  distribution  of  the  light  in  the  case  of  the 
uniformly  illuminated  disc  excites  certain  other  traces,  td. 
Calling  <ra  and  a-d  the  visual  appearances  of  sphere  and 
disc  respectively,  and  r  the  common  area  of  the  retina 
stimulated,  we  have 

<r,  =  4>(r,t,)  and  o-a=<f>(r,td); 

and  the  sensible  shape  of  the  two  sensa  takes  different 
forms,  viz.,  the  solid  spherical  form  and  the  flat  round 
form.  Conversely,  suppose  we  are  looking  at  a  per- 
spective drawing  of  a  cube  on  a  flat  bit  of  paper.  If 
we   happen    to    be   thinking    mainly    of   solids,    as   we 


POSITIONS   AND   SHAPES   OF   SENSA       295 

generally  are,  a  trace,  4,  left  by  past  experiences  of 
touching  cubes,  will  tend  to  be  excited  ;  if  we  are  think- 
ing mainly  of  the  flat  bit  of  paper  a  different  trace, 
tp  will  tend  to  be  excited.     The  two  visual  sensa, 

Sc  =  <t>{r,tc)  and  s  =  <f>(r,t/), 

will  then  differ  in  the  specific  form  that  their  sensible 
shape  takes. 

(c)  Visual  Distance. — We  can  now  pass  to  the  question 
of  visual  distance,  which  is  more  important  for  our 
present  purpose,  and  about  which  almost  exactly  the 
same  controversy  has  arisen.  We  have  been  told 
ad  nauseam  since  the  days  of  Berkeley  that  we  do  not 
see  objects  at  a  distance  from  ourselves,  but  that  the 
perception  of  distance  by  sight  is  simply  associated 
images  of  tactual  and  kinesthetic  sensations.  I  take 
this  to  mean  that  distance  is  not  an  intrinsic  property 
of  our  visual  fields,  as  colour,  size,  and  shape  are. 
Now  it  is  perfectly  obvious  to  me  that  I  do  sense 
different  patches  of  colour  at  different  visual  distances. 
When  it  is  said  that  we  do  not  see  distances  out  from 
the  body,  the  only  sense  in  which  it  is  true  is  that,  in 
monocular  vision,  there  is  nothing  in  the  retinal  stimulus 
which  is  uniquely  correlated  with  the  distance  of  the 
source  of  light  from  my  eye.  In  binocular  vision 
there  is,  I  suppose,  parallax  between  the  two  retinal 
impressions.  To  make  the  case  that  I  am  arguing 
against  as  strong  as  possible,  I  will  confine  myself  to 
monocular  vision. 

It  is  true  that,  if  I  fix  a  stick  6  inches  long  at  6  feet 
from  my  eye,  its  projection  on  my  retina  is  the  same 
as  that  of  a  stick  1  foot  long  held  at  12  feet  from  my 
eye  and  parallel  to  the  first.  The  one  factor  of  length 
in  the  retinal  impression  has  to  represent  the  two  factors 
of  length  and  distance  in  the  physical  object.  This  is, 
of  course,  still  clearer  if  we  keep  one  end  of  the  stick 
fixed  and  move  the  other  end  about  in  various  directions 
in  Space.     The  various  projections  on   the   retina  are 


296  scientific  thought 

of  many  different  lengths  ;  but  all  these  various  pro- 
jections could  equally  have  been  produced  by  sticks  of 
suitable  lengths,  with  their  directions  all  confined  to 
the  plane  parallel  to  the  observer's  body.  Hence  there 
is  nothing  in  the  retinal  impression  to  distinguish 
between  a  number  of  sticks  of  various  lengths  put  in 
various  directions  in  a  plane  parallel  to  the  body,  and 
a  single  stick  with  one  end  at  a  fixed  distance  and  the 
other  turned  in  various  directions  in  Space.  The  con- 
clusion drawn  is  that  distance  out  from  the  body  is 
not  an  attribute  of  visual  sensa  as  such,  like  length 
and  breadth;  the  distance  that  is  apparently  "seen" 
consists  of  associated  images  of  kinesthetic  and  tactual 
experiences  that  have  been  enjoyed  in  the  past. 

We  must  make  much  the  same  criticisms  on  this 
argument  as  we  have  already  made  on  the  argument 
to  prove  that  there  is  no  such  quality  as  visual  solidity, 
(i)  Whatever  may  be  the  history  of  the  process,  it  is 
now  a  fact  that  one  visual  sensum  is  visibly  remoter 
than  another,  and  that  a  stick  6  inches  long  and  6  feet 
away  looks  different  from  a  parallel  stick  i  foot  long 
and  12  feet  away.  (2)  This  sensible  distance  is  not 
now  analysable  into  a  sensum  of  a  certain  size  and 
no  distance,  together  with  revived  images  of  past  kin- 
esthetic and  tactual  sensations.  Visual  distance  is  as 
simple  and  unitary  a  quality  in  itself  (whatever  may 
be  true  of  its  conditions)  as  visual   length  or  breadth. 

(3)  It  is  extremely  difficult  to  believe  that  visual  sensa 
started  with  no  such  quality  as  distance,  and  then 
acquired  an  extra  quality,  perfectly  interchangeable 
with  their  former  qualities  of  length  and  breadth, 
through  association  with  experiences  of  another  sense. 

(4)  The  fact  that  there  is  nothing  in  the  retinal  stimulus 
which  is  uniquely  correlated  with  distance  in  no  way 
proves  that  visual  sensa  do  not,  from  the  very  first, 
have  some  form  of  visual  distance.  It  is  equally  true 
that  there  is  nothing  in  the  retinal  stimulus  that 
uniquely  corresponds  to   the   length  or  breadth  of  the 


POSITIONS   AND   SHAPES   OF   SENSA       297 

object  at  which  we  are  looking  ;  yet  the  present  theory 
does  not  hesitate  to  hold  that  length  and  breadth  are 
genuine  qualities  of  visual  sensa.  In  fact,  nothing 
but  prejudice  can  make  us  suppose  that,  because  a 
physiological  stimulus  has  only  n  dimensions,  the 
sensum  which  is  correlated  with  it  cannot  have  more 
than  n  dimensions.  It  is,  therefore,  perfectly  open  to 
us  to  hold  that  all  visual  sensa  have,  of  their  very 
nature,  some  visual  distance  or  other.  The  only  problem 
is  to  account  for  the  fact  that  here  and  now  one  visual 
sensum  has  one  sensible  distance  and  another  visual 
sensum  has  another.  (5)  To  account  for  this  we  have 
to  remember  that,  on  any  view,  it  is  not  the  retinal 
stimulus  itself,  but  a  process  in  the  brain,  which  is  the 
last  link  in  the  train  of  events  which  ends  with  a  visual 
sensation.  This  being  so,  it  is  not  unreasonable  to 
suppose  that  the  total  physiological  conditions  of  any 
visual  sensation  include  (a)  a  set  of  brain-states  which 
correspond  by  transmission  to  the  events  in  an  excited 
area  of  the  retina;  and  (b)  certain  brain-states  which  are 
independent  of  the  present  retinal  stimulus.  Among  the 
latter  are  traces  left  by  past  experiences  of  sight,  touch, 
movement,  etc.  ;  and  these  play  an  important  part  in 
determining  the  particular  visual  distance  that  a  given 
visual  sensum  shall  have.  It  is  thus  perfectly  intelligible 
that  the  sensible  length  and  distance  of  two  sensa  should 
differ  when  the  retinal  stimulus  is  of  the  same  size 
and  shape,  and  conversely.  This  is  simply  another 
instance  of  the  same  general  principle  which  we  have 
already  seen  at  work  in  the  case  of  sensible  motion  and 
rest  and  in  that  of  visual  solidity. 

A  special  difficulty  with  which  we  must  now  deal, 
has  been  felt  about  ascribing  distance  to  visual  sensa. 
It  is  argued  that  distance  is  essentially  a  relation  between 
two  terms,  and  that  a  relation  cannot  literally  be  sensed 
unless  both  its  terms  are  also  sensed.  Thus  we  do  not 
visually  sense  a  given  line,  unless  we  visually  sense 
both  ends  of  it.     Now  we  certainly  do  not  visually  sense 

u 


298  SCIENTIFIC  THOUGHT 

our  own  retina,  and  therefore  it  is  impossible  that  we 
should  visually  sense  the  distance  of  visual  sensa  from 
them.  This  is  a  perfectly  sound  argument,  and  to  meet 
it  we  must  draw  certain  distinctions. 

(i)  The  first  thing  to  recognise  is  that  the  awareness 
of  visual  distance  is  primarily  an  awareness  of  the 
distance  between  two  visual  sensa,  and  is  not  an  aware- 
ness of  the  distance  of  either  of  them  from  our  retina. 
It  is  perfectly  true  that  the  distance  of  sensa  from  our 
retina  is  not  sensed  by  sight.  Indeed,  it  is  only  possible 
to  srive  a  meaning  to  the  notion  of  distance  between  a 
visual  sensum  and  something,  like  the  retina,  which  is 
not  a  sensum  at  all,  in  a  highly  Pickwickian  sense.  All 
I  am  asserting  is  that,  when  I  open  my  eyes,  I  am  aware 
of  a  visual  field  in  which  different  parts  have  different 
depths.  What  I  sense  as  visual  distance  is  the  difference 
of  depth  between  two  sensa  in  this  field. 

(2)  We  must  therefore  distinguish  between  visual 
depth  and  visual  distance.  Depth  is  a  sensible  quality, 
not  a  sensible  relation.  Visual  distance  is  a  sensible 
relation  between  two  visual  sensa,  founded  upon  the 
difference  of  their  respective  visual  depths.  When  we 
sense  two  sensa  with  different  visual  depths  we  ipso 
facto  sense  the  relation  of  visual  distance  between  them. 

If  we  only  sense  a  single  visual  sensum  (say  a  luminous 
flash  on  a  perfectly  dark  night)  we  do  not  sense  distance, 
but  we  do  sense  depth.  It  is,  of  course,  quite  true  that 
it  is  extremely  difficult  to  estimate  depth  accurately 
apart  from  distance.  But  there  is  nothing  odd  in  this. 
It  is  extremely  difficult  to  estimate  length  accurately 
except  by  comparing  an  object  with  some  other.  Never- 
theless, objects  do  have  lengths  of  their  own,  and  the 
relations  between  them  which  we  notice  when  we  com- 
pare and  measure,  are  founded  on  the  lengths  of  each 
of  them. 

(3)  Sensa  are  at  no  distance  from  our  retina,  not  in 
the  sense  that  they  are  at  zero  distance  from  it,  as  the 
points  of  contact  of  two  billiard  balls  are  from  each  other 


POSITIONS   AND   SHAPES   OF   SENSA       299 

when  they  hit,  but  in  the  sense  that  the  concept  of 
visual  distance  does  not  apply  at  all  to  anything  but 
pairs  of  visual  sensa.  They  are  at  no  distance  apart 
in  the  kind  of  way  in  which  it  is  true  that  my  belief 
that  2x2  =  4  is  at  no  distance  from  my  desire  for  my 
tea.  A  Pickwickian  sense  of  distance  can  be  defined 
in  which  it  is  true  generally  to  say  that  visual  sensa  of 
less  depth  are  nearer  to  my  eye  than  visual  sensa  of 
greater  depth.  But  this  Pickwickian  sense  involves  a 
reference  to  movement  and  other  things  which  we  have 
yet  to  consider.  The  interpretation  of  the  depth  of  a 
single  visual  sensum  in  terms  of  distance  between  it 
and  the  eye  is,  of  course,  greatly  helped  by  the  fact  that, 
when  two  sensa  of  different  depth  are  both  sensed,  the 
correlated  relation  of  visual  distance  between  them  is 
also  immediately  cognised. 

I  have  spoken  at  some  length  about  visual  motion 
and  rest,  solidity,  and  distance,  for  three  reasons  :  (i) 
They  illustrate  the  extreme  complexity  of  the  relations 
between  sensa  (if  there  be  such  things,  as  we  are  assuming 
throughout  this  book)  and  physical  objects  and  processes, 
and  show  that  the  past  history  and  present  expectations 
of  the  percipient  must  be  supposed  to  be  partial  con- 
ditions of  some  of  the  qualities  and  relations  of  sensa. 
This  cuts  out  at  once  any  of  those  cheap  and  easy  forms' 
of  naive  realism  which  are  produced  in  mass  and  ex-  • 
ported  in  bulk  from  the  other  side  of  the  Atlantic,  (ii) 
The  problem  of  the  perception  of  distance  and  solidity 
by  sight  is  an  intrinsically  interesting  and  very  complex 
one,  and  we  have  at  least  shown  that  many  venerable 
arguments  on  these  subjects  rest  on  assumptions  which 
are  not  convincing  when  clearly  stated,  (iii)  The  con- 
clusions which  we  have  reached  about  visual  distance 
and  solidity  are  of  the  utmost  importance  for  our 
immediate  purpose,  viz.,  a  discussion  of  the  concepts  of 
position  and  shape,  as  applied  to  sensa  on  the  one  hand 
and  to  physical  objects  on  the  other. 

My  view  is  that  nearly  all  the  general  concepts  that  we 


300  SCIENTIFIC   THOUGHT 

use  in  dealing  with  Space,  e.g.,  distance,  direction,  place, 
shape,  etc.,  come  from  sight,  whilst  the  notion  of  one 
Space  and  the  particular  quantitative  values  which  these 
general  concepts  assume  in  special  cases  are  due  mainly 
to  touch  and  to  movement.  Series  of  kinesthetic  sensa- 
tions are  not,  as  such,  experiences  of  distance,  direction, 
etc.;  and  I  do  not  see  how  they  could  ever  be  interpreted 
in  such  terms  unless  the  necessary  concepts  had  already 
been  supplied  by  sight.  Before  going  further,  I  will 
sum  up  our  conclusions  and  sketch  the  general  outline 
of  the  view  that  I  take. 

(a)  The  physical  world  is  conceived  as  comprising 
at  any  moment  a  number  of  co-existing  objects  of 
various  shapes  and  sizes  in  various  spatial  relations  to 
each  other,  (b)  The  concepts,  in  terms  of  which  this 
view  is  stated,  come  mainly  from  sight,  and  could 
hardly  have  arisen  apart  from  it.  Sight  supplies  each 
of  us  at  each  moment  with  an  extended  visual  field  in 
which  there  are  outstanding  coloured  patches  of  various 
shapes  and  sizes.  These  co-exist ;  are  in  many  cases 
sensibly  solid  ;  and  have  various  spatial  relations  to 
each  other  in  three  dimensions,  which  relations  are 
directly  sensed,  (e)  These  visual  experiences,  however, 
need  much  supplementation  before  they  can  give  rise 
to  the  traditional  concept  of  physical  Space.  In  the 
first  place,  visual  shape,  size,  distance,  etc.,  are  not 
quantitatively  very  definite.  Again,  Space  is  not 
thought  of  as  either  momentary  or  private.  It,  and 
the  objects  in  it,  are  thought  of  as  public  property 
which  all  observers  can  perceive.  And  it  is  thought 
of  as  the  permanent  container  in  which  physical  objects 
exist,  persist,  change,  and  move.  Thus  it  is  necessary 
to  connect  up  with  each  other  (i)  the  successive  visual 
fields  of  the  same  observer,  and  (ii)  the  contemporary 
visual  fields  of  different  observers.  This  fact  may  well 
make  us  anticipate  that  the  traditional  separation  of 
Space  and  Time  is  not  an  ultimate  fact,  but  is  a  con- 
venient fiction,  which  works  as  well  as  it  does  because 


POSITIONS  AND   SHAPES   OF   SENSA      301 

of  certain  simplifying  conditions  which   are   generally 
fulfilled    in    everyday    life.       (d)    The    connecting    link 
between    various   visual  fields    I    believe  to   be   mainly 
experiences  of  bodily  movement  and  of  touch.     These 
also  enable  us  to  give  quantitative  definiteness  to  the 
mainly  qualitative  concepts  which  we  derive  from  sight. 
(e)  These  series  of  movement-sensations  are  not  them- 
selves sensations  of  spatial  relations.     They  are  series 
in    Time,    whereas    spatial    relations   are    conceived    to 
link  contemporary  terms.     They  are  interpreted  spatially, 
in  terms  of  the  concepts  which  sight  alone  can  supply, 
through  their  association  with  visual   experience.     (/) 
The    accurate    quantitative    detail,    and    the    unity    of 
physical  Space,  as  conceived  by   us,    are  thus  due  to 
the  intimate  association  of  sight  with  touch  and  move- 
ment-sensations.      But  the   traces    of  the  latter  do   not 
work  simply    by   calling   up  judgments   or   images    of 
past   or    possible    movements    and    touch    experiences. 
They  also  continually  modify  the  actual   properties  of 
our  visual  sensa  ;  so  that  the  sensa  connected    with  a 
given  retinal  disturbance  may  come  to  acquire  different 
visual    shape,    size,   and    depth,  from   that  which    they 
at  first  had.     {g)   I    do   not,   of  course,   mean   that  the 
spatial    attributes    of   visual    sensa    can    be    indefinitely 
modified  by  association  with  other  experiences,  or  that 
such  association  does  not  often  express  itself  by  mere 
judgment,  without  modification   of  the  qualities  of  the 
sensa.      For  instance,   it  is  true  that  if  I  look  at  what 
I  believe  to  be  a  round  object  in  a  considerably  oblique 
direction,  the  visual  sensum  is  not  rendered  round  by 
the  traces  of  past  experiences,  but  remains  visibly  ellip- 
tical.    What  the  traces  do  here   is  not  to   modify  the 
sensum,   but  merely   to  produce   the  judgment  that    I 
am  in  fact  dealing  with  a  round  physical  object.     The 
meaning    of  roundness   is    mainly   based  on   visual   ex- 
periences ;  the  fact  that  I  apply  the  concept  of  roundness 
and   not  that  of  ellipticity    to  the    perceived   object    is 
mainly  due  to  the  associated  traces  of  past  tactual  and 


302  SCIENTIFIC   THOUGHT 

motor  experiences  ;  but  the  latter  only  modify  my  judg- 
ment about  a  physical  object  in  this  case,  and  do  not 
actually  render  the  visual  sensum  round.  This  may 
be  contrasted  with  the  case  of  looking  through  a 
homogeneous  medium  at  an  object  which  is  believed  to 
be  still,  and  turning  my  head.  Here  the  traces  left  by 
tactual  and  kinesthetic  experiences,  which  I  have  had 
in  the  past  in  connexion  with  similar  retinal  stimuli, 
do  prevent  the  sensum  from  having  any  sensible  move- 
ment. If  the  medium  be  not  in  fact  homogeneous, 
these  traces  will  automatically  supply  an  "over-correc- 
tion," and  the  sensa  will  visibly  move.  (//)  On  the 
whole,  we  may  say  that  traces  of  past  experiences  do 
tend  to  modify  the  qualities  of  visual  sensa  in  such  a 
direction  that  they  approximate  more  closely  to  those 
which  we  believe  the  object  at  which  we  are  looking 
possesses.  Often  the  approximation  is  very  imperfect; 
but,  as  a  rule,  this  makes  little  difference  to  the  judg- 
ments that  we  make  about  physical  objects  on  the  basis 
of  our  sensa.  (/)  In  any  case,  the  spatial  attributes 
that  we  ascribe  to  a  physical  object,  on  the  basis  of  a 
present  stimulus  and  the  traces  of  past  experiences, 
gain  their  whole  meaning  from  sensa  and  their  proper- 
ties, and  in  the  main  from  the  properties  of  visual  sensa. 
I  may  judge  that  I  am  looking  at  a  round  penny 
because  I  am  sensing  an  elliptical  sensum  ;  but  what 
I  mean  by  calling  it  "round,"  is  that  it  has  the  same 
sort  of  shape  as  certain  visual  sensa  that  I  have  sensed 
in  the  past  {e.g.  when  I  look  straight  down  on  pennies). 
U)  We  must  further  remember  that,  in  ninety-nine  cases 
out  of  a  hundred,  the  result  of  association,  whether 
it  modifies  the  present  sensum  or  not,  is  not  to  produce 
an  explicit  judgment  about  a  physical  object  and  its 
properties,  but  to  guide  us  to  appropriate  actions. 
When  we  say  that  an  elliptical  sensum,  together  with 
traces  of  past  experiences,  leads  us  to  judge  that  we 
are  looking  at  a  round  physical  object,  this  is  generally 
an  over-intellectual  statement  of  the  facts.     The  peculiar 


POSITIONS   AND   SHAPES   OF   SENSA       303 

experience  of  judging  or  believing  may  not  arise  in  our 
minds  at  all,  and  probably  will  not,  if  we  are  at  the 
time  more  interested  in  action  than  in  reflection — as  the 
present  state  of  the  world  proves  most  people  to  be 
at  most  times.  What  really  happens  is  that  we  act  as 
we  might  reasonably  have  been  expected  to  act  if  we 
had  made  such  and  such  a  judgment. 

The  Concept  of  Place  :  (a)  Sensible  Place. — Let  us  now 
deal  in  detail  with  the  concept  of  place,  as  applied  to 
sensa  and  to  physical  objects.  We  will  start  with 
visual  sensa.  The  fundamental  meaning  of  "place 
for  visual  sensa  is  their  place  in  the  visual  field  of  the 
observer  who  senses  them.  This  I  shall  call  Sensible 
Visual  Place.  We  shall  also  find  it  convenient  to  say 
that  such  and  such  a  coloured  patch  is  sensibly  present  at 
a  certain  place  in  a  visual  field.  Sensible  presence  is 
(a)  directly  experienced  by  sight ;  (b)  is  literal  and  un- 
analysable, not  Pickwickian  ;  and  (c)  is  private  to  a 
single  observer,  in  the  sense  that  it  only  applies  to  the 
sensa  of  his  field.  It  is  a  relation  between  a  sensum, 
which  is  part  of  a  field,  and  the  rest  of  the  field.  Two 
different  men  have  different  visual  fields,  and  the  same 
man  has  different  fields  at  different  times.  A  given 
field  may  be  said  to  last  as  long  as  the  specious  present 
of  the  observer  whose  field  it  is.  We  shall  have  to  go 
fully  into  this  matter  when  we  deal  with  the  concepts 
of  date  and  duration,  as  applied  to  sensa  and  to  physical 
objects.  In  the  present  chapter  I  shall  make  the 
simplifying  assumption  that  our  successive  fields  are 
literally  momentary.  This  is  certainly  not  true,  for  a 
momentary  field  is  something  that  can  only  be  defined 
by  Extensive  Abstraction  ;  but  it  is  best  to  deal  with 
one  difficulty  at  a  time. 

I  have  already  said  that  it  seems  to  me  that  the 
visual  field,  with  its  various  coloured  patches  standing 
out  at  different  depths  and  in  different  directions  against 
a  more  neutral  background,  is  the  sensible  basis  which 


4 


. 


304  SCIENTIFIC   THOUGHT 

alone  gives  meaning  to  the  concept  of  Space.  The 
concept  of  Space  is  that  of  a  perfectly  unique  kind  of 
whole  of  co-existing  parts,  and,  if  we  had  never  been 
sensibly  acquainted  with  a  concrete  individual  instance 
of  such  a  whole,  we  could  never  have  formed  the  con- 
cept. The  visual  field  seems  to  me  to  be  an  instance, 
and  the  only  instance,  of  a  space-like  whole  with  which 
we  are  directly  acquainted.  Now,  of  course,  once  a 
concept  has  been  acquired  through  sensible  acquaintance 
with  a  particular  instance  of  it,  it  can  be  applied  by 
thought  to  wholes  which  are  never  sensed  as  such, 
but  are  only  conceived  by  reflection  on  experiences 
which  come  to  us  piecemeal.  In  order  to  apply  the 
concept  to  such  wholes,  many  modifications  in  detail 
may  be  necessary,  and  these  will  be  suggested  by  the 
characteristics  of  the  various  experiences  which  we  are 
synthesising  under  the  concept  of  a  quasi-spatial  whole. 
For  example,  if  you  ask  a  scientist  what  he  under- 
stands by  the  statement  that  an  atom  consists  of  a  number 
of  electrons  arranged  in  a  characteristic  pattern  in 
Space,  he  will  not  be  able  to  answer  you  by  defining 
his  meaning  in  terms  of  other  concepts.  But  he  will  be 
able  to  answer  you  by  exemplifying  what  he  means.  He 
can  ask  you  to  look  up  at  the  sky  on  a  clear  night.  He 
can  then  say  that  he  thinks  of  the  electrons  as  analogous 
to  the  little  twinkling  dots  in  your  visual  field,  and  that 
he  thinks  of  them  as  forming  a  pattern  in  Space,  in  the 
sense  in  which  those  little  dots  form  a  pattern  in  your 
visual  field.  In  fact,  a  bit  of  matter  is  to  physical  Space 
as  a  visual  sensum  is  to  a  visual  field.  This  is  the 
fundamental,  non-Pickwickian  sense  in  which  things  are 
conceived  to  occupy  places  in  Space.  What  we  have 
now  to  consider  is  the  facts  about  our  sensa  and  the  other 
experiences  which  encourage  us  to  extend  the  applica- 
tion of  this  concept  beyond  the  visual  field  and  its 
sensa.  *\ 

(b)  Compresence\of  Visual  Sensa  from  different  Fields. — 
If  I   look  at  a   penny,   and   either  stand  still   or  walk 


POSITIONS  AND   SHAPES   OF   SENSA       305 

about,  I  sense  a  successive  series  of  visual  fields.  In 
each  of  these  there  is  a  sensum  which  is  an  appearance 
of  the  penny.  Again,  if  a  number  of  observers  look 
at  the  penny  together,  there  are  as  many  different  visual 
fields  at  any  moment  as  there  are  observers.  Each 
contains  a  sensum  which  is  an  appearance  of  the  penny. 
We  say  that  the  appearances  in  the  successive  fields  of 
each  observer,  and  the  appearances  in  the  contemporary 
fields  of  the  various  observers,  are  in  a  certain  sense  all 
"in  the  same  place,"  and  we  say  that  this  is  the 
"place  where  the  penny  is."  It  is  evident  that  facts 
such  as  I  have  just  been  describing  are  the  sensible 
basis  of  such  statements  as  that  I  "  go  on  seeing  the 
same  penny,"  and  that  other  people  and  myself  "  see  the 
same  penny  together."  If  there  were  no  such  correla- 
tions between  the  successive  fields  of  myself  and  between 
the  contemporary  fields  of  several  observers,  there  would 
be  no  ground  for  making  assertions  of  this  kind. 

Now  it  is  quite  clear  that  when  I  say  that  a  number 
of  sensa  from  different  fields  are  in  the  same  place,  I 
cannot  be  talking  of  "sensible  place,"  as  described 
above,  for  that  concept  refers  essentially  to  the  relation 
between  a  sensum  and  its  own  field.  We  must,  there- 
fore, try  to  find  the  exact  cash-value,  in  terms  of  sensible 
experience,  of  the  statements  {a)  that  the  various  visual 
sensa  are  in  the  same  place  ;  and  {b)  that  this  is  the  place 
where  the  physical  penny  is.  By  considering  abnormal 
cases,  like  mirror  images,  we  shall  see  that  sometimes 
the  first  is  true  when  the  second  is  false.  But  we  will 
begin  with  more  ordinary  cases. 

Very  often  the  successive  visual  fields  of  an  observer 
are  largely  similar.     In  particular,  there  may  be  a  series  of 

sensa  s1 sn  in  his  successive  fields/^ fm 

which  are  very  much  alike.  Let  us  take  the  case  of  a 
man  who  would  be  said  to  be  looking  directly  at  some  rest- 
ing luminous  object  through  a  homogeneous  medium. 
What  sort  of  visual  sensa  will  he  sense?  To  start  with, 
a  certain  sensum  s0  in  the  field  f0  may  attract  his  atten- 


306  SCIENTIFIC  THOUGHT 

tion.  This  may  be  somewhere  to  the  side  of  the  field. 
Suppose  he  turns  his  head  so  that,  as  we  say,  he  is  now 
looking  at  the  object  of  which  this  sensum  is  an  appear- 
ance. What  happens  is  that  he  turns  his  head  until  he 
is  aware  of  a  field/1?  in  the  middle  of  which  is  a  sensum 
sv  which  in  colour,  shape,  etc.,  very  much  resembles 
the  sensum  s0,  which  originally  attracted  his  attention. 
This  will  have  a  certain  sensible  depth.  Suppose  that 
he  now  begins  to  walk,  "  following  his  nose."  He  will 
sense  a  series  of  visual  fields,  of  which  the  following 
propositions  will  generally  be  true,  (i)  In  any  one  of 
these  fr  there  will  be  a  sensum  sr  in  the  middle,  closely 
resembling  s1  in  shape  and  colour,     (ii)  The    sensible 

depths  of  the  successive  sensa  ^ sn  will  steadily 

diminish,  whilst  their  brightness,  distinctness,  and  size 
will  increase,  (iii)  This  increase  in  distinctness  and  size 
will  go  on  up  to  a  maximum,  say  in  the  sensum  sn  of 
the  field  fn.  (iv)  If  he  now  goes  further,  various  new 
and  startling  things  will  begin  to  happen.  He  will 
often  find  that,  if  he  stretches  out  his  hand  in  front  of 
him,  he  will  sense  tactual  sensa,  correlated  in  shape 
with  the  visual  sensum.  He  may  also  burn  his  fingers 
badly.  He  will  generally  find  that  his  path  is  blocked. 
(v)  If  he  manages  to  get  past  the  obstacle  he  will  find 
that  his  field  fa+x  contains  no  sensum  sn+v  like  those  of 

the  series  sx sn.     (vi)  Very  often  he  will  be  able 

to  sense  a  field  _/"',l+1,  which  does  contain  a  sensum  s'n+1  of 
the  right  kind,  provided  that  he  turns  right  round.  The 
essence  of  the  process,  then,  is  a  succession  of  visual 
fields,  each  containing  at  its  centre  one  of  a  series  of 
qualitatively  similar  sensa  of  steadily  diminishing  depth 
and  increasing  brightness  and  clearness,  followed  by  a 
great  discontinuity  and  the  beginning  of  new,  though 
often  correlated,  sensations. 

Next,  let  us  suppose  that  on  another  occasion  the 
man  does  not  try  to  turn  his  head  so  as  to  sense  a  visual 
field  with  a  sensum  like  s0  in  the  middle  of  it.  Let  him, 
instead,  walk  in  some  other  direction,  and  let  him  stop 


POSITIONS   AND   SHAPES   OF   SENSA       307 

at  some  point  in  this  course.  Call  his  visual  field  at 
that  time  <£„.  4>n  may  or  may  not  contain  a  sensum  like 
s0.  If  it  does,  the  sensum  will  certainly  not  be  in  the 
middle  of  the  field,  and  will  probably  be  a  very  distorted 
projection  of  s0.  But,  on  either  alternative,  he  will 
generally  be  able,  by  suitably  turning  his  head,  to  sense 
a  field  f'v  in  the  middle  of  which  there  is  a  sensum  s'v 
which  is  a  good  deal  like  s0,  though  not  as  a  rule  so 

much  like  it  as  the  sensa  of  the  series  j^ sn  are 

like  each  other.  (As  we  say,  he  is  seeing  a  different 
side  of  the  object.)     If  he  now  follows  his  nose,  he  will 

in  general  sense  a  series  of  visual  fields  f\ f'„, 

in  the  middle  of  each  of  which  is  a  sensum  of  a  series 

s\ /„.     This   series  will    have   the   same   sort 

of  internal    relations   as   the   series  sx s„,  and 

will  end  up  in  the  same  catastrophic  way.  Now  our 
solitary  observer  will  often  find  that,  wherever  he 
starts,  he  can,  by  suitable  head-turning,  sense  such 
a  series  of  sensa.  He  thus  comes  to  recognise  a  central 
region  of  discontinuity,  to  which  he  can  walk  from  any 
position,  and  to  which  he  passes  through  series  of 
similar  visual  sensa  of  decreasing  depth  and  increasing 
brightness. 

Now  he  will  find  this  notion  of  a  central  volume  rein- 
forced by  some  of  his  other  senses.  The  two  other 
senses  that  act  at  a  distance  are  hearing  and  the  feeling 
of  radiant  heat.  They  have  interesting  differences  from 
each  other  and  from  sight,  which  will  be  worth  mention- 
ing. Let  us  begin  with  sound.  There  is  an  auditory 
continuum  from  which  particular  noises  stand  out,  as 
particular  coloured  patches  stand  out  from  the  sight 
continuum.  But,  whilst  patches  of  colour  have  definite 
shapes  and  sizes,  noises  do  not.  It  is  extremely  hard 
to  state  the  vague  spatial  characteristics  of  a  field  of 
sound.  Differences  of  direction  in  it  can  certainly  be 
sensed,  but  each  sound  seems  to  fill  the  whole  sound- 
field,  though  one  is  more  intensely  present  in  one  part 
of  it  and  another  in   another   part.     Coloured  patches 


3o8  SCIENTIFIC   THOUGHT 

in  the  same  visual  field  do  not  interpenetrate.  Two 
different  colours  cannot  be  sensibly  present  in  the  same 
place  in  the  same  visual  field.  A  colour  is  either 
sensibly  present  in  a  place  or  it  is  not.  There  is  no 
question  of  degree.  But  each  sound  seems  to  be  present 
everywhere  in  the  auditory  field,  though  it  is  "more" 
present  in  some  parts  than  in  others.  This  difference 
between  the  sensible  presence  of  sounds  and  of  colours 
leads  to  a  difference  in  the  way  in  which  common-sense 
supposes  them  to  be  present  in  physical  Space. 
Common-sense  says  that  the  colours  that  it  sees  are 
spread  out  over  the  surfaces  which  it  can  touch.  It 
refuses  to  say  that  they  are  present  in  the  medium 
between  this  and  the  observer's  body.  But  common- 
sense  does  not  hold  that  the  noise  of  a  bell  is  spread  out 
over  the  surface  of  the  bell,  or  even  that  it  is  confined 
to  the  volume  of  the  bell.  I  think  it  would  prefer  to 
say  that  the  noise  is  present  throughout  the  whole 
surrounding  air,  and  that  there  is  merely  "  more  of  it 
per  unit  volume  "  as  we  approach  the  bell. 

Apart  from  this  very  important  difference,  to  which 
we  shall  have  to  return,  there  are  striking  likenesses 
between  sight  and  hearing.  If  we  sense  a  sound  s0  {e.g. 
the  auditory  appearance  of  a  tolling  bell)  we  can  turn 
our  heads  in  such  a  way  that  a  similar  sensum  s1 
"  occupies  the  middle  of  the  auditory  field."  If  we  then 
follow  our  noses  we  shall,  as  a  rule,  sense  a  succession 

of  auditory  fields  fx fn,  each  of  which  contains 

at  its  centre  one  member  of  a  series  of  auditory  sensa 
st s„.  These  are  qualitatively  alike  and  of  in- 
creasing loudness,  though  I  do  not  think  we  can  say 
that  there  is  anything  corresponding  to  the  continual 
decrease  in  sensible  depth  which  we  should  find  in  a 
series  of  visual  sensa.  After  you  have  reached  a  certain 
stage  in  this  series  you  will  generally  find  that,  on 
stretching  out  your  hands  in  front  of  you,  you  get 
tactual  sensa,  and  that,  as  you  do  so,  the  sound  ceases 
or    is    modified.       Exactly    parallel    results    to    those 


POSITIONS   AND   SHAPES   OF   SENSA       309 

described  in  the  case  of  sight  are  found,  when  we 
approach  from  different  starting-points,  or  pass  the 
obstacle  in  which  such  series  generally  end.  Thus 
auditory  sensa  equally  lead  us  to  the  notion  of  "centres." 
Now  in  very  many  cases,  whether  you  move  under  the 
guidance  of  your  visual  sensa  or  under  that  of  your 
auditory  sensa,  you  will  end  up  with  similar  tactual 
sensations  after  a  similar  series  of  kinesthetic  sensations. 
This  happens,  e.g.  if  we  first  look  at  a  sounding  bell 
with  our  ears  stopped,  and  then  unstop  our  ears  and 
shut  our  eyes.  Thus  we  come  to  think  of  centres  of 
discontinuity  which  can  be  approached  from  all  sides, 
and  which  are  not  merely  centres  for  colour  or  for 
sound,  but  are  centres  for  both. 

If  we  now  ask  ourselves  why  colours  are  held  to  be 
on  the  bounding  surfaces  of  such  central  volumes,  and 
not  anywhere  else,  whilst  sounds  are  held  to  be  both 
in  and  all  round  the  sounding  centre,  the  answer  is 
plain.  Visual  sensa  have  sensible  depth  ;  this  steadily 
diminishes  in  the  successive  sensa  that  we  sense  as  we 
approach  a  centre,  but  never  vanishes  altogether  till  we 
are  too  near  the  centre  to  sense  any  sensum  of  the  series 
at  all.  On  the  other  hand,  noises  have  no  fixed 
boundaries  ;  they  do  not  exclude  each  other  from  the 
same  sensible  place  ;  and  they  do  not,  I  think,  have 
sensible  "depth."  We  have  thus  no  ground  for  saying 
that  we  approach  the  sound  when  we  approach  the  sound- 
ing centre.  A  part  of  the  sound  is  held  to  be  wherever 
we  are  when  we  hear  it ;  it  merely  is  present  in  greater 
density  at  places  nearer  the  sounding  centre. 

Let  us  next  say  a  word  or  two  about  our  sensation 
of  radiant  heat.  We  have  here  series  of  sensa  of  the 
same  kind  as  we  have  with  sound.  They  lead  us  again 
to  the  notion  of  centres  of  discontinuity,  and  in  general 
to  centres  which  are  common  to  radiant  heat,  sound, 
and  sight.  But  there  is  one  interesting  and  important 
peculiarity  in  the  case  of  heat.  If  we  start  at  a  distance 
from    a   centre    we    feel    a    heat    sensum  ;    and,    as   we 


310  SCIENTIFIC   THOUGHT 

approach,  our  successive  heat  sensa  are  more  and  more 
intense,  in  the  usual  way.  Now,  as  usual,  when  we 
get  to  a  certain  point  in  the  series  we  can  sense  tactual 
sensa,  if  we  stretch  out  our  hands  in  front  of  us.  These 
sensa  will  usually  be  intensely  and  painfully  hot.  The 
interesting  point  is  that,  in  this  case,  heat  is  felt  both  in 
the  surrounding  space  and  on  the  surface  of  the  central 
volume.  There  is  no  sensible  depth  in  the  field  of  heat 
sensa,  so  that,  as  with  sound,  we  do  not  localise  the 
successive  sensa  on  the  central  volume.  On  the  other 
hand,  when  we  do  feel  the  central  volume,  the  tactual 
sensa  are  themselves  hot.  So  the  heat  is  regarded  as 
both  filling  the  surrounding  space  and  residing  in  or  on 
the  central  volume.  Now  common-sense  regards  what 
can  be  felt  as  the  physical  object  par  excellence,  and  the 
place  to  which  one  has  to  move  in  order  to  sense  the 
tactual  sensa  as  the  place  of  the  object.  Owing  to  the 
fact  of  visual  depth,  and  its  gradual  decrease  as  such 
central  volumes  are  approached,  common-sense  regards 
all  the  successive  visual  sensa  as  localised  on  this 
volume.  It  therefore  says  that  the  central  volume  is 
coloured,  not  that  it  causes  colour.  In  the  case  of  the  bell 
it  does  not  say  that  this  is  endowed  with  sound,  but  that 
it  is  the  cause  of  the  surrounding  space  being  filled  with 
sound.  In  the  case  of  heat  it  thinks  of  the  central 
volume  as  both  being  hot  and  causing  the  surrounding 
space  to  be  filled  with  heat.  The  discrete  side  of  the 
common-sense  view  of  the  physical  world  is  based  on 
the  peculiarities  of  the  visual  field,  and  on  the  fact  that 
long  intervals  of  free  movement  often  come  between 
tactual  sensations.  The  continuous  side  of  the  common- 
sense  view  of  the  physical  world  is  based  on  the 
peculiarities  of  the  fields  of  radiant  heat  and  sound. 
Heat  sensations  in  some  way  form  a  connecting  link 
between  the  two  aspects  of  nature,  since  they  are  felt 
both  on  and  between  the  centres  of  discontinuity. 

It  is  obvious  that  these  two  sides  of  the  common-sense 
view  correspond  to  real  facts  in  nature.     But  we  may 


POSITIONS   AND   SHAPES   OF   SENSA       311 

reasonably  suspect  that  the  separation  between  them 
has  been  made  too  sharp,  as  all  separations  that  are 
made  primarily  in  the  interests  of  practice  tend  to 
be.  As  a  matter  of  fact,  the  common-sense  view  has 
been  based  mainly  on  experiences  of  touch,  sight,  and 
movement.  Pervasive  media,  like  air  and  ether,  have 
only  been  recognised  in  historical  times.  Thus  the 
continuous  and  transmissive  side  of  nature  has  had  to 
be  fitted  into  a  prehistoric  metaphysic  of  the  external 
world,  made  up  mainly  to  deal  with  our  experiences  of 
visible  and  tangible  volumes  with  sharp  outlines. 
Atomic  theories  are  so  much  more  comfortable  to  most 
of  us  than  hydrodynamic  theories,  because  they  fit  in 
so  much  better  with  the  scheme  that  we  have  inherited 
from  the  practical  philosophers  of  the  Stone  Age.  We 
learn,  as  time  goes  on,  that  light  itself  travels  through 
a  medium  with  a  velocity,  that  colours  seen  depend  on 
events  in  central  volumes,  just  as  do  sounds  heard,  and 
that  these  colours  may  turn  up  in  places  where  no 
correlated  tactual  sensa  can  be  felt.  All  this  will  have 
to  be  dealt  with  later,  more  especially  when  we  come 
to  treat  of  date  and  duration.  But,  in  the  meanwhile, 
we  may  offer  the  suggestion  that  a  good  deal  of  our 
difficulty  with  the  philosophy  of  the  external  world  is 
due  to  the  fact  that  we  are  trying  to  fit  new  data  into  a 
scheme  based  on  experiences  which  did  not  include 
them,  and  which  ignored  or  minimised  the  sensible 
facts,  such  as  images,  shadows,  echoes,  etc.,  to  deal 
with  which  new  concepts  are  needed.  In  just  the  same 
way  we  insist  on  forcing  the  facts  of  modern  society  into 
the  ethical  and  political  framework  of  a  simpler  age, 
without  even  the  excuse  that  this  "works  well  in 
practice." 

So  far,  we  have  confined  ourselves  to  the  case  of  a 
solitary  observer,  immersed  in  a  homogeneous  medium, 
such  as  air,  and  dealing  with  resting  objects.  These 
are,  of  course,  very  common  and  practically  important 
conditions,  and  the  corresponding  experiences  are  there- 


312  SCIENTIFIC   THOUGHT 

fore  common,  and  have  left  their  traces  deeply  on  every- 
one. I  have  tried  to  show  that  such  an  observer  will 
soon  reach  the  notion  of  "centres  of  discontinuity," 
dotted  about  in  various  places  which  he  can  reach  by 
movement ;  and  that  his  successive  visual  sensa  fall 
into  series  which  we  will  localise  on  the  surfaces  of  these 
central  volumes.  Further,  we  have  seen  that  the  senses 
of  hearing  and  of  feeling  heat  will  reinforce  this  notion, 
and  will  lead  him  to  recognise  these  centres  as  common 
to  the  sensa  of  different  senses.  In  particular,  heat  and 
sound  will  combine  to  give  him  the  notion  of  centres 
surrounded  with  "physical  fields."  Sight,  for  reasons 
mentioned  above,  does  not  give  to  unsophisticated  people 
the  notion  of  a  physical  field  ;  and  when  the  advance  of 
science  makes  it  necessary  to  introduce  this,  consider- 
able difficulties  are  felt  in  reconciling  the  omnipresence 
and  the  finite  velocity  of  the  light  field  with  the  strict 
localisation  of  colours  on  central  volumes  remote  from 
the  observer.  We  may  say,  if  we  like,  that  colour 
belongs  physically  to  the  continuous  side  of  nature,  but 
that  it  has  so  far  belonged  epistemologically  to  the  discrete 
side  of  nature. 

We  can  now  pass  to  the  case  of  a  number  of  observers  ; 
and  thence  to  the  more  complex  cases  of  non-homo- 
geneous media,  which  considerably  "stain  the  white 
radiance "  of  our  original  view  about  sight  and  the 
localisation  of  its  objects.  Even  with  the  solitary 
observer  in  the  homogeneous  medium  we  have  passed 
to  a  new  meaning  of  "place"  for  visual  sensa.  The 
first  and  most  primitive  meaning  was  the  place  of  a  single 
visual  sensum  in  its  own  visual  field.  We  have  passed 
beyond  this  to  a  group  of  visual  sensa,  each  selected 
out  of  different  sensible  fields  of  the  same  observer. 
The  members  of  such  a  group  are  said  to  be  in  the 
same  place,  through  their  correlation  with  each  other 
and  with  the  movements  of  the  observer.  The  "place" 
referred  to  here  is  clearly  not  a  place  in  any  visual  field, 
but  is  a  place  in  the  continuum  of  possible  positions  of 


POSITIONS   AND   SHAPES   OF   SENSA       313 

the  observer's  body.  And  the  presence  of  a  visual 
sensum  at  such  a  place  is  not  an  ultimate  unanalysable 
relation,  like  its  sensible  presence  at  a  place  in  its  own 
visual  field.  On  the  contrary,  we  have  just  been 
analysing  the  meaning  of  the  statement  that  a  visual 
sensum  is  present  at  a  certain  place  in  the  movement 
continuum,  and  have  found  that  it  means  that  the 
sensum  in  question  is  one  of  a  set  of  sensa  belonging 
to  successive  visual  fields  and  connected  with  each 
other  and  with  the  observer's  movements  in  the  ways 
indicated  above. 

When  a  set  of  visual  sensa  from  successive  fields  of  a 
single  observer  have  the  sort  of  relations  that  we  have 
been  describing,  we  will  say  that  they  are  optically 
compresent  with  respect  to  that  observer.  Each  member 
of  the  set  may  be  said  to  be  optically  present  at  the 
place  in  the  continuum  of  possible  positions  of  the 
observer's  body  which  he  reaches  when  the  character 
of  the  set  begins  to  change  abruptly.  Looking  at  the 
matter  from  the  point  of  view  of  this  place  in  the  move- 
ment-continuum, we  may  say  that  it  is  optically  occupied 
by  sensa  of  such  and  such  a  kind  from  such  and  such 
a  direction.  When  we  have  a  number  of  such  sets, 
which  all  converge  on  a  central  volume  wherever  the 
observer  may  start,  we  will  say  that  this  place  is 
"  optically  fillecV  with  sensa  of  a  certain  kind.  We  shall 
see  later  that  a  place  may  be  optically  occupied  without 
being  optically  filled.  We  have  seen  that,  as  a  rule, 
when  a  place  in  the  movement-continuum  is  optically 
filled,  correlated  tactual  sensa  are  present  at  that  place. 
(We  have  not  as  yet  considered  what  is  meant  by 
saying  that  tactual  sensa  are  present  at  a  place  in  the 
movement-continuum,  but  we  will  for  the  moment  take 
this  notion  for  granted.  We  have  also  not  as  yet  ade- 
quately discussed  the  notion  of  place  in  the  movement- 
continuum.     To  these  points  we  shall  return  later.) 

Now,    under   normal   conditions,    we   can    not   only 
find  groups  of  optically  compresent  sensa  in   the  sue- 


314  SCIENTIFIC   THOUGHT 

cessive  visual  fields  of  a  single  observer.     We  can  also 
find  something  of  the  same  kind  in  the  fields  of  different 
observers.      Let   us  consider  what   is   meant   by   saying 
that  the  sensa  sA  and  s,.,  belonging  to  visual  fields /ii  and 
fn  of  the  observers  A  and  B  respectively,  are  in  the  same 
place.     We  will  suppose  that  A  and  B  have  turned  their 
heads  in  such  directions  that  st  is  in  the  middle  of/,  and 
sB  in  the  middle  o(fn.      If  they  change  places  and  repeat 
the  process,   A's  new  sensum  will,  as  a  rule,   resemble 
B's  old   one  in   shape,  and   conversely.     Suppose  that, 
when  they  have  both  turned  their  heads  so  as  to  sense 
fields   with    these   correlated    sensa    at    their   respective 
centres,  they  start  to  walk,  following  their  noses.      Let 
A  do  this  till   he  senses  the  sensum   .?,",   which   is  the 
most  distinct  of  the  series.      Let  him  then  stop,  and  let 
B  now  start  to  follow  his  nose.     B's  body  will,  in  general, 
get  nearer  and  nearer  to  A's,  and  by  the  time  that  B 
senses  his  most  distinct  sensum  s ;;,  they  will  be  nearly 
in    contact.      If  they    now    follow    up   their    respective 
courses  they  will  certainly  run  into  each  other.     If  they 
both  stretch  out  their  hands  they  will,  in  general,  both 
sense  tactual  sensa  correlated  in  shape  with  their  visual 
sensa.     Thus  the    notion    of  a  common    centre    in    the 
movement-continuum,    at    which    a    number    of    visual 
sensa  are  optically  compresent,   is  extended  to  include 
series  of  optically  compresent  sensa  belonging   to   the 
fields  of  different   observers  as   well   as  to  those   of  a 
single  observer. 

Now  it  will  be  noticed  that  the  place  which  a  group 
of  optically  compresent  sensa  are  said  to  occupy  is 
defined  by  bodily  movement.  I  have  called  the  con- 
tinuum of  possible  positions  of  an  observer's  body  "the 
movement-continuum."  I  think  that  "place,"  in  the 
physical  sense,  refers  primarily  to  places  in  this  con- 
tinuum. Before  we  can  deal  with  the  more  complicated 
cases  of  visual  sensa  sensed  by  an  observer  who  is  not 
surrounded  by  a  homogeneous  medium,  we  must  get 
clearer   about   the    notion    of  place    in    the    movement- 


POSITIONS   AND   SHAPES   OF   SENSA       315 

continuum.  The  experiences  of  turning  one's  head  so 
much  and  then  walking  so  far  in  a  straight  line  are  not 
in  themselves  spatial  experiences.  They  are  simply 
series  of  kinesthetic  and  muscular  sensations,  different 
stages  of  which  fall  into  different  specious  presents. 
They  last  for  sensibly  different  times,  and  tire  us  to 
sensibly  different  degrees.  How  do  they  come  to  lead 
to  the  notion  of  a  continuum  of  physical  places,  which 
are  common  property  to  all  the  observers  and  are  co- 
existent? We  cannot  fully  deal  with  this  question  till 
we  have  dealt  with  the  dates  and  durations  of  sensa 
and  of  physical  objects  ;  but  we  can  at  least  say  this 
much :  These  series  of  successive  kinesthetic  sensa- 
tions would  not  lead  to  the  notion  of  a  continuum  of 
contemporary  places  if  it  were  not  for  their  correlation 
with  experiences  of  sight.  All  the  fundamental  con- 
cepts needed  for  dealing  with  Space  have  their  origin, 
and  their  only  literal  exemplification,  in  the  visual  field. 
Space  is  thought  of  as  a  whole  of  contemporary  parts, 
spread  out  at  various  distances  and  in  various  directions. 
A  whole  of  this  kind  is  sensed,  if  I  am  right,  at  each 
moment  by  sight,  and  in  no  other  way.  Turnings  of 
the  head  are  interpreted  in  terms  of  direction  because 
(a)  different  sensa  do  have  different  visible  directions 
in  the  same  visual  field  ;  and  (b)  because  with  every 
turn  of  the  head  is  correlated  a  change  in  the  sensible 
position  of  some  sensum  within  the  field  of  view.  Or, 
to  put  it  more  accurately,  when  we  turn  our  heads  a 
field  y^,  with  a  sensum  sx  at  a  certain  sensible  place  in  it, 
can  be  replaced  by  a  field  f2,  with  a  similar  sensum  s2 
in  a  different  place  in  it,  e.g.  in  the  middle.  Again, 
a  series  of  kinesthetic  sensations  is  interpreted  as  the 
traversing  of  a  physical  line  of  a  certain  length  by  the 
observer,    because    the    sensible   depths    of  the   similar 

sensa   sx sn    in    the    middle    of   the    successive 

fields  f\ fn   continually  diminish  as  the  series 

lasts    longer.       Sight    and    movement    are   thus   under 
reciprocal  obligations.     Were  it  not  for  sight,  with  its 


J 


16  SCIENTIFIC   THOUGHT 


extended  fields  of  contemporary  parts  with  different 
sensible  depths  and  in  different  sensible  directions,  we 
should  lack  the  very  concepts  needed  for  interpreting 
the  movement-continuum  spatially.  On  the  other  hand, 
were  it  not  for  the  existence  of  groups  of  visual  sensa, 
correlated  with  each  other  and  with  movements,  in  the 
way  described,  we  should  never  have  reached  the  notion 
of  the  optical  compresence  in  the  same  place  of  visual 
sensa  from  different  fields. 

But,  although  the  facts  about  visual  sensa  which 
lead  to  the  recognition  of  "centres"  in  which  groups 
of  visual  sensa  are  optically  compresent,  are  necessary 
in  order  that  the  movement-continuum  may  be  inter- 
preted spatially,  we  must  not  suppose  that  all  places 
in  the  movement-continuum  are  optically  full  or  even 
optically  occupied  at  all.  The  vast  majority  of  them 
are  not.  Moreover,  some  which  are  optically  occupied 
from  several  directions  are  yet  not  centres  at  which 
correlated  tactual  sensa  are  present.  Let  me  illustrate 
the  first  point.  If  I  direct  my  movements  by  a  certain 
series  of  optically  compresent  sensa  in  the  way  described, 
but  stop  before  I  reach  the  end  of  the  series,  I  have 
reached  a  place  in  the  movement-continuum.  But  I 
have  not  arrived  at  the  place  in  which  the  sensa  of 
this  series  are  optically  compresent,  and  when  I  stretch 
out  my  hands  I  may  feel  nothing  at  all.  And  the  place 
in  the  movement-continuum  at  which  I  have  stopped 
may  quite  well  not  be  occupied  by  any  visual  sensa 
of  any  series.  What  do  we  say  under  such  circum- 
stances? We  say  that  we  have  indeed  reached  a 
physical  place,  for  we  have  walked  so  far,  and  in  such 
and  such  a  direction.  But  we  add  that  this  place  is 
neither  optically  nor  tactually  occupied.  If  no  places 
had  been  optically  or  tactually  occupied,  we  should 
almost  certainly  not  have  interpreted  the  movement- 
continuum  spatially,  or  have  arrived  at  anything  like 
our  present  conception  of  the  external  world.  As  it  is, 
a  large   number,  though   a  minority,  of  places   in   the 


POSITIONS   AND   SHAPES   OF   SENSA       317 

movement-continuum  are  optically  occupied  ;  many  are 
optically  filled  ;  and  most  of  these  are  also  centres  for 
sound  and  heat,  and  are  also  tactually  occupied.  This 
fact  gives  us  the  contrast  between  the  filled  and  the 
empty  parts  of  the  movement-continuum,  and  helps  us 
to  conceive  it  as  a  Space  dotted  about  with  physical 
objects  in  definite  places  and  with  definite  boundaries. 
We  are  now  in  a  position  to  deal  with  the  less 
usual  forms  of  optical  presence.  These  arise  when,  as 
the  physicist  would  say,  we  are  surrounded  by  a  non- 
homogeneous  medium.  Our  present  task,  however,  is 
to  describe  as  accurately  as  possible  the  actual  facts 
about  our  visual  sensa,  and  not  to  offer  causal  explana- 
tions of  them  in  terms  of  their  correlations  with  physical 
events.  To  begin  with  a  very  simple  case,  let  us 
suppose  that  I  am  looking  at  the  image  of  a  luminous 
point  in  a  plane  mirror.  I  can,  as  before,  turn  my 
head  in  such  a  way  that  I  sense  a  visual  field  fx  with 
a  sensum  sx  in  the  middle  of  it,  similar  to  the  sensum 
s0  that  originally  attracted  my  attention.  Having  done 
this,  I  can,  as  before,  follow  my  nose.  Up  to  a  point 
my  experiences  will  be  exactly  like  those  which  we 
have  already  described.     There  will  be  the  same  kind 

of  series  of  sensa  sx sn,  qualitatively  much  alike, 

each  in  the  middle  of  its  field,  of  steadily  decreasing 
visual  depth,  and  so  on.  But  at  a  certain  stage  in  the 
series  I  shall  suddenly  sense  certain  tactual  sensa,  quite 
uncorrelated  with  the  visual  sensa  of  the  series  {i.e.  I 
shall  "bump  into  the  mirror").  This  is  illustrated  by 
the  figure  below  : 


If  I,  or  anyone  else,  were  to  start  from  B  instead 
of    from    A,    the    same    sort   of    experiences   would    be 


318  SCIENTIFIC   THOUGHT 

enjoyed.  Tliis,  however,  is  by  no  means  all.  A  and 
B  might  both  have  experiences  of  this  kind  if  they 
were  both  looking  directly  at  some  source  of  light 
through  a  thin  sheet  of  transparent  glass.  The  differ- 
ence is  the  following:  In  the  former  case,  if  A  or  B 
break  through  or  get  round  the  mirror  and  try  to 
continue  their  course,  there  will  be  nothing  in  their 
visual  fields  corresponding  to  the  visual  sensa  that  led 
them  up  to  the  mirror.  (That  is  to  say,  their  visual 
experiences,  as  they  move  along  the  dotted  part  of  the 
line  AI  or  BI,  are  quite  different  from  those  which  they 
had  when  they  traversed  the  undotted  parts  of  these 
lines.)  If  there  were  merely  a  thin  sheet  of  transparent 
glass  at  M,  and  A  and  B  were  viewing  through  it  a 
source  of  light  at  I,  the  series  of  visual  sensa  would 
go  on  steadily  after  they  had  broken  through  or  got 
round  the  obstacle. 

The  next  point  to  notice  is  that  the  courses  of  A, 
B,  C,  etc.,  who  start  from  the  same  side  of  the  mirror, 
really  do  converge  on  a  common  place  in  the  movement- 
continuum.  If  they  pursued  them  through  the  mirror 
or  the  glass  they  really  would  meet  at  I.  The  difference 
in  the  two  cases  would  be  this  :  If  they  were  looking 
at  something  directly  through  a  thin  piece  of  glass,  the 
series  of  visual  sensa  of  each  of  them  would  end  at  about 
the  time  when  their  bodies  came  in  contact  with  each 
other,  and  correlated  tactual  sensa  could  be  sensed  by 
each  if  he  stretched  his  hand  forward.  If  they  are  look- 
ing at  a  mirror-image  the  series  of  visual  sensa  which 
leads  them  up  to  the  mirror  not  only  ceases  abruptly  as 
soon  as  they  get  through  or  past  it ;  they  also  find 
that,  when  they  meet,  they  either  sense  no  tactual  sensa 
at  all,  or,  if  they  sense  any,  these  are  quite  uncorrelated 
with  the  visual  sensa  that  originally  guided  them  on 
their  respective  ways.  If  they  want  to  sense  correlated 
tactual  sensa,  they  will  have  to  go  to  quite  a  different 
place  in  the  movement-continuum,  and  one  that  is  not 
on  their  course  of  movement  at  all,  viz.,  the  place  O 


POSITIONS   AND   SHAPES   OF   SENSA       319 

in  the  figure.  Now  this  place  O,  which  is  on  A's  and 
B's  side  of  the  mirror,  is  also  a  place  in  which  visual 
sensa,  much  like  those  that  guided  A  and  B  up  to  the 
mirror,  are  optically  compresent.  But,  as  we  have 
remarked,  it  is  in  quite  a  different  direction  from  those 
followed  by  A  and  B  ;  and  people  who  walked  up  to 
it  would  sense  tactual  sensa  correlated  with  the  visual 
sensa  that  led  them  to  it,  and  therefore  also  correlated 
with  the  visual  sensa  that  led  A  and  B  away  from  it 
towards  I. 

There    is    one    further   point   to    notice   about    I    as 
compared    with    O.       Not    only   are    there    no    tactual 
sensa  at  I  correlated  with  the  visual   sensa  that  guide 
observers    from  the  other  side  of  the  mirror   on    their 
paths     towards    I  ;     there    is    also     a     purely    optical 
peculiarity   about    I.     The    place    O    is   optically  filled 
with  visual  sensa   of  the    kind  in    question.     That    is, 
any   observer,    no    matter    in    what   direction    he    may 
approach  O,  will  sooner  or  later  begin  to  sense  a  series 
of  visual  sensa  of  this  kind,  which  are  optically  com- 
present at  O.     This  is  far  from   being  true  of  I.      I  is 
not  a  centre  which  is  occupied  by  visual  sensa  of  the 
kind  in  question  for  all  observers,  or  even  for  the  latter 
parts  of  the  course  of  any  observer.     People  at  the  back 
of  the  mirror,  who  look  directly  at  the  place  I,   either 
see  nothing  there  or  else  they  sense  sensa  which  have  no 
resemblance  to  those  which  A  and  B  sense  on  the  earlier 
part  of  their  courses.     Again,  A  and  B,  during  the  latter 
part  of  their  courses,  sense  no  such  sensa  as  they  did 
when  they  were  on  the  reflecting  side  of  the  mirror.    We 
must  say,  then,  that  I  is  occupied  by  the  sort  of  sensa  that 
constitute    the    mirror-image,  from    certain    places,   but 
by  no    means    from    all  ;    whilst    it    may  be  filled  with 
visual  sensa  of  quite  a  different  kind.     On    the   other 
hand,  O  is  not  merely  occupied,  but  is  filled,  with  such 
visual  sensa  as  constitute  the  mirror-image.     (For  the 
moment  I  neglect  the  inversion  of  the  image,  which  of 
course    makes   a   characteristic   difference   between    the 


320  SCIENTIFIC   THOUGHT 

sensa  that  till  O  and  the  otherwise  similar  sensa  that 
optically  occupy  1  from  places  on  the  reflecting  side  of 
the  mirror.) 

We  may  sum  up  the  peculiarities  of  mirror-images 
with  respect  to  place,  as  follows:  (i)  The  usual  correla- 
tion between  visual  and  tactual  sensa  breaks  down. 
Usually,  when  visual  sensa  are  optically  com  present 
at  a  certain  place,  correlated  tactual  sensa  can  be  sensed 
by  an  observer  who  walks  up  to  that  place.  If,  however, 
you  want  to  sense  tactual  sensa  correlated  with  the 
visual  sensa  that  constitute  a  mirror-image,  you  must 
go  to  quite  a  different  place  from  that  at  which  these 
visual  sensa  are  optically  compresent.  This  is,  of  course, 
puzzling,  because  unusual  ;  but  there  is  no  theoretical 
difficulty  in  the  fact  that  two  sorts  of  sensa,  which  are 
generally  compresent,  should  sometimes  not  be  so. 
People  whom  we  meet  are  generally  compresent  with 
their  trousers,  but  this  rule  is  liable  to  break  down  in 
swimming-baths.  (ii)  The  optical  places  of  mirror- 
images  are  never  optically  filled  with  the  sensa  that 
constitute  the  image,  but  are  only  occupied  by  such 
sensa  from  certain  directions  and  from  the  remoter 
places  on  these  directions.  On  the  other  hand,  they 
may  be  at  the  same  time  optically  filled  with  visual 
sensa  that  are  not  in  the  least  like  the  mirror-image, 
but  are  correlated  with  tactual  sensa  which  can  be 
sensed  by  people  who  walk  to  these  places. 

We  can  now  ask :  What  is  it  precisely  that  the 
laws  of  geometrical  optics  tell  us  about  mirror-images? 
The  answer  is  simple.  They  tell  us  where  sources 
would  have  to  be  placed,  and  what  tangible  shapes 
they  would  need  to  have,  in  order  that  an  observer 
who  stands  in  a  given  position  shall  continue  to  sense 
the  same  visual  sensum  when  the  heterogeneous  medium, 
with  which  he  is  in  fact  surrounded,  is  replaced  by  air. 
If  we  like  to  use  the  convenient  language  of  the  general 
Theory  of  Relativity,  we  can  say  that  the  introduction 
of    suitable    sources    in    suitable    places    in    a    homo- 


POSITIONS   AND   SHAPES   OF   SENSA      321 

geneous  medium  will  always  "transform  away"  {i.e. 
be  equivalent  to)  the  effects  of  any  heterogeneous 
medium  for  any  one  visual  sensum  of  any  one  observer 
in  any  one  position.  In  favourable  cases  the  trans- 
formation may  apply  to  many  sensa  of  many  observers 
in  many  positions.  But  no  arrangement  of  sources  in 
a  homogeneous  medium  will  be  equivalent  to  the 
effects  of  a  heterogeneous  medium  for  all  observers 
in  all  positions.  For  instance,  if  we  remove  the  mirror 
M  and  put  a  luminous  point  of  the  right  colour  at  I, 
A's  and  B's  visual  sensa  will  be  unchanged  ;  but  very 
different  sensa  will  now  be  introduced  into  the  fields 
of  observers  at  the  back  of  the  mirror.  The  laws  of 
geometrical  optics  are  then  simply  the  rules  according 
to  which  we  can  calculate  the  tactual  shapes  and  the 
positions  of  such  hypothetical  sources  as  would  trans- 
form away  the  effects  of  a  heterogeneous  medium  for 
a  given  sensum  of  a  given  observer  in  a  given  place 
in  the  movement-continuum. 

(c)  The  Relation  of  Optical  Occupation. — I  think  that 
we  are  now  in  a  position  to  go  a  step  further  in  our 
analysis  of  the  optical  places  of  visual  sensa.  We 
notice  that  three  types  of  case  can  arise,  ranging  from 
the  completely  normal,  through  the  mildly  abnormal, 
to  the  wildly  abnormal,  (i)  There  is  the  case  of  seeing 
things  by  direct  vision  in  a  homogeneous  medium. 
Here  all  observers  in  all  directions  (provided  they  be 
not  too  far  off)  can  sense  very  similar  sensa,  and  can 
bring  them  into  the  middles  of  their  respective  fields 
of  view  ;  and  the  paths  of  all  these  observers  converge 
to  a  common  place  in  the  movement-continuum,  at  which 
all  the  sensa  of  all  these  series  are  optically  compresent. 
The  proviso  that  the  observers  are  not  to  be  too  far  off 
is  added  in  order  to  allow  for  the  possible  interposition 
of  opaque  obstacles  between  the  place  where  the  observer 
is  and  the  centre  of  optical  compresence.  If  a  luminous 
point  be  inside  a  room,  it  is  true  that  the  place  where  it 
is  said  to  be  is  optically  occupied  by  sensa  of  similar 


322  SCIENTIFIC   THOUGHT 

quality  from  all  directions;  it  is  not  true,  however,  that 
it  is  occupied  by  such  sensa  from  all  places  on  any  one 
of  these  directions.  It  is  not  so  occupied  from  places 
that  are  outside  the  room.  What  we  can  say  is  that 
there  is  some  finite  distance  r,  such  that  the  place  in 
question  is  optically  occupied  by  such  sensa  from  all 
places  within  a  sphere  of  radius  r  drawn  with  this  place 
as  centre.     The  figure  below  illustrates  this  restriction. 

The  dotted  parts  of  the  lines  are 
the  positions  from  which  P  is  not 
----*     optically  occupied  by  sensa  of  the 
sort  with  which  it  is  optically  filled, 
(ii)  In    the    case    of    seeing    a 
*  mirror-image    there    is    a    certain 

place  behind  the  mirror  which  (a)  is  occupied  by 
similar  visual  sensa  from  many,  but  not  from  all, 
directions  which  converge  on  the  point,  (b)  It  is  only 
occupied  by  visual  sensa  of  this  kind  from  certain  places 
on  any  one  of  these  directions,  and  no  series  of  such 
places  extends  up  to  the  place  where  the  image  is  said 
to  be.  On  the  contrary,  these  series  always  end  abruptly 
at  a  finite  distance  from  the  place,  (c)  The  place  of  the 
mirror-image  may,  though  it  need  not,  be  also  a  place 
of  complete  optical  compresence  from  all  directions. 
But,  if  so,  the  sensa  with  which  it  is  optically  filled 
will  be  quite  unlike  those  which  optically  occupy  it 
from  places  on  the  reflecting  side  of  the  mirror.  In 
the  figure  below,  M  is  a  mirror,  N  an  opaque  obstacle, 
and  I  the  place  of  a  mirror-image.  The  full  thick  part 
of  a  line  represents  the  places  on  it  from  which  I  is 
optically  occupied  by  the  sensa  which  constitute  the 
mirror-image.  The  full  thin  part  represents  the  places 
from  which  it  is  optically  occupied  by  sensa  of  the  sort 
with  which  it  is  optically  filled.  The  dotted  parts 
represent  places  from  which  it  is  occupied  by  neither 
kind  of  sensa. 

(iii)  Lastly,  with  distorted   mirrors  or  other  kinds  of 
more  heterogeneous  media,  any  observer  may  find  that 


POSITIONS   AND   SHAPES   OF   SENSA      323 

he  has  continually  to  turn  his  head  at  each  step,  if  he 
wants  to  sense  a  series  of  visual  fields  with  at  all  similar 
sensa  at  their  centres.     In  such  cases  the  observers  will 


also  generally  find   that  their  sensa  are   affected   with 
sensible  movement  as  they  turn  their  heads. 

We  thus  have  a  series  of  cases,    ranging  from   the 
complete  tameness  of  (i)  to  the  extreme  wildness  of  (iii). 
Now    it    seems   to   me   that  the  psychological   and   the 
logical  order  are  here  opposite  to  each  other.      Psycho- 
logically   our  concept  of  Space,   and    of  the  places  of 
things  in  it,  is  built  on  (i),  i.e.,  on  the  commonest  and 
most  practically  important  cases.      If  these  had  been  less 
common  and  less  practically  important,    it   is  doubtful 
whether   we   should    have    reached    anything   like   our 
present    view   of   the   external    world.       But,    logically 
considered,  it  is  the  wild  cases,  of  type  (iii),  that  are  of 
fundamental  importance.      It  seems  pretty  clear  that  the 
normal  cases  can  only  arise  when  certain  special  simpli- 
fying conditions  are  fulfilled,  viz.,  those  which  we  sum 
up  by  saying  that  the  medium  is  homogeneous.     These 
special    conditions    mask    the    real    complexity    of  the 
relations    involved  ;    whereas    the    wilder   cases   exhibit 
these   relations   in   their  most  general   form.     There  is 
some    hope   that,    if  we  treat  the  wild  cases  as  funda- 


324  SCIENTIFIC  THOUGHT 

mental,  we  may  be  able  to  deal  with  the  normal  ones 
as  specially  simplified  instances  of  a  more  general 
relation  ;  as,  e.g,y  a  circle  may  be  regarded  as  a  specially 
simplified  case  of  an  ellipse.  But  there  is  very  little 
hope  that,  if  we  take  the  relations  involved  in  the  normal 
cases  as  fundamental,  we  shall  be  able  to  interpret  the 
abnormal  cases  in  terms  of  them.  And,  as  Critical 
Philosophers,  it  is  our  business  to  try  to  deal  with  all 
the  facts,  and  not  to  hush  up  the  existence  of  abnormal 
sensa,  as  though  they  were  the  peccadillos  of  a  Cabinet 
Minister. 

We  can  now  say  something  about  the  logical 
characteristics  of  the  relation  of  optical  occupation,  (i) 
It  is  a  relation  between  a  visual  sensum  on  the  one 
hand  and  a  place  in  the  movement-continuum  on  the 
other.  (2)  It  is  a  many-one  relation.  This  means  that 
a  given  sensum  s  can  only  occupy  optically  one  place 
in  the  movement-continuum,  but  one  place  in  the 
movement -continuum  can  be  optically  occupied  at 
the  same  time  by  many  sensa.  (3)  I  think  we  must 
also  hold  that  the  relation  of  optical  occupation  is 
irreducibly  triadic.  This  means  that  any  complete 
statement,  which  asserts  this  relation  to  hold,  involves 
three  terms,  viz.,  the  sensum,  the  place  that  it  optically 
occupies,  and  a  third  term.  My  reason  for  saying  this 
is  the  following:  The  statement  that  the  place  p  is 
optically  occupied  by  the  sensum  s  seems  to  be  incom- 
plete ;  the  full  statement  would  seem  to  be  that  p  is 
optically  occupied  by  s  from  q,  where  q  is  the  place  in 
the  movement-continuum  occupied  by  the  observer's 
body.  We  see  this  more  clearly  if  we  state  exactly 
what  we  mean  when  we  say  that  s  optically  occupies  p. 
s  will  be  a  sensum  which  is  sensibly  present  in  a  certain 
observer's  visual  field  at  the  time.  This  observer  will, 
in  fact,  be  in  a  certain  place  q.  To  define  the  direction 
of  p,  the  place  optically  occupied  by  s,  we  have  to 
suppose  that  the  observer  turns  till  he  senses  a  visual 
field  with  a  sensum  s',  similar  to  s,  in  its  centre.     The 


POSITIONS   AND   SHAPES   OF   SENSA       325 

direction  of  p  is  then  the  direction  in  which  he  would 
start  to  walk  if  he  followed  his  nose.  The  distance  of  p 
is  determined  by  the  sensible  depth  of/  in  the  observer's 
visual  field.  It  is  the  distance  that  he  would  have  to 
walk  to  reach  a  source  if,  in  fact,  the  medium  were  homo- 
geneous and  s'  were  due  to  the  transmission  of  light 
directly  from  this  source  to  his  eye.  It  seems  therefore 
that  the  full  meaning  of  the  statement  that  s  is  optically 
present  atp  cannot  be  understood  without  a  reference  to 
the  place  q  occupied  by  the  observer  in  whose  visual  field 
s  is  sensibly  present.  If  so,  the  relation  of  optical  occupa- 
tion is  triadic,  and  the  minimum  complete  statement  is 
that  s  occupies/  from  q. 

Of  course,  in  a  great  many  cases,  if  the  observer 
were  to  walk  to  a  place  />,  thus  determined,  he  would 
not  find  any  centre  of  discontinuity  there  which  could 
be  taken  as  the  source  of  his  original  sensum  s.  And,  in 
many  cases,  he  would  not  find  that  a  series  of  sensa  like 
s  were  sensibly  present  in  the  middle  of  his  successive 
visual  fields  as  he  moved  in  the  line  from  q  to  /.  This, 
however,  does  not  prove  that  our  definition  of  optical 
occupation  is  wrong.  It  merely  shows  that  the  fact  that 
a  sensum  s  occupies/  optically  from  q  is  no  guarantee  that 
p  is  physically  occupied  by  anything  closely  connected 
with  s.  This  we  already  knew  from  our  experiences 
with  mirrors  and  other  types  of  non-homogeneous 
medium. 

We  must  not  be  frightened  of  triadic  relations,  for 
there  are  plenty  of  other  examples  of  them  in  daily  life. 
The  relation  of  giving  is  an  example,  since  it  essentially 
involves  a  giver,  a  gift,  and  a  recipient.  The  minimum 
intelligible  statement  which  asserts  the  relation  of  giving 
is  of  the  form  "  x  gives  y  to  z."  It  is  true  that  we  some- 
times use  apparently  simpler  phrases,  like  "  Smith  gives 
to  the  Additional  Curates'  Fund  "  ;  but  these  are  clearly 
elliptical,  and,  when  fully  stated,  appear  in  the  form 
"Smith  gives  something  to  the  Additional  Curates' 
Fund."     Of  course,  whenever  x,  y,  and   z  stand  in   a 


326  SCIENTIFIC   THOUGHT 

» 

triadic  relation,  this  involves  certain  dyadic  relations 
between  them  by  pairs;  but  the  assertion  of  the  triadic 
relation  is  not  analysable  into  the  conjoint  assertion  of 
these  dyadic  relations.  The  latter  are  derived  from  the 
former,  and  the  former  is  not  built  up  out  of  the  latter. 
Contrast  the  relation  of  "  uncle  "  with  that  of  "  giving." 
Both  involve  three  terms.  For  to  say  that  x  is  uncle  of 
.;  means  that  x  is  brother  of  some  third  person  j,  who  is 
a  parent  of  s.  This  does  not  make  the  avuncular 
relation  triadic  ;  for  it  is  completely  analysable  into  the 
conjoint  assertion  of  these  two  dyadic  relations,  and 
they  are  not  merely  derived  from  it. 

Now  we  are  very  liable  to  ignore  the  fact  that  a 
relation  is  polyadic  and  to  treat  it  as  dyadic.  This 
happens  if  two  of  the  terms  mainly  interest  us  and  the 
rest  are  uninteresting  or  generally  constant.  When 
this  condition  ceases  to  be  fulfilled  we  are  liable  to  find 
apparent  contradictions,  which  can  only  be  avoided  by 
recognising  the  polyadicity  of  the  relation.  When  we 
say  that  A  is  to  the  right  of  B,  we  often  ignore  the  fact 
that  we  are  really  asserting  a  triadic  relation  between 
A,  B,  and  our  own  hands.  Eventually  we  meet  some- 
one as  sane  as  ourselves,  who  insists  that  A  is  to  the 
left  of  B.  This  is  a  contradiction,  until  we  take  into 
account  the  neglected  third  term,  which  is  different  in 
the  two  cases,  and  see  that  both  parties  may  be  right 
when  their  full  meanings  are  made  explicit. 

If  we  accept  the  view  that  the  relation  of  optical 
occupation  between  visual  sensa  and  places  in  the  move- 
ment-continuum is  triadic,  there  is  no  difficulty  in  the 
fact  that  a  place  may  be  at  once  optically  filled  with 
sensa  of  a  certain  kind  and  optically  occupied  from 
many  places  with  sensa  of  quite  a  different  kind,  which 
have  no  connexion  with  the  physical  filling  of  this  place. 
P  is  optically  filled  with  sensa  of  the  kind  k  if  there  is  a 
closed  surface  in  the  movement-continuum  such  that  it 
contains  P,  and  such  that  P  is  optically  occupied  by 
sensa  of  the  kind  k  from  all  places  between  the  outside 


POSITIONS   AND   SHAPES   OF   SENSA      327 

of  P  and  the  inside  of  this  surface.  This  is  quite  com- 
patible with  the  fact  that  there  are  other  places  in  the 
movement-continuum  from  which  P  is  not  occupied  by 
sensa  at  all.  It  is  also  quite  compatible  with  P  being 
optically  occupied  from  many  other  places  with  sensa 
of  a  different  kind  k '.  This  is  what  happens  in  the  case 
of  mirror-images.  With  a  plane  mirror  the  situation  is 
as  follows  :  There  is  a  set  of  places  from  each  of  which 
a  sensum  of  the  kind  k'  is  optically  present  at  P. 
These  places  are  on  lines  of  approach  which  converge 
on  P.  But  (a)  all  the  lines  on  which  such  places  are 
situated  are  confined  within  a  certain  solid  angle  with  P 
as  vertex  ;  and  (/;)  even  for  lines  within  this  region  the 
series  of  places  from  which  sensa  of  the  kind  k'  are 
optically  present  at  P  does  not  reach  P,  but  stops  short 
at  a  finite  distance  from  it. 

The  question  might  now  perhaps  be  raised:  "  Is  it 
enough  to  suppose  that  the  relation  between  a  visual 
sensum  and  a  place  which  it  occupies  in  the  movement- 
continuum  is  triadic?"  Ought  we  not,  in  the  case  of 
the  mirror-image,  for  instance,  to  bring  in  the  positions 
of  the  source  and  the  mirror  as  well  as  that  of  the 
observer,  and  thus  make  the  relation  at  least  pentadic? 
This  is  a  plausible  question,  but  I  think  that  it  rests  on 
a  confusion.  Undoubtedly,  if  we  want  to  predict  in  what 
place  a  sensum  of  a  certain  kind  will  be  optically  present 
from  the  place  of  a  certain  observer  we  need  to  know 
the  positions  of  the  source  and  the  mirror.  But  these 
are  not  involved  in  the  meaning  of  the  statement  that 
such  and  such  a  sensum  is  optically  present  in  such  and 
such  a  place.  We  saw  that  a  reference  to  the  place 
of  the  observer  is  an  essential  part  of  the  meaning 
of  this  statement.  But  the  parts  played  by  the  source 
and  the  mirror  are  merely  causal  and  not  constitutive. 
This  is  clear  from  the  fact  that  we  have  been  able  to 
give  a  satisfactory  definition  of  optical  occupation  with- 
out mentioning  the  positions  of  the  source  or  the  mirror. 
The  way    in    which    these   do    become    relevant   is   the 


328  SCIENTIFIC   THOUGHT 

following  :  The  positions  of  the  source  and  of  the  mirror 
do  determine  causally,  according  to  the  physical  laws 
of  light,  the  sensible  place  of  the  sensum  s  in  o's  visual 
field.  And  the  place  p  in  the  movement-continuum, 
which  is  optically  occupied  by  s  from  where  the  observer 
is,  depends  (by  definition)  on  the  sensible  place  of  s  in  o's 
visual  field.  But  it  is  one  thing  to  say  that  the  positions 
of  the  source  and  the  mirror  are  factors  which  causally 
determine  the  nature  of  the  sensum  which  optically 
occupies  a  particular  place  /  from  another  place  q,  and 
quite  another  thing  to  say  that  the  positions  of  source 
and  mirror  have  to  be  stated  before  the  proposition  that 
s  optically  occupies/  from  q  can  be  understood.  If  the 
latter  were  true,  the  relation  between  a  sensum  and  its 
optical  place  would  be  at  least  pentadic,  for  the  minimum 
intelligible  statement  about  optical  occupation  would  be 
of  the  form  "  s  optically  occupies  /  from  q  with  respect 
to  the  medium  m  and  the  source  o-."  But  this  does  not 
seem  to  be  true,  and  therefore  I  see  no  reason  at  present 
to  hold  that  the  relation  of  optical  occupation  is  more 
than  triadic. 

(d)  Physical  Place. — Having  dealt  with  the  puzzling, 
but  most  illuminating,  case  of  abnormal  optical  occupa- 
tion, we  can  now  treat  the  places  of  physical  objects. 
Before  the  notion  of  physical  place  can  be  profitably 
discussed,  we  must  form  a  clearer  idea  of  what  we  mean 
by  a  physical  object.  For  a  physical  place  is  the  sort 
of  place  that  can  be  occupied  by  a  physical  object.  So 
far  we  have  simply  contrasted  physical  objects  with  the 
sensa  which  are  their  appearances.  But  it  may  well  be 
that  "  physical  object,"  in  this  sense,  is  a  somewhat  loose 
term,  and  covers  several  different  kinds  of  entity.  We 
must  even  be  prepared  for  the  possibility  that  what 
common-sense  calls  a  physical  object  may  be  really  a 
number  of  correlated  objects  of  fundamentally  different 
kinds. 

That  this  is  so  will  be  plain,  I  think,  if  we  compare 
the  following  four  entities  :  a  particular  visual  appear- 


POSITIONS   AND   SHAPES   OF   SENSA       329 

ance  of  a  certain  penny  ;  an  image  of  the  penny  in  a 
plane  mirror  ;  what  common-sense  understands  by  the 
penny;  and  the  atoms,  electrons,  etc.,  which  science 
asserts  to  be  the  ultimate  physical  constituents  of  the 
penny.  The  first,  no  one  would  think  of  calling  a 
physical  object.  The  second  would  not  indeed  be 
called  a  physical  object  ;  but  it  is  much  more  than  a 
mere  sensum.  It  can  be  "seen"  by  a  number  of 
different  observers  from  different  places  in  exactly  the 
same  sense  in  which  the  penny  itself  can  be  seen.  And 
it  has  a  certain  persistence  and  independence.  It  is,  in 
fact,  a  group  of  closely  correlated  visual  sensa,  and  a 
certain  place  in  the  movement-continuum  is  optically 
occupied  by  members  of  this  group  from  a  great  many 
places,  although  it  is  not  filled  by  them.  We  refuse  to 
call  it  a  physical  object,  because  of  the  lack  of  complete 
optical  filling,  and  because  of  the  absence  of  correlated 
tactual  sensa  when  we  come  to  the  place  which  is  opti- 
cally occupied  by  sensa  of  such  a  group.  I  will  call 
such  a  thing  as  a  mirror-image  a  Partial  Optical  Object: — 
optical,  because  it  consists  wholly  of  visual  sensa; 
partial,  because  it  does  not  optically  fill  the  place  which 
it  optically  occupies. 

Now  what  common-sense  understands  by  a  physical 
object,  such  as  a  penny,  is  something  more  than  this 
in  two  ways  at  least.  (1)  It  involves  a  Complete  Optical 
Object,  for  the  place  where  the  penny  is  said  to  be  is 
optically  filled  with  correlated  brown  elliptical  and  round 
sensa.  (2)  It  involves  something  more,  which  is  not 
optical  at  all.  The  place  in  the  movement-continuum 
which  is  marked  out  for  us  by  being  filled  with  the 
complete  optical  object  very  often  resists  our  efforts  to 
move  into  it.  It  is  often  a  centre  for  sound  and  radiant- 
heat  sensa.  And,  as  a  rule,  we  sense  tactual  sensa  of 
characteristic  shape  and  of  some  temperature  or  other 
when  we  come  to  this  place.  It  is  very  exceptional  for 
condition  (1)  to  be  fulfilled  without  condition  (2);  though 
I  suppose  we  may  say  that  condition  (2)  is  evanescent 

Y 


SCIENTIFIC    THOUGHT 

in  the  case  of  clouds  and  wisps  of  coloured  vapour. 
Lei  us  call  the  penny,  as  common-sense  understands 
it,  a  Perceptual  Object.  Now  the  important  thing  to 
notice  is  that  a  perceptual  object  is  really  not  one  single 
homogeneous  object,  present  in  a  place  in  the  movement- 
continuum  in  one  single  sense  of  "presence."  It  is 
a  number  of  interconnected  objects  of  different  types, 
and  the  different  kinds  of  object  included  in  it  are  present 
in  different  senses  in  the  place  where  the  perceptual 
object  is  said  to  be.  I  will  call  the  various  correlated 
objects  which  together  constitute  a  perceptual  object 
constituents  of  the  perceptual  object.  It  would  be  mis- 
leading to  call  them  parts  of  it,  because  this  would 
suggest  that  they  literally  fit  together  to  fill  up  the 
place  in  which  the  perceptual  object  is  said  to  be.  This 
could  not  be  true,  because  they  are  of  radically  different 
kinds,  and  are  in  this  place  in  radically  different  senses. 
Take,  for  example,  the  perceptual  object  which  is  what 
common-sense  means  by  a  penny.  One  constituent  of 
this  is  a  complete  optical  object.  This  consists  of  visual 
sensa.  Each  of  these  is  literally  present  only  at  a  place 
in  its  own  visual  field.  The  optical  object  is  only 
present  at  the  place  in  the  movement-continuum  in  the 
sense  that  this  place  is  optically  filled  by  the  visual 
sensa  which  together  make  up  the  complete  optical 
object.  Another  constituent  of  the  perceptual  penny 
is  a  group  of  tactual  sensa.  Each  of  these  is  literally 
present  only  in  its  own  tactual  sense-field.  The  whole 
group  is  present  at  the  place  where  the  penny  is  said 
to  be,  in  some  Pickwickian  sense  which  we  have  not 
yet  defined,  but  which,  from  the  nature  of  the  case, 
cannot  be  identified  either  with  sensible  presence  or 
with  optical  presence.  It  is  because  the  perceptual 
object  is  not  one  homogeneous  thing,  but  a  complex 
of  correlated  constituent  objects  of  various  types,  that 
science  finds  it  necessary  to  pass  beyond  the  perceptual 
objects  of  common-sense.  This  does  not  mean,  as  we  are 
liable  to  think,  that  the  latter  are  "unreal."    It  only  means 


POSITIONS   AND   SHAPES   OF   SENSA       331 

that  they  are  unsuitable  units  for  scientific  purposes, 
though  admirably  convenient  units  for  the  purposes  of 
everyday  life.  This  leads  us  to  the  last  meaning  of 
"physical  object,"  viz.,  what  Whitehead  calls  Scientific 
Objects.  (Though  I  use  this  convenient  expression  of 
Whitehead's,  and  mean  it  to  apply  to  much  the  same 
things  as  he  applies  it  to,  it  does  not  necessarily  follow 
that  he  would  agree  with  the  account  that  I  am  going 
to  give  of  the  concept  of  such  objects.) 

Science  tells  us  that  a  penny  "consists  of"  large 
numbers  of  colourless  particles,  moving  about  with  great 
velocities  in  characteristic  ways.  This  is  understood 
both  by  science  and  common-sense  to  mean  that  the 
colourless  particles  are  parts  of  the  perceptible  brown 
penny  in  the  same  literal  sense  in  which  a  visual 
appearance  of  the  King's  head  is  a  part  of  the  visual 
appearance  of  the  penny.  It  would  be  difficult  to 
accept  this  interpretation,  even  on  a  naively  realistic 
view  of  pennies  and  our  perception  of  them.  It  is  not 
easy  to  believe  that  the  brown  continuous  surface  of  the 
penny,  which,  on  that  view,  we  sense,  can  literally  be 
composed  of  colourless  particles.  Anyhow,  this  simple- 
minded  interpretation  of  the  scientific  statement  becomes 
impossible  when  we  remember  that  the  perceptual 
penny  is  not  one  homogeneous  object,  but  is  a  complex 
of  connected  constituent  objects  of  different  types, 
which  all  occupy  a  place  in  the  movement-continuum  in 
different  Pickwickian  senses.  It  is  clear  that  nothing 
could  be  a  part  of  all  the  constituents  of  a  perceptual 
object  in  any  one  sense  of  the  word  "part,"  whether 
literal  or  Pickwickian.  If  it  be  literally  part  of  one  of 
the  constituents,  it  can  only  be  a  part  of  the  others  in  as 
many  different  Pickwickian  senses  as  there  are  different 
types  of  constituent.  Moreover,  some  at  least  of  the 
constituents  are  such  that  nothing  could  literally  be  a 
part  of  them.  One  constituent,  e.g.,  of  a  perceptual 
object  is  a  complete  optical  object.  Nothing  could 
claim  to  be  a  literal  part  of  this  except  one  of  the  visual 


332  SCIENTIFIC   THOUGHT 

appearances  of  the  perceptual  object.  And  even  these 
are  not  literally  parts  of  the  complete  optical  object.  A 
visual  appearance  of  a  penny  is  a  "part"  of  the  complete 
optical  object  only  in  the  sense  that  the  latter  is  a  group 
of  optically  compresent  sensa  of  which  this  appearance 
is  one  member.  But  the  various  members  do  not  literally 
fit  together  to  make  up  a  surface,  and  therefore  they 
are  not  literally  parts  of  the  complete  optical  object. 

We  can  now  return  to  the  statement  that  perceptual 
objects,  like  pennies,  are  "composed  of"  scientific 
objects,  like  electrons.  From  what  we  have  just  said, 
this  cannot  mean  more  than  that  the  scientific  objects  are 
literally  parts  of  one  of  the  constituents  of  a  perceptual 
object.  It  is  further  quite  clear  that  they  are  not  literally 
parts,  or  even  members,  of  the  optical  constituent  of  the 
perceptual  object.  This,  I  take  it,  is  why  there  is  no 
objection  to  the  view  that  a  brown  penny  is  composed 
of  colourless  electrons.  The  brownness  belongs  to  the 
optical  constituent  ;  and  the  electrons  are  not  literally 
parts  of  this,  but  at  most  of  some  other  constituent  of 
the  perceptual  object. 

Now  I  think  that  by  a  scientific  object  we  mean 
something  that  literally  occupies  a  place  in  the  move- 
ment-continuum. And  by  this  I  mean  that  it  occupies 
it  in  the  same  indefinable  way  in  which  a  sensum 
occupies  its  sensible  place  in  its  own  field.  If  this  be 
right,  the  relation  between  the  place  of  the  perceptual 
object  and  its  component  scientific  objects  may  be  stated 
as  follows  :  The  perceptual  object  marks  out  a  certain 
region  in  the  movement-continuum  by  the  presence  in 
this  region  of  its  various  constituents.  These  con- 
stituents are  all  present  in  this  place  in  different  ways, 
and  these  ways  are  all  definable  and  Pickwickian.  We 
have  attempted  to  define  the  way  in  which  the  optical 
constituent  is  present,  because  this  is  the  most  difficult 
and  important  case.  Science  conceives  that  the  regions 
in  the  movement-continuum,  thus  marked  out,  are  liter- 
ally occupied  by  certain  objects  which  have  an  important 


POSITIONS   AND   SHAPES   OF   SENSA       333 

causal  bearing  on  the  nature  of  the  sensa  which  occupy 
such  regions  in  their  various  Pickwickian  ways.  These 
supposed  objects,  defined  as  the  literal  occupants  of 
places  in  the  movement-continuum,  are  what  we  mean 
by  scientific  objects.  And  a  perceptual  object  is  com- 
posed of  certain  scientific  objects,  in  the  sense  that  the 
latter  literally  occupy  that  region  of  the  movement- 
continuum  which  the  constituents  of  the  former  occupy 
in  Pickwickian  senses. 

(e)  Summary  of  Conclusions  about  Place. — There  is  one 
and  only  one  literal  sense  of  "  being  in  a  place."  This 
is  not  definable,  but  it  is  exemplified  in  our  sense- 
experience  most  clearly  in  the  presence  of  a  visual 
sensum  at  a  certain  sensible  place  in  its  visual  field. 
The  concept  of  being  in  a  place  is  based  on  our  sensible 
acquaintance  with  such  instances  as  this.  It  can  then 
be  applied  in  thought  to  types  of  object  and  of  con- 
tinuum which  we  cannot  sense  as  simultaneous  wholes. 
Again,  there  is  one  and  only  one  kind  of  place  which 
we  deal  with  when  once  we  leave  individual  sensa  and 
their  fields  and  pass  to  physical  objects  in  the  widest 
sense  of  the  term.  This  is  a  place  in  the  continuum 
of  possible  positions  of  our  bodies  as  we  move.  This 
continuum  is  not  sensed  as  a  simultaneous  whole  ;  but 
our  successive  experiences  of  motion  are  synthesised 
under  the  concept  of  a  spatial  whole,  through  analogy 
with  visual  fields  which  we  can  sense  simultaneously. 
Now,  although  there  is  only  one  literal  sense  of  being 
in  a  place  ;  and  although  by  "  place  "  we  always  mean 
"place  in  the  movement- continuum,  spatially  con- 
ceived," so  soon  as  we  leave  the  individual  sense-field  ; 
still  there  are  many  derivative,  definable,  and  Pick- 
wickian senses  of  "  being  in  a  place."  Whenever  we 
talk  of  any  sensum  occupying  a  place  in  the  movement- 
continuum,  we  are  using  terms  in  a  Pickwickian  manner, 
and  are  bound  to  define  them.  And  for  different  kinds 
of  sensa  different  Pickwickian  kinds  of  occupation  will 
have  to  be  defined. 


334  SCIENTIFIC   THOUGHT 

Now  there  are  certain  correlations  between  the  sensa 
of  successive  fields  sensed  by  the  same  observer,  between 
contemporary  sensa  of  different  observers,  and  between 
sensa  of  different  kinds,  which  constantly  occur  in  real 
life,  and  make  these  definitions  possible  and  useful. 
But  we  are  liable  to  overlook  cases  where  these  correla- 
tions break  down  in  whole  or  in  part,  and  thus  to 
produce  an  illusory  simplification.  This  mistake  is 
avoided  by  considering-  such  facts  as  mirror-images. 
We  found  that  the  perceptual  objects  of  everyday  life 
are  not  homogeneous,  but  are  really  composed  of  a 
number  of  correlated  constituent  objects,  all  occupying, 
in  various  Pickwickian  senses,  the  same  region  of  the 
movement-continuum.  A  mirror-image  bears  a  close 
resemblance  to  the  complete  optical  object  which  is  one 
of  the  constituents  of  an  ordinary  perceptual  object.  It 
differs  from  a  perceptual  object  in  three  ways:  (i)  It 
is  not  a  complete  optical  object,  but  only  a  partial  one. 

(2)  The  place  which  it  optically  occupies    is    not   also 
occupied  by  correlated  tactual  and  other  types  of  object. 

(3)  There  is  good  reason  to  think  that  the  place  of  a 
perceptual  object  is  literally  occupied  by  certain  scientific 
objects,  which  are  intimately  connected  causally  with  the 
sensa  which  occupy  this  place  in  Pickwickian  ways.  In 
the  case  of  a  mirror-image,  the  place  which  is  optically 
occupied  by  the  sensa  which  make  up  the  image  may 
or  may  not  also  be  literally  occupied  by  scientific  objects. 
But,  on  either  alternative,  the  nature  of  the  sensa  is  not 
causally  determined  by  the  scientific  objects  which  occupy 
this  place,  and  is  causally  determined  by  the  scientific 
objects  which  occupy  certain  other  places,  viz.,  the  places 
where  the  source  and  the  mirror  are  perceptually  present. 
Finally,  just  as  a  place  in  the  movement-continuum  may 
be  optically  occupied  without  containing  any  relevant 
scientific  objects,  so  there  may  be  many  places  in  the 
movement-continuum  which  contain  important  scientific 
objects  without  beingeitheropticallyortactually  occupied. 
If  there  had  been  no  perceptual  objects,  or  if  the  relevant 


POSITIONS   AND   SHAPES   OF   SENSA       335 

scientific  objects  had  not  as  a  rule  occupied  the  region 
marked  out  for  us  by  the  perceptual  objects  to  which 
they  are  most  relevant,  we  should  hardly  have  reached 
the  notion  of  scientific  objects  at  all.  But,  once  having 
reached  this  notion  from  reflecting  on  perceptual  objects, 
there  is  no  reason  why  we  should  not  apply  it  to  regions 
which  are  not  occupied  by  perceptual  objects  at  all. 
Nevertheless,  this  is  a  late  development  of  human 
thought,  which  has  happened  well  within  historical 
times,  whereas  the  recognition  of  perceptual  objects  is, 
of  course,  prehistoric  and  almost  certainly  pre-human. 

The  Concept  of  Shape.— It  remains  to  consider  what 
is  meant  by  "  shape,"  and  what  is  the  exact  cash  value 
of  common  statements  about  shape,  such  as  "This 
penny  is  round."  The  notion  of  shape  is  one  of  the 
many  points  where  the  traditional  separation  between 
Space  and  Time  wears  very  thin.  This  is  readily  seen 
if  we  ask:  "  What  is  the  shape  of  a  cloud  of  coloured 
vapour?"  As  the  outlines  of  a  cloud  are  continually 
shifting,  there  is  nothing  that  can  strictly  be  called  the 
shape  of  it.  We  can,  however,  divide  up  the  history 
of  the  cloud  into  shorter  and  shorter  successive  sections, 
and  talk  of  the  shape  of  each  of  these.  Shape  only 
becomes  a  perfectly  definite  concept  when  it  refers  to 
a  momentary  extended  object  ;  it  can  therefore  only  be 
defined  strictly  by  the  use  of  Extensive  Abstraction. 
It  is  true,  however,  that  there  are  many  objects, 
such  as  pennies,  for  which  the  shapes  of  successive 
momentary  sections  are  practically  identical  over  a 
long  slice  of  history.  In  such  cases  we  can  talk  of 
the  shape  of  the  object.  We  can  say  that  a  penny  has 
a  definite  shape,  and  that  this  is  circular.  We  have 
now  to  consider  the  precise  meaning  of  such  statements. 

(a)  Sensible  Shape. — Just  as  there  is  one  and  only 
one  non-Pickwickian  sense  of  being  in  a  place,  so  there 
is  only  one  literal  sense  of  having  a  shape.  We  cannot 
define  "shape"  in  its  literal  sense,  any  more  than  we 


336  SCIENTIFIC   THOUGHT 

can  define  "being  in  a  place "  in  its  literal  sense. 
But  we  can  and  do  become  acquainted  with  concrete 
instances  of  shape  in  our  sense-fields.  The  literal 
meaning  of  shape  is  best  illustrated  by  a  visual  sensum 
which  persists  unchanged  throughout  the  whole  of 
the  short  duration  of  a  single  sense-field.  It  will  be 
remembered  that,  in  the  present  chapter,  we  are  making 
the  simplifying  assumption  that  sense-fields  and  the 
sensa  which  they  contain  are  literally  momentary. 
This  assumption  will  be  corrected  in  the  next  chapter. 
But  in  the  meanwhile  we  may  say  that  Sensible  Shape 
is  the  sort  of  shape  possessed  by  visual  and  other 
sensa,  and  that  this  is  the  fundamental  meaning  of 
shape. 

{U)   Optical  Shape. — We  talk  of  a  number  of  different 
observers  "seeing  the  same  object  from  different  places." 
We  have  already  discussed  the  cash  value  of  this  state- 
ment with  sufficient  accuracy  for  the  purpose  of  defining 
optical  occupation.     For  the  present  purpose  we  must 
go   a    little   further   and   draw   a  distinction   which  we 
have  hitherto  ignored  for  the  sake  of  simplicity.     When 
several  people  are  said  to  "see  the  same  object,"  this 
sometimes  means  that  they  all  "see  the  same  part  of 
the  object,"  and    it   sometimes  means  that  they   "see 
different  parts  of  the   same   object."     Moreover,  when 
they  are  seeing  different   parts  of  the  same  object,   it 
would    be    held   that   sometimes   the    parts  which   they 
see    are    entirely    separate,    and    that    sometimes   they 
partially  overlap  each  other.     The  following  examples 
will    illustrate   these    distinctions:    (i)    If    a    penny    be 
laid  on  the  table  and  a  number  of  people  stand  round 
and  look  at  it,    we   should   say  that  they  all   "see   the 
whole  of  the   upper  surface  of  the  penny."      (2)  If  I 
am    in    my   rooms  with  the  door   shut,   and   I   look  at 
the  door  from   inside  the   room   whilst  you   look  at   it 
from  outside  in   the  passage,  we  should  be  said  to  be 
"seeing   wholly   separate    parts   of    the   same   object." 
(3)   If  a  cricket-ball  be  put  on  the  table  and  a  number 


POSITIONS   AND   SHAPES   OF   SENSA      337 

of  people  stand  round  and  look  at  it,  we  should  say 
that  they  all  "see  partially  different  parts  of  it,  but 
that  the  parts  seen  by  adjacent  observers  partially  over- 
lap." It  is  quite  evident  that  these  three  different 
types  of  statement  express  three  genuinely  different 
situations,  all  of  which  often  arise  in  real  life.  On  the 
naive  view,  that  we  literally  sense  parts  of  the  surfaces 
of  physical  objects  when  we  look  at  them,  the  meanings 
of  such  statements  are  tolerably  obvious.  But  we  have 
long  ago  deserted  that  view  ;  and  indeed  one  of  the 
reasons  which  made  us  do  so  was  the  differences  in 
sensible  shape  of  the  sensa  of  various  observers  who 
were  all  "seeing  the  whole  of  the  upper  surface  of  a 
penny."  It  is  therefore  necessary  for  us  to  define  Pick- 
wickian senses  in  which  such  statements  are  true. 

A  and  B  may  be  said  to  see  the  same  part  of  a 
perceptual  object  when  the  visual  sensa  sA  and  sB,  which 
are  the  appearances  of  this  object  to  A  and  B  respectively, 
are  optically  present  in  precisely  the  same  region  of  the 
movement-continuum.  It  might  be  said:  "How  is 
this  possible,  when  sA  may  be  circular  and  sB  elliptical  ; 
or,  again,  both  may  be  circular,  but  sA  much  bigger 
than  j^?"  This  objection  rests  on  a  confusion  between 
optical  and  literal  occupation.  There  is  nothing  in  the 
definition  of  optical  occupation  to  prevent  precisely  the 
same  region  of  the  movement-continuum  being  optically 
occupied  from  different  places  with  sensa  of  various 
sensible  shapes  and  sizes.  What  would  be  impossible 
is  that  either  (a)  the  same  place  in  a  sense-field  should 
be  sensibly  occupied  by  two  sensa  of  different  shape  or 
size  ;  or  (d)  that  the  same  region  of  the  movement-con- 
tinuum should  be  physically  occupied  by  scientific 
objects  of  different  shape  or  size.  It  is  now  easy  to  deal 
with  the  other  two  cases.  We  see  wholly  different  parts 
of  a  perceptual  object  if  the  visual  sensa,  which  are  the 
appearances  of  this  object  to  us,  are  optically  present  in 
wholly  separate  regions  of  the  movement-continuum. 
Lastly,   A  and  B  see  partially   overlapping  parts  of  a 


338  SCIENTIFIC   THOUGHT 

perceptual  object  if  (n)  the  sensa  .v.,  and  s„  are  optically 
present  in  different  regions  of  the  movement-continuum  ; 
(/>)  these  regions  partly  overlap  ;  and  (c)  the  overlapping 
part  is  optically  occupied  by  a  part  of  sA  and  by  a 
part  of  .<•  .  What  we  must  clearly  understand  is  that 
literally  it  is  nonsense  to  suggest  that  the  various 
sensa  which  constitute  a  complete  optical  object  them- 
selves overlap  and  together  make  up  a  single  surface. 

It  is  hardly  worth  while  to  take  great  trouble  to 
define  the  optical  shape  of  a  perceptual  object.  This 
would  involve  defining  some  Pickwickian  sense  in  which 
we  could  talk  of  the  shape  of  the  complete  optical  object 
which  is  a  constituent  of  the  given  perceptual  object. 
Now  common-sense  would  admit  that  no  one  can  literally 
see  the  whole  of  any  perceptual  object  from  any  one 
position.  And  it  would  admit  that  the  visual  shape  and 
size  of  any  part  depend  on  the  position  of  the  observer. 
In  fact  we  only  use  visual  shape  and  size  as  indications 
(trustworthy  enough  under  normal  conditions,  if  suit- 
ably corrected)  of  the  shape  of  the  perceptual  object. 
And  by  the  shape  of  the  perceptual  object  common- 
sense  understands  its  felt  shape.  It  is  possible,  and 
perhaps  useful,  to  define  the  optical  shape  and  size  of  a 
part  of  a  perceptual  object  from  a  given  direction.  This 
might  be  done  as  follows  :  If  we  look  at  the  place  where 
a  perceptual  object  is,  bring  the  visual  appearance  of 
the  object  into  the  middle  of  our  visual  field,  and  then 
follow  our  noses,  we  do  sense  a  series  of  visual  fields,  each 
containing  an  appearance  of  the  object.  These  sensa, 
as  we  have  already  seen,  do  increase  to  a  maximum 
of  size  and  brightness  as  we  approach  the  place  which 
they  optically  occupy.  We  might,  perhaps,  take  the 
size  and  shape  of  the  largest  and  clearest  sensum  of 
such  a  series  as  what  is  meant  by  the  optical  size  and 
shape  from  a  given  direction  of  a  certain  part  of  the 
perceptual  object.  But  I  do  not  think  that  it  would  be 
possible  to  generalise  this  definition,  so  as  to  give  a  mean- 
ing to  the  size  and  shape  of  a  complete  optical  object. 


POSITIONS   AND   SHAPES   OF   SENSA       339 

(c)  Physical  Shape. — We  have  said  that  common- 
sense  identifies  the  "  real  "  shape  of  a  perceptual  object 
with  its  felt  shape.  This  statement  requires  a  good 
deal  of  analysis.  The  first  thing  to  notice  is  that  we 
are  much  more  inclined  to  believe  that  we  feel  literal 
parts  of  the  surfaces  of  physical  objects  than  that  we 
see  them.  Mirror-images,  and  the  variations  of  visual 
shape  and  size  with  the  position  of  the  observer,  make 
it  fairly  evident,  even  to  common-sense,  that  visual  sensa 
are  not  literally  parts  of  the  surfaces  of  perceptual 
objects,  though,  of  course,  common-sense  does  not  under- 
stand what  radical  changes  a  consistent  application  of 
this  conclusion  involves.  But  we  are  convinced  that 
what  we  touch  is  literally  a  part  of  the  surface  of  a 
physical  object.  I  believe  that,  with  suitable  explana- 
tions and  qualifications,  some  such  view  can  be  held  ; 
but  we  must  gradually  work  up  to  it,  and  make  the 
necessary  distinctions  as  we  go  along. 

(1)  There  are  tactual  fields,  just  as  there  are  visual 
fields.  And  within  them  there  are  sometimes  out- 
standing tactual  sensa,  with  recognisable  sensible  shape 
and  position  within  the  field.  Tactual  sensa  stand  out 
from  the  rest  of  the  tactual  field,  if  they  be  markedly 
different  in  temperature  or  in  "feel"  from  the  rest. 
These  remarks  would  be  illustrated  by  laying  one's 
hand  on  a  table  with  a  small  bit  of  ice  lying  on  it  or 
with  a  nail  sticking  up  from  it.  In  each  case  we  should 
sense  a  tactual  field  with  a  certain  outstanding  tactual 
sensum  at  a  certain  sensible  place  within  it.  In  the 
first  case  the  sensum  would  stand  out  by  its  coldness 
from  the  background,  and  it  would  have  a  sensible 
shape.  In  the  second  a  sensum  would  stand  out  from 
the  background  by  its  peculiar  "prickly  feel."  But,  in 
the  ordinary  man,  the  tactual  field  is  much  less  clearly 
differentiated  than  the  visual  field,  and  sensible  tactual 
position  and  shape  are  far  vaguer  than  the  sensible 
shapes  and  positions  of  visual  sensa.  Very  possibly 
this  is  not  true  of  blind  men.     The  tactual  field,  such 


340  SCIENTIFIC  THOUGHT 

as  we  have  just  been  describing,  is  connected  with  what 
psychologists  call  "  passive  touch  "  ;  audit  is  generally 
admitted  that  passive  touch  by  itself  gives  very  vague 
information  about  shape  and  size. 

(2)  Just  as  visual  sensa  are  literally  present  only  in 
their  own  fields,  so  tactual  sensa  are  literally  present 
only  in  tactual  fields.  When  we  say  that  there  is  a  cold 
round  tactual  sensum  at  a  certain  place  in  the  movement- 
continuum,  we  are  necessarily  speaking  in  a  Pickwickian 
sense,  as  much  as  when  we  say  that  there  is  an  elliptical 
brown  visual  sensum  there.  This  Pickwickian  sense 
is  fairly  obvious.  A  certain  tactual  sensum  may  be  said 
to  occupy  that  place  in  the  movement-continuum  to 
which  I  have  to  move  my  hand  before  I  can  sense 
this  sensum.  The  total  region  in  which  a  certain 
perceptual  object  is  present  may,  in  this  sense,  be 
occupied  in  different  parts  by  a  great  number  of  different 
tactual  sensa  from  contemporary  fields  of  different 
observers  and  from  successive  fields  of  a  single  observer. 
The  whole  of  such  a  group  of  tactual  sensa  would  be 
the  Tangible  Constituent,  which,  along  with  the  complete 
optical  object  and  perhaps  other  constituents,  makes  up 
the  perceptual  object. 

(3)  It  would  generally  be  admitted  that  it  is  by 
"  active  touch,"  i.e.,  by  passing  our  fingers  over  surfaces 
that  we  learn  about  the  "real  shapes"  of  objects  like 
pennies.  Now  active  touch  is  partly  a  movement- 
experience  and  partly  a  tactual  experience.  The  purely 
tactual  side  of  it  is  illustrated  in  isolation  in  passive 
touch,  and  we  have  seen  how  very  little  it  has  to  tell 
the  normal  man  about  shape  and  size.  But  active 
touch  is  movement  of  very  much  the  same  kind  as  we 
experience  when  we  walk  about,  accompanied  by  sensa- 
tions of  temperature,  pressure,  "sharpness,"  "  blunt- 
ness,"  etc.  We  find  that  there  are  certain  regions  of 
the  movement-continuum  into  which  we  cannot  enter  or 
push  our  hands.  Our  previously  free  course  is  stopped. 
This    stoppage    is    accompanied    and    emphasised    by 


POSITIONS   AND   SHAPES   OF   SENSA       341 

tactual  sensations  of  various  kinds.  It  is  always 
accompanied  by  pressure-sensations,  which  grow  in 
intensity  the  more  we  try  to  penetrate  the  region  in 
question.  When  we  actively  feel  a  body  we  are  trying 
to  penetrate  a  certain  region  of  the  movement-continuum 
from  various  directions,  and  are  failing  to  do  so.  And 
our  failure  is  marked  bv  characteristic  tactual  sensations. 
The  points  on  its  surface  are  the  points  at  which 
attempted  courses  of  further  movement  are  stopped. 
Thus,  it  seems  to  me  that  what  we  feel  when  we  are  said 
to  be  actively  exploring  a  certain  perceptual  object  is 
a  closed  surface  in  the  movement-continuum.  The  felt 
boundaries  are  the  boundaries  of  a  volume  which  is  in 
the  movement-continuum  in  the  same  literal  sense  in 
which  a  tactual  sensum  is  in  its  tactual  field  or  a  visual 
sensum  in  its  visual  field.  The  optical  constituent  and 
the  tangible  constituent  of  the  perceptual  object  are  on 
the  surface  of  this  felt  region  in  their  respective  Pick- 
wickian ways,  whilst  relevant  scientific  objects  are 
within  this  region  in  a  perfectly  literal  sense. 

There  is  one  important  point  to  remember  here. 
The  experience  of  being  stopped  when  we  try  to  pene- 
trate a  certain  region  of  the  movement-continuum  from 
various  directions  is  not  one  simultaneous  experience, 
but  is  a  series  of  successive  attempts  and  failures,  accom- 
panied by  characteristic  tactual  sensations.  On  the 
other  hand,  the  region  which  we  are  said  to  feel  is  con- 
ceived as  a  network  of  contemporary  points.  If  we  had 
not  got  the  concepts  of  shape  and  volume  from  our 
visual,  and  in  a  much  smaller  degree,  our  tactual  fields, 
we  should  never  have  been  able  to  interpret  these 
successive  stoppages  as  a  network  of  contemporary 
points  in  a  kind  of  space.  This  is  simply  a  further 
illustration  of  the  general  fact,  already  noted,  that  apart 
from  the  characteristic  peculiarities  of  visual  fields 
and  their  correlations  with  our  bodily  movements  we 
should  never  have  interpreted  the  movement-continuum 
spatially  at  all. 


342  SCIENTIFIC   THOUGHT 

(//)  Summary  of  Conclusions  about  Shape. — Shape 
has  a  perfectly  definite  meaning  only  as  applied  to 
extensive  wholes  of  co-existent  parts.  It  is  therefore 
impossible  to  deal  with  it  adequately  apart  from  time. 
Strictly  speaking,  only  momentary  extended  events 
have  shape,  and  we  can  only  talk  of  the  shape  of  a 
persistent  object  on  the  assumption  that  successive 
momentary  sections  of  its  history  are  extended  events 
with  the  same  shape.  Leaving  these  temporal  compli- 
cations aside  till  the  next  chapter,  we  may  say  that  we 
reach  the  concept  of  shape  by  acquaintance  with 
particular  instances  of  it  in  the  form  of  visual  and  (to 
a  much  less  degree)  tactual  sensa.  Having  reached 
the  concept  in  this  way,  we  can,  as  usual,  proceed  to 
apply  it  to  other  cases  which  we  cannot  sense. 

The  notion  of  the  shape  of  a  perceptual  object  has 
the  same  kind  of  confusion  as  the  perceptual  object 
itself.  For  the  latter  is  a  compositum  of  constituent 
objects  of  various  types.  Each  of  these  constituent 
objects  will  have  a  shape  only  in  a  Pickwickian  sense, 
if  at  all.  And  the  Pickwickian  sense  will  be  different 
for  each  different  type  of  constituent  object.  It  proved 
to  be  unprofitable,  and  perhaps  impossible,  to  define 
a  meaning  for  the  shape  of  the  optical  constituent  or 
the  tangible  constituent.  In  fact,  what  is  meant  by  the 
shape  of  a  perceptual  object  seems  not  to  be  the  shape 
of  any  of  its  constituent  objects.  It  is  rather  the  shape 
of  a  certain  region  of  discontinuity  within  the  move- 
ment-continuum. This  is  the  region  on  whose  surface 
the  optical  and  tangible  components  of  the  perceptual 
object  are  present  in  the  Pickwickian  senses  of 
"presence"  appropriate  to  each.  And  within  this 
volume  are  supposed  to  reside  those  scientific  objects 
which  are  mainly  relevant  in  determining  the  optical 
and  tangible  filling  of  the  region. 

The  boundaries  of  such  regions  of  the  movement- 
continuum  are  learnt  by  active  exploration.  Attempts 
at  further  movement  are  here  stopped,  and  the  stoppage 


POSITIONS   AND   SHAPES   OF   SENSA       343 

is  emphasised  by  the  accompanying  tactual  sensations. 
The  interpretation  of  these  successive  stoppages  as  a 
network  of  contemporary  points  within  the  movement- 
continuum  involves  the  application  of  concepts  derived 
mainly  from  the  visual  field,  and  the  same  is  true  of 
the  spatial  interpretation  of  the  movement-continuum 
itself.  The  shapes  of  visual  sensa  are  taken  as  indica- 
tions of  the  shape  of  this  region  in  the  movement- 
continuum,  but  are  admitted  by  common-sense  to  need 
correction,  a  correction  which  we  apply  automatically 
and  properly  in  familiar  cases. 

This  is  as  far  as  we  can  profitably  go  without  con- 
sidering the  temporal  characteristics  of  sensa,  physical 
objects,  and  physical  events.  With  these  we  shall  deal 
in  the  next  chapter. 

The  following  additional  works  may  be  consulted 
with  advantage : 

G.  F.  STOUT,  Manual  of  Psychology,  Book  III.  Part  II.,  Caps. 

III.  and  IV. 
W.  James,  Principles  of  Psychology,  Chapter  on  Space. 
Berkeley,  Theory  of  Vision. 


CHAPTER   X 

"  She  is  settling  fast,"  said  the  First  Lieutenant  as  he  returned 
from  shaving. 

"  Fast,  Mr  Spoker  ?  "  asked  the  Captain.      "  The  expression 

is  a   strange   one,   for  Time    (if   you    will   think  of    it)    is   only 

relative." 

(R.  L.  Stevenson,  The  Sinking  Ship.) 

The  Dates  and  Durations  of  Sensa  and  of 
Physical  Objects  and  Events 

We  have  now  to  raise  the  same  kind  of  questions  about 
date  and  duration  as  we  have  just  been  raising  about 
place  and  shape.  As  in  the  last  chapter  we  were 
learning  something  fresh,  not  only  about  Matter,  but 
also  about  Space,  so  here  we  are  going  to  dig  beneath 
the  traditional  concepts  of  Time  and  Change  which 
were  treated  in  Chapter  II.  We  shall  also  be  correcting 
certain  simplifying  assumptions  which  were  made  in 
the  last  chapter,  such,  e.g.,  as  the  assumption  that  our 
successive  sensible  fields  are  literally  momentary. 

Comparison  of  Spatial  and  Temporal  Characteristics 
of  Sensa. — Let  us  begin  with  the  temporal  characteristics 
which  belong  to  sensa  in  the  same  direct  and  literal 
way  in  which  sensible  place  in  their  own  fields  belongs 
to  them.  There  are  three  ways  in  which  temporal 
characteristics  are  more  pervasive  than  spatial  ones, 
(i)  Only  objects  have  places  and  shapes  in  a  literal  or 
even  a  Pickwickian  sense.  Mental  acts,  like  believing, 
wishing,  etc.,  neither  have  sensible  places,  such  as 
sensa  have  in  their  own  fields,  nor  are  they  commonly 
held  to  be  in  physical  Space,  even  in  a  Pickwickian 
sense.     This  is  denied  by  Alexander,  but  I  am   quite 

344 


DATE   AND   DURATION  345 

unconvinced  by  his  arguments.  It  is  no  doubt  possible 
to  give  a  Pickwickian  meaning  to  the  statement  that  our 
mental  acts  are  in  our  heads,  but  we  make  so  little 
scientific  use  of  such  statements  that  it  is  hardly  worth 
troubling  to  do  so.  On  the  other  hand,  it  seems  to  me 
that  mental  acts  have  dates  in  the  same  literal  sense  as 
sensa  and  other  objects,  which  are  not  acts.  When  I 
say  that  I  began  to  think  of  my  dinner  at  the  moment 
when  I  heard  a  noise,  I  am  asserting  that  a  certain  act 
of  thought  and  a  certain  sensation  of  sound  were  con- 
temporary ;  and  this  is  an  expression  of  an  immediate 
experience,  and  has  nothing  Pickwickian  about  it. 
(ii)  The  spatial  characteristics  of  the  sensa  of  one  sense 
do  not  literally  extend  to  those  of  another  sense,  even 
in  the  case  of  a  single  observer.  My  visual  sensa  have 
places  in  my  visual  field,  and  my  tactual  sensa  have 
places  in  my  tactual  field  ;  there  is  no  place  in  which 
both  are  literally  present.  We  do,  indeed,  come  to  say 
that  certain  visual  sensa  are  compresent  with  certain 
tactual  ones  ;  but,  as  we  have  seen,  this  only  means 
that  both  are  present,  in  different  Pickwickian  senses,  in 
a  region  of  the  movement-continuum.  This  is  not  the 
kind  of  fact  that  can  be  directly  sensed.  On  the  other 
hand,  it  does  seem  to  me  that  temporal  relations  do 
literally  connect  sensa  belonging  to  different  senses  of 
the  same  observer.  I  can  often  judge  quite  immediately 
that  a  certain  noise  that  I  sense  is  contemporary  with 
a  certain  flash  that  I  sense,  and  is  later  than  a  certain 
twinge  of  toothache  which  I  remember.  Here  I  seem 
to  be  using  the  names  of  these  temporal  relations  quite 
literally,  and  in  no  Pickwickian  sense.  On  the  other 
hand,  temporal  relations  do  not  literally  stretch  across 
from  one  observer  to  another.  You  and  I  may  judge 
that  two  visual  sensa,  one  of  which  was  sensed  by  you 
and  the  other  by  me,  were  contemporary  ;  and  you  may 
judge  that  your  visual  sensum  was  contemporary  with 
a  twinge  of  toothache  that  you  felt.  But  my  flash  and 
yours  are  not  contemporary,  in  the  same  literal  sense 


346  SCIENTIFIC   THOUGHT 

in  which  your  flash  and  your  toothache  are  con- 
temporary. Temporal  relations  between  the  sensa 
or  the  mental  acts  of  two  different  observers  have  to 
be  defined  in  terms  of  a  good  manv  other  facts  beside 
the  two  which  they  are  said  to  relate,  just  as  we  found 
with  spatial  relations  between  the  sensa  of  different 
observers,  (iii)  Spatial  relations  do  not  literally  extend 
from  the  sensa  of  one  field  of  a  certain  observer  to  the 
sensa  of  a  later  field  of  the  same  sense  of  the  same 
observer.  It  is  only  in  a  Pickwickian  sense  that  we 
can  say  that  a  certain  visual  sensum  of  mine  is  corn- 
present  with  another  visual  sensum  of  mine,  which 
belongs  to  a  later  field.  On  the  other  hand,  direct 
memory  seems  often  to  bridge  the  gap  between  two 
of  our  sensa  of  different  dates,  and  to  enable  us  to 
judge  directly  that  one  is  literally  later  than  the  other. 

Sensible  Duration  :  (a)  Sensa  and  Sense-objects. — We 
assumed  temporarily,  and  for  the  sake  of  simplicity, 
in  the  last  chapter  that  our  successive  sensible  fields 
are  literally  momentary,  and  that  a  sensum  in  one  field 
is  ipso  facto  different  from  any  sensum  in  another  held. 
We  must  now  get  behind  these  simplifying  assumptions. 
The  second  of  them  is  partly  a  matter  of  definition. 
It  is  obvious  that  what  is  now  past  cannot  be  precisely 
and  numerically  the  same  as  what  is  now  present,  even 
though  the  sensible  qualities  and  shapes  of  both  should 
be  exactly  the  same,  and  though  they  should  occupy 
precisely  similar  sensible  places  in  their  respective 
sensible  fields.  I  am  therefore  justified  in  using  the 
term  "sensum  "  in  such  a  way  that  they  shall  be  called 
different  sensa.  This  is,  of  course,  without  prejudice 
to  the  fact  that  the  resemblances  and  the  continuity 
between  the  members  of  a  series  of  different  sensa  in 
successive  fields  may  be  such  that  it  is  possible  and 
useful  to  speak  of  a  single  persistent  sense-object,  of 
whose  history  the  sensa  of  the  series  are  different  and 
successive    slices.       When    there    is   a   series    of  sensa 


DATE   AND   DURATION  347 

sr s„  in  a  set  of  successive  fields  of  an  observer 

O,  and  when  there  is  enough  qualitative  likeness  between 
adjacent  sensa  of  the  series,  we  can  say  that  a  sense- 
object  S  exists  and  persists,  and  that  these  sensa  are 
successive  parts  of  its  history.  If  all  the  sensa  of  the 
series  be  indistinguishable  in  their  qualities,  we  can 
say  that  the  sense-object  S  has  persisted  unchanged 
throughout  a  certain  duration.  If  the  successive  sensa 
have  different  places  in  their  respective  fields,  and  if 
certain  further  conditions  be  fulfilled,  we  can  say  that 
the  sense-object  S  has  moved.     The  sort  of  continuity 

that  is  required  of  the  sensa  s1 s„  in  order  that 

they  shall  all  count  as  parts  of  the  history  of  a  single 
sense-object  S,  is  that  the  nearer  together  two  sensa 
are  in  the  series  the  more  alike  are  their  sensible  places 
in  their  respective  fields.  If  this  condition  be  fulfilled, 
we  say  that  there  is  a  single  sense-object,  and  if  the 
successive  sensible  places  are  different,  we  say  that  it 
has  moved.  We  can,  of  course,  remember  the  place  of 
a  sensum  sr  in  its  field  fr,  and  compare  it  with  that  of 
sr+1  in  its  field  fr+1.  This  is  not  generally  an  act  of 
deliberate  memory  and  comparison,  but  we  automatically 
notice  if  sr+1's  position  in/,.+1  is  greatly  different  from  s^s 
position  in  fr.  If  the  fields  which  come  after  a  certain 
field/,,  do  not  contain  sensa  with  the  right  sort  of  resem- 
blance and  continuity  with  the  previous  s's,  we  say  that 
the  sense-object  S  has  ceased  to  exist.  As  we  have 
already  explained,  nothing  that  has  ever  existed  really 
ceases  to  exist.  The  parts  of  its  history  that  have  be- 
come, merely  recede  into  the  more  and  more  distant 
past ;  and  nothing  that  henceforward  becomes,  is  of 
such  a  nature  that  it  adds  on  to  these  past  events  to 
make  a  continuation  of  that  particular  sense-object.  It 
were  therefore  less  misleading  to  say  that  the  sense- 
object  in  question  ceases  to  persist.  The  past,  like 
the  unhappy  Theseus,  "  Sedet,  ceternumque  sedebit" 

(/>)  Duration    of  Sense-fields   and  of  Sensa. — On    the 
assumption  that  sensible:  fields  are  literally  momentary, 


348  SCIENTIFIC  THOUGHT 

it  follows  that  sensa  are  also  literally  momentary.  But 
this  assumption  must  now  be  dropped,  and  we  must 
come  closer  to  the  actual  facts  of  sensible  experience. 
A  sensible  event  has  a  finite  duration,  which  may 
roughly  be  defined  as  the  time  during  which  it  is  sensed, 
as  distinct  from  being  remembered.  The  two  kinds 
of  act  are  markedly  different  when  a  long  gap  of  time 
separates  the  act  of  remembering  from  the  object  re- 
membered. As  the  time-lapse  between  act  and  object 
decreases,  the  distinction  between  sensing  and  remember- 
ing grows  fainter,  and  no  absolutely  sharp  line  can  be 
drawn  where  one  ends  and  the  other  begins.  Still, 
it  is  certain  that  what  can  be  sensed  at  any  moment 
stretches  a  little  way  back  behind  that  moment.  This 
is  the  phenomenon  to  which  we  have  already  referred 
as  the  Specious  Present.  I  do  not  find  the  accounts 
of  the  Specious  Present  given  by  psychologists  very 
clear,  and  I  shall  therefore  try  to  illustrate  the  matter 
in  my  own  way,  which  will  lead  us  to  definitions  of 
momentary  fields  and  momentary  acts  of  sensing.  It 
is  obvious  that,  if  we  are  to  hold  that  all  object-events 
are  really  of  finite  duration,  and  that  momentary  objects 
are  to  be  defined  by  Extensive  Abstraction,  we  ought 
to  take  up  the  same  attitude  towards  acts.  I  shall 
begin  by  assuming  literally  momentary  acts  of  sensing, 
and  shall  then  correct  this  abstraction. 

Let  us  represent  the  history  of  O's  acts  by  a  directed 
line  OO.  Let  us  represent  the  history  of  his  sensible 
fields  by  a  parallel  line  ce.  Let  Ox,  on  the  upper  line, 
represent  a  momentary  act  of  sensing  done  by  O  at 
a  moment  t\.  I  take  it  to  be  a  fact  that  this  act  grasps 
an  event  of  finite  duration  which  stretches  back  from 
the  moment  t\  to  a  moment  tlf  which  is  earlier  by  an 
amount  t.  This  duration  t  is  the  length  of  O's  Specious 
Present.  I  call  this  event  exe'v  and  I  represent  the  act 
of  sensing  which  grasps  it  as  a  whole  by  the  right- 
angled  triangle  ^O^,  with  exe\  as  base  and  01  as 
vertex. 


DATE   AND   DURATION 


349 


Let  us  now  suppose  that,  at  a  slightly  later  date 
(separated  by  less  than  the  length  of  the  Specious 
Present),  O  performs  another  act  of  sensing.  We  will 
represent  this  by  the  dotted  triangle  e20./.2,  which  is 
similar  to  exOxe\.  This  grasps  an 
event  of  duration  t,  stretching 
back  from  the  moment  when  the 
act  happens.  The  event  is  repre- 
sented by  e2e2.  Now  it  is  evident 
that  there  is  a  part  e2e\,  which  is 
common  to  the  two  events  e1e'1 
and  e2e2.  This  part  is  sensed 
by  both  the  acts  Ox  and  0.2.     On 

the  other  hand,  there  is  a  part  exe2  of  the  first  event 
which  is  not  sensed  by  the  second  act,  and  a  part 
e\e'2  of  the  second  event  which  is  not  sensed  by  the 
first  act.  It  will  be  noticed  that  the  duration  of  e2e\, 
the  event  which  is  sensed  by  both  Ox  and  02,  is  such 
that,  when  added  to  the  time  that  elapses  between  the 
two  acts,  it  makes  up  the  duration  of  O's  Specious 
Present.  If  we  finally  take  an  act  On,  separated  from 
Ox  by  the  length  of  the  Specious  Present,  the  event  ene'n 
which  it  grasps  has  nothing  in  common  with  exe\,  except 
the  single  point  which  is  labelled  both  e\  and  eH.  Thus, 
if  two  acts  of  sensing  by  O  be  separated  by  the  length 
of  O's  Specious  Present,  the  only  "  event  "  that  is  sensed 
in  both  of  them  is  a  "  momentary  event."  In  general, 
we  notice  that  the  shorter  the  time-lapse  between  two 
of  O's  acts  of  sensing,  the  longer  is  the  event  which  is 
sensed  in  both  of  them  ;  and  that,  as  the  lapse  tends 
to  nothing,  the  duration  of  the  event  tends  to  t. 

(c)  Momentary  Fields  and  Momentary  Acts  of  Sensing. — 
We  are  now  able  to  remove  the  supposition  of  literally 
momentary  acts,  and  to  define  by  Extensive  Abstraction 
both  momentary  acts  and  momentary  fields.  If  the 
reader  will  look  back  at  the  diagram  he  will  see  that 
the  event  e2e'v  which  is  common  to  the  two  acts  of 
sensing  Ox  and  02,  is  a  fortiori  common  to  Ox  and  any 


350  SCIENTIFIC   THOUGHT 

act  that  happens  between  Oj  and  0.2.  For  it  will  be  a 
proper  part  of  the  longer  event  which  is  common  to 
this  pair  of  more  closely  adjacent  acts.  If  we  imagine 
a  continuous  series  of  momentary  acts  between  Oa  and 
(X  we  can  regard  them  as  momentary  sections  of  an 
act  or  process  of  finite  duration,  and  can  say  that  the 
finite  event  eie\  is  present  throughout  the  whole  of  this 
process  of  sensing.  The  parts  exe2  and  c\e\  form  a  kind  of 
penumbra  ;  the  latter  was  not  present  at  the  beginning, 
and  the  former  is  not  present  at  the  end,  of  this  finite 
process  of  sensing ;  but  the  part  c./\  is  present  all 
through.  A  momentary  sensible  field  may  thus  be 
roughly  defined  as  the  limit  which  the  event  that  is 
present  throughout  the  whole  of  a  process  of  sensing 
approaches,  as  the  duration  of  the  process  of  sensing 
approaches  to  the  length  of  the  observer's  Specious 
Present.  The  reference  to  limits  can  then  be  got  rid 
of  in  the  usual  way  by  Extensive  Abstraction.  The 
momentary  field  e\  might  finally  be  defined  as  follows  : 
It  is  a  class  of  events  such  that  each  member  of  it  is 
present  throughout  the  whole  of  some  process  of  sensing 
which  begins  at  t\  and  does  not  last  longer  than  O's 
Specious  Present. 

In  the  same  kind  of  way  we  can  define  a  momentary 
act  of  sensing.  The  longer  an  event  the  shorter  is  the 
process  of  sensing  throughout  the  whole  of  which  it  is 
present.  As  the  length  of  the  sensed  event  approaches 
that  of  the  Specious  Present,  the  duration  of  the  process 
of  sensing  throughout  the  whole  of  which  the  event  is 
present  approaches  to  nothing.  We  could,  therefore, 
roughly  define  a  momentary  act  of  sensing  as  the  limit 
which  a  process  of  sensing  approaches  as  the  duration 
of  the  event  which  is  present  throughout  the  whole  of 
this  process  approaches  to  that  of  the  observer's  Specious 
Present.  The  reference  to  limits  can  then  be  got  rid  of 
in  the  usual  way.  The  momentary  act  Ox  might  ulti- 
mately be  defined  as  follows  :  It  is  a  class  of  acts  such 
that  throughout  each  member  of  it  there  is  present  some 


DATE  AND   DURATION  351 

event  which  ends  at  t\  and  does  not  last  longer  than  the 
duration  of  O's  Specious  Present. 

In  real  life  we  may  assume  that  our  acts  of  sensing 
are  not  momentary,  but  are  processes  that  last  for  a 
finite  time.  What  we  choose  to  count  as  one  process 
of  sensing,  of  course,  depends  on  many  factors,  of  which 
the  most  important  is  probably  unity  of  interest.  If  our 
account  of  the  Specious  Present  be  right,  the  funda- 
mental fact  is  that  a  process  of  sensing  which  lasts  for 
a  finite  time  (provided  it  be  shorter  than  the  duration 
of  the  Specious  Present)  will  actually  sense  a  certain 
event  of  finite  duration  throughout  the  whole  time  that 
the  process  lasts.  Since,  however,  we  have  succeeded 
in  defining  momentary  acts  and  momentary  sensible 
fields  in  terms  of  processes  of  sensing  and  sensible 
fields  of  finite  duration,  we  are  henceforth  at  liberty 
to  use  the  momentary  conceptions  whenever  we  find  it 
convenient  to  do  so. 

(d)  Sensible  Change. — We  are  now  in  a  position  to  deal 
with  sensible  change  and  movement.  We  have  already 
defined  what  is  meant  by  the  statement  that  a  sense- 
object  has  changed  or  moved.  We  saw  that  it  depended 
on  a  comparison  between  the  sensible  positions  and 
other  qualities  of  sensa  in  successive  fields.  But  it  is 
a  notorious  fact  that  we  do  not  merely  notice  that  some- 
thing has  moved  or  otherwise  changed  ;  we  also  often 
see  something  moving  or  changing.  This  happens  if  we 
look  at  the  second-hand  of  a  watch  or  look  at  a  flickering 
flame.  These  are  experiences  of  a  quite  unique  kind  ; 
we  could  no  more  describe  what  we  sense  in  them  to  a 
man  who  had  never  had  such  experiences  than  we  could 
describe  a  red  colour  to  a  man  born  blind.  It  is  also 
clear  that  to  see  a  second-hand  moving  is  a  quite  different 
thing  from  "seeing"  that  an  hour-hand  has  moved. 
In  the  one  case  we  are  concerned  with  something  that 
happens  within  a  single  sensible  field  ;  in  the  other  we 
are  concerned  with  a  comparison  between  the  contents 
of  two  different  sensible  fields.     Now  we  have  just  seen 


352  SCIENTIFIC   THOUGHT 

that,  in  the  total  event  which  is  sensed  by  a  process 
that  lasts  for  less  time  than  the  duration  of  the  Specious 
Present,  there  is  a  finite  part  which  is  sensibly  present 
throughout  the  whole  process  of  sensing-.  Even  if  a 
certain  process  of  sensing  goes  on  for  longer  than  a 
Specious  Present,  there  will  be  parts  of  it  that  are 
shorter  than  the  duration  of  a  Specious  Present,  and 
some  event  of  finite  duration  will  be  sensed  throughout 
any  one  of  these  shorter  parts  of  the  total  process.  Let 
us  consider  any  such  finite  event,  which  is  sensed 
throughout  the  whole  of  a  finite  process  of  sensing. 
It  will  constitute  a  sensible  field,  and  it  lasts  for  a 
finite  time.  It  can  therefore  be  divided  into  successive 
fields  of  shorter  duration,  which  together  make  it  up. 
If  anything  in  one  of  its  earlier  sections  be  qualitatively 
different  from  anything  in  any  of  its  later  sections  there 
will  be  change  within  the  original  finite  field.  But  the 
whole  of  this  field  is  sensed  throughout  a  finite  process 
of  sensing.  Thus  the  qualitative  differences  between 
its  earlier  and  its  later  sections  will  be  sensed  together  ; 
i.e.  the  observer  will  actually  sense  the  changing  and 
will  not  merely  notice  that  something  has  changed. 
We  can  now  easily  see  why  a  change  must  surpass  a 
certain  minimum  speed  if  it  is  to  be  sensed  as  such. 
If  a  change  takes  place  slowly,  this  means  that  closely 
adjacent  events  are  qualitatively  very  little  different 
from  each  other.  It  may  therefore  happen  that  two 
events  are  not  qualitatively  distinguishable  by  us  unless 
they  are  separated  by  more  than  the  duration  of  a 
Specious  Present.  If  this  be  so,  these  two  qualitatively 
distinguishable  sections  of  a  single  long  event  are  too 
far  separated  to  be  sensed  together  even  by  a  momentary 
act.  A  fortiori  they  could  not  be  sensed  throughout  the 
whole  of  any  process  of  sensing  which  lasts  for  a  finite 
time,  as  all  real  acts  of  sensing  do.  Thus  we  may  be 
able  in  such  a  case  to  judge  by  memory  and  comparison 
that  something  has  changed,  but  we  shall  not  be  able 
to  sense  its  changing. 


DATE   AND   DURATION  353 

The  fact  that,  in  favourable  cases,  changes  can 
actually  be  sensed,  is  of  great  importance  in  developing 
the  concept  of  change  in  general.  A  sufficiently  short 
act  of  sensing  senses  a  field  of  finite  duration.  This 
field  is  divisible  into  earlier  and  later  parts,  which  to- 
gether make  it  up.  Now,  since  I  sense  this  finite  field 
as  a  whole,  I  actually  sense  the  way  in  which  its  earlier 
half  joins  up  with  its  later  half  to  make  up  the  whole. 
By  analogy  with  this,  I  am  able  to  conceive  how  two 
successive  adjacent  fields,  which  no  act,  however  short, 
can  sense  together,  are  joined  up  with  each  other  in 
nature  to  form  a  single  long  event.  I  thus  interpret 
those  qualitative  differences,  which  I  can  notice  only 
between  successively  sensed  fields,  in  terms  of  the 
changes  which  I  can  actually  sense  within  a  field  that 
is  short  enough  to  be  sensed  as  a  whole  by  an  act  of 
finite  duration.  If  there  were  no  sensible  change,  it 
would  still  be  true  that  a  sufficiently  short  act  of  sensing 
senses  a  field  of  finite  duration  ;  but  it  would  be  ex- 
tremely difficult  for  us  to  recognise  that  this  was  divisible 
into  successive  shorter  sections  which  join  up  with  each 
other  to  make  the  finite  field.  For  there  would  be  no 
recognisable  qualitative  difference  between  the  earlier 
and  the  later  sections.  In  this  case,  it  would  be  ex- 
tremely difficult  for  us  to  conceive  the  way  in  which  a 
finite  field,  which  is  now  sensed,  joins  on  to  an  earlier 
finite  field,  which  is  now  only  remembered.  It  would 
be  proportionately  difficult  for  us  to  interpret  any 
qualitative  differences  that  we  might  find  between  two 
such  fields  in  terms  of  slow  continuous  change. 

(e)  Conclusions  about  Sensible  Duration. — We  have  now, 
I  think,  got  all  the  facts  that  are  needed  to  deal  with 
the  concept  of  the  duration  of  sensa.  A  sensible  field 
is  the  total  event  that  is  sensed  throughout  the  whole 
of  any  process  of  sensing.  No  process  which  lasts  for 
longer  than  the  duration  of  a  Specious  Present  senses 
a  single  sensible  field,  and  no  sensible  field  can  last 
longer  than  the  duration  of  a  Specious  Present.      But, 


354  SCIENTIFIC   THOUGHT 

on  the  other  hand,  every  process  of  sensing  that  lasts 
for  a  shorter  time  than  a  Specious  Present  senses 
throughout  the  whole  of  it  a  sensible  field  of  finite 
duration.  Since  we  can  always  divide  up  a  process 
of  sensing  into  successive  bits,  each  of  which  is  shorter 
than  a  Specious  Present,  we  can  always  divide  up  the 
total  event  that  an  observer  has  sensed  in  the  course  of 
a  long  process  of  sensing  into  successive  sensible  fields, 
each  of  a  finite  duration  less  than  that  of  the  Specious 
Present.  There  is  thus  a  maximum  possible  duration 
for  a  sensible  field,  but  any  sensible  field  is  divisible 
into  shorter  fields  which  join  together  at  their  ends  to 
make  up  the  whole.  This  divisibility  is  made  obvious 
to  us  by  the  fact  of  sensible  change,  and  the  mode  of 
junction  of  successive  adjacent  fields  is  conceived  to  be 
analogous  to  that  which  is  actually  sensed  in  the  case 
of  the  earlier  and  the  later  half  of  a  single  sensible  field. 
Now  we  have  already  seen  that  even  a  momentary 
sensible  field  (especially,  for  example,  a  visual  one)  is 
spatially  extended.  We  have  now  seen  that  any  real 
sensible  field  has  a  certain  duration,  which  cannot 
exceed  that  of  the  observer's  Specious  Present.  It  is 
thus  also  temporally  "extended."  It  may  thus  be 
regarded  as  a  four-dimensional  spatio-temporal  whole. 
I  define  a  sensum  as  a  part  of  a  sensible  field.  Now, 
if  we  consider  an  ordinary  three-dimensional  volume, 
like  a  cube,  and  neglect  the  question  of  duration 
altogether,  wre  see  that  anything  that  is  literally  a  part 
of  it  must  be  a  three-dimensional  volume  too.  For  it 
is  only  such  things  that  could  literally  fit  together  to 
make  up  the  cube.  Plane  sections  of  the  cube  are  not 
parts  of  it  in  this  literal  sense,  though  it  is  perfectly 
easy  to  define  by  Extensive  Abstraction  Pickwickian 
senses  in  which  planes,  lines,  and  points  can  be  truly 
and  usefully  said  to  be  "parts"  of  volumes.  In  the 
same  way,  it  is  clear  that  the  only  sort  of  thing  that 
can  literally  be  a  part  of  a  spatio-temporal  whole,  like 
a  sensible  field,  must  be  something  that  is  extended  in 


DATE   AND   DURATION  355 

time  as  well  as  in  space.  Any  actual  sensum  is  there- 
fore extended  both  spatially  and  temporally.  Granted 
that  no  sensum  is  to  be  held  to  last  longer  than  the 
sensible  field  of  which  it  is  a  part,  we  have  still  to  ask 
what  is  meant  by  the  statement  that  one  sensum  persists 
through  the  whole  of  a  certain  sensible  field  and  that 
another  sensum  does  not.  The  following  cases  can 
arise:  (i)  A  certain  place  in  a  sensible  field  may  be 
occupied  by  a  sense-quality  {e.g.,  a  colour  of  a  certain 
definite  shade,  brightness,  and  saturation)  throughout 
the  whole  duration  of  the  sensible  field.  We  should 
then  say  that  a  sensum  of  this  colour  has  persisted  and 
rested  in  one  sensible  place  throughout  the  whole 
duration  of  the  field.  Of  such  a  sensum  we  can  only 
say  that  it  cannot  last  longer  than  the  sensible  field  of 
which  it  is  a  part  (and  therefore  not  longer  than  the  dura- 
tion of  a  Specious  Present),  though,  of  course,  it  may 
be  continued  by  qualitatively  indistinguishable  sensa, 
occupying  similar  sensible  places  in  successive  sensible 
fields,  (ii)  A  certain  place  might  be  sensibly  occupied 
by  a  continuously  changing  sense-quality  throughout 
the  whole  duration  of  the  sensible  field.  This  means 
roughly  that,  if  we  divide  up  the  history  of  this  place 
throughout  the  duration  of  the  field  into  successive 
thinner  sections,  any  two  sections  will  be  occupied  by 
a  different  sense-quality,  but  the  thinner  we  make  the 
sections  the  more  nearly  alike  will  be  the  sense-qualities 
that  occupy  this  place  throughout  adjacent  sections. 
In  this  case  we  should  actually  "sense  the  change  of 
quality."  The  sensible  identity  of  place,  and  the 
continuity  of  the  sense-quality,  would  generally  be 
regarded  as  sufficient  to  justify  us  in  saying  that  a 
single  sensum  has  persisted  throughout  the  sensible 
field  and  has  rested  in  one  sensible  place,  but  that  it 
sensibly  and  continuously  changes  in  qualityv  (iii) 
It  might  be  possible  to  divide  the  history  of  a  certain 
sensible  place  in  a  sensible  field  into  three  successive 
sections,  of  which  the  first  is  occupied  by  a  quality  qv 


356  SCIENTIFIC  THOUGHT 

the  second  by  a  markedly  different  quality  q.,,  and  the 
third  by  a  markedly  different  quality  q:i.  We  should 
then  say  that  there  were  three  successive  sensa,  each  of 
which  persisted  for  so  long,  and  then  was  succeeded  by 
another.  If  the  middle  one  of  these  sections  should 
be  excessively  short,  we  could  say  that  we  had  sensed 
a  " sense-flash  of  quality  q.,  at  this  sensible  place."  (iv) 
It  might  happen  that,  as  we  divide  up  the  sensible  field 
into  successive  thinner  sections,  we  find  that  in  each 
section  there  is  a  sensible  place  occupied  by  the  same 
sense-quality.  Moreover,  the  shapes  of  these  sensible 
places  might  be  indistinguishable.  But  the  sensible 
places  occupied  by  this  quality  in  successive  sections 
of  the  sensible  field  might  differ.  And  it  might  be 
found  that  the  thinner  we  made  the  sections  the  more 
nearly  alike  were  the  sensible  places  occupied  by 
this  quality  in  adjacent  sections.  On  the  grounds  of 
this  continuity  of  place  and  identity  of  shape  and 
sensible  quality,  we  should  be  justified  in  saying  that 
we  were  dealing  with  a  single  sensum,  which  persists 
throughout  the  whole  of  the  sensible  field.  But  we 
should  actually  sense  its  movement ;  and  should  there- 
fore say  that  a  moving  sensum  of  such  and  such  shape 
and  sensible  quality  persisted  throughout  the  whole  of 
this  sensible  field.  In  real  life  it  is  unlikely  that  the 
shapes  of  the  successive  places  would  be  exactly  alike, 
or  that  precisely  the  same  sense-quality  would  occupy 
each  of  them.  But,  provided  that  the  change  of  shape 
and  of  sense-quality  was  continuous  in  the  sense  defined 
above,  we  should  still  say  that  we  were  dealing  with  a 
single  sensum  ;  but  should  add  that  it  changes  sensibly 
in  shape  and  quality  as  it  sensibly  moves.  Of  course 
a  moving  or  qualitatively  changing  sensum  need  not 
persist  throughout  the  whole  of  a  sensible  field,  any 
more  than  a  resting  or  qualitatively  fixed  one  need  do 
so.  The  change  may  begin  after  the  beginning  and 
end  before  the  end  of  the  sensible  field  in  question. 

I  think  that  we  have  now  said  all  that  is  necessary 


DATE   AND   DURATION  357 

about  the  duration  of  sensa.  As  in  all  questions  of 
duration,  the  answer  depends  in  part  on  mere  matters  of 
definition.  When  we  ask  how  long  so  and  so  lasts,  we 
have  first  to  lay  down  our  criterion  of  identity  for  so 
and  so.  If  anything  lasts  at  all,  the  successive  parts 
of  its  history  are  necessarily  numerically  different,  or 
they  could  not  be  successive.  Our  criterion  of  identity 
must,  therefore,  depend  on  identity  of  quality,  in  a  wide 
sense  of  that  word,  which  includes  shape  and  place. 
Thus  the  question  is:  "How  much  qualitative  differ- 
ence can  we  allow  between  successive  slices  of  a  long 
event  before  it  ceases  to  be  appropriate  to  call  the  whole 
event  the  history  of  so  and  so?"  Obviously,  this  is  a 
question  which  admits  of  various  answers;  but  no  one 
holds  that  complete  qualitative  identity  of  successive 
events  is  necessary  if  they  are  all  to  be  regarded  as 
parts  of  the  history  of  one  persistent  object.  I  have 
defined  the  word  sensum  in  such  a  way  that  nothing 
which  cannot  be  sensed  throughout  the  whole  of  some 
process  of  sensing  is  to  be  called  one  sensum,  no  matter 
how  great  the  qualitative  resemblance  and  the  con- 
tinuity between  successive  slices  of  this  long  event  may 
be.  Such  a  long  event  may  count  as  the  history  of  a 
single  sense-object ;  because  the  kind  of  identity  needed 
for  the  persistence  of  a  sense-object,  as  defined  by  me, 
is  different  from  that  required  for  the  persistence  of  a 
sensum.  Within  these  limits,  however,  I  have  not 
considered  that  complete  identity  of  place,  shape,  or 
sense-quality  is  essential  to  the  identity  of  a  sensum. 
I  therefore  recognise  the  existence  of  sensibly  moving 
and  sensibly  changing  sensa.  Since  the  experiences 
of  sensible  change  and  movement  are  peculiar  and 
important,  and  since  they  occur  within  fields  that  are 
sensed  as  wholes  by  processes  of  sensing  of  finite 
duration,  this  seems  to  be  the  most  reasonable  course 
to  take.  Anyone  who  disapproves  of  it  has  merely  to 
make  appropriate  modifications  in  his  definition  of  the 
word  sensum  ;  he  will  still  have  to  recognise  and  deal  as 


358  SCIENTIFIC   THOUGHT 

best    he    ran    with    all   the    facts    which    we   have    been 
passing  under  review. 

Dating  of  Sensa. — We  can  now  turn  to  the  subject 
of  date.  The  notion  of  date  only  becomes  perfectly- 
definite  when  we  deal  with  momentary  events  ;  and  no 
actual  events  are  momentary.  It  therefore  has  to  be 
defined  by  Extensive  Abstraction.  We  will  first  con- 
sider the  dating  of  sensa  which  are  sensed  by  a  single 
observer,  and  we  will  then  pass  to  the  concept  of 
temporal  relations  between  sensa  of  different  observers. 
When  a  meaning  can  be  assigned  to  the  statement  that 
a  sensum  sv  which  is  sensed  by  01}  is  contemporary 
with  sv  which  is  sensed  by  O,,  and  later  than  s3,  which 
was  sensed  by  03,  it  will  be  possible  to  see  what  is 
meant  by  the  notion  of  a  date  which  is  neutral  as 
between  various  observers.  But  I  must  just  say  a 
word  about  the  dates  of  acts  of  sensing. 

(a)  Temporal  Relation  between  Act  of  Sensing  and 
Sensum.  —  If  the  reader  will  refer  back  to  the  diagram, 
by  wrhich  we  illustrated  the  facts  of  the  Specious  Present, 
he  will  see  that  we  there  tacitly  assumed  that  a 
momentary  act  of  sensing  would  be  contemporary  with 
the  end-point  of  the  finite  event  which  it  senses.  This 
is  implied  by  making  lines,  like  01c\  in  the  diagram, 
normal  to  the  line  of  objects  sensed.  I  suppose  that  it 
is  possible  that  an  act  of  sensing  might  be  later  by  a 
finite  amount  than  the  whole  of  the  event  that  it  senses. 
It  could  not,  of  course,  on  our  view  of  the  future,  be 
earlier  than  any  part  of  what  it  senses.  For,  when  the 
act  is  present,  there  is  nothing  later  than  it ;  and  to 
sense  what  has  not  yet  become,  would  be  literally  to 
sense  nothing.  Our  assumption  seems  to  be  the  most 
reasonable  one  to  make.  On  the  one  hand,  there  is, 
so  far  as  I  know,  nothing  conclusive  against  it.  On 
the  other  hand,  the  distinguishing  mark  of  an  act  of 
memory  is  that  it  is  separated  by  a  finite  time-lapse  from 
the  latest  part  of  the  event  which  it  remembers.      Hence, 


DATE   AND   DURATION  359 

any  other  assumption  than  that  which  we  made,  would 
render  it  difficult  to  distinguish,  even  in  theory,  between 
an  act  of  sensing  and  an  act  of  remembering.  The 
practical  difficulty  which  there  sometimes  is  in  drawing 
this  distinction  can  easily  be  accounted  for  on  our  view. 
We  can  well  suppose  that,  as  the  gap  between  an  act 
of  remembering  and  the  end  of  the  event  remembered 
gets  shorter  and  shorter,  it  will  be  more  and  more 
difficult  to  distinguish  the  act  of  remembering  from  an 
act  of  sensing,  in  which,  if  we  are  right,  the  gap 
vanishes  altogether.  I  shall  therefore  take  it  that  the 
assumption  tacitly  made  in  the  diagram  is  justified.  In 
general,  then,  we  may  say  that  the  beginning  of  a  pro- 
cess of  sensing,  throughout  the  whole  of  which  an 
event  of  finite  duration  is  sensed,  is  contemporary  with 
the  end  of  the  event  in  question.  Thus,  in  the  diagram, 
Ox,  the  beginning  of  the  act  C^O.,,  is  contemporary 
with  e'v  the  end  of  the  event  e.-,e'v  which  is  sensed 
throughout  the  whole  of  this  process.  This  will  suffice 
as  to  the  connexion  between  the  dates  of  an  act  of 
sensing  and  of  an  event  sensed  by  it  ;  a  question  to 
which  nothing  comparable  arises  when  we  deal  with 
Space,  since  mental  acts  do  not  have  places,  as  they 
have  dates. 

(d)  Temporal  Relations  within  a  Sense-field. — Having 
cleared  this  point  out  of  the  way,  let  us  consider 
the  dating  of  sensa  that  are  sensed  during  the  life- 
history  of  a  single  observer.  This  inquiry  falls  into 
two  parts.  We  have  first  to  consider  the  dating  of 
sensa  that  fall  within  a  single  sensible  field  of  the 
observer,  and  then  to  consider  the  extension  of  this  to 
sensa  that  do  not  fall  into  the  same  sensible  field  but  into 
successive  ones.  I  must  first  clear  up  a  slight  ambiguity 
in  the  term  sensible  field.  In  the  last  chapter  we  counted 
the  fields  of  two  different  senses,  e.g.,  an  auditory  and  a 
visual  field  of  the  same  observer,  as  different  sensible 
fields  which  do  not  form  parts  of  a  single  larger  whole. 
This  is  true  as  regards  spatial  characteristics,  which  we 


36o  SCIENTIFIC   THOUGHT 

were  then  considering- ;  since  sensible  spatial  relations 
do  not  connect  the  sensa  of  one  sense  with  those  of 
another.  But,  as  regards  temporal  characteristics,  the 
distinction  between  the  sensible  fields  of  different  senses 
ceases  to  be  of  importance.  A  noise  that  I  sense 
auditorily  may  be  sensibly  and  literally  contemporary 
with  a  flash  of  colour  that  I  sense  visually.  We  can 
therefore  say  that  the  special  sensible  fields  of  the  various 
senses  form  parts  of  a  single  general  sensible  field,  so  far 
as  temporal  characteristics  are  concerned.  When  I 
speak  of  a  sensible  field  in  the  sequel,  I  shall  mean  a 
o-eneral  sensible  field,  unless  the  context  makes  it  plain 
that  I  am  referring  to  some  special  one,  such  as  that  of 
sight  or  that  of  hearing-. 

Let  us  then  take  a  certain  sensible  field  of  a  certain 
observer.  As  we  have  explained,  this  is  of  finite 
duration  and  its  parts  of  finite  duration  are  sensa.  Some 
of  these  endure  throughout  the  whole  of  it,  others  do 
not.  Of  two  sensa,  neither  of  which  endures  through- 
out the  whole  of  this  field,  one  may  be  completely 
separated  from  the  other,  i.e.,  one  may  cease  and  some 
third  sensum  may  intervene  before  the  other  begins. 
On  the  other  hand,  the  end  of  one  may  exactly  coincide 
with  the  beginning  of  the  other.  Or,  finally,  the  two 
may  partially  or  totally  overlap.  These  various  temporal 
relations  between  sensa  of  finite  duration  that  fall  into 
the  same  sensible  field  can  be  and  are  directly  sensed, 
just  as  the  spatial  relations  between  two  coloured  patches 
in  the  same  visual  field  can  be.  Two  sensa  would  be 
said  to  be  sensibly  simultaneous  if  each  completely  overlaps 
the  other.  If  one  sensum  only  partially  overlaps  another, 
there  is  a  shorter  part  of  one  which  completely  over- 
laps and  is  completely  overlapped  by  a  certain  shorter 
part  of  the  other.  Thus  these  two  parts  will  be  sensibly 
simultaneous,  though  the  wholes  are  not.  It  will  be 
seen  that  sensa  which  are  sensibly  simultaneous  both 
persist  through  the  same  slice  of  the  sensible  field.  As 
this  slice  is   made  thinner  and  thinner,  the  sensa  that 


DATE  AND   DURATION  361 

persist  through  it  are  made  shorter  and  shorter.  Pro- 
ceeding to  the  limit,  we  get  the  notion  of  exact  simul- 
taneity between  momentary  events.  The  reference  to 
limits  can  then  be  removed  by  Extensive  Abstraction. 
The  details  of  the  process  will  be  found  in  Whitehead. 

{b)  Temporal  Relations  within  a  Sense-history. — We 
can  see  roughly  how,  in  this  way,  the  sensa  that  fall 
within  a  single  sensible  field  can  be  arranged  in  a 
temporal  order  and  dated.  We  have  now  merely  to 
extend  this  to  successive  fields  of  the  same  observer. 
Any  sensum  in  a  later  field  is  later  than  any  sensum 
in  an  earlier  field.  A  field  is  later  than  another  if  it 
was  sensed  when  the  other  could  only  be  remembered. 
(This  is  not  the  meaning  of  being  later,  as  we  have 
seen,  but  it  is  a  criterion  of  it  that  we  can  and  do  use 
in  practice.)  Now  we  have  seen  that  earlier  and  later 
sections  of  any  one  sensible  field  can  be  distinguished 
and  dated.  Successive  fields  of  the  same  observer  are 
conceived  as  joining  on  to  each  other  in  the  same  way 
in  which  successive  sections  of  the  same  field  are  actually 
sensed  to  join  up  with  each  other  and  to  constitute  that 
field.  Thus  we  conceive  of  the  total  event,  that  is 
gradually  and  piecemeal  sensed  by  an  observer  in  the 
course  of  his  life,  as  being  completely  analogous  in  its 
temporal  characteristics  to  those  short  sections  of  it 
which  can  be  sensed  as  wholes  throughout  the  whole  of 
a  single  process  of  sensing. 

The  particular  duration  of  an  observer's  Specious 
Present  may  fairly  be  regarded  as  a  peculiarity  of 
himself  or  of  his  species.  It  is  known  that  this  duration 
is  much  the  same  for  all  men  under  normal  conditions. 
It  is  known  that  it  is  short  as  compared  with  the  dura- 
tion of  most  events  that  are  practically  interesting  to  us, 
but  long  as  compared  with  that  of  many  events — such  as 
a  single  vibration  of  an  electron — which  are  of  great 
scientific  importance.  (These  statements  can,  of  course, 
only  receive  a  perfectly  definite  meaning  at  a  later  stage, 

when  the  temporal  characteristics  of  physical  objects  and 

2  A 


362  SCIENTIFIC   THOUGHT 

events  have  been  discussed.)  In  the  meanwhile  it  is  a 
fact  that  we  can  easily  conceive  of  Specious  Presents 
which  are  longer  than  our  own.  In  particular,  we  can 
imagine  ourselves  replaced  by  an  observer  who  differs 
in  no  respect  from  us  except  that  his  Specious  Present 
covers  the  whole  of  his  history.  Such  a  man  would  still 
distinguish  the  present  from  the  past  and  the  future, 
and  the  less  from  the  more  remote  past.  But,  whilst  the 
distinction  between  present  or  past  and  future  would  be 
as  important  for  him  as  for  us,  since  it  is  the  distinction 
between  something  and  nothing,  the  difference  between 
present  and  past  would  be  much  less  important  for  him 
than  for  us.  With  us  the  sinking  of  an  event  into  the 
past  is  accompanied  by  a  change  in  our  mode  of 
cognising  it.  We  have  to  cognise  it  by  memory  or 
inference,  if  at  all  ;  and  the  further  it  sinks  into  the  past 
the  vaguer  is  our  knowledge  of  it  likely  to  become. 
But  the  hypothetical  observer  would  sense  the  whole  of 
his  past  history  at  every  moment,  and  therefore  would 
have  the  same  full  knowledge  of  its  earliest  parts  as  of 
those  that  have  only  just  become.  This  conception  of 
an  observer  with  an  indefinitely  long  Specious  Present 
is  useful,  because  we  conceive  the  whole  content  of  our 
history  to  be  such  as  this  observer  would  sense  it  to  be. 

(c)  Neutral  Temporal  Relations. — We  have  now  to 
deal  with  the  temporal  relations  between  sensa  of 
different  observers.  Let  us  call  the  whole  series  of 
sensible  fields  which  an  observer  O  senses  in  the  course 
of  his  life,  O's  sense-history.  We  have  seen  that,  within 
any  sense-history,  momentary  sections  can  be  defined 
and  dated  by  Extensive  Abstraction.  We  have  now 
to  take  into  account  the  existence  of  a  number  of  ob- 
servers, each  with  his  own  sense-history.  Our  task  is 
to  treat  the  temporal  relations  between  a  certain  event 
in  one  sense-history  and  a  certain  event  in  another. 
Let  us  start  with  the  fundamental  relation  of  simul- 
taneity. This  is  illustrated  in  its  most  literal  sense  by 
sensa  in  the  same  field  ;  the  question  is,  how  far  it  can 


DATE  AND   DURATION  363 

be  extended  to  a  pair  of  sensa,  one  from  the  field  of 
one  observer  and  the  other  from  the  field  of  another 
observer. 

We  will  begin  by  pointing  out  a  complication  which 
did  not  arise  over  spatial  relations.  When  we  dis- 
cussed in  the  last  chapter  the  meaning  of  the  statement 
that  visual  sensa  from  several  different  fields  are  "in 
the  same  place,"  it  was  clear  that  we  were  giving  a 
definition  and  not  a  mere  test.  This  is  perfectly  evident 
from  the  following  consideration  :  Two  different  visual 
appearances  of  a  penny  are  at  once  sensibly  present 
in  different  places  and  optically  present  in  the  same 
place.  This  would  be  a  sheer  contradiction  if  optical 
and  sensible  presence  had  the  same  meaning.  Thus, 
when  we  say  that,  under  such  and  such  conditions, 
two  visual  sensa  are  optically  compresent,  the  con- 
ditions are  part  of  the  definition  of  what  is  meant  by 
"optical  compresence."  It  is  impossible  to  hold  that 
optical  presence  really  means  the  same  thing  as  sensible 
presence,  and  that  the  conditions  mentioned  are  simply 
tests,  by  which  we  can  establish  that  this  relation  holds 
in  cases  where  the  evidence  of  direct  sense-awareness 
fails  us. 

Now,  when  we  deal  with  temporal  relations,  and  try 
to  state  the  conditions  under  which  two  sensa  in  different 
sense-histories  are  said  to  be  contemporary,  it  is  by 
no  means  obvious  whether  we  are  defining  a  new  sense 
of  simultaneity,  or  merely  giving  a  test  by  which  the  fact 
of  simultaneity,  in  the  old  sense  of  the  word,  can  be  estab- 
lished in  cases  where  it  cannot  be  directly  sensed.  I 
think  that  failure  to  distinguish  clearly  these  two  possi- 
bilities has  caused  much  confusion  in  the  writers  and 
readers  of  books  on  the  Theory  of  Relativity.  It  is 
very  much  more  plausible  to  hold  that  "simultaneity" 
always  means  the  same  in  all  its  applications,  than  to 
hold  that  "compresence"  means  the  same  always  and 
everywhere.  For  it  is  admitted  that  sensa  belonging 
to  different   senses   of  the  same  observer  can  be  con- 


364  SCIENTIFIC   THOUGHT 

temporary  with  each  other,  in  precisely  the  same  way 
in  which  two  visual  or  two  tactual  sensa  of  the  same 
observer  can  be  contemporary.  It  is  therefore  not 
glaringly  absurd  to  suggest  that  sensa  belonging  to 
different  sense-histories  may  be  contemporary  in  the 
same  way  in  which  sensa  in  the  same  sense-history  can 
be  so.  In  that  case  the  conditions  under  which  two 
sensa  belonging  to  different  sense-histories  are  said 
to  be  simultaneous  do  not  define  a  new  meaning  of 
u  simultaneity,"  but  merely  give  a  test  for  simultaneity, 
in  the  old  meaning  of  the  word,  which  we  use  in  those 
unfavourable  cases  where  the  relation  cannot  be  directly 
sensed. 

The  only  way  of  deciding  between  the  two  alter- 
natives would  be  the  following  :  The  relation  of  sensible 
simultaneity  has  certain  logical  characteristics.  For 
instance,  it  is  transitive,  i.e.,  if  A  has  it  to  B,  and  B  has 
it  to  C,  then  A  necessarily  has  it  to  C.  If  we  found  that 
"  simultaneity,"  as  tested  by  the  conditions  commonly 
laid  down,  did  not  have  all  these  logical  characteristics, 
we  could  conclude  that  we  were  dealing  with  a  new 
meaning  of  "  simultaneity."  This  would  not,  of  course, 
preclude  the  possibility  that  sensa  from  different  sense- 
histories  have  also  in  fact  the  relation  of  simultaneity,  in 
the  original  sense.  But  it  would  show  that  the  conditions 
laid  down  were  not  a  test  for  that  relation.  And  it 
might  turn  out  that  no  conditions  that  we  could  think 
of  would  be  a  test  for  that  relation  between  sensa  belong- 
ing to  different  histories.  In  that  case,  it  would  be  a 
mere  personal  idiosyncrasy  to  hold  that  simultaneity,  in 
the  original  sense,  ever  holds  between  sensa  in  different 
histories  ;  and  it  would  be  better  to  regard  the  conditions 
laid  down  as  defining  a  new  sense  of  "  simultaneity." 
For  the  present  we  must  confine  ourselves  to  the  question 
of  fact:  "Under  what  conditions  do  people  hold  that 
sensa  from  different  sense-histories  are  contemporary?" 
We  may  later  on  raise  the  question  whether  these  condi- 
tions are  simply  a  test  for  simultaneity,  in  the  original 


DATE   AND   DURATION  365 

sense  of  the  word,  or  whether  they  define  a  new  meaning 
of  "  simultaneity."  I  will  use  the  vague  word  determine, 
to  cover  both  "  being  a  test  for  "  and  "  being  a  condition 
of"  so  and  so. 

Under  what  conditions  do  two  observers  in  fact 
judge  that  they  sense  two  contemporary  sensa?  Often 
two  men  assert  that  they  both  "see  the  same  flash"  or 
"  hear  the  same  noise."  If  this  means  literally  that  the 
two  men  sense  precisely  and  numerically  the  same  visual 
or  auditory  sensum,  and  if  their  statement  be  true  when 
so  interpreted,  it  is  easy  to  lay  down  the  conditions 
under  which  sensa  from  their  respective  sense-histories 
would  be  said  to  be  simultaneous.  If  A's  twinge  of 
toothache  be  sensibly  contemporary  with  this  common 
sensum,  and  B's  twinge  of  stomach-ache  be  also  sensibly 
contemporary  with  it,  we  might  say  that  A's  toothache 
and  B's  stomach-ache  are  neutrally  contemporary  with 
each  other. 

Now  there  is  no  doubt  at  all  that  it  is  under  condi- 
tions of  this  kind  that  sensa  belonging  to  different  sense- 
histories  are  said    to    be    "simultaneous."     But  it  will 
take  us  some  time  to  find  the  exact  meaning  of  these 
conditions,  and  to  make  sure  what  are  the  properties  of 
"simultaneity"  thus  established.      Evidently  the  first 
question  that  arises  is  :  What  is  meant  by  the  common 
statement  that  two  observers  "  hear  the  same  noise"  or 
"  see  the  same  flash  "?     Do  they  mean  that  they  sense 
a  single  sensum  which  is  common  to  the  sense-histories 
of  both  of  them  ?     And,  whether  they  mean  it  or  not, 
is  it  ever  true?     As  ordinary  people  do  not  explicitly 
draw  a  distinction  between  sensa  and  physical  objects, 
it  is  difficult  to  say  whether  they  mean  that  they  sense 
a  common  visual  sensum  when  they  assert  that  they  see 
the  same  flash.      But,  as  it  is  quite  certain  that  by  words 
like  "  seeing  "  and   "hearing,"  people  commonly  mean 
to  refer  to  acts  of  perceiving  and  not  to  acts  of  sensing, 
it  is  probable  that  by  "the  same  flash"  or  "the  same 
noise"  they  intend  to  refer  to  a  common  physical  eve?it 


366  SCIENTIFIC   THOUGHT 

and  not  necessarily  to  a  common  sensum.  In  that  case 
no  such  simple  interpretation  of  the  statement  that  A's 
toothache  and  B's  stomach-ache  are  contemporary,  as  was 
offered  above,  can  be  accepted.  For  we  should  need  to 
know  how  to  determine  whether  two  sensa  are  con- 
temporary with  the  same  physical  event  before  we  could 
determine  whether  they  are  contemporary  with  each 
other.  Now,  at  present,  all  that  we  know  is  what  is 
meant  by  one  sensum  of  an  observer  being  simultaneous 
with  another  sensum  of  //W  observer.  Hence  to  determine 
neutral  simultaneity  between  two  sensa  in  terms  of  the 
simultaneity  of  each  with  a  common  physical  event  tells 
us  nothing,  since  it  involves  simultaneity  in  a  sense 
which  has  not  yet  been  determined. 

Let  us  then  ask  ourselves  what  is  the  exact  cash 
value  of  the  statement  that  A  and  B  hear  the  same  noise. 
I  would  like  to  point  out  at  the  beginning  that  nothing 
that  has  been  said  so  far  about  sensa  and  sensible  fields 
precludes  the  possibility  that  one  and  the  same  sensum 
should  be  in  several  sensible  fields  of  different  observers. 
A  sensum  is  defined  as  a  part  of  some  sensible  field  ; 
this  clearly  leaves  open  the  possibility  that  two  or  more 
sensible  fields,  sensed  by  different  observers,  might  have 
a  part  in  common.  If  so,  there  are  sensa  common  to 
several  fields  of  several  different  observers.  Whether 
this  is  an  actual  fact  remains  to  be  seen. 

It  is  fairly  easy  to  show,  subject  to  certain  subtle 
qualifications,  that  when  a  number  of  observers  say  that 
they  hear  the  same  noise  and  that  they  see  the  same 
flash,  this  cannot  mean  both  that  they  all  sense  the  same 
auditory  sensum  and  that  they  all  sense  the  same  visual 
sensum.  For,  as  we  shall  see  in  a  moment,  it  is  very 
difficult  to  reconcile  this  view  with  all  the  facts.  Let  us 
suppose  that  I  fire  a  pistol,  and  that  there  is  a  number 
of  other  observers  dotted  about  at  different  places.  All 
the  observers,  including  myself,  will  sense  a  short 
auditory  sensum  and  a  short  visual  sensum.  These 
will  be  sensibly  contemporary  for  me  ;  for  an  observer 


DATE   AND   DURATION  367 

at  some  distance  from  me  they  will  only  partially  over- 
lap, the  visual  sensum  beginning  before  the  auditory 
one  does  so.  For  an  observer  still  further  off,  the  visual 
sensum  will  totally  precede  the  auditory  one,  though 
both  may  be  in  the  same  sensible  field.  Finally,  for  a 
very  distant  observer  the  visual  sensum  may  fall  into  a 
different  (and  earlier)  field  from  that  into  which  the 
auditory  sensum  falls.  Nevertheless,  all  the  observers, 
on  comparing  notes,  will  say  that  they  heard  the  same 
noise  and  saw  the  same  flash.  Now,  if  this  literally 
means  that  there  is  one  single  visual  sensum  which 
they  all  sense,  and  one  single  auditory  sensum  which 
they  all  sense,  we  shall  have  to  hold  that  the  same  pair 
of  sensa  can  be  both  sensibly  simultaneous,  partially 
overlapping,  and  completely  separated  in  time.  Now 
these  relations  seem  to  be  incompatible  with  each  other, 
and  therefore  we  seem  forced  to  conclude  that,  when 
several  observers  say  that  they  see  the  same  flash  and 
hear  the  same  noise,  this  cannot  mean  both  that  they  all 
sense  one  and  the  same  visual  sensum,  and  that  they  all 
sense  one  and  the  same  auditory  sensum.  Theoretically, 
it  would  be  possible  to  interpret  one  of  these  statements 
{e.g.,  that  they  all  saw  the  same  flash)  in  this  literal  way, 
provided  we  did  not  interpret  the  other  (viz.,  that  they 
all  heard  the  same  noise)  literally.  But,  even  apart 
from  the  additional  facts  which  have  led  physicists  to 
ascribe  a  finite  velocity  to  light  as  well  as  to  sound, 
such  a  course  would  hardly  be  reasonable.  If  at  least 
otie  of  the  statements,  that  we  all  hear  the  same  noise 
and  that  we  all  see  the  same  flash,  must  be  interpreted 
in  some  Pickwickian  manner,  it  is  hardly  reasonable  to 
suppose  that  the  other  can  be  interpreted  literally. 

Is  there  any  way  out  of  the  conclusion  that  to  hear 
the  same  sound  and  to  see  the  same  flash  cannot  mean 
that  a  number  of  observers  literally  sense  a  single  visual 
and  a  single  auditory  sensum  ?  So  far  as  I  can  see,  there 
are  at  least  two  alternative  wavs  in  which  this  conclusion 
could  be  avoided.      One  would  be  to  hold  that  sensa  can 


;..S  SCIENTIFIC    THOUGHT 

be  sensed  at  various  times  after  they  have  ceased  to 
persist,  and  that  the  further  a  man  is  from  a  source  of 
sound,  the  greater  is  the  gap  between  his  act  of  sensing 
and  the  end  of  the  auditory  sensum  which  it  senses.  I 
do  not  think  that  this  is  a  satisfactory  alternative,  for 
reasons  which  I  have  given  earlier  in  this  chapter,  when 
I  tried  to  justify  the  view  that  the  beginning  of  a  process 
of  sensing,  throughout  which  a  finite  event  is  sensed, 
is  contemporary  with  the  end  of  that  event. 

The  second  alternative  is  a  much  more  important 
one.  It  is  to  adopt  the  usual  expedient,  which  has 
already  been  mentioned  as  useful  when  two  entities  seem 
to  have  incompatible  relations  to  each  other.  This 
expedient  is  to  assume  that  what  has  been  taken  to  be 
a  dyadic  relation  between  these  two  entities  is  really 
irreducibly  polyadic,  and  involves  some  other  term  or 
terms  beside  the  two  entities  in  question.  It  is  un- 
doubtedly true  that  the  same  pair  of  sensa  cannot  be 
simultaneous,  and  partially  overlapping,  and  wholly 
separated,  -with  respect  to  the  sense-history  of  a  single 
observer.  But  suppose  that  this  pair  of  sensa  belongs 
to  the  sense-histories  of  several  observers,  and  that  the 
temporal  relations  in  question  are  really  irreducibly 
triadic.  Suppose  that  the  minimum  intelligible  state- 
ment that  can  be  made  about  the  temporal  relations  of 
two  sensa  in  a  sense-history  is  of  the  form  "  sx  is  con- 
temporary with  s2  (or  partially  overlaps  it,  or  wholly 
succeeds  it,  as  the  case  may  be)  with  respect  to  the 
sense-history  //."  In  that  case  there  need  be  no  incon- 
sistency in  the  same  pair  of  sensa  being  contemporary 
with  respect  to  one  sense-history,  partially  overlapping 
with  respect  to  another,  and  completely  separated  with 
respect  to  a  third  sense-history.  We  see  then  that  our 
argument  from  the  facts  of  sound  does  not  conclusively 
prove  that,  when  a  number  of  observers  say  that  they 
all  hear  the  same  sound  and  see  the  same  flash,  they 
cannot  all  be  sensing  precisely  the  same  auditory 
sensum  and  precisely  the  same  visual  sensum.     It  does, 


DATE  AND   DURATION  369 

however,  tie  us  down  to  one  of  two  alternatives.  Either 
this  conclusion  must  be  accepted,  or  we  must  give  up  the 
common-sense  notion  that  the  temporal  relations  between 
the  sensa  in  the  same  sense-history  are  dyadic,  and  must 
substitute  for  it  the  view  that  they  are  at  least  triadic, 
and  that  the  third  term  which  is  always  involved  is  some 
sense-history  in  which  both  the  sensa  are  contained. 

Is  there  any  way  of  deciding  between  these  two 
alternatives?  I  think  that  we  can  at  least  show  that 
the  second  alternative  could  not  stand  by  itself,  but 
would  need  to  form  part  of  a  general  Multiple  Relation 
theory  of  sensible  appearances.  The  various  observers 
in  my  example  do  not  really  all  sense  auditory  sensa 
which  are  exactly  alike  in  quality.  Both  the  auditory 
and  the  visual  sensa  which  are  sensed  by  very  distant 
observers  are  much  fainter  than  those  which  are  sensed 
by  me  and  by  observers  near  me.     Now,  on  the  sensum  v 

theory,  sensa  have  all  the  qualities  that  they  appear  to  \^/ 
have.  What  really  differs  in  quality  cannot  be  numeri-  \^ 
cally  identical  ;  hence  a  faint  sensum  cannot  be  the  same  .  ^^"^) 
sensum  as  a  loud  one,  however  much  alike  they  may 
be  in  other  respects.  This  argument  would  not  be  5 
conclusive  on  a  Multiple  Relation  theory  of  sensible 
appearance ;  because,  on  such  a  theory,  sensa  need 
not  have  the  qualities  that  they  seem  to  have.  But  I 
am  deliberately  ignoring  Multiple  Relation  theories 
of  sensible  appearance  in  this  book,  in  order  to  test 
Sensum  theories,  as  Cardinal  Newman  tested  the 
Thirty-nine  Articles  to  see  how  much  Catholic  Truth 
they  could  be  made  to  contain.  I  am  as  indifferent  as 
he  was  to  the  possibility  of  the  subject  of  my  experi- 
ment blowing  up  at  the  end  of  the  process  ;  for  negative 
results  are  often  as  valuable  as  positive  ones.  Accord- 
ingly, I  think  I  may  conclude  that,  on  the  Sensum 
theory  of  sensible  appearance,  it  cannot  be  true  that 
when  a  number  of  observers  say  that  they  see  the 
same  flash  or  hear  the  same  noise  they  literally  sense  a 
single  visual  or  auditory  sensum  common  to  all  of  them. 


370  SCIENTIFIC   THOUGHT 

On  either  alternative  the  determination  of  neutral 
simultaneity  between  A's  toothache  and  B's  stomach- 
ache is  going  to  be  a  much  harder  job  than  it  would  be 
if  the  facts  about  sound  (and  as  we  shall  see  later,  about 
light)  were  different.  If  what  we  call  the  same  noise  be 
really  a  group  of  auditory  sensa,  the  simultaneity  of  A's 
toothache  and  of  B's  stomach-ache  with  this  noise  only 
means  that  the  former  is  sensibly  contemporary  with  a 
certain  auditory  sensum  sensed  by  A,  and  that  the  latter 
is  sensibly  contemporary  with  a  different  auditory  sensum 
sensed  by  B.  It  is  true  that  these  two  auditory  sensa 
are  both  members  of  a  group  of  sensa  which  are  so  con- 
nected with  each  other  that  the  whole  is  called  one  noise. 
But  it  is  by  no  means  obvious  that  this  rather  indirect 
relation  between  A's  toothache  and  B's  stomach-ache  will 
have  the  kind  of  properties  that  we  demand  of  simul- 
taneity. The  same  difficulty  arises  if  we  suppose  that 
there  is  literally  only  one  auditory  sensum,  which  is 
sensed  by  both  A  and  B,  and  that  the  relation  of 
sensible  simultaneity  is  triadic.  The  fact  that  A's 
toothache  is  contemporary  with  a  certain  auditory 
sensum  with  respect  to  A's  sense-history,  and  that 
B's  stomach-ache  is  contemporary  with  the  same 
auditory  sensum  with  respect  to  B's  sense-history,  does 
indeed  constitute  a  relation  between  the  toothache  and 
the  stomach-ache.  But  there  seems  no  particular  reason 
to  expect  that  this  relation  will  have  the  kind  of  pro- 
perties that  we  demand  of  simultaneity. 

Let  us  begin  by  imagining  a  set  of  observers  who 
tried  to  determine  neutral  simultaneity  entirely  by 
sound.  We  need,  not  suppose  them  to  be  blind,  but 
we  will  suppose  that  they  have  no  means  of  producing 
flashes  of  light  either  by  igniting  combustible  things 
or  by  opening  and  shutting  opaque  shutters.  A 
number  of  them  hear  what  they  call  the  same  noise. 
They  all  sense  short,  outstanding  auditory  sensa. 
These  are  very  similar  in  quality  and  are  connected 
with  a  common  centre  in  the  way  described  in  the  last 


DATE   AND   DURATION  371 

chapter.  They  agree  that  any  pair  of  sensa  belonging 
to  the  sense-histories  of  different  observers  shall  count 
as  neutrally  simultaneous  provided  that  one  is  sensibly 
contemporary  with  one  member  of  such  a  group  of 
auditory  sensa  and  that  the  other  is  sensibly  con- 
temporary with  one  member  of  the  same  group  of 
auditory  sensa.  What  properties  will  neutral  simul- 
taneity, so  determined,  possess? 

In  the  first  place,  it  will  be  necessary  slightly  to 
extend  this  way  of  determining  neutral  simultaneity, 
so  as  to  deal  with  the  various  auditory  sensa  that 
constitute  a  single  noise.  If  we  are  going  to  allow 
them  to  have  any  neutral  temporal  relations  to  each 
other,  we  must  suppose  that  they  are  all  neutrally  con- 
temporary, or  we  shall  get  into  difficulties.  For  suppose 
that  any  two  sensa,  s\  and  j2,  belonging  to  different 
sense-histories,  were  neutrally  contemporary,  as  deter- 
mined by  the  present  method.  This  will  mean  that  st 
is  sensibly  contemporary  with  one  auditory  sensum  and 
that  s.2  is  sensibly  contemporary  with  another  auditory 
sensum,  and  that  these  two  auditory  sensa  belong  to 
a  single  noise.  Now,  unless  we  hold  that  the  two 
auditory  sensa  in  question  are  neutrally  contemporary 
with  each  other,  we  shall  have  to  admit  that  two 
neutrally  contemporary  sensa  can  be  respectively 
sensibly  simultaneous  with  two  auditory  sensa  which 
are  neutrally  successive  to  each  other.  This  does  not 
accord  with  the  view  of  neutral  temporal  relations  as 
a  consistent  extension  of  the  sensible  temporal  relations 
that  hold  between  sensa  in  the  same  sense-history.  We 
must  therefore  determine  neutral  simultaneity,  on  the 
present  method,  as  follows:  Two  sensa  in  different 
sense-histories  are  neutrally  contemporary  if  (a)  they 
are  two  auditory  sensa  belonging  to  the  same  noise  ; 
or  (b)  they  are  respectively  sensibly  simultaneous  with 
two  auditory  sensa  which  belong  to  the  same  noise. 
Would  such  a  mode  of  determination  be  satisfactory? 

Let   A  and  B  be   two  observers   at   a   considerable 


372  SCIENTIFIC  THOUGHT 

distance  apart,  and  let  there  be  a  bell  near  A  and 
another  bell  near  B.  Let  the  strokes  of  both  bells  be 
audible  to  both  observers.  We  will  call  them  "  A's 
bell  "and  "  B's  bell"  respectively.  Suppose  that  A's 
bell  ring's  and  that  B  hears  the  noise.  It  may  happen 
that  B's  bell  rings  at  such  a  date  that  he  hears  its  stroke 
at  the  same  time  as  he  hears  the  stroke  of  A's  bell.  If 
so,  A  will  hear  this  stroke  of  B's  bell  sensibly  later  than 
the  stroke  of  his  own  bell.  Call  A's  sensum  of  the 
stroke  of  A's  bell  aA)  A's  sensum  of  the  stroke  of  B's 
bell  ain  B's  sensum  of  the  stroke  of  A's  bell  bA,  and 
B's  sensum  of  the  stroke  of  B's  bell  bB.  Then  by 
definition  we  have  : 

(i)  aA  is  neutrally  contemporary  with  bA  ; 

(2)  a,,  is  neutrally  contemporary  with  b„  ; 
and,  by  the  terms  of  the  experiment,  we  have 

(3)  bn  is  sensibly  contemporary  with  bA. 
Under  these  circumstances  we  should  find  that 

(4)  aB  is  sensibly  later  than  aA. 

Now,  if  neutral  simultaneity  be  just  an  extended 
application  of  sensible  simultaneity,  we  should  expect 
that  (2)  and  (3)  would  together  imply  that  aB  is  neutrally 
contemporary  with  b A.  Combining  this  with  (1),  we 
should  expect  to  find  that  aA  and  aB  were  sensibly 
simultaneous.  But  this  contradicts  the  fact  stated  in 
(4).  In  fact,  if  we  determine  neutral  simultaneity  in 
this  way,  we  shall  find  that  two  sensa  in  the  same 
sense-history  can  be  neutrally  simultaneous  respectively 
with  two  sensa  in  another  sense-history,  which  are 
sensibly  simultaneous  with  each  other  ;  and  yet  the 
first  pair  of  sensa  are  not  sensibly  simultaneous  with 
each  other,  but  are  sensibly  successive.  Thus  neutral 
simultaneity,  determined  by  this  method,  cannot  be  a 
mere  extension  of  sensible  simultaneity.  This  can 
only  be  got  over  if  we  admit  that,  when  two  people 
"  hear  the  same  noise,"  the  auditory  sensum  of  the  one 
who  is  nearer  the  source  is  neutrally  earlier  than  that 


DATE  AND   DURATION  373 

of  the  one  who  is  further  away  from  it.  But,  as  soon 
as  we  admit  this,  the  purely  auditory  determination  of 
neutral  simultaneity  has  been  given  up  ;  for  we  cannot 
determine  in  purely  auditory  terms  the  neutral  temporal 
relations  between  auditory  sensa  which  belong  to  "the 
same  noise."  We  have  to  introduce  spatial  measure- 
ment, and  the  notion  of  influences  travelling  out  from 
sources  with  a  finite  velocity.  The  intimate  linkage  of 
Space  and  Time  becomes  evident  here,  as  in  so  many 
places. 

So  far  then  we  see  that,  if  observers  tried  to  determine 
neutral  temporal  relations  by  sound  alone,  they  would 
be  forced  to  the  view  that  what  they  call  the  same  noise 
is   a   set   of  auditory  sensa  of  different  neutral    dates  ; 
these    dates   depending    on    the   distance    between    the 
observer   who   senses  a  sensum  of  the  group  and   the 
source  of  the    noise.     This   fact  was  early  recognised 
about  sound  for  several  reasons,     (i)  Sound  travels  so 
slowly  that  the  difficulties  pointed  out  above  are  quite 
obvious  to  ordinary  observers  at   reasonable  distances 
apart,  and    provided    with    no   delicate  apparatus,     (ii) 
Sounds,  as  we  have  seen,  are  not  thought  of  as  confined 
to  a  central  volume,  but  as  being  in  all  the  space  that 
surrounds  their  source.     Each  observer  is  thought  of 
as  sensing  the  particular  part  of  this  physical  field  of 
sound   which  is  "where  he  is  at  the  moment."     It  is 
thus   natural   enough  to  think  of  this  physical  field  as 
travelling   out   from    the  centre   and  reaching  different 
observers   at   different   times.      (iii)    Again,    the   phen- 
omenon of  echoes  makes  the  notion  of  the  velocity  of 
sound    pretty   obvious    to  anyone.     An    echo    is  quali- 
tatively very  much  like  the  original  sound  with  which 
it  is  obviously  connected.     But  it  is  separated  from  it, 
as  a  rule,  by  a  distinct  sensible  interval.     This  naturally 
suggests  something  travelling  from  the   observer   to  a 
wall  (for  instance),  and    then  travelling   back    to  him. 
(iv)  Lastly,  we  are  not  like  the  observers  in  our  example. 
We  can   produce  flashes  of  light  by  various  means  at 


374  SCIENTIFIC   THOUGHT 

will.  Now,  if  a  number  of  observers  count  two  sensa 
as  neutrally  contemporary  with  each  other,  when  each 
is  sensibly  contemporary  with  the  same  flash  of  light 
that  they  all  see,  they  will  not,  in  ordinary  life,  get  into 
difficulties  which  arise  for  observers  who  try  to  define 
neutral  simultaneity  by  means  of  sound.  But,  of  course, 
if  they  do  this,  they  will  be  obliged  to  recognise  that«the 
various  auditory  sensa  which  they  sense  when  they  say 
that  they  all  hear  the  same  noise  are  not  neutrally  con- 
temporary. It  is,  in  fact,  by  a  combination  of  ight- 
signals  and  sound-signals  that  the  velocity  of  sound  is 
generally  measured. 

The  next  step  that  naturally  suggests  itself  is  to 
determine  the  neutral  simultaneity  between  two  sensa 
in  different  sense-histories,  as  the  relation  which  holds 
between  the  two  when  each  is  sensibly  contemporary 
with  some  sensum  of  the  group  which  constitutes  a 
single  flash  of  light.  If  we  adopt  this  method,  we  shall 
have  to  begin  by  extending  it  slightly  in  the  same 
direction,  and  for  the  same  reasons  as  we  extended  the 
auditory  method  of  determining  neutral  simultaneity. 
That  is,  we  shall  have  to  assume  that  two  visual  sensa 
belonging  to  the  same  flash  are  neutrally  contemporary, 
or  we  shall  get  into  difficulties.  We  may  therefore  give 
the  following  as  the  visual  definition  of  neutral  simul- 
taneity :  Two  sensa,  belonging  to  different  sense- 
histories,  are  neutrally  contemporary,  if  (i)  they  are  two 
visual  sensa  of  a  group  which  constitutes  a  single  flash  ; 
or  (ii)  are  respectively  sensibly  simultaneous  with  two 
visual  sensa  which  belong  to  such  a  group. 

There  is,  I  think,  no  doubt  that  this  is  the  way  of 
determining  neutral  simultaneity,  with  which  we  all 
work  in  practice,  except  in  extremely  delicate  scientific 
investigations  or  in  cases  where  distances  of  astronomical 
order  of  magnitude  are  under  discussion.  Nevertheless, 
we  all  know  that  no  scientist  would  accept  it  as  ultimately 
satisfactory.  He  would  point  to  the  facts  which  are 
alleged  to  prove  that  light  travels  with  a  finite  velocity 


DATE   AND   DURATION  375 

as  a  conclusive  objection  to  the  definition.  The  asser- 
tion that  light  travels  with  a  finite  velocity  implies, 
inter  alia,  that  there  is  an  extremely  important  sense  in 
which  the  various  sensa  of  observers  in  different  places 
who  see  the  same  flash  are  not  simultaneous  but  succes- 
sive. The  above  definition  of  neutral  simultaneity  is 
therefore  unsatisfactory,  because  it  leads  us  to  call  sensa 
simultaneous,  which  are  in  some  very  important,  but  as 
yet  undefined  sense,  successive. 

Let  us  then  consider  this  definition  and  the  facts  that 
are  held  to  render  it  inappropriate.  In  the  first  place, 
there  are  two  things  to  be  said  in  its  favour:  It  is  not 
circular,  and  it  does  not  directly  conflict  with  our 
judgments  about  sensible  temporal  relations,  as  the 
attempted  auditory  definition  did.  It  would,  of  course, 
be  circular  if  we  could  not  define  what  we  mean  by  "  the 
same  flash "  without  introducing  temporal  relations 
between  sensa  in  different  sense-histories.  But  we  can 
define  "the  same  flash"  without  this.  A  number  of 
observers  may  be  said  to  see  the  same  flash  when  the 
following  conditions  are  fulfilled  :  (i)  Each  is  aware  of 
a  single  outstanding  visual  sensum  of  very  short  dura- 
tion, (ii)  These  sensa  are  all  qualitatively  very  much 
alike,  (iii)  They  are  all  optically  compresent  at  a 
common  centre,  in  the  sense  defined  in  the  last  chapter. 
(The  first  condition  seems  to  be  enough  to  secure  that 
we  are  all  dealing  with  a  single  flash,  and  that  different 
observers  are  not  seeing  similar  but  successive  flashes. 
For,  if  successive  flashes  were  being  sent  out,  some  at 
least  of  the  observers  would  sense  two  or  more  qualita- 
tively similar  sensa  which  were  sensibly  successive.) 

Again,  there  is  nothing  in  our  light-experiences  to 
correspond  to  the  case  that  we  adduced  of  two  distant 
observers  hearing  two  bells,  and  one  of  them  finding 
his  auditory  sensa  sensibly  contemporary,  and  the  other 
finding  the  auditory  sensa  belonging  to  the  two  noises 
sensibly  successive.  We  can  only  deal  with  pairs  of 
observers  separated  by  distances  of  a  few  miles  ;  and 


3/0  SCIENTIFIC   THOUGHT 

for  such  distances  there  is  no  conflict  between  sensible 
temporal  relations  and  neutral  temporal  relations  as 
determined  by  light-signals. 

It  is  therefore  possible  to  determine  neutral  simul- 
taneity visually  without  committing  a  circle  and  without 
conflict  with    any  judgments   of  sensible   simultaneity 
that  we  can  make.     The  conflict  is  with  the  facts  that 
prove  that  light  has  a  finite  velocity.     What  are  these 
facts  and  what  do  they  prove?     When  people  say  that 
light  travels  with  a  finite  velocity  they  mean  that  some 
change  moves  from  a  distant  centre  to  the  observer  and 
that  his  visual  sensum  begins  as  soon  as  this  change 
reaches   him  and  goes  on  till  it  ceases  to  reach  him. 
By  a  single  flash  they  think  of  a  single  event  at  the 
source  (e.g.,  the  opening  of  a  shutter)  and  the  change 
that  travels   out  from  this.     Let  us    consider  the  facts 
and  arguments  which  are  supposed  to  prove  this.     We 
may  take  three  typical  examples.     These  are  Fizeau's 
experiment,  with  a  rotating   cogwheel   and   a    mirror ; 
Romer's    argument    from    the    times    that    apparently 
elapse    between    successive    eclipses    of    a   satellite   of 
Jupiter  ;  and  Bradley's  argument  from  the  shift  in  the 
apparent   positions    of    the   fixed    stars.     These    three 
arguments  are  placed  in  order  of  simplicity.     The  first 
keeps  the  source  and  the  observer  relatively  at  rest  for 
the   whole   time,    and    literally    consists    in    producing 
"  light-echoes,"  and  showing  that  there  is  a  time-lapse 
between    them    and    the    flash    of    which    they   are   the 
"echoes."     The  second  depends   on  the    fact   that   an 
observer  and  a  certain  source  are  at  different  distances 
apart   at    different   times   of    year.     The    last   depends 
on    the   relative    velocity   of   source   and    observer,    and 
belongs  rather  to  the  subject  of  the  next  chapter  than 
to  the  limits  within  which  we  are  at  present  confining 
ourselves.      I  must  state  as  shortly  as  possible  the  facts 
on  which  these  arguments  are  based,  so  that  we  may 
be  able  to  see  what  exactly  they  assume  in  order  to 
reach  their  conclusion. 


DATE   AND   DURATION  377 

(i)  Fizeaiis  Experiment. — Light  is  sent  through  a  hole, 
in  front  of  which  is  a  cogwheel.  When  one  of  the  teeth 
of  the  wheel  is  in  front  of  the  gap,  light  cannot  pass  ; 
otherwise  it  can.  The  light  travels  some  considerable 
distance,  and  is  then  reflected  back  along  its  old  course, 
and  the  image  is  viewed  from  behind  the  cogwheel.  If 
the  passage  of  the  light  between  the  source  and  the 
mirror  and  back  again  be  instantaneous,  the  image  will 
be  visible,  no  matter  how  fast  the  cogwheel  revolves  ; 
for  if  no  time  has  elapsed,  the  cogwheel  cannot  have 
moved  any  distance  since  the  flash  left  it  and  before  the 
light  returned  to  it.  The  gap  cannot,  therefore,  have 
become  shut,  in  the  meanwhile,  by  the  rotation  of  the 
cogwheel.  But  if  any  finite  time  elapses  between  the 
departure  and  the  return  of  the  light,  it  must  be  possible 
to  cause  the  original  gap  to  be  replaced  by  the  next 
tooth  by  the  time  that  the  light  returns,  provided  that 
the  cogwheel  has  moved  fast  enough.  In  that  case  no 
image  will  be  seen.  If  the  speed  of  the  wheel  be  now 
increased  enough,  the  image  ought  again  to  be  seen, 
since  the  wheel  will  have  turned  so  far  in  the  time  taken 
by  the  passage  of  the  light  that  the  next  gap  will  be  in 
position  to  admit  the  reflected  beam  when  it  returns.  It 
is  found  that  the  image  can  be  made  to  disappear  by 
rotating  the  wheel  fast  enough,  that  it  can  be  made  to 
reappear  by  rotating  the  wheel  faster,  and  that  the 
wheel  needs  to  be  rotated  faster  and  faster  the  nearer 
the  mirror  is  to  the  source,  in  order  to  make  the  image 
disappear.  All  these  facts  are  what  we  should  expect  if 
the  reflected  sensum  depends  on  the  passage  of  some- 
thing with  finite  velocity  from  source  to  mirror,  and  from 
mirror  to  observer,  and  begins  when  this  something 
reaches  the  observer's  eye,  and  does  not  end  till  it  ceases 
to  reach  his  eye. 

It  is  clear  that  the  result  of  the  experiment  does  not 
bear  directly  on  the  question  of  the  neutral  temporal 
relations  between  two  sensa  of  observers  who  see  the 
same  flash.     For  we  are  actually  dealing  with  a  single 

2  B 


;-s  SCIENTIFIC   THOUGHT 

sensum  (the  reflected  image)  of  a  single  observer.  The 
connexion,  however,  is  this:  It  is  argued  that  the  result 
of  the  experiment  shows  that  any  visual  sensum  begins 
when  something  that  has  started  from  a  source  reaches 
the  observer,  and  that  this  something  takes  a  finite 
time  to  travel.  The  various  visual  sensa  that  together 
constitute  a  single  flash  are  simply  those  sensa  which 
begin  to  be  sensed  by  various  observers  when  something 
that  left  a  source  at  a  certain  moment  reaches  them.  If 
the  observers  are  at  different  distances  from  the  source, 
their  various  sensa  will  be  correlated  with  different  stages 
in  this  process  of  transmission.  Hence,  there  is  an  im- 
portant sense  in  which  what  is  called  one  flash  is  a 
group  of  successive  sensa.  It  would,  therefore,  be  incon- 
venient to  determine  neutral  simultaneity  in  such  a  way 
that  all  the  sensa  in  a  single  flash  would  count  as 
neutrally  simultaneous. 

Thus  a  single  flash  of  light  comes  to  be  treated  as 
a  set  of  successive  sensa,  because  different  sensa  in  the 
set  are  held  to  be  correlated  with  different  stages  in  a 
certain  process  of  transmission  from  the  source  through 
the  surrounding  Space. 

(ii)  Router's  Argument. — The  earth  and  the  planet 
Jupiter  revolve  about  the  sun  in  approximately  the 
same  plane  and  approximately  in  circles.  Jupiter  has 
a  much  larger  orbit  than  the  earth,  and  takes  much 
longer  to  complete  it.  Thus,  at  certain  times,  the  two 
are  in  the  position  shown  below, 

S/        E/  J/ 


and  at  other  times  they  are  in  the  position  shown  below. 
The  first  is  called  a  conjunction  and  the  second  an 
opposition. 

Eg      S2  Je 

Jupiter  has  satellites  which  revolve  round  it  as  the 
moon  does   round  the  earth.     When  a  satellite  moves 


DATE   AND   DURATION  379 

into  the  shadow  on  the  far  side  of  Jupiter  from  the  sun, 
it  is  eclipsed,  and  becomes  invisible  to  us.  Now  it 
is  found  that  the  number  of  eclipses  that  take  place 
between  a  conjunction  and  the  next  opposition  is  the 
same  as  the  number  that  take  place  between  an 
opposition  and  the  next  conjunction.  But  there  is 
quite  a  marked  difference  (about  33  minutes)  between 
the  total  times  that  elapse  from  the  first  to  the  last  of 
these  eclipses  in  the  two  cases. 

Now  the  eclipse  of  a  satellite  is  comparable  to  the 
shutting  of  a  shutter.  The  movement  of  the  earth 
ensures  that  the  observer  on  it  is  at  different  distances 
from  this  shutter  at  different  times  of  year.  He  is 
nearer  to  it  at  the  time  of  conjunction  than  he  is  at  the 
time  of  opposition  by  the  whole  diameter  of  the  earth's 
orbit.  If  we  suppose  that  the  visual  sensum  ceases  to 
persist  as  soon  as  the  shutter  is  closed,  we  can  only 
explain  the  facts  by  supposing  a  periodic  change  in  the 
time  of  revolution  of  the  satellite.  This  would  be 
extremely  difficult  to  fit  in  with  the  facts  that  we  believe 
about  the  laws  of  mechanics  and  the  forces  acting  on 
the  satellites.  If,  however,  we  assume  that  the  visual 
sense-object  persists  after  the  shutter  is  closed,  for  a 
time  which  increases  with  the  distance  between  the 
observer  and  the  shutter,  we  can  fully  account  for  the 
divergence  of  33  minutes,  without  needing  to  suppose 
that  the  periodic  time  of  the  satellite  changes  as  Jupiter 
progresses  in  its  orbit.  The  time-lapse  between  an 
eclipse  and  the  cessation  of  the  corresponding  visual 
sense-object,  which  is  necessary  to  account  for  the 
33  minutes'  discrepancy,  can  easily  be  calculated  ; 
and,  if  the  radius  of  the  earth's  orbit  be  known,  the 
velocity  of  light  can  be  determined.  It  is  found  to  be 
approximately  the  same  as  that  deduced  from  Fizeau's 
experiment.  Here  there  is  no  complication  about 
mirror-images  ;  we  simply  have  a  source  and  an 
observer  which  are  at  different  distances  apart  at 
different  times  of  year. 


38o  SCIENTIFIC   THOUGHT 

Once  again  the  result  of  the  argument  does  not  bear 
directly   on    the   question    whether   it    is  appropriate   to 
determine  neutral   simultaneity   in  such  a  way  that  the 
various  sensa  which    constitute   a  single  flash  of   light 
shall  be  all  neutrally  contemporary.     We  are  not  deal- 
ing with  two  observers   seeing  a  single  flash  ;    on  the 
contrary,  we  are  dealing  with  a  single  observer  who  sees 
three  different  flashes  (if  an  eclipse  may  by  courtesy  be 
called  a  flash)  at  widely  different  dates  in   his  history. 
There     is,     however,     an     indirect     connexion.       The 
argument  is,  that  you  must  either  abandon  certain  very 
well-established    laws   of   motion,    or   assume   that   the 
occurrence  of  visual  sensa  depends   on  the  motion    of 
something  from  the  source  to  the  observer.     The  visual 
sense-object   lasts    so    long   as   any  of  this  something 
meets   the    eye,    no    matter  what    may   have    happened 
to  the  source  in  the  meanwhile.     On  this  assumption, 
you  can  account  for  the  facts  without  abandoning  the 
familiar  laws  of  motion.      But,  as  before,   if  you  make 
this    assumption,    you    must    suppose    that    what    we 
call  a  single  flash  is  a  group  of  sensa  correlated  with 
various  stages    in    the  process  of  transmission   of  this 
something.      And,   on    that   supposition,    it    is    unsatis- 
factory to  determine  neutral  simultaneity  by  a  method 
which  presupposes  that  the  various  sensa  which  belong 
to  a  single  flash  are  neutrally  simultaneous. 

(iii)  The  Aberration  Argument. — It  is  found  that,  if 
the  fixed  stars  be  observed  night  after  night,  their 
apparent  positions  undergo  a  periodic  change.  Each 
describes  a  closed  curve  in  the  course  of  a  year.  Now 
the  apparent  position  of  a  star  is,  of  course,  the  optical 
place  of  the  visual  sensum  which  is  an  appearance  to 
us  of  the  star.  The  direction  of  this  place  will  be 
determined  by  the  direction  in  which  we  have  to  point 
our  telescope  in  order  to  bring  this  visual  sensum  into 
the  middle  of  our  visual  field.  Now,  of  course,  we  might 
suppose  that  all  the  fixed  stars  are  describing  closed 
curves  in   the  time   which   it  takes  the  earth  to   move 


DATE   AND   DURATION 


381 


round  the  sun.  But  this  would  be  a  most  extraordinary 
state  of  affairs,  and  it  is  not  one  that  we  readily  accept. 
Now  it  happens  that  the  facts  can  be  quite  easily  ex- 
plained on  the  same  assumption  as  before  about  light. 

Let  S  be  a  star,  and  let  the  line  OO  represent  the 
course  of  a  moving-  observer  with  a  telescope.  In  the 
first  figure  we  will  suppose  that  he  is  pointing  his 
telescope  at  the  physical  place  of  the  star.  At  a  certain 
moment  let  his  position  be  O,  and  let  light  from  the 
star  have  reached  lv  a  point  in  the  middle  of  the  far 
end  of  his  telescope.  At  a  slightly  later  moment  let 
his  position  be  02.     The  light  will  then  have  got  to  /2 


*s 


//„ 


°,   °e 


ftp/ 


O,    q,   03  o4 


/%& 


in  its  original  straight  line,  and  will  no  longer  be  passing 
down  his  telescope  at  all.  It  is  clear  then  thatv  if  the 
moving  observer  points  his  telescope  at  the  physical 
place  of  the  star,  he  will  see  no  star  at  all.  Suppose 
now  that  he  tilts  his  telescope  forward  by  an  appropriate 
amount  in  the  direction  of  his  movement.  Let  Ov  02, 
03,  04  represent  four  successive  positions  of  the  tele- 
scope, and  /1}  /.,,  /3,  /4,  the  four  corresponding  positions 
in  the  course  of  the  light  which  is  travelling  from  the 
star.  It  is  clear  from  the  figure  that  the  light  will  pass 
down  the  telescope  and  meet  his  eye,  provided  that  he 
slopes  the  telescope  forward  at  an  angle  to  his  course, 
whose  tangent  is  cjv,  where  c  is  the  velocity  of  light 
and  v  is  that  of  the  observer.  Now  an  observer  on  the 
earth  is  moving  with  it  in  the  course  of  a  year  round 
a  closed  curve  —  the  earth's  orbit  —  with  considerable 


382  SCIENTIFIC  THOUGHT 

velocity.  It  is  thus  easy  to  understand  that,  although 
the  physical  place  of  a  star  remains  constant,  the  optical 
places  of  the  sensa  by  which  the  star  appears  to  us  will 
vary  in  the  course  of  the  year,  and  will  repeat  their 
variations  over  and  over  again  in  that  period.  From 
the  speed  of  the  earth  in  its  orbit  and  the  amount  of  the 
aberration  of  a  star,  it  is  easy  to  calculate  the  velocity 
of  light.  It  is  once  more  found  to  be  the  same,  within 
the  limits  of  experimental  error,  as  that  found  by  Romer's 
argument  and  by  Fizeau's  method. 

This  argument  is  of  particular  interest  to  us,  not 
merely  in  connexion  with  the  question  of  neutral  dating, 
but  also  as  reinforcing  the  distinction  that  has  already 
been  drawn  on  other  grounds  between  physically  and 
optically  occupied  places.  We  introduced  that  dis- 
tinction originally  because  of  facts  which  are  found 
to  arise  when  the  medium  surrounding  an  observer  is 
non-homogeneous.  We  now  see  that  the  optical  place 
of  a  visual  appearance  and  the  physical  place  of  its 
source  may  be  different,  even  when  the  medium  is 
homogeneous,  if  the  source  and  the  observer  be  in 
relative  motion. 

Let  us  now  consider  what  these  arguments  have  to 
teach  us.  (i)  We  see  that  three  extremely  different 
lines  of  argument  tend  to  the  conclusion  that  visual 
sensa  are  connected  with  something  that  is  transmitted 
from  a  source  to  an  observer  with  a  finite  velocity. 
And  they  all  lead  to  approximately  the  same  numerical 
value  for  this  velocity.  Now,  in  each  separate  case, 
there  is  no  doubt  that  the  facts  could  be  explained 
without  taking  this  particular  view  about  light,  provided 
we  made  some  other  assumption.  But,  in  the  first  place, 
each  of  these  assumptions  would  conflict  with  some  law 
of  Nature  which  has  been  well  established  in  other  cases. 
And,  in  the  second  place,  these  assumptions  would  be 
quite  disconnected  with  each  other  ;  each  would  be  an 
independent  piece  of  "cooking."  On  the  other  hand, 
a  single  assumption  as  to  the  nature  of  light  explains 


DATE  AND   DURATION  383 

all  these  very  different  facts,  and  reconciles  them  with 
the  established  natural  laws  with  which  they  would 
otherwise  conflict.  Thus  the  hypothesis  in  question  is 
established  about  as  solidly  as  any  scientific  hypothesis 
can  be.  The  simple-minded  scientist  may  think  that  I 
have  needlessly  laboured  this  point ;  but  I  have  deliber- 
ately insisted  on  it,  because  I  know  that  some  eminent 
"realist"  philosophers,  finding-  that  the  finite  velocity 
of  lierht  "stains  the  white  radiance"  of  their  theories  of 
perception,  are  inclined  in  private  to  deny  it,  or  at  least 
to  "damn  with  faint  praise,  assent  with  civil  leer." 

(ii)    We    notice   that  the  finite  velocity   of  light   is 
never  proved  directly  ;  but  always  by  the  argument  that, 
unless   it  be  true,  certain  observable  facts  will   not  be 
reconcilable  with  well  verified  laws  about  the  motion  of 
matter.     The  only  direct  way  to  verify  the  proposition 
would  be  for  two  observers  to  stand  at  a  distance  apart, 
see  the  same  flash  of  light,  and  find  that  their  respective 
visual  sensa  were  not  contemporary.     Now  there  is  both 
a  practical  and  a  theoretical   difficulty  about  any  such 
experiment.      The   theoretical    difficulty   is   this.      The 
two  observers  would   need   to  be    provided   with  some 
means  of  marking,   and   thus  comparing,  the  dates  of 
their  respective  sensa.     Suppose  that  the  means  adopted 
were  two  stop-watches.     This  would  be  useless,  unless 
they  had  reason  to  suppose  that  the  two  watches  agreed 
in  their  zero  points  and  were  going  at  the  same  rate. 
They  might,  of  course,  set  the  watches  in  synchronism 
when  they  are  both  together  ;  but  what  guarantee  have 
they  that  they  will   remain   in   synchronism  when  one 
has   been   carried  a    long  distance   away?      To  assume 
that  they  do,   is  to  make  an  assumption  which   is  con- 
tradicted   by   quite    gross    experiences.       To   test   their 
synchronism  after  they  have  been  separated,  can  only 
be  done  by  means  of  light  or  electrical  signals  ;    and 
there  is  obviously  a  circle  in  setting  two  watches  by  light- 
signals  and  then  using  them  to  test  whether  two  visual 
sensa  belonging  to  the  same  flash  are  contemporary  or 


;S.,  SCIENTIFIC   THOUGHT 

successive.  The  only  way  out  of  this  difficulty  would  be 
if  both  observers  could  observe  a  certain  pair  of  flashes, 
and  if  one  of  them  should  find  that  his  two  visual  sensa 
were  sensibly  simultaneous,  and  the  other  should  And 
that  his  two  visual  sensa  were  sensibly  successive.  But, 
in  practice,  this  cannot  be  done,  because  of  the  great 
velocity  of  light  and  the  fact  that  the  only  observers 
who  can  compare  notes  with  each  other  are  confined  to 
the  earth's  surface.  Thus  it  seems  clear  to  me  that  the 
neutral  simultaneity  of  visual  sensa  belonging  to  the 
same  flash  is  denied  wholly  and  solely  because  it  con- 
flicts with  another  system  of  dating  which  depends  on 
certain  alleged  laws  of  motion. 

(iii)  It  is  evident  that  if  we  accept  the  view  that  the 
various  sensa  belongingto  the  same  flash  are  not  neutrally 
simultaneous,  we  shall  have  to  admit  either  that  two 
sensa  which  seem  simultaneous  may  not  really  be  so,  or 
that  two  sensa  which  are  neutrally  successive  may  be 
sensibly  simultaneous.  The  latter  alternative  would 
prevent  neutral  temporal  relations  from  being  consistent 
extensions  of  sensible  temporal  relations,  and  we  shall 
therefore  not  take  it,  unless  we  are  forced  to  do  so.  Now 
there  is  nothing  in  the  Sensum  theory  of  sensible  appear- 
ance to  force  us  to  the  second  alternative.  A  sensum 
belonging  to  a  certain  flash  and  a  sensum  belonging 
to  its  reflected  flash,  seem  to  us  to  be  sensibly  simul- 
taneous. If  the  physical  theory  of  light  be  accepted,  the 
latter  is  neutrally  a  little  later  than  the  former.  But  the 
sensible  simultaneity  of  two  sensa  only  means  that  each 
exactly  overlaps  the  other  in  their  common  sensible 
field.  Now  the  notion  of  exactness  ahvays  involves  a 
negative  factor  ;  it  means  that  no  part  of  the  one  sensum 
sticks  out  beyond  the  end  of  the  other.  And  we  saw, 
when  dealing  with  the  general  theory  of  sensa,  that 
there  is  no  reason  why  negative  judgments  about  sensa 
should  be  infallible.  Thus,  two  sensa  may  often  seem 
to  be  sensibly  quite  simultaneous,  when  really  one  begins 
a  little  later  and  ends  a  little  later  than  the  other. 


DATE   AND   DURATION  385 

We  see  then  that  the  question  of  a  neutral  dating  of 
events  in  different  sense-histories  leads  inevitably  to  the 
question  of  motion,  whether  it  be  the  transmission  of 
those  changes  which  are  connected  with  sound  and  light, 
or  the  motion  of  ordinary  physical  bodies  through  Space. 
Thus  the  separation  of  Space  and  Time,  with  which  we 
started,  which  has  been  wearing  thinner  and  thinner  as 
the  argument  has  advanced,  has  now  broken  down 
altogether.  This  does  not  mean  that  there  is  no  differ- 
ence between  temporal  and  spatial  relations  ;  but  it  does 
mean  that  it  is  impossible  to  apply  the  concept  of  a 
single  Space  to  Nature  without  referring  through  Motion 
to  Time,  and  that  it  is  equally  impossible  to  date  the 
events  of  Nature  in  a  single  Time  without  referring 
through  Motion  to  Space.  And  this,  it  will  be  noted, 
is  one  of  the  characteristic  features  of  the  Theory  of 
Relativity. 

To  sum  up  :  If  I  want  to  determine  neutral  temporal 
relations  between  an  event  which  is  in  my  sense-history 
but  not  in  yours,  and  an  event  which  is  in  your  sense- 
history  but  not  in  mine,  the  only  possible  way  seems  to 
be  to  find  something  which  is  common  to  the  sense- 
histories  of  both  of  us,  and  to  determine  the  neutral 
temporal  relations  between  the  two  "private'"  events 
by  means  of  their  respective  sensible  relations  to  this 
"public"  event.  At  first  sight  this  seems  perfectly 
plain  sailing,  since  there  are  events,  like  noises  and 
flashes,  which  are  admittedly  "public"  in  a  way  in 
which  headaches  and  toothaches  are  not.  If  it  were 
really  true  that,  when  we  say  that  we  "hear  the  same 
noise  "  or  "  see  the  same  flash,"  there  is  a  single  auditory 
or  visual  sensum  in  all  our  sense-histories,  it  would  be 
easy  to  determine  neutral  simultaneity  in  this  way. 
And,  since  it  would  have  the  same  logical  properties 
as  sensible  simultaneity,  it  would  be  reasonable  to  hold 
that  it  is  really  the  same  relation,  and  that  the  pro- 
posed method  of  determination  is  simply  a  test  and  not 
a  definition  of  a  new  kind  of  relation.     But,  although  it 


;>N<>  SCIENTIFIC   THOUGHT 

is  not  logically  impossible  that  a  single  sensum  might  be 
in  a  number  of  different  sense-histories,  eloser  observa- 
tion of  the  facts  makes  it  almost  impossible  to  believe  that 
a  noise  or  a  Hash  really  is  a  single  sensum.  Moreover, 
it  seems  impossible  to  hold  that  it  is  even  a  group  of 
contemporary  sensa.  Thus,  such  methods  of  determina- 
tion, though  practically  useful  for  most  purposes,  owing 
to  the  considerable  velocity  of  sounds  and  the  very  great 
velocity  of  light,  are  not  theoretically  satisfactory. 

Temporal  Characteristics  of  Physical  Events. — The 
further  development  of  this  subject  must  be  left  to  the 
next  two  chapters,  but  it  is  possible  in  the  meanwhile  to 
say  something  about  the  durations  and  dates  of  physical 
objects  and  events.  A  single  flash  of  light  or  a  single 
noise  may  be  called  a.  perceptible  physical  event.  When  a 
man  says  that  he  sees  a  flash  of  light,  he  does  not  mean 
either  {a)  merely  that  he  senses  a  certain  visual  sensum, 
or  (/;)  that  he  sees  the  movement,  e.g.,  of  an  electron  at 
the  source  which  is  responsible  for  the  flash.  For  (a) 
he  admits  that  other  people  can  see  the  same  flash, 
whereas  we  have  found  reason  to  think  that  two  people 
who  see  the  same  flash  do  not  sense  the  same  visual 
sensum.  And  (d),  so  far  from  admitting  that  he  saw 
the  movement  of  the  electron,  he  would  say  that  this 
is  invisible,  and  that  he  only  believes  it  to  have  taken 
place  on  the  authority  of  a  scientific  theory  which  he 
does  not  himself  understand.  Thus,  to  see  a  flash  means 
something  more  than  to  sense  a  visual  sensum,  and 
something,  partly  more  and  partly  less,  than  to  perceive 
the  motion  of  an  electron.  An  angel  might  perceive  the 
motion  of  the  electron  and  see  no  flash,  whilst  a  man 
sees  the  flash  and  does  not  perceive  the  motion  of  the 
electron.  Seeing  the  flash  involves  sensing  the  sensum 
and  also  something  more.  It  involves  the  excitement 
of  traces  connected  with  similar  experiences  in  the  past. 
These  may  or  may  not  actually  produce  the  explicit 
perceptual  judgment  that  other  observers  are  sensing 


DATE  AND   DURATION  387 

similar  sensa  which  are  optically  in  the  same  place, 
and  that  some  movement  has  happened  in  that  place. 
But,  whether  these  judgments  actually  arise  or  not,  the 
observer  will  tend  to  behave  in  a  way  in  which  it  would 
be  reasonable  to  behave  if  he  had  explicitly  made  these 
judgments.  If  such  judgments  be  not  true  in  a  particular 
case,  we  say  that  the  observer  is  mistaken  in  his  belief 
that  he  has  seen  a  flash  of  light,  even  though  he  has 
sensed  a  short,  bright  visual  sensum.  Thus  a  man 
who  "sees  stars,"  because  he  has  hit  his  head  against 
a  post,  senses  a  bright  visual  sensum,  but  would  be 
deceiving  himself  and  others  if  he  said  that  he  had  seen 
a  flash  of  light. 

A  perceptible  physical  event,  like  a  flash  or  a  noise, 
may  therefore  be  defined  as  a  certain  group  of  sensa 
having  certain  similarities  to  each  other  and  certain 
neutral  spatial  relations.  Nearly  always  they  will  be, 
in  some  sense,  compresent  at  a  certain  place  in  Space. 
We  have  seen  that,  as  a  rule,  they  will  not  all  be 
neutrally  simultaneous,  but  that  their  neutral  dates  will 
depend  upon  the  positions  of  the  various  observers  who 
sense  them.  To  perceive  such  a  perceptible  event 
means  (a)  to  sense  a  sensum  belonging  to  such  a  group  ; 
and  (b),  in  consequence  of  the  traces  left  by  similar 
experiences  in  the  past,  either  explicitly  to  judge  that  it 
is  a  member  of  such  a  group,  or  to  act  as  it  would 
be  appropriate  to  act  if  one  had  explicitly  made  this 
judgment. 

(a)  Dates  of  Perceptible  Physical  Events. — Now,  since 
a  perceptible  physical  event  consists  of  a  number  of 
sensa  of  different  neutral  dates,  it  is  obvious  that  the 
question:  "What  is  the  date  of  a  certain  perceptible 
physical  event?"  can  only  be  answered  in  a  more  or 
less  Pickwickian  manner.  To  give  any  answer  to  it 
we  must  notice  the  two  following  facts  :  The  neutral 
dates  of  the  sensa  in  such  a  group  are  none  of  them 
earlier  than  the  date  of  a  certain  physical  movement, 
such  as  the  opening  of  a  shutter.      If  we  include  in  the 


,ss  SCIENTIFIC  THOUGHT 

flash  not  only  actual  sensa  but  the  sensa  of  possible 
observers,  the  dates  of  the  various  sensa  would  approach 
the  date  of  this  movement  at  the  source  as  their  lower 
limit.  This  date  might,  therefore,  be  defined  as  "the 
date  at  which  the  perceptible  physical  event  begins.''' 
The  second  point  to  notice  is  that,  where  a  group  of 
sensa  have  later  and  later  neutral  dates  as  the  observer 
is  further  and  further  from  the  source,  the  sensa  in 
question  are  fainter  and  fainter.  Thus  the  dates  of  the 
sensa  which  constitute  a  single  noise  approach  a  limit 
where  we  are  dealing  with  an  observer  so  remote  that 
he  can  only  just  sense  a  sensum  of  the  group.  This 
does  not  give  an  absolutely  sharp  date  which  may  be 
taken  as  "the  date  at  which  the  perceptible  physical 
event  ends"  because  the  question  of  the  different  acute- 
ness  of  different  observers  comes  in.  Still  it  is  clear 
that  in  this  way  we  could  define  approximately  the 
date  at  which  such  an  event  ends.  The  duration  of  a 
perceptible  physical  event  may  then  be  defined  as  the 
time  that  elapses  between  its  beginning  and  its  end. 

(if)  Relative  Dates  of  Act  of  Perceiving  and  Event 
Perceived. — Next  we  see  that,  although  the  beginning 
of  an  act  of  sensing  may  be  regarded  as  contemporary 
with  the  end  of  the  sensible  field  that  is  sensed  through- 
out  the  whole  of  it,  there  is  not  the  same  simple  relation 
between  the  date  of  an  act  of  perceiving  and  the  date  of 
the  physical  event  perceived  by  it.  This  is  obvious, 
since  there  is  nothing  that  can  appropriately  be  called 
the  date  of  a  perceptible  physical  event.  We  may 
reasonably  identify  the  date  of  an  act  of  perceiving 
with  that  of  the  act  of  sensing  on  which  it  is  based. 
So  that,  in  general,  all  we  can  say  is  that  an  act  of 
perceiving  is  later  than  the  beginning  and  earlier 
than  the  end  of  the  physical  event  that  it  perceives. 
It  is  very  common  to  suppose  that  an  act  of  perceiving 
must  be  contemporary  with  the  event  perceived.  This 
is,  of  course,  a  mere  mistake,  due  to  a  confusion 
between  an  act  of  sensing,  whose  object  is  a  sensum, 


DATE   AND   DURATION  389 

and  an  act  of  perceiving,  whose  object  is  a  physical 
event. 

There  is  one  more  confusion  to  be  pointed  out 
before  we  leave  this  subject.  It  might  be  said  :  "  Does 
not  a  physical  event,  such  as  a  flash  of  light,  persist 
for  ever  once  it  has  started?"  I  answer  that  the  move- 
ment that  is  transmitted  from  the  source  and  is  corre- 
lated with  the  various  visual  sensa  of  the  group,  may 
very  well  go  on  for  ever.  But  this  movement,  of  what- 
ever nature  it  may  be,  is  not  the  flash  of  light.  A  flash 
of  light  is  a  perceptible  object ;  the  movement  in  the 
ether  is  not  perceptible — by  us  at  any  rate.  It  is  merely 
silly  to  say  that  a  certain  perceptible  event  lasts  for  ever, 
because  a  certain  imperceptible  event,  with  which  it  is 
closely  connected,  does  so. 

(c)  Scientific  Events. — This  naturally  brings  us  to 
the  question  of  the  dates  and  durations  of  imperceptible 
physical  events.  We  know  that  perceptible  physical 
events,  such  as  flashes  of  light,  are  supposed  to  be 
intimately  connected  with  movements  of  electrons  and 
changes  in  the  ether  which  we  cannot  perceive.  These 
are  much  more  important  theoretically  to  the  scientist 
than  perceptible  events.  The  epistemological  relation 
between  the  two  is  the  following:  It  is  by  observing 
and  noting  the  relations  between  perceptible  events 
that  we  infer  the  existence  of  these  imperceptible  events, 
which,  following  Whitehead,  I  will  call  scientific  events. 
Instead  of  stating  the  laws  of  Nature  as  direct  relations 
between  perceptible  events,  we  analyse  these  relations 
into  the  relative  product  of  two  different  kinds  of  rela- 
tions, viz.,  (a)  those  of  scientific  events  to  each  other,  and 
(b)  those  of  scientific  events  to  perceptible  events.  This 
process  seems  to  be  indispensable,  if  we  are  to  deal 
satisfactorily  with  Nature  at  all.  The  relations  between 
perceptible  events  are  very  complex,  and  few  simple 
and  invariable  laws  can  be  stated  about  them.  On  the 
other  hand,  the  relations  of  imperceptible  events  to  each 
other  and  to  perc'eptible  events  are  reasonably  simple, 


390  SCIENTIFIC   THOUGHT 

and  laws  of  very  wide  range  can  be  stated  about  them. 
We  can  then  use  these  hypothetical  laws  to  predict 
what  perceptible  events  will  be  perceived  under  assigned 
perceptible  conditions.  In  so  far  as  the  predicted 
events  actually  take  place,  our  hypothesis  about  imper- 
ceptible events  and  their  laws  is  strengthened.  It  is 
very  easy  for  a  scientist,  who  constantly  deals  with 
scientific  events  and  sees  their  great  practical  and 
theoretical  importance,  to  fall  into  the  mistake  of 
supposing  that  they  alone  are  "  real."  This  is  a  great 
error.  The  actual  position  is  this :  The  existence  of 
sensa  is  absolutely  certain,  and  those  positive  sensible 
properties  which  they  seem  to  have  they  certainly  do 
have,  if  the  Sensum  theory  be  accepted  at  all.  The 
existence  of  some  perceptible  physical  events  is  prac- 
tically certain,  if  we  are  prepared  to  accept  the  existence 
of  other  observers  and  to  believe  what  they  tell  us 
about  their  sensa.  But,  in  any  particular  case,  an 
observer  who  thinks  that  he  perceives  a  certain  physical 
event  may  be  mistaken.  For  he  may  sense  a  sensum 
of  a  certain  kind  and  mistakenly  suppose  that  it  is  one 
of  a  group  of  connected  sensa,  when  really  it  is  "wild" 
and  isolated.  Lastly,  since  imperceptible  physical 
events  are  only  assumed  in  order  to  fill  the  gaps 
between  the  various  sensa  of  single  perceptible  events 
and  to  connect  different  perceptible  events  with  each 
other,  it  is  clear  that  our  certainty  that  there  are  such 
and  such  imperceptible  events  cannot  logically  exceed 
our  certainty  that  there  are  such  and  such  percep- 
tible ones. 

There  is  a  connecting  link  between  purely  percep- 
tible events,  like  flashes  of  light,  and  purely  scientific 
events,  like  the  movements  of  electrons  and  ether-waves. 
This  link  is  the  unperceived  parts  of  perceptible  events. 
We  defined  a  flash  as  a  certain  group  of  visual  sensa, 
and  we  said  that  its  duration  was  the  time  that  elapses 
between  the  earliest  and  the  latest  of  these  sensa.  But, 
it  must  be  admitted  that  the  really  important  point  about 


DATE   AND   DURATION  391 

perceptible  events  is  not  the  actual  sensa  in  the  group, 
but  the  possible  sensa.  Actually  only  a  few  of  the 
sensa  in  such  groups  are  sensed  by  anyone,  and  it  may 
quite  well  happen  that  only  one  of  them  is  sensed.  The 
perceptual  judgment  does  not  assert  that  other  sensa  of 
the  group  are  sensed,  but  only  that  they  would  be  by 
any  observer  sufficiently  like  ourselves  placed  in  any 
suitable  position.  Thus  the  cash  value  of  the  statement 
that  perceptible  events  persist,  even  when  no  one  happens 
to  sense  any  sensum  of  the  group,  is  that  whenever  a 
suitable  observer  is  present  at  any  position  in  a  certain 
spatio-temporal  region,  he  will  sense  a  member  of  the 
group.  We  are  not  content  with  this  merely  hypo- 
thetical assertion.  We  assume  that  if  any  observer  at 
any  position  of  a  certain  spatio-temporal  region  will 
sense  a  sensum  of  a  certain  group,  this  must  be  because 
something  independent  of  all  observers  is  going  on  at 
all  positions  in  this  region.  This  assumption  rests 
partly  on  our  passion  for  spatio-temporal  continuity. 
When  there  is  a  close  connexion  between  events  in 
different  places  and  of  different  dates,  we  feel  that  the 
gaps  between  them  must  be  filled  in  somehow.  And 
this  conviction  is  strongly  reinforced  if  we  find  that 
any  observer  who  takes  up  his  position  at  random 
within  the  spatio-temporal  region  in  question  equally 
senses  a  member  of  the  group. 

We  must  notice,  moreover,  that  the  presence  of  an 
observer  is  found  to  be  irrelevant  to  most  chains  of 
physical  causation.  If  I  put  a  kettle  on  the  fire  and 
watch  both,  the  perceptible  event  of  the  fire  burning 
is  followed  after  a  certain  time  by  the  perceptible  event 
of  the  kettle  boiling.  If  I  and  all  other  observers  go 
away  for  a  time  and  then  return,  we  find  that  the  kettle 
has  boiled  after  the  same  lapse  of  time.  These  and 
millions  of  other  experiences  show  that  the  gaps 
between  the  sensa  belonging  to  a  perceptible  event 
are  filled  by  something  that  produces  just  the  same 
effects  as  if  we  were  present.     Thus,  even  at  the  level 


392  SCIENTIFIC   THOUGHT 

of  common-sense,  a  perceptible  physical  event  is  thought 
of  as  a  group  of  sensa  connected  by  events  that  go  on 
in  the  absence  of  observers.  Common-sense  is  very 
vague  as  to  the  nature  of  these  unperceived  parts  of 
perceptible  events.  I  think  that  it  generally  supposes 
in  a  rather  half-hearted  way  that  they  are  of  the  same 
nature  as  the  parts  that  are  actually  sensed.  How  far 
such  a  view  can  be  maintained  cannot  be  decided  until 
we  have  dealt  with  the  physiological  conditions  of  sensa. 
But,  at  any  rate,  we  can  say  that  it  seems  essential  to 
suppose  that  something  bridges  these  gaps  ;  and  science 
professes  to  determine  more  and  more  accurately  the 
nature  of  this  something.  Whether  it  has  the  properties 
of  sensa  or  not,  it  certainly  has  the  properties  of  scientific 
events,  subject  of  course  to  the  possibility  of  scientific 
theories  being  wrong  on  points  of  detail. 

In  the  last  chapter  I  said  that  scientific  objects  are 
conceived  to  have  shapes  and  to  occupy  places  in  the 
movement-continuum  in  the  same  literal  way  in  which 
visual  sensa  are  immediately  sensed  to  have  shapes  and 
to  occupy  sensible  places  in  their  fields.  In  fact,  the 
concepts  of  what  I  will  now  call  Scientific  Space  and 
scientific  physical  objects  are  constructed  together  in 
an  inseparable  union.  They  are  constructed  on  the 
analogy  of  sensa  and  their  fields  out  of  data  derived 
from  the  sense-experiences  of  many  observers  through 
various  senses  and  at  various  times.  Exactly  similar 
remarks  apply,  mutatis  mutandis,  to  the  concepts  of 
what  I  will  call  Scientific  Time  and  scientific  events. 
Scientific  Time  is  conceived  by  analogy  with  a  sense- 
history  ;  scientific  events  are  conceived  to  have  dates  in 
Scientific  Time  as  sensa  have  dates  in  the  sense-history 
of  the  observer  who  senses  them  ;  scientific  objects  are 
conceived  to  have  duration  in  Scientific  Time  as  sense- 
objects  have  duration  in  a  sense-history.  There  is  one 
difference,  however.  For  reasons  already  stated,  it  is 
impossible  that  sensa  should  literally  occupy  places  in 
scientific  space,  though  it  may  not,  of  course,  be  im- 


DATE   AND   DURATION  393 

possible  to  construct  a  space-like  whole  of  more  than 
three  dimensions,  in  which  sensa  of  all  kinds,  and 
scientific  objects,  literally  have  places.  If  so,  I  suppose 
that  Scientific  Space  would  be  one  kind  of  section  of 
such  a  quasi-space,  and  e.g.,  a  visual  field  would  be 
another  kind  of  section  of  the  same  quasi-space.  But, 
if  such  a  construction  can  be  made  at  all,  I,  at  any  rate, 
am  not  capable  of  doing  the  trick.  On  the  other  hand, 
it  is  not  obviously  impossible  that  sensa  should  literally 
have  dates  and  durations  in  the  same  Scientific  Time  as 
scientific  events  ;  for,  as  we  have  seen,  temporal  relations 
are  much  more  pervasive  than  spatial  relations.  The 
scientific  dates  of  sensa  would  seem  to  be  the  dates  at 
which  certain  scientific  events  happen  in  the  brain  of 
the  observer  who  senses  these  sensa.  Unless  there  be 
some  positive  inconsistency  between  the  temporal  rela- 
tions of  such  scientific  events  and  the  sensible  temporal 
relations  of  the  corresponding  sensa,  there  seems  no 
reason  to  reject  the  naive  view  that  the  temporal  re- 
lations between  sensa  in  our  own  sense-history,  with 
which  we  become  acquainted  through  sensation  and 
memory,  are  literally  the  same  as  the  temporal  relations 
between  the  corresponding  scientific  events  in  our  brains. 
Whether  this  view  can  be  held,  is  a  question  which  must 
be  reserved  for  a  later  chapter. 

Duration  of  Physical  Objects. — We  have  now  said 
all  that  can  be  said  with  profit  about  the  dates  and 
durations  of  physical  events  before  dealing  with  motion 
and  the  union  of  Space  with  Time.  It  remains  to  say 
something  about  the  durations  of  physical  objects  or 
"  things."  A  thing,  as  we  have  seen,  is  simply  a  long 
event,  throughout  the  course  of  which  there  is  either 
qualitative  similarity  or  continuous  qualitative  change, 
together  with  a  characteristic  spatio-temporal  unity. 
A  sense-object,  as  defined  earlier  in  the  chapter,  is  an 
example  of  such  a  long  event ;  though,  for  reasons  which 
will  appear  in  a  moment,  it  would  hardly  be  called  a 

2  c 


394  SCIENTIFIC  THOUGHT 

"  thing,"  und  it  is  certainly  not  "  physical."  Thus  the 
dividing  line  between  events  and  thing's  cannot  be 
very  sharply  drawn  in  theory.  Nevertheless,  we  can 
draw  a  rough  practical  distinction,  and  it  is  useful  to 
do  so,  in  order  not  to  depart  too  far  from  common 
speech. 

(a)  Perceptual  Objects. — A  flash  of  light  would  be 
called  a  perceptual  event,  but  not  a  perceptual  thing  or 
object.  This  is  because  each  person  who  sees  the  flash 
senses  a  single  short  sensum,  and  not  a  series  of  sensa 
in  successive  fields  which  join  up  with  each  other  to 
form  a  sense-object  of  decent  duration.  This  is  true, 
although,  as  we  have  seen,  the  flash  itself  as  a  per- 
ceptible event  has  considerable  duration,  which  may 
extend  to  thousands  of  years.  Thus  one  point  about  a 
perceptible  object  is  that  it  must  be  capable  of  being 
perceived  for  a  long  time  by  the  same  observer.  And 
this  means  that  its  appearance  to  him  must  be  not 
merely  a  sensum  but  a  sense-object.  Again,  a  perceptible 
thing  is  always  understood  to  combine  a  number  of 
connected  qualities  which  can  only  be  perceived  by 
different  senses.  An  observer  might  see  a  mirror- 
image  for  an  hour  at  a  time,  but  he  would  never  say 
that  he  was  seeing  a  physical  object,  so  long  as  he  knew 
that  it  was  a  mirror-image.  For  he  would  know  that, 
if  he  went  to  the  place  where  it  is  optically  present,  he 
would  sense  no  correlated  tactual  sensa,  and  that  there 
would  be  no  relevant  scientific  objects  there. 

Of  course,  as  I  have  already  hinted,  these  criteria 
are  not  theoretically  satisfactory.  What  we  count  as 
a  perceptible  object  may  be  moving  so  fast  that  we 
sense  only  one  short  sensum  in  connexion  with  it. 
Conversely,  an  observer  who  moved  in  the  right  direction 
with  the  velocity  of  light  would  continually  sense  sensa 
connected  with  a  single  flash,  so  that  he  would  be 
aware  of  a  sense-object  of  considerable  duration,  and 
might  therefore  be  inclined  to  say  that  he  was  seeing  a 
perceptible  thing  and  not   merely  a  perceptible  event. 


DATE   AND   DURATION  395 

Still,  the  criteria  that  we  have  just  laid  down  work  in  a 
great  many  cases  and  will  do  for  our  present  purpose. 

We  can  now  improve  the  definition  of  a  perceptual 
object  which  we  gave  in  the  last  chapter,  where  we 
deliberately  overlooked  for  the  moment  complications 
due  to  time.  We  still  cannot  give  a  perfectly  satis- 
factory definition,  because  we  have  not  yet  dealt 
properly  with  the  movement  of  physical  objects  and 
observers  and  the  consequent  displacement  of  visual 
sensa  in  the  movement-continuum.  We  will  assume 
for  the  present  that  we  are  confining  ourselves  to  a 
resting  object  and  resting  observers,  and  we  shall  not 
attempt  to  remove  this  restriction  until  the  next  chapter. 
Suppose  that  a  scientific  event  of  the  kind  which  is 
connected  with  a  single  flash  of  light  were  to  happen 
at  a  certain  moment  at  a  certain  place  in  scientific 
space.  Suppose  that  observers  were  dotted  about  in  all 
directions  and  at  all  distances  around  this  place.  Then 
it  is  true  that  the  place  in  question  would  be  optically 
occupied  by  visual  sensa  from  all  directions  for  a  very 
long  time.  But  it  would  be  optically  occupied  only 
for  a  moment  by  visual  sensa  from  a  given  distance. 
At  any  given  moment  the  sensa  which  occupied  the 
place  would  occupy  it  from  places  on  a  certain  sphere 
surrounding  it,  and  at  a  later  moment  it  would  be 
occupied  only  by  sensa  from  places  on  a  larger  sphere. 
It  would  never  be  occupied  at  once  by  sensa  from  places 
on  two  such  spheres.  If  there  were  a  persistent  optical 
object,  instead  of  a  mere  flash,  at  the  place,  this  place 
would  be  optically  occupied  at  a  given  moment  from 
many  different  distances  as  well  as  from  all  directions. 
We  might  regard  a  persistent  optical  object  as  a  con- 
tinuous series  of  successive  flashes.  Each  flash  is 
itself  a  series  of  successive  sensa  belonging  to  different 
fields,  and  the  later  a  sensum  is  in  its  flash  the  further 
off  is  the  place  from  which  it  is  present  at  the  luminous 
centre.  Thus  there  are  two  temporal  series  to  be  con- 
sidered :  (1)  The  series  of  flashes  which  together  make 


396  SCIENTIFIC   THOUGHT 

up  the  history  of  the  persistent  optical  object  ;  and  (2) 
the  series  of  successive  sensa  which  together  make  up 
a  single  flash.  It  is  obvious  that  an  early  sensum 
belonging  to  a  later  flash  and  a  late  sensum  belonging 
to  an  earlier  flash  may  be  simultaneous  with  each  other. 
The  former  will  be  optically  present  at  the  centre  from 
a  near  place,  and  the  latter  will  be  optically  present  at 
the  centre  from  a  more  remote  place.  Thus  the  centre 
is  optically  occupied  by  sensa  from  different  distances  at 
the  same  moment.  Imagine  for  simplicity  a  visible 
object  of  very  small  spatial  dimensions,  which  we  can 
treat  as  a  point.  Suppose  it  lasted  for  a  time  T,  and 
that  a  time  /  has  now  elapsed  since  it  began  to  exist. 
Then  the  places  from  which  sensa  are 
present  at  this  point  at  the  moment  /  are 
all  the  points  contained  in  the  volume 
between  a  pair  of  spheres  with  the 
point  as  centre  and  ct  and  c  (7  +  T)  as 
radii.  (Here  c  is  the  velocity  of  light.) 
The  diagram  will  make  this  plain. 

At  this  moment  sensa  from  the  first  flash  in  the 
history  of  the  object  will  be  present  at  P  from  places  on 
the  outer  sphere,  and  sensa  from  the  last  flash  in  its 
history  will  be  present  at  P  from  places  on  the  inner 
sphere.  Sensa  of  intermediate  flashes  will  be  present 
at  P  from  places  in  the  volume  contained  between  the 
two  spherical  surfaces.  Thus  the  thickness  of  this  solid 
shell  of  places,  from  which  sensa  are  contemporaneously 
present  at  P,  is  characteristic  of  the  duration  of  the 
optical  object.  From  places  within  the  smaller  sphere 
there  are  no  longer  any  sensa  present  at  P,  and  from 
places  outside  the  larger  sphere  there  are  not  yet  any 
sensa  present  at  P.  The  "  shell  "  will  continually 
spread  out  from  the  centre,  but  it  will  always  remain  of 
the  same  "thickness,"  and  this  thickness  is  character- 
istic of  the  duration  of  the  optical  object. 

So  far,  we  have  confined  our  attention  to  the  places 
from  which  sensa  are  present  at  a  given  place  at  a  given 


DATE   AND   DURATION  397 

moment.  But  we  can  equally  well  regard  the  whole 
situation  from  another  point  of  view.  We  can  consider 
the  moments  at  which  sensa  are  present  at  a  given  place 
from  a.  given  place.  In  the  case  of  a  flash  each  observer 
senses  just  one  sensum,  which  is  optically  present  at 
the  place  where  the  flash  is  said  to  be.  In  the  case  of 
a  persistent  optical  object  all  the  observers  will  be  aware 
in  course  of  time,  not  merely  of  a  single  sensum,  but 
of  a  sense-object.  And  the  duration  of  this  sense-object 
would  commonly  be  identified  with  that  of  the  optical 
object.  The  sense-object  in  this  case  is  a  group  of 
successive  visual  sensa  in  a  single  sense-history,  one 
of  which  belongs  to  each  of  the  successive  flashes  into 
which  the  history  of  the  persistent  optical  object  can  be 
analysed  by  Extensive  Abstraction.  It  is  clear  that  we 
must  distinguish  between  (1)  the  duration  of  an  optical 
object  from  a  place,  and  (2)  the  total  duration  of  an  optical 
object.  The  former  is  simply  the  duration  of  the  sensible 
object  which  is  the  appearance  of  the  optical  object 
to  an  observer  at  that  place.  But  an  optical  object, 
however  short  its  duration  from  any  one  place,  has  an 
enormously  great  duration,  when  you  take  into  account 
all  the  sensa  which  belong  to  it  from  all  places.  Its 
total  duration  is  the  time  that  elapses  between  the  earliest 
and  the  latest  visual  sensum  which  belongs  to  it.  And 
this,  even  in  the  case  of  a  momentary  flash,  may  amount 
to  millions  of  years.  A  flash,  in  the  limit,  has  only 
duration  of  the  second  kind  ;  a  persistent  optical  object 
has  both  kinds  of  duration. 

We  can  now  define  a  persistent  complete  optical  object, 
subject  to  the  limitations  about  motion  which  we  have 
already  indicated.  Such  an  object  is  a  group  of  visual 
sensa  of  various  dates,  correlated  with  each  other,  and 
having  the  following  properties:  (1)  There  is  a  certain 
closed  contour  in  Scientific  Space  (the  "  place  occupied 
by  the  optical  object"),  such  that  every  member  of  this 
group  of  sensa  is  optically  present  at  some  part  of  its 
surface  from  somewhere.     (2)  Every  part  of  this  contour 


398  SCIENTIFIC   THOUGHT 

is  optically  occupied  from  somewhere  by  some  member 
(or  members)  of  the  group.  (3)  At  any  moment  after 
the  optical  object  has  started  to  exist,  any  part  of  this 
central  contour  is  occupied  by  sensa  of  the  group  from 
all  the  places  within  a  certain  volume.  This  volume  is 
bounded  by  two  closed  surfaces,  both  of  which  contain 
the  place  occupied  by  the  optical  object.  After  the 
optical  object  has  completed  its  history,  the  thickness  of 
this  volume  is  a  measure  of  the  duration  of  the  object 
from  any  point.  (4)  From  any  point  a  certain  part  of 
the  central  contour  is  occupied  by  a  series  of  successive 
sensa,  forming  a  sense-object  in  the  sense-history  of  an 
observer  who  stays  at  this  point.  The  duration  of  this 
sense-object  is  the  duration  of  the  optical  object  from 
this  place. 

To  define  a  non-persistent  complete  optical  object,  i.e. 
a  complete  optical  event,  or  "flash,"  we  leave  clauses 
(1)  and  (2)  standing,  and  modify  clauses  (3)  and  (4)  as 
follows:  In  (3)  substitute  "on  a  certain  surface"  for 
"within  a  certain  volume."  In  (4)  substitute  "a  single 
sensum  "  for  "a  series  of  successive  sensa,"  and  omit 
the  rest  of  the  clause.  Finally,  a  mirror-image  of  a 
chair  or  a  pin  would  be  a  persistent  incomplete  optical 
object,  whilst  a  mirror-image  of  a  flash  would  be  a  non- 
persistent  incomplete  optical  object. 

We  said  in  the  last  chapter  that  an  ordinary  per- 
ceptual object,  like  a  penny,  as  understood  by  common- 
sense,  is  really  a  composition  consisting  of  a  number  of 
correlated  constituent  objects  of  various  kinds,  all 
occupying  a  place  in  the  movement-continuum  in  their 
various  appropriate  Pickwickian  ways.  This  place, 
moreover,  is  conceived  to  be  literally  occupied  by  cor- 
related scientific  objects  ;  and  the  difference  between 
science  and  common-sense  is  largely  a  difference  in 
the  amount  of  knowledge  which  the  two  claim  to  have 
about  these  scientific  objects.  It  is  obvious  that  some 
of  the  constituents  of  a  perceptual  object  may  cease 
to  persist  while  others  remain.     Again,  a  place  where 


DATE   AND   DURATION  399 

a  perceptual  object  has  once  been,  may  continue  to  be 
haunted  from  certain  places  by  its  ghost,  in  the  form 
of  its  optical  constituent.  The  compositeness  of  a 
perceptual  object  infects  the  notion  of  "its"  duration 
with  an  incurable  vagueness.  We  can  make  accurate 
statements  about  the  durations  of  its  constituents,  and 
we  can  make  accurate  statements  about  the  durations 
of  the  correlated  scientific  objects,  but  the  perceptual 
object  of  common-sense  is  too  much  a  mixture  of  non- 
homogeneous  constituents  to  be  worth  treating  very 
seriously  as  a  whole. 

We  saw  that  an  observer  can  very  well  be  mistaken 
in  thinking  that  he  perceives  a  physical  event  of  a 
certain  kind,  because  this  implies  a  reference  beyond 
the  sensum  which  he  senses  to  other  sensa,  actual  and 
possible,  of  other  observers.  A  fortiori,  we  can  be  mis- 
taken in  supposing  that  we  perceive  a  certain  physical 
thing  ;  and  this  can  happen  even  when  we  are  quite 
right  in  thinking  that  we  perceive  a  physical  event  or 
a  series  of  them.  Such  mistakes  take  various  forms, 
and  contain  various  amounts  of  error,  (i)  We  may 
mistake  a  partial  for  a  complete  optical  object,  i.e.,  we 
may  think  that  a  certain  place  is  optically  occupied  from 
all  directions  when  really  it  is  occupied  only  from  one 
or  from  a  restricted  range  of  directions.  This  happens 
in  optical  illusions  which  really  deceive  us.  (ii)  If  we 
make  this  mistake  we  shall  almost  certainly  make  the 
further  mistake  of  supposing  that  the  place  in  question 
is  also  occupied  by  correlated  tactual  and  other  con- 
stituents, that  it  is  a  centre  for  sound  and  radiant  heat, 
and  that  it  is  occupied  literally  by  scientific  objects 
specially  correlated  with  our  visual  sensa.  Actually 
the  most  relevant  scientific  objects  will  be  at  some 
remote  place,  (iii)  We  may  make  very  grave  mistakes 
about  time.  We  practically  always  think  that  physical 
things  have  endued  and  remained  in  the  same  place 
longer  than  our  visual  perceptions  really  justify  us  in 
believing.     If  an  ordinary  man  sees  a  star  in  a  certain 


400  SCIENTIFIC   THOUGHT 

optical  place,  he  assumes  that  it  must  have  been  there 
at  least  up  to  the  time  when  he  ceases  to  see  it.  This 
is  of  course  unjustified.  My  visual  sensa  are  indeed 
optically  present  at  this  place  at  the  time  when  I  sense 
them,  and  for  as  long  as  I  go  on  sensing  them.  But, 
in  saying  that  the  star  is  there  at  that  time,  I  am  assert- 
ing much  more  than  this.  I  am  asserting  that  other 
types  of  constituent  object  are  also  there,  and  that  the 
place  is  now  occupied  by  correlated  scientific  objects 
and  events.  This  may  happen  to  be  true,  but  it  is  not 
justified  by  my  visual  perception  alone.  The  star  may 
have  blown  up  or  moved  elsewhere  since  the  light  left 
it.  The  first  statement  implies  that  there  is  now  no 
centre  occupied  by  scientific  objects  correlated  with  my 
present  visual  sensa.  The  second  implies  that  there  is 
still  a  centre  occupied  by  events  of  this  kind,  but  that 
it  is  no  longer  at  the  place  where  the  optical  object  is 
present.  The  facts  of  aberration  show  that  such  diver- 
gences between  the  place  of  a  perceptual  event  and 
that  of  the  thing  with  which  it  is  connected,  may  arise 
through  mere  movement  of  the  observer. 

{b)  Scientific  Objects. — It  is  admitted  that  ordinary 
perceptual  objects,  like  pennies  and  chairs,  begin  to 
exist,  last  for  so  long,  and  then  come  to  an  end.  In 
the  chapter  on  Time  and  Change  in  Part  I,  I  tried  to 
explain  what  exactly  is  meant  by  saying  of  any  object 
that  it  began  to  exist,  lasted  so  long,  and  came  to  an 
end.  Now  perceptual  objects  are  supposed  to  be  con- 
nected with  scientific  objects  in  the  way  described 
earlier  in  the  present  chapter.  And  the  total  scientific 
object  specially  connected  with  any  perceptual  object 
is  believed  to  be  a  very  complex  whole  of  related 
parts.  Such  structures  have  more  or  less  stability, 
once  they  are  formed  ;  but  they  do  begin  to  exist  and 
come  to  an  end  under  suitable  conditions.  We  shall 
have  to  distinguish  between  scientific  objects  of  various 
orders.  The  sort  of  scientific  object  which  is  specially 
connected  with  a  perceptual  object,  like  a  chair,  may  be 


DATE   AND   DURATION  401 

called  a  first  order  object.  It  is  supposed,  as  we  know, 
to  consist  of  a  great  many  molecules  arranged  in 
a  pattern  in  space.  These  may  be  called  second  order 
objects.  Each  molecule  is  supposed  to  consist  of  a 
number  of  atoms,  characteristically  arranged  in  space 
and  moving  in  characteristic  ways  in  time.  These 
atoms  are  third  order  objects.  Finally,  each  atom  is 
supposed  to  be  an  arrangement  of  positive  and  negative 
electrons,  with  characteristic  types  of  motion.  These 
are  fourth  order  objects  ;  and  it  is  of  course  possible  that 
they  are  themselves  complicated  structures  composed 
of  fifth  order  objects. 

Such  a  hierarchy  represents  real  facts  about  Nature. 
The  simplest  way  to  look  at  it  is  the  following  :  Many 
agents,  such  as  the  presence  of  a  sufficiently  prosperous 
profiteer  on  the  seat,  will  break  up  a  chair  without 
affecting  the  molecules  of  cellulose  of  which  it  is  com- 
posed. Other  agents,  such  as  heat,  will  break  up  the 
cellulose  molecules,  but  leave  the  atoms  of  carbon, 
hydrogen,  and  oxygen  of  which  they  are  made,  un- 
altered. A  very  few  agents  will,  with  great  difficulty, 
break  up  the  atoms  themselves  into  their  constituent 
electrons.  So  far  as  I  know,  no  agent  yet  employed 
will  break  up  an  electron,  though  it  is  possible  by 
heroic  methods  to  knock  pieces  off  the  nucleus  of  an 
atom.  Thus  the  orders  in  the  hierarchy  of  scientific 
objects  are  the  stages  where  certain  disintegrating 
agents,  which  have  previously  been  effective,  cease  to 
be  so.  Chairs  really  are  permanent  under  a  great 
variety  of  conditions,  cellulose  molecules  under  a  greater 
variety,  carbon  atoms  under  a  still  greater  range,  and 
electrons  under  all  variations  that  have  been  tried. 

Now,  for  our  present  purpose,  the  important  thing 
to  notice  is  that  scientific  objects  of  different  orders  need 
different  minimal  spaces  and  durations  to  live  in.  This 
is  generally  recognised  in  regard  to  space,  though  it  is 
stated  in  a  rather  misleading  way,  e.g.,  that  "  molecules 
are  divisible  and  electrons  are  not."     It  is  equally  true 


402  SCIENTIFIC   THOUGHT 

of  time,  and  it  is  one  of  Whitehead's  great  merits  to 
have  pointed  this  out  clearly.      I  will  first  explain  what 
is  meant  by  this  statement  as    regards   space.      If  you 
divide  up  the  space  which  is  occupied  by  a  chair  into 
two  parts,  neither  of  these  parts  will  be  occupied  by  a 
chair,  though  one  may  be  occupied  by  a  leg  and  another 
by  a  seat.     Again,  you  could  divide  up  the  space  occupied 
by  a  chair  into  partitions,  each  of  which  was  occupied  by 
a  cellulose  molecule.      If  you  further  subdivided  one  of 
these  divisions  you  would  find  that  some  of  your  sub- 
divisions were  occupied  by  a  hydrogen  atom,  some  by 
a  carbon  atom,  some  by  an  oxygen  atom,  and  some  by 
nothing  at  all.     When  a  person  says  that  a  molecule  is 
divisible  in  space,  whilst   an    electron  is   not,  what  he 
means,  over  and  above  the  fact  that  one  has  been  experi- 
mentally split  up  and  that  the  other  has  not,  is  roughly 
the  following:  If  you  take  a  space  containing  one  and  only 
one  molecule  and  nothing  else,  you  can  divide  it  into  a 
set  of  exhaustive  and  mutually  exclusive  partitions,  such 
that  there  is  a  positive  difference  of  quality  between  the 
contents  of    some  of  these  partitions  and  the  contents 
of  others.       [E-g-,  the  contents  of  one   may  have  the 
"hydrogen    quality,"    that    of    another    the    "oxygen 
quality,"  and  so  on.     Of  course,  some  of  your  partitions 
may  have   no   contents   at   all.)     If  you    take   a   space 
containing  one  electron   and   nothing  else,  then  either 
(i)  all  sets  of  exhaustive  and  mutually    exclusive  par- 
titions into  which  you  can  divide  the  space  are  occupied 
by  contents  of  the  same  quality,  or  (2)  you  can  divide 
the  space  into  two   mutually  exclusive  and  exhaustive 
partitions,  one  of  which  is  empty  whilst  the  other  has 
the   property  (1).     What   is   called    "indivisibility"   is 
really  rather  homogeneity  of  quality  for    all  spatial  sub- 
divisions below  a  certain   maximum.      Whether  in   fact 
an   electron  answers  to    this   definition   is,   of  course,  a 
matter  for  empirical  investigation. 

Now,  as  Whitehead  has  pointed  out,  we   have  the 
same  distinction  among  objects  as    regards  division  of 


DATE   AND   DURATION  403 

their  history  into  successive  slices.  There  are  many 
types  of  object  whose  characteristic  qualities  need  a 
certain  minimum  of  duration  to  inhere  in.  E.g.,  memory 
is  one  of  the  outstanding  features  of  the  sort  of  thing 
that  we  call  a  "mind."  It  is,  therefore,  clear  that  the 
very  notion  of  a  "  momentary  mind  "  is  nonsense.  Now 
the  same  is  true  of  any  scientific  object  which  is  partly 
characterised  by  some  special  type  of  motion.  Suppose 
that  a  certain  kind  of  atom  consisted  of  a  nucleus  and 
an  electron  rotating  about  it  at  a  certain  characteristic 
rate.  Such  an  atom  would  need  at  least  the  duration 
of  one  complete  rotation  to  display  its  characteristic 
properties.  The  history  of  such  an  atom  is  a  "  pattern  " 
in  time,  just  as  the  momentary  arrangement  of  electrons 
and  nucleus  is  a  pattern  in  space.  If  the  duration  of 
one  complete  rotation  be  sliced  up  into  adjacent  successive 
parts,  the  contents  of  the  parts  will  differ  in  quality  from 
the  contents  of  the  whole. 

On  the  other  hand,  there  may  well  be  objects  which 
are  temporally  homogeneous.  This  would  mean  that, 
however  you  choose  to  divide  up  their  history,  the 
contents  of  all  the  slices  are  the  same  as  each  other  and 
as  the  whole  in  quality.  Many  types  of  scientific  object 
then  have  a  characteristic  minimum  duration  as  well 
as  a  characteristic  minimum  extension. 

Now  science  regards  the  ultimate  scientific  objects 
as  being  spatio-temporally  homogeneous.  And  it 
assumes  that  these  ultimate  scientific  objects  never 
begin  or  end.  Thus  the  ultimate  scientific  objects  are 
regarded  as  eternal  in  the  sense  of  existing  throughout 
all  time.  The  only  ultimate  scientific  changes  are  the 
groupings  and  regroupings  of  such  objects  according 
to  a  single  set  of  fundamental  laws.  Whether  this 
assumption  be  true,  and  whether  it  be  self-evident,  I  do 
not  profess  to  know.  But  I  believe  we  may  assert  (as 
I  have  pointed  out  elsewhere,  and  as  Mr  Keynes  has 
independently  and  much  more  clearly  shown  in  his 
Treatise  on  Probability)  that,  without  some  such  assump- 


404  SCIENTIFIC   THOUGHT 

tion,  it  is  impossible  to  justify  the  confidence  which 
we  feel  in  the  results  of  "  well-established  "  inductions. 
I  do  not  propose  to  pursue  this  subject  further  here. 

In  the  next  chapter  I  shall  say  what  I  can  about 
Motion,  and,  in  the  next  but  one,  I  shall  discuss  the 
concept  of  Space-Time,  from  which  Scientific  Space 
and  Scientific  Time  are  two  abstractions  of  different 
types. 

The  following  additional  works  may  be  consulted 
with  advantage  : 

B.  A.  W.  Russell,  Lectures  on  the  External  World,  Lectures 

III.  and  IV. 
A.  N.  Whitehead,  Principles  of  Natural  Knowledge,  Part  IV. 
S.  Alexander,  Space,  Time  and  Deity,  Book  I. 
A.  A.  ROBB,  Absolute  Relations  of  Time  and  Space. 


CHAPTER    XI 

"  Oh,  how  glorious  and  resplendent, 
Fragile  Body,  shalt  thou  be  !  " 

(Hymns  Ancient  and  Modern.) 

Sensible  and  Physical  Motion 

In  the  last  chapter  I  touched  incidentally  on  the 
sensible  motion  of  sensa  within  their  own  fields.  Both 
in  it  and  in  the  chapter  before  I  talked  of  the  motion  of 
our  bodies,  and  said  that  the  concept  of  physical  Space 
is  based  on  such  motions,  interpreted  spatially  by 
analogy  with  our  visual  fields.  I  propose  now  to  go 
considerably  more  into  detail  about  these  matters  ;  to 
consider  exactly  how  the  concepts  of  physical  Space 
and  Motion  are  connected,  on  the  one  hand  with  our 
bodily  movements,  and  on  the  other  with  the  positions 
and  movements  of  our  sensa  in  their  fields  ;  and  finally 
to  work  up  to  the  concept  of  physical  Space-Time. 
We  shall  find  that  the  consideration  of  our  own  bodies 
and  of  the  bodies  of  other  observers  who  can  communi- 
cate with  us  about  their  experiences  fills  a  gap  in  our 
concept  of  physical  objects,  and  is  an  essential  factor 
in  the  development  of  the  concept  of  physical  Space. 

General    Remarks    about    Change    and    Motion. — 

When  we  say  that  something  changes,  or,  more 
particularly,  that  it  moves,  we  imply  a  certain  identity 
and  a  certain  difference.  There  must  be  enough 
identity  for  us  to  be  able  to  say  that  we  are  dealing 
with  the  same  object,  in  spite  of  the  movement  or  other 
change.  And  there  must  be  some  difference  between 
one  part  of  the  history  of  the  object  and  others,  or  we 


4o6  SCIENTIFIC   THOUGHT 

should  not  say  that  it  had  changed  or  moved.  Change 
is  a  more  general  concept  than  movement,  since  move- 
ment is  simply  change  of  position  in  space.  We  will, 
therefore,  begin  with  change  in  general. 

In  ordinary  life  we  distinguish  between  an  object 
and  its  history,  and  we  are  inclined  to  think  that  the 
former  is  logically  prior  to  the  latter.  We  say,  e.g., 
that  there  is  a  certain  object,  such  as  a  penny,  and  that 
it  may  either  rest  or  move,  keep  bright  or  tarnish, 
and  so  on.  These  events,  we  say,  "happen  to"  the 
object,  and  its  history  is  just  all  the  events  that  happen 
to  it.  You  might,  we  think,  have  an  object  without  a 
history,  but  you  could  not  have  a  history  without  an 
object.  I  believe  this  to  be  a  profound  mistake,  which 
arises  from  taking  "history"  in  too  narrow  a  sense. 
An  object,  separated  from  its  history,  is  clearly  not  the 
kind  of  thing  that  could  possibly  exist.  Every  object 
that  is  not  merely  momentary  has  a  history  of  some 
kind,  and  no  merely  momentary  object  could  really 
exist.  "  Object,"  apart  from  "history,"  is  therefore  as 
much  an  abstraction  as  "  history,"  apart  from  "  object." 
Of  course  some  histories  are  very  tame,  e.g.,  that  of  a 
penny  which  keeps  in  one  place  and  never  varies  in  its 
other  qualities.  Others  are  more  exciting,  e.g.,  that  of 
a  penny  which  moves  about,  gets  bent  and  defaced, 
and  is  finally  dropped  into  the  collection-plate.  Now 
we  are  inclined  to  identify  history  with  exciting,  i.e., 
variable,  history.  We  then  identify  the  object  with 
the  tame  tracts  of  its  history  ;  and  forget  that  these  are 
history  at  all,  because  they  are  so  uniform.  But  really 
all  that  literally  exists  is  strands  of  history,  some  tamer 
and  some  more  exciting. 

Now  it  is  conceivable  that  there  might  have  been 
succession  but  no  history.  If  so,  there  would  have 
been  neither  an  object  nor  a  plurality  of  objects.  Let 
us  consider  a  fragment  of  the  whole  course  of  Nature, 
lasting  for  an  hour.  Let  us  imagine  it  cut  up  into 
successive  slices,  each  lasting  for  a  second.     Theoreti- 


SENSIBLE   AND   PHYSICAL   MOTION       407 

cally  there  are  three  possibilities,  (i)  We  might  find 
that  the  contents  of  any  adjacent  pair  of  seconds  had  no 
particular  resemblance  either  in  whole  or  in  part.  And 
we  might  still  find  the  same  result  if  we  took  shorter 
and  shorter  divisions.  In  that  case  we  could  hardly 
talk  of  history  at  all  ;  there  would  merely  be  a  perfectly 
chaotic  hail  of  events,  (ii)  We  might  find  that  there 
was  considerable  qualitative  resemblance  between  the 
whole  contents  of  any  adjacent  pair  of  seconds,  and  that 
this  resemblance  increased  as  we  took  shorter  and 
shorter  sub-divisions.  But  we  might  have  to  compare 
the  contents  of  each  second  en  bloc.  We  mio-ht  not  be 
able  to  divide  it  into  clearly  distinguishable  co-existing 
parts.  In  that  case  we  should  say  that  there  is  a  history 
(of  the  world  as  a  whole),  but  that  there  is  not  a 
number  of  distinct  strands  of  history.  We  could  then 
talk  of  an  object,  which  endures  and  perhaps  changes, 
viz.,  the  universe;  but  not  of  a  number  of  distinct 
objects,  (iii)  We  might  find,  as  we  actually  do,  that 
the  content  of  each  second  is  distinguishable  into 
different  co-existing  parts,  and  that  a  certain  part  of 
the  content  of  one  is  hooked  on  to  a  certain  part  of  the 
content  of  the  next  by  close  qualitative  resemblance. 
Under  this  head  I  include  resemblance  of  shape  and 
position,  as  well  as  resemblance  of  colour,  temperature, 
etc.  We  should  then  say,  not  only  that  there  is  a 
history  of  the  world  as  a  whole,  but  also  that  there  are 
various  distinct  strands  of  history.  Each  strand  would 
be  called  the  history  of  such  and  such  an  object,  but 
this  does  not  mean  that  there  is  another  existent,  viz., 
"the  object,"  beside  the  strand  itself.  It  is  only 
because  there  are  such  strands  that  we  can  talk  of  a 
plurality  of  objects.  The  world  as  a  whole  would  have 
a  history,  partly  because  it  is  composed  of  such  strands 
of  history.  But  its  history  is  more  than  the  sum  total 
of  a  number  of  distinct  strands  lying  side  by  side.  If 
there  be  causal  and  other  regularities  which  hold 
throughout   the  whole    period    under   discussion,  there 


408  SCIENTIFIC  THOUGHT 

will  be  characteristic  relations  between  the  strands, 
and  the  history  of  the  world  as  a  whole  would  have 
more  unity  and  complexity  than  is  implied  by  the 
simple  statement  that  it  is  composed  of  such  and  such 
parallel  strands. 

Whenever  we  talk  then  of  "objects,"  the  funda- 
mental fact  is  the  existence  of  distinct  strands  of  history. 
A  given  object  is  a  certain  strand,  pervaded  by  a  certain 
special  unity  and  continuity,  which  characterise  it  and 
mark  it  out  from  strands  of  other  kinds.  To  say  that  a 
certain  object  has  not  changed  in  any  respect  is  to  say 
that  all  the  successive  slices  of  a  certain  strand  are 
qualitatively  indistinguishable  from  each  other.  An 
unchanging  object  is  thus  a  completely  uniform  strand  of 
history.  To  say  that  a  certain  object  has  moved,  but 
has  not  otherwise  changed,  is  to  say  that  the  positional 
qualities  of  successive  slices  of  a  certain  strand  are 
progressively  different.  A  moving  object  is  therefore  a 
positionally  non-uniform  strand. 

Now  it  happens,  of  course,  that  there  are  many  distinct 
strands  which  are  so  much  alike  in  the  characters  of 
their  slices,  and  in  the  type  of  unity  that  pervades  them, 
that  they  are  called  histories  of  objects  of  the  same  kind. 
Yet  some  of  these  strands  may  be  positionally  uniform, 
whilst  others  are  positionally  non-uniform.  An  example 
would  be  given  by  a  resting  and  a  moving  penny. 
Again,  a  strand  which  has  enough  unity  and  continuity 
throughout  to  count  as  the  history  of  a  single  object 
may  yet  for  some  part  of  its  length  be  positionally 
uniform  and  for  others  be  positionally  non-uniform. 
An  example  would  be  a  penny  which  sometimes  keeps 
still  and  sometimes  moves.  I  think  that  it  is  partly  in 
consequence  of  such  facts  that  we  tend  to  separate 
objects  from  their  histories,  and  to  treat  their  histories 
as  something  more  or  less  external,  which  may  or  may 
not  "happen  to"  them.  A  given  penny  really  is  a 
certain  definite  strand  of  history,  positionally  uniform 
if  it  be  a  resting  penny,   positionally  non-uniform  if  it 


SENSIBLE   AND   PHYSICAL   MOTION       409 

be  a  moving  penny,  and  so  on.  But  you  can  always 
find  plenty  of  other  strands  of  history  sufficiently  like 
this  one  in  their  non-positional  qualities  to  be  called 
histories  of  pennies,  and  yet  uniform  where  this  history 
is  positionally  non-uniform.  You  tend  to  identify  the 
first  penny  with  a  uniform  history,  such  as  the  second 
penny,  and  to  regard  the  non-uniform  part  of  the  first 
pennyas  something  that  "happened  to"  it,  but  was  not 
a  part  of  it.  The  real  fact,  however,  is  that  the  first 
penny  is  the  first  strand  and  nothing  else,  and  the 
second  penny  is  the  second  strand  and  nothing  else. 
Of  course  the  general  characteristic  of  "  being  a  penny  " 
is  common  to  both,  since  it  is  the  general  type  of 
qualitative  character  which  pervades  all  such  strands  ; 
but  this  is  a  universal,  not  a  particular  existent  ;  and 
when  people  talk  of  "objects,"  and  say  that  they  rest 
or  move,  they  are  certainly  not  primarily  talking  about 
universal  characteristics  but  about  particular  existents. 

It  is  evident  then  that  every  object  has  a  time- 
dimension  as  well  as  any  space-dimensions  that  it 
may  have.  There  is  nothing  mysterious  about  this  ;  it 
means  no  more  than  that  every  existing  object,  whether 
at  rest  or  in  motion,  is  a  strand  of  history  with  some 
duration.  The  question  whether  it  is  a  changing  or 
an  unchanging  object  is  simply  the  question  whether 
successive  slices  of  the  strand,  normal  to  the  time- 
dimension,  are  exactly  alike  or  progressively  different 
in  quality.  The  notion  of  an  object  with  nothing  but 
spatial  dimensions  is  an  abstraction.  You  can  divide 
up  the  object  into  thinner  and  thinner  slices  normal  to 
its  time-dimension,  and  these  slices  will  approximate, 
as  you  make  them  thinner  and  thinner,  to  purely  spatial 
figures.  In  the  limit  each  will  be  a  purely  spatial 
figure,  in  general  of  three  dimensions.  But  these  are 
not  the  object,  nor  are  they  literally  even  parts  of  it. 
The  object  is  the  whole  four-dimensional  strand  of 
history.        And    these    momentary    spatial    figures   are 

"parts"  of  the  object  only  in  the  Pickwickian  sense  in 

2  D 


4io  SCIENTIFIC   THOUGHT 

which  plane  sections  of  an  ordinary  solid  are  "parts" 
of  the  solid.  A  person  who  refuses  to  identify  an  object 
with  its  whole  history  must  either  identify  it  with  a 
momentary  section  of  that  history  or  with  a  uniform  slice 
of  it.  If  he  does  the  former,  the  object  is  a  mere  abstrac- 
tion, incapable  of  existence.  If  he  does  the  latter,  his 
restriction  to  the  uniform  part  of  the  whole  strand  of 
history  is  clearly  arbitrary. 

If  it  should  happen  that  all  the  successive  momentary 
sections  of  an  object  have  the  same  shape,  you  can  call 
this  the  shape  of  the  object.  But,  if  they  have  different 
shapes,  there  is  nothing  that  can  be  called  the  shape  of 
the  object.  A  penny  and  a  mist  are  both  objects  ;  but, 
whilst  you  can  talk  of  the  shape  of  the  former,  you 
cannot  talk  of  the  shape  of  the  latter. 

Motion  and  Rest  in  Visual  Fields  and  Sense-histories. 
— After  these  general  remarks  about  the  nature  of  objects 
and  their  motion  or  rest,  we  can  consider  the  various 
types  of  motion  and  rest  which  happen  within  our  visual 
fields  and  sense-histories. 

(a)  Motion  and  Rest  of  Visual  Sensa. — A  single  sense- 
field  lasts  for  a  finite,  though  short,  time.  Spatially  it 
is  of  three  dimensions.  It  is  therefore  a  four-dimensional 
spatio-temporal  whole.  In  sensing  it,  we  thus  sense 
directly  a  four-dimensional  whole  with  three  spatial 
dimensions  and  one  temporal.  A  sensum  is  an  outstand- 
ing part  of  the  total  content  of  a  sense-field.  It  has  some 
duration,  which  cannot  be  greater  than  that  of  the  sense- 
field,  and  it  has  spatial  extension.  It  is  therefore  in 
general  a  four-dimensional  object.  Now,  as  we  have 
seen,  a  visual  sensum  may  shift  its  position  in  its  own 
field  or  not.  If  it  does,  it  is  affected  with  sensible  motion, 
otherwise  it  is  sensibly  at  rest.  Thus  all  visual  sensa 
are  four-dimensional  objects,  and  those  that  are  affected 
with  sensible  motion  are  positionally  non-uniform  objects. 
Just  as  we  cannot  see  at  once  an  object  of  more  than  a 
certain  size,  so  we  cannot  sense  by  one  act  an   object 


SENSIBLE   AND   PHYSICAL   MOTION       411 

that  exceeds  the  duration  of  a  Specious  Present,  whether 
it  be  uniform  or  non-uniform.  In  sensing  a  resting 
sensum  we  are  aware  in  one  act  of  a  positionally  uniform 
four-dimensional  object  of  short  duration  ;  in  sensing  a 
moving  sensum  we  are  aware  in  one  act  of  a  positionally 
non-uniform  four-dimensional  object  of  short  duration. 
Thus,  sensible  motion  is  the  way  in  which  the  positional 
non-uniformity  of  a  four-dimensional  object  presents 
itself  to  us  when  this  non-uniformity  is  "sharp"  enough 
to  be  noticeable  within  the  duration  of  a  single  sense- 
field. 

(b)  Motion  and  Rest  of  Visual  Sense-objects.  —  Our 
successive  visual  fields  join  up  with  each  other  to 
form  a  single  sense-history,  as  already  described.  This 
is  simply  a  four-dimensional  whole,  of  the  same  general 
nature  as  a  single  visual  field,  but  of  greater  duration. 
It  cannot,  of  course,  be  sensed  as  a  whole,  though  some 
of  its  earlier  slices  may  be  remembered  while  its  latest 
slice  is  being  sensed.  Now,  when  a  certain  resting 
sensum  has  occupied  a  certain  position  throughout  the 
whole  of  one  field,  similar  sensa  may  occupy  exactly 
similar  positions  in  a  series  of  successive  fields.  Just 
as  the  fields  join  up  to  give  one  sense-history,  of  which 
they  are  successive  slices,  so  these  resting  sensa  join 
up  to  give  a  single  sense-object,  of  which  they  are 
successive  slices.  This  will  be  a  positionally  uniform 
sense-object,  and  may  be  described  as  a  sense-object 
which  rests  in  the  space  of  the  observer  s  sense- history. 

Now  it  may  happen  that  there  is  a  series  of  more 
or  less  similar  sensa  in  a  series  of  successive  fields,  but 
that  they  occupy  progressively  dissimilar  positions  in 
their  respective  fields.  And  it  may  be  that  the  thinner 
two  fields  are  and  the  nearer  they  are  together,  the  less 
is  the  dissimilarity  between  the  positions  of  the  sensa 
of  this  set  which  belong  to  these  fields.  On  these  con- 
ditions the  sensa  of  the  set  still  join  up  to  form  a  sense- 
object  of  which  they  are  successive  slices.  But  this 
sense-object  is    positionally   non-uniform,   and    may   be 


412  SCIENTIFIC   THOUGHT 

described  as  a  sense-object  which  moves  in  the  space  of  the 
observers  sense-history.  Often  there  is  no  sensible  non- 
uniformity  in  the  individual  sensa  of  such  a  group, 
although  they  join  up  to  form  a  positionally  non-uniform 
sense-object.  On  the  other  hand,  it  often  happens  that 
each  of  the  component  sensa  of  a  moving  sense-object 
is  itself  affected  with  sensible  motion  in  its  own  field. 
It  is  reasonable  to  suppose  that,  even  in  the  former  case, 
the  component  sensa  are  really  not  quite  positionally 
uniform  objects,  but  that  their  departure  from  uniformity 
is  not  "sharp"  enough  to  be  sensed  as  movement  within 
the  sense-field. 

Now,  it  is  very  important  to  notice  that  the  move- 
ment of  sensa  in  their  fields  and  of  sense-objects  in  the 
spaces  of  their  sense-histories  is  the  ultimate  empirical 
basis  of  the  concept  of  absolute  motion.  The  sensible 
motion  of  a  sensum  in  its  field  really  is  something 
absolute  ;  it  does  not  simply  consist  in  the  fact  that 
this  sensum  alters  its  spatial  relations  to  other  sensa 
in  the  field,  though,  of  course,  it  involves  this  as  a 
necessary  consequence.  This  is  quite  clear,  from  the 
following  example:  Suppose  I  am  looking  at  the  sky, 
and  a  shooting  star  darts  across.  I  am  aware  of  a 
field  ;  and  within  this  are  sensa  which  are  the  appear- 
ances of  the  other  stars,  and  a  sensum  which  is  the 
appearance  of  the  shooting  star.  The  latter  is  affected 
with  sensible  motion,  whilst  the  former  are  not.  Now, 
if  the  sensible  motion  simply  consisted  in  a  change  of 
relative  position  within  the  field,  it  would  be  perfectly 
symmetrical,  and  it  would  be  impossible  to  say  that 
the  shooting  star  sensum  sensibly  moves  and  that  the 
other  sensa  do  not.  But  it  is  quite  clear  that  in  fact 
we  do  sense  an  intrinsic  peculiarity  of  the  shooting 
star  sensum  which  is  not  present  in  the  others.  Thus, 
sensible  motion  and  rest  are  something  absolute  and 
intrinsic,  not  merely  relational  ;  and  I  take  it  that  this 
fact  is  at  the  basis  of  the  concepts  of  absolute  motion 
and    rest.       It    does    not,    of    course,    follow   that    the 


SENSIBLE   AND   PHYSICAL   MOTION       413 

concept  thus  formed  really  is  applicable  beyond  sense- 
fields  and  sense-histories.  It  may  well  be  that  the 
absolute  motion  or  rest  of  a  sense-object  in  the  space 
of  my  sense-history  is  connected  with  merely  relative 
motion  between  my  body  and  other  physical  objects. 
This  does  not  alter  the  fact  that  the  motion  of  the 
sense-object  in  the  space  of  my  sense-history  is  itself 
absolute,  and  not  a  mere  change  of  relation  to  other 
contents  of  the  history.  We  shall  consider  this  question 
at  a  later  stage  in  the  chapter. 

Correlations  between  the  Motions  of  Visual  Objects 
and  the  Kinesthetic  Sensations  of  an  Observer. — The 
best  way  to  approach  this  complicated  subject  seems 
to  be  by  taking  special  cases  as  illustrations.  Taking 
a  single  observer  and  a  single  physical  object,  we 
can  begin  by  distinguishing  four  cases  which  con- 
stantly happen  :  (A)  The  observer  stands  still,  and 
(i)  watches  a  resting  physical  object,  or  (ii)  watches 
a  moving  physical  object.  (B)  The  observer  moves 
bodily,  and  (i)  watches  a  resting  physical  object,  or 
(ii)  watches  a  moving  physical  object.  These  four 
cases  must  be  distinguished  from  each  other  by  certain 
differences  in  our  sensible  experiences,  and  I  shall  begin 
by  pointing  out  the  peculiarities  of  each  in  turn. 

(A)  There  are  two  kinds  of  kinesthetic  sensation, 
one  connected  with  walking,  and  the  other  with  turning 
the  head.  I  will  call  them  respectively  translational  and 
rotational  kinassthetic  sensations.  The  A-cases  are  all 
alike  in  the  fact  that  the  observer  feels  no  translational 
kinesthetic  sensations. 

(i)  When  a  resting  observer  watches  a  resting 
physical  object  he  finds  that,  once  having  turned  his 
head  so  as  to  sense  a  field  with  a  visual  appearance  of 
this  object  in  the  middle  of  it,  he  must  henceforth  keep 
his  head  still  if  he  wants  to  go  on  sensing  fields  with 
similar  sensa  at  their  centres.  That  is,  in  order  that 
the  physical  object  may  appear  in  his  sense-history  as  a 


414  SCIENTIFIC   THOUGHT 

resting  sense-object,  he  must  henceforth  keep  free  from 
rotational  kinesthetic  sensations.  If  at  any  moment 
he  chooses  to  start  turning  his  head,  the  physical  object 
will  still  continue  for  a  time  to  appear  in  his  visual 
sense-history.  But  the  visual  sensa  by  which  it  appears 
will  occupy  progressively  dissimilar  places  in  his  suc- 
cessive fields.  Moreover,  they  may  be  affected  with 
sensible  motion  within  their  fields.  Thus,  in  this  case, 
the  physical  object  still  appears,  for  a  time  at  least,  as 
a  visual  sense-object  in  the  observer's  sense-history. 
But  its  appearance  is  now  a  positionally  non-uniform, 
i.e..,  a  moving,  sense-object. 

There  are  also  certain  points  to  be  noticed  about  the 
shapes,  etc.,  of  the  successive  sensa  in  this  sense-object. 
While  the  observer  keeps  his  head  still,  the  successive 
sensa  will  be  indistinguishable  in  shape,  unless,  of 
course,  physical  changes  are  going  on  in  the  object. 
But  when  he  moves  his  head,  the  successive  appear- 
ances will  differ  in  shape  ;  they  will  be  more  and  more 
distorted  as  he  turns  his  head  more,  and  as  they  occupy 
more  eccentric  positions  in  his  successive  fields.  Thus, 
when  he  turns  his  head,  the  sense-object  by  which  the 
physical  object  appears  in  his  sense-history  is  not  only 
positionally  non-uniform  ;  it  is  also  non-uniform  as 
regards  shape.  There  is  another  difference  between  the 
successive  sensa,  which  I  will  just  mention  here  and  deal 
with  more  fully  later.  They  do  not  differ  merely  in 
the  fact  that  each  is  a  distortion  of  the  original  central 
sensum.  Very  often  there  is  something  in  the  later 
sensa  to  which  nothing  corresponded  in  the  earlier 
ones,  and  conversely.  This  is  the  sensible  basis  of 
the  fact  which  we  express  by  saying  that,  as  we  turn 
our  heads,  "fresh  parts  of  the  object  come  into  view, 
whilst  others  which  were  formerly  visible  cease  to 
be  so." 

A  final  and  very  important  point  to  notice  is  that, 
in  the  present  case,  by  exactly  reversing  the  series  of 
rotational  kinesthetic  sensations  I  exactly  reverse  the 


SENSIBLE   AND   PHYSICAL   MOTION       415 

series  of  sensa,  and  end  up  with  a  field  like  that  from 
which  I  started,  with  a  sensum   like  the  original  one 
in   its  centre.      I   can   do    this  as   often   as   I   like,   and 
always  with  the  same  result.     Again,  I  can  move  my 
head    from    its    initial    position    in    a    great   variety   of 
ways,  which  are  distinguished  for  me  by  characteristic 
differences    in    my    rotational     kinesthetic    sensations. 
Each  such  way  will  involve  a  non-uniform  sense-object 
of    the    kind    described  ;    and    each,    on    reversal,    will 
bring:  me  back  to  a  field  like  that  with  which  I  started. 
But  there  are  characteristic  differences  of  detail  between 
the  various  non-uniform  sense-objects  which  correspond 
to  the  various  series  of  rotational  kinesthetic  sensations, 
(ii)  When  I  stand  still  and  watch  a  moving  physical 
object,  I  find  that  I  must  keep  turning  my  head  if  I  want 
to    keep   the    successive   appearances    of    the    physical 
object  in  the  centres  of  my  successive  fields.     And    I 
must  do  this  in  a  perfectly   definite   way.     Moreover, 
there  is  a  difference  between  the  sense-object  which  I 
sense  in  this  case  and  in  the  last.      In  the  last  case,  if 
I  keep  my  head  still,  I  sense  a  completely  uniform  sense- 
object.      In  the  present,  the  sense-object  never  is  com- 
pletely uniform  ;   it  is  not  even  completely  uniform  in 
position.     What  we  should  find  would  be  this  :  There 
would   be  a  steady  increase,  a  steady  decrease,  or  the 
one  followed  by  the  other,   in  the  sizes  and  depths  of 
the   sensa.     There   will   be    distortion   in   their  shapes. 
There  will  be   variations  in  brightness.     And,  finally, 
the  later  sensa  will  have  parts  to  which  nothing  corre- 
sponds in  the  earlier,  and  conversely. 

Suppose  now  that,  at  a  certain  moment,  I  stop 
moving  my  head.  From  that  moment  the  successive 
appearances  of  the  physical  object  will  begin  to  occupy 
dissimilar  positions  in  my  successive  fields.  Very 
probably  each  will  have  sensible  motion  in  its  own 
field.  And  the  distortion  of  later  sensa,  and  the 
addition  of  new  and  dropping  of  old  features,  will  be 
greatly  accelerated.       In   fact,   the  physical   object  will 


416  SCIENTIFIC   THOUGHT 

henceforth  appear  as  an  extremely  non-uniform  sense- 
object,  both  positionally  and  in  other  respects.  Very 
soon  it  will  cease  to  appear  at  all  in  my  sense-history, 
i.e.,  the  later  parts  of  the  sense-history  will  be  fields 
containing  no  sensa  connected  with  this  physical  object. 
When  this  is  so,  I  could,  as  a  rule,  start  again  at  will 
to  sense  a  field  with  an  appearance  of  this  physical 
object  at  its  centre.  In  order  to  do  this,  I  shall  have 
to  turn  my  head  to  a  definite  extent,  independent  of 
my  choice.  And,  when  I  do  at  length  sense  another 
field  with  a  sensum  of  the  required  kind  in  the  middle 
of  it,  I  shall  find  that  this  sensum  differs  in  shape, 
brightness,  depth,  etc.,  from  the  one  that  was  in  the 
middle  of  the  last  field  which  I  sensed  before  I  stopped 
turning  my  head. 

(B)  The    B-cases    resemble  each    other,    and    differ 
from    the    A-cases,    in    that    the    observer   experiences 
translatory  as  well  as  rotational  kinesthetic  sensations, 
(i)  If  a  man  walks,  and  wants  to  keep  his  eye  on  a 
resting    physical    object,    he    will    find    that    he    must 
continually  turn  his  head  as  he  walks.     And  the  amount 
of  rotational  kinesthetic  sensation  needed  is  correlated 
with  the  amount  of  translational  kinesthetic  sensation 
experienced.      Provided  he  turns  his  head  properly,  the 
physical  object   will   appear   in    his  sense-history  as  a 
partly,   but  only  partly,   uniform    sense-object.      It   will 
not   be   uniform   in    depth    or   brightness.      There  will 
also  be    distortion   and   revelation    of   new   parts.     But 
the  sensa  will  be  at  the  centres  of  his  successive  fields. 
If  he  walks,  and   keeps  his   head   and   eyes   fixed,   the 
physical   object   will   appear    in    his    sense-history  as   a 
moving  sense-object,  and  possibly  the  constituent  sensa 
may   have    sensible    motion    in    their    respective  fields. 
The   non-uniformity   in    respect  of  shape  will   be  very 
much    greater    than    when    he    keeps    his   eye   on    the 
physical  object,  and  soon  this  will  cease  to  appear  at 
all   in  his  sense-history.     After  it  has  disappeared   he 
can   again   sense  a  field  with  a  sensum   of  the  group 


SENSIBLE  AND   PHYSICAL   MOTION       417 

at  its  centre,  provided  he  turns  his  head  properly.  The 
amount  of  rotational  kinesthetic  sensation  needed  for 
this  purpose  will  be  completely  determined  by  the 
nature  and  amount  of  translational  kinesthetic  sensation 
which  he  has  experienced  since  he  ceased  turning  his 
head.  Lastly,  the  sensum  which  will  occupy  the  middle 
of  his  present  field  will  never  be  exactly  like  that  which 
occupied  the  middle  of  the  field  which  he  was  sensing 
when  he  stopped  turning  his  head.  There  will  be 
differences  in  shape,  depth,  brightness,  etc.  ;  and  there 
will  be  parts  to  which  nothing  corresponded  in  the 
last  sensum,  and  conversely. 

It  is  obvious  that,  on  the  visual  side,  there  is  a 
close  analogy  between  B  (i)  and  A  (ii),  i.e.,  between 
the  visual  experiences  of  a  moving  observer  watching 
a  resting  object  and  those  of  a  resting  observer  watching 
a  moving  object.  There  is  also  a  partial  resemblance 
between  the  rotational  kinesthetic  sensations,  since  both 
of  them  are  obliged  to  keep  moving  their  heads  in  a 
certain  way  in  order  to  keep  the  appearances  of  the 
physical  object  in  the  centres  of  their  successive  fields. 
The  difference  is  that  in  A  (ii)  the  rotational  kin- 
esthetic sensation  needed  is  absolutely  independent  of 
the  observer's  volition,  whilst  in  B  (i)  it  is  indirectly 
dependent  on  his  volition.  It  is  primarily  dependent 
only  on  the  amount  and  kind  of  his  translational  kin- 
esthetic sensations  ;  but  these  in  turn  are  dependent  on 
his  will,  since  he  can  walk  as  he  chooses.  This  gap, 
however,  is  bridged  by  the  case  of  observers  whose 
bodies  are  carried  about  in  trains,  motor  cars,  etc. 
Their  movements  do  not  involve  translational  kinesthetic 
sensations,  and  here  the  analogy  between  B  (i)  and  A 
(ii)  becomes  practically  complete.  Such  facts  as  this 
analogy  lie  at  the  basis  of  the  concept  of  the  relativity 
of  physical  motion. 

(ii)  When  an  observer  moves  about  and  keeps  his 
eye  on  a  moving  physical  object  he  will  find  that  the 
nature  and  amount  of  kinesthetic  sensation  needed  are 


418  SCIENTIFIC  THOUGHT 

determined  partly,  but  only  partly,  by  his  translational 
kinesthetic  sensations.  He  will  sometimes  have  to  turn 
his  head  more  quickly,  and  sometimes  less  quickly  than 
if  he  were  walking  in  the  same  way  and  keeping  his  eye 
on  a  resting  physical  object.  If  he  were  to  retrace  his 
steps,  and  then  walk  over  his  old  course  again,  it  would 
be  useless  to  repeat  the  same  head-movements  which  he 
made  on  the  previous  occasion.  If  he  did  this,  it  is  very 
likely  that  the  physical  object  would  no  longer  appear 
in  his  sense-history  at  all  ;  and,  even  if  it  did  so,  it 
would  certainly  not  appear  in  the  form  of  a  sense-object 
whose  successive  sensa  occupied  the  centres  of  his 
successive  fields. 

There  is  a  very  important  point  to  notice  about  these 
B-cases.  In  them  the  observer  has  both  translational 
and  rotational  kinesthetic  sensations.  Now  these  fall 
into  pairs  of  correlated  series  in  the  following  way  :  The 
successive  appearances  of  a  physical  object  can  be  kept 
at  the  centres  of  one's  successive  fields  in  an  infinite 
variety  of  different  ways,  all  of  which  involve  different 
combinations  of  translational  and  rotational  kinesthetic 
sensations.  Take  first  a  resting  physical  object,  (a) 
Its  successive  visual  appearances  can  be  kept  in  the 
centres  of  one's  successive  visual  fields  by  suitably 
turning  the  head  and  henceforth  moving  neither  the 
head  nor  the  body.  (/3)  A  similar  result  (though  not  an 
identical  one)  can  be  produced  by  walking  in  innumer- 
able different  ways,  and  at  the  same  time  continually 
turning  the  head  in  correlated  ways.  Lastly,  (y)  there 
is  one  and  only  one  way  of  walking  without  turning  the 
head  which  will  produce  similar  results,  though,  of  course, 
this  one  way  may  be  pursued  at  different  rates.  This  is 
what  we  call  "walking  straight  up  to  the  object."  (a) 
and  (y)  are  two  extreme  cases  of  the  huge  group  included 
under  (/3).  It  must  be  noticed  that  the  various  combina- 
tions of  correlated  rotational  and  translational  kinesthetic 
sensations  are  not  absolutely  equivalent  in  their  results 
on    the    sense -object    by    which    the    physical    object 


SENSIBLE   AND   PHYSICAL   MOTION       419 

appears  in  the  observer's  sense-history.  The  (a)-method 
gives  a  completely  uniform  sense-object.  Each  of  the 
(/3)-methods  gives  a  somewhat  different  sense  -  object. 
All  these  sense-objects  are  non-uniform  in  shape  and 
depth  ;  for  different  component  sensa  will  have  different 
depths  in  their  respective  fields.  Moreover,  there  is 
always  that  difference  between  successive  sensa  which 
we  describe  by  saying  that  we  "  see  fresh  parts  and  lose 
sight  of  some  which  we  saw  before."  Lastly,  the 
(y)-method  gives  a  sense-object  which  is  uniform,  in  the 
sense  that  there  is  no  distortion  between  the  successive 
sensa  which  constitute  it.  But  each  of  these  sensa  has 
a  larger  size  and  a  smaller  depth  than  the  one  before, 
whilst  there  will  be  a  progressive  increase  in  brightness. 
In  spite  of  this,  there  may  be  the  difference  which  we 
should  express  by  saying  that  the  earlier  sensa  "  reveal 
parts  of  the  physical  object  which  cease  to  be  revealed 
by  the  later  ones." 

Somewhat  similar  remarks  apply  to  the  correlation 
between  rotational  and  translational  kinesthetic  sensa- 
tions in  watching  a  moving  physical  object.  But  there 
are  certain  differences,  (a)  Its  successive  appearances 
cannot  be  kept  in  the  centres  of  our  successive  fields  if 
we  neither  walk  nor  turn  our  heads.  (/3)  If  we  choose 
to  do  both,  there  are  innumerable  combinations  of  the 
two  which  will  produce  the  required  kind  of  sense- 
object.  But  the  rotational  kinesthetic  sensations  which 
have  to  be  combined  with  a  given  set  of  translational 
sensations  for  this  purpose  are  not  the  same  as  they 
would  be  if  we  were  looking  at  a  resting  object.  In  fact, 
no  general  rule  of  correlation  can  be  laid  down  without 
bringing  in  an  additional  factor,  viz.,  the  motion  of  the 
physical  object  itself,  (y)  There  is  one  and  only  one 
way  of  keeping  the  successive  appearances  of  a  moving 
physical  object  in  the  centres  of  our  successive  fields  with- 
out continually  turning  our  heads,  and  that  is,  of  course, 
by  walking  parallel  to  its  line  of  motion  at  a  suitable 
pace.     The  particular  series  of  kinesthetic  sensations 


420  SCIENTIFIC   THOUGHT 

needed  for  this  purpose  varies,  of  course,  with  the  motion 
of  the  particular  physical  object  which  is  being  watched. 
By  the  (y)-method,  and  by  it  alone,  does  a  moving 
physical  object  appear  to  us  as  a  completely  uniform 
sense-object. 

There  is  thus  a  close  resemblance  between  the  cases 
A  (i)  and  B  (ii)  (y).  So  far  as  the  visual  object  is  con- 
cerned, they  are  precisely  alike.  The  difference  is  that  in 
A  (i)  a  completely  uniform  sense-object  requires  complete 
absence  of  both  kinds  of  kinesthetic  sensation,  whilst 
in  B  (ii)  (y)  it  requires  a  characteristic  series  of  trans- 
lational  kinesthetic  sensations.  The  gap  here  is  to 
some  extent  bridged,  as  in  the  analogy  between  A  (ii) 
and  B  (i),  by  the  fact  that  an  observer's  body  may  be 
carried  parallel  to  another  physical  object  without  effort 
of  his  own.  This  happens,  e.g.,  when  an  observer  in 
a  moving  train  keeps  his  eye  on  a  certain  window  of  a 
carriage,  moving  at  the  same  rate  and  in  the  same 
direction  on  a  parallel  line.  Here  we  have  another 
sensible  fact  which  lies  at  the  basis  of  the  concept  of 
the  relativity  of  physical  motion. 

(b)  Summary  of  Facts  elicited  in  the  last  Sub-section. 
We  have  been  discussing  the  sensible  experiences, 
both  visual  and  kinesthetic,  which  make  an  observer 
say  sometimes  that  he  stands  still  and  watches  a  resting 
body,  sometimes  that  he  stands  still  and  watches  a 
moving  body,  sometimes  that  he  moves  and  watches  a 
resting  body,  and  sometimes  that  he  moves  and  watches 
a  moving  body.  The  most  important  general  conclusion 
that  emerges  is  that  there  is  a  mixture  of  arbitrariness 
and  compulsion  in  all  such  cases,  and  that  it  is  the 
particular  character  of  the  mixture  which  causes  us 
to  make  now  one  and  now  another  of  these  four  types 
of  statement. 

(i)  I  can  always,  if  I  choose,  sense  a  series  of  visual 
fields,  each  of  which  contains  an  appearance  of  an 
assigned  physical  object  at  its  centre,  (ii)  I  can  always, 
if  I  choose,  sense  a  series  of  fields  in  which  successive 


SENSIBLE  AND   PHYSICAL   MOTION       421 

appearances  of  the  assigned  physical  object  occupy 
progressively  more  dissimilar  sensible  positions.  But 
(iii),  once  I  have  decided  which  kind  of  sense-object  I 
want  to  sense,  conditions  are  imposed  on  my  kinesthetic 
sensations,  which  I  must  simply  accept.  And  these 
imposed  conditions  vary  from  case  to  case.  Sometimes 
I  must  keep  my  head  and  body  still  if  I  want  to  sense 
a  completely  uniform  sense-object ;  sometimes  I  must 
move  bodily  to  secure  this  result.  If  the  latter,  I 
cannot  move  just  as  I  like  ;  only  one  way  of  moving 
will  secure  the  result  in  a  given  case,  and  the  right  way 
will  vary  from  occasion  to  occasion.  Then  (iv)  there 
are  various  mixtures  of  rotational  and  translational 
kinesthetic  sensations  which  will  cause  the  physical 
object  to  appear  as  a. partially  uniform  sense-object  with 
its  successive  sensa  at  the  centres  of  my  successive 
fields.  But  (v)  the  sense-object  will  not  be  uniform 
in  depth,  shape,  brightness,  etc.  And  (vi)  not  every 
mixture  of  translational  and  rotational  kinassthetic  sensa- 
tions will  secure  even  this  result.  If  I  arbitrarily  choose 
to  experience  a  certain  series  of  translational  kinesthetic 
sensations,  the  amount  and  speed  of  the  rotational 
kinesthetic  sensations  needed  will  always  be  partly 
and  sometimes  wholly  determined  by  the  former  series. 
Similar  remarks  apply,  mutatis  mutandis  if  we  arbitrarily 
choose  a  certain  series  of  rotational  kinesthetic  sensa- 
tions, (vii)  Sometimes  when  we  deliberately  confine 
ourselves  to  rotational  kinesthetic  sensations,  i.e.,  when 
we  deliberately  stand  still  and  merely  turn  our  heads, 
we  find  that  as  often  as  we  completely  reverse  the  series 
a  qualitatively  unchanged  appearance  of  the  given 
physical  object  occupies  the  centre  of  our  final  visual 
field.  On  other  occasions  we  find  that,  if  we  have  once 
turned  our  heads  and  thus  ceased  to  sense  an  appearance 
of  a  certain  physical  object  at  the  centre  of  our  field, 
mere  reversal  of  the  original  series  of  rotational  kin- 
esthetic sensations  will  not  suffice  to  restore  a  similar 
field.      In  such  cases  the  amount  and  kind  of  rotational 


422  SCIENTIFIC   THOUGHT 

kinesthetic  sensation  needed  for  the  purpose  are 
independent  of  our  choice,  and  vary  from  one  object 
to  another,  (viii)  When,  in  spite  of  our  best  endeavours, 
the  physical  object  fails  to  appear  in  our  visual  sense- 
history  as  a  completely  uniform  sense-object,  the  kind 
of  non-uniformity  in  depth,  shape,  brightness,  etc., 
which  it  displays  is  independent  of  our  choice.  It  is 
determined  partly  by  the  particular  mixture  of  trans- 
lational  and  kinesthetic  sensations  which  we  have 
chosen  out  of  the  whole  set  which  will  keep  the 
successive  appearances  in  the  centres  of  the  successive 
fields.  As  a  rule,  it  is  not  wholly  determined  by  this, 
but  is  partly  determined  by  another  factor  which  is 
quite  independent  of  us.  This  other  factor  is  what 
we  come  to  know  as  "the  physical  motion  of  the  body 
at  which  we  are  looking." 

It  is  this  mixture  of  arbitrary  choice  and  subsequent 
external  compulsion  which  is  at  the  basis  of  our  dis- 
tinction between  "objective  physical  motion  and  rest," 
and  "subjective  sensible  motion  and  rest."  I  shall 
now  go  into  this  important  matter  a  little  more  fully, 
taking  some  important  special  cases  which  we  have 
so  far  touched  on  only  incidentally. 

(c)  Successive  Sensible  Appearances  of  Co-existing  Physical 
Objects. — We  have  already  seen  that,  when  a  physical 
object  moves  away  from  us  while  we  stand  still  and 
keep  our  eyes  on  it,  it  never  appears  in  our  sense- 
history  as  a  completely  uniform  sense-object,  although 
its  successive  appearances  are  in  the  centres  of  our 
successive  fields.  I  am  not  at  present  concerned  with 
the  non- uniformity  of  the  sense -object  in  respect  to 
depth  or  brightness.  Nor  am  I  now  concerned  with  that 
kind  of  non-uniformity  which  may  be  described  as  "dis- 
tortion" of  the  successive  appearances  as  compared  with 
the  appearance  in  some  standard  field  of  the  sense- 
history,  i.e.,  with  the  kind  of  variation  which  takes  place 
in  the  successive  appearances  of  the  upper  surface  of 
a  penny  as  it  moves  away  from  us  while  we  keep  our 


SENSIBLE   AND   PHYSICAL   MOTION       423 

eyes  on  it.  What  I  want  to  discuss  is  that  kind  of 
change  which  we  describe  by  saying  that,  as  time  goes 
on,  we  see  parts  of  the  object  which  we  could  not  see 
before,  and  cease  to  be  able  to  see  parts  of  it  which 
we  could  see  before. 

As  far  as  our  visual  sensa  are  concerned,  there  is 
no  particular  difficulty  in  describing  such  experiences. 
We  sense  a  series  of  sensa  which  have  enough  con- 
tinuity with  each  other  to  count  as  successive  slices  of 
a  single  sense-object.  But,  although  closely  adjacent 
sensa  of  the  series  are  barely  distinguishable  in  quality, 
those  at  some  distance  apart  differ  in  the  following 
way  :  The  earlier  has  some  parts  to  which  nothing 
corresponds  in  the  later,  and  the  later  has  some  parts 
to  which  nothing  corresponds  in  the  earlier.  The  real 
problem  is  this:  These  sensa  are  successive;  when  the 
last  is  present  the  first  is  past.  But  we  suppose  that 
the  part  of  the  first  to  which  nothing  corresponds  in 
the  second,  and  the  part  of  the  second  to  which  nothing 
corresponds  in  the  first,  are  appearances  of  co-existing 
parts  of  the  physical  object.  Why  do  we  assert  physical 
co-existence  on  a  basis  of  sensible  succession?  Since 
the  spatial  parts  of  physical  objects  are  themselves 
physical  objects,  and  the  spatial  parts  of  sensa  are 
themselves  sensa,  we  may  generalise  the  problem  as 
follows  :  Under  what  conditions  do  two  successive  sensa 
justify  us  in  asserting  the  existence  of  two  contemporary 
physical  objects? 

This  question  is,  of  course,  roughly  equivalent  to 
a  very  famous  one  discussed  by  Kant  in  the  Analytic 
of  Principles  of  his  Critique  of  Pure  Reason.  I  think 
that  Kant  hit  on  one  very  important  part  of  the  answer, 
but  that  other  important  factors  are  involved  beside  the 
one  which  he  stresses.  Moreover,  the  Sage  of  Konigs- 
berg  did  not  number  clearness  of  exposition  among  his 
many  merits,  so  that  it  will  be  well  worth  while  to 
discuss  the  whole  question  afresh.  Let  us  take  a  very 
simple  concrete  example.     From  where    I   am   sitting, 


424  SCIENTIFIC   THOUGHT 

if  I  look  straight  in  front  of  me,  the  middle  of  my 
visual  field  is  occupied  by  an  appearance  of  a  certain 
picture.  The  rest  of  the  field  consists  almost  wholly 
of  a  cream-coloured  background,  which  is  an  appear- 
ance of  the  wall.  In  this  field  there  is  nowhere  an 
appearance  of  a  door.  If  I  turn  my  head  enough  to 
the  left  I  sense  a  field  whose  general  background  is 
much  as  before.  But,  in  the  middle  of  it,  is  an  appear- 
ance of  a  door,  and  nowhere  in  it  is  there  an  appearance 
of  the  picture.  From  where  I  sit  it  is  impossible  for 
these  two  physical  objects  to  be  represented  by  simul- 
taneous visual  appearances  in  a  single  field.  Neverthe- 
less, I  judge  them  to  co-exist,  although  their  appearances 
are  always  successive. 

Now,  first  of  all,  what  does  my  judgment  of  co- 
existence really  profess  to  assert?  It  does  not,  I  think, 
mean  that  the  part  of  the  history  of  the  picture  which 
appears  to  me  when  I  look  in  one  direction,  and  the 
part  of  the  history  of  the  door  which  appears  to  me 
when  I  look  in  the  other  direction,  are  contemporary. 
If  physical  objects  exist  and  endure,  they  must  be  strands 
of  history,  just  as  sense-objects  are,  i.e.,  they  must  be 
extended  in  time.  And  a  sensum  is  presumably  an 
appearance  of  a  short  slice  of  the  history  of  a  physical 
object.  Now,  apart  from  complications  about  the  velocity 
of  light,  it  is  reasonable  to  suppose  that  successive  sensa 
are  appearances  of  successive  slices  of  physical  history  ; 
and  I  think  we  always  do  assume  this  in  the  absence 
of  special  reasons  to  the  contrary.  Thus  the  judgment 
that  the  picture  and  the  door  co-exist,  although  their 
appearances  are  successive,  does  not  mean  that  the 
successive  appearances  reveal  contemporary  slices  of 
their  histories.  What  it  means  is  this  :  The  history 
of  the  picture  has  gone  on  while  I  turned  to  the  door  ; 
and,  when  the  door  appears  to  me,  there  is  a  slice 
of  picture-history  contemporary  with  the  slice  of  door- 
history  which  now  appears  to  me,  and  practically  indis- 
tinguishable in  quality  from  the  slice  of  picture-history 


SENSIBLE   AND   PHYSICAL   MOTION       425 

which  appeared  to  me  when  I  last  looked  toward  the 
picture.  Conversely,  the  door-history  extends  back- 
wards from  the  slice  which  is  now  appearing  to  me  ; 
and  there  is  a  slice  of  it  which  is  contemporary  with 
the  slice  of  picture-history  which  appeared  to  me  when 
I  formerly  looked  at  the  picture.  So  what  we  are  really 
asserting  is  that  the  picture-history  extends  forward  for 
some  time  with  practically  no  qualitative  variation  after 
the  last  slice  that  has  appeared  to  me,  and  that  the 
door-history  extends  backwards  for  some  time  with  prac- 
tically no  qualitative  variation  before  the  first  slice  that 
appeared  to  me. 

Now,  I  have  already  said  that  I  do  not  profess  to  be 
able  to  prove  that  such  assumptions  are  ever  true.  If 
anyone  says  that  the  existence  of  long  strands  of  physical 
history  of  almost  uniform  character  does  not  follow  logic- 
ally from  the  mere  existence  at  certain  times  of  picture- 
sensa  and  at  other  times  of  door-sensa,  I  heartily  agree. 
I  can  only  answer  that  we  all  do,  in  fact,  assume  that 
sensa  are  appearances  of  short  slices  of  things  which 
last  longer  than  themselves,  and  that  we  can  neither 
refute  this  assumption,  get  rid  of  it  in  practice,  nor 
stir  a  step  without  it.  What  we  can  do,  however,  is  to 
state  the  special  conditions  under  which  we  hold  that 
successive  sensa  are  appearances  of  co-existing  physical 
objects  (in  the  sense  defined  above),  and  show  that, 
subject  to  the  general  assumption  just  mentioned,  these 
conditions  are  reasonable. 

I  find  that  over  a  long  period  of  time  I  sense  a  practi- 
cally uniform  picture-sense-object,  whenever  I  look  in 
a  certain  direction.  Moreover,  I  can  look  away  and  then 
look  back  again  after  all  kinds  of  different  intervals,  and 
I  still  find  a  similar  sense-object.  Exactly  similar  remarks 
apply,  mutatis  mutandis,  to  the  sense-object  by  which  the 
door  appears  to  me.  Now,  theoretically,  there  are  four 
possibilities  :  (i)  My  looking  in  a  certain  direction  is  a 
sufficient  as  well  as  a  necessary  condition  for  producing 

a  field  with  a  picture-sensum  in  the  middle  of  it.     (ii) 

2  E 


426  SCIENTIFIC   THOUGHT 

The  occurrence,  at  a  certain  moment,  of  a  field  with  a 
picture-sensum  at  the  middle  of  it,  is  a  necessary  and 
sufficient  condition  of  my  turning  my  head  at  that 
moment  in  a  certain  direction,  (iii)  There  is  a  certain 
event  which  (a)  causes  me  to  turn  in  the  given  direction 
whenever  it  occurs,  and  (/3)  produces  the  picture-sensum 
at  the  same  time,  (iv)  The  head-turning,  and  the  pro- 
duction of  the  sensum  when  I  have  turned,  are  the 
results  of  two  causally  independent  series. 

We  will  first  give  familiar  examples  of  these  various 
possibilities.  Suppose  that  on  a  certain  day  I  pass  a 
certain  building  several  times  at  various  intervals,  and 
that  on  each  occasion  a  brick  falls  on  my  head  as  I  pass. 
It  might  be  (i)  that  my  passing  shakes  down  a  loose 
brick,  which  would  not  otherwise  have  fallen.  Or  (ii) 
that  whenever  I  see  that  a  brick  is  about  to  fall,  I  am 
so  much  interested  that  I  rush  to  the  spot,  and  that 
nothing  else  ever  takes  me  there.  Or  (iii)  that  I  go  to 
the  place  when  and  only  when  a  workman  who  is  working 
there  calls  me,  and  that  he  throws  down  a  brick  when 
and  only  when  I  get  there,  because  he  is  a  "class- 
conscious  proletarian  "  and  regards  me  as  a  "  lackey  of 
the  bourgeoisie."  Or  (iv)  it  might  be  that  my  journeys 
to  the  place  and  the  falling  of  the  bricks  belong  to 
causally  independent  series.  Now  I  might  be  able  to 
cut  out  the  first  three  alternatives  by  reflecting  on  the 
facts.  I  might  know  that  I  am  not  heavy  enough  to 
shake  bricks  down  by  passing  underneath.  I  might 
know  that  I  had  not  gone  to  the  place  because  I  saw 
that  a  brick  was  going  to  fall,  and  I  might  know  that 
no  workman  had  called  me  or  thrown  the  bricks  at  me. 
I  might  be  able  to  explain  why  I  had  passed  there  on 
each  occasion  without  needing  to  refer  to  anything  going 
on  at  the  place  whatever. 

Supposing  that  this  is  so,  only  one  explanation  of 
the  facts  would  be  reasonable,  viz.,  that  a  fairly  steady 
stream  of  bricks  has  probably  been  falling  for  most  of 
the  day.     It  is  almost  incredible  that  each  of  my  visits 


SENSIBLE   AND   PHYSICAL   MOTION       427 

to  the  place  should  happen  to  coincide  with  the  fall  of 
a  brick,  granted  that  the  causes  of  the  visits  and  of  the 
falls  are  quite  independent,  unless  many  more  bricks 
fall  than  the  few  that  I  happen  to  "stop."  Now  let  us 
apply  this  argument  to  the  sensible  appearance  of  the 
picture  and  of  the  door.  It  is  certain  that  merely  to 
look  in  a  given  direction  is  not  sufficient  to  produce  one 
particular  sensum  in  the  middle  of  my  visual  field  ;  for 
at  other  times  I  can  look  in  the  same  direction  and  sense 
no  such  sensum  (e.g.,  if  someone  has  moved  the  picture). 
It  is  also  certain  that  the  occurrence  of  the  sensum  does 
not  make  me  turn  my  head  in  that  direction  ;  on  the 
contrary,  I  often  turn  my  head  simply  in  order  to  see 
whether  I  shall  again  sense  the  same  kind  of  sensum 
as  before.  And,  in  general,  I  know  why  I  turn  my 
head  on  each  occasion,  and  can  see  that  my  act  is  com- 
pletely determined  by  causes  which  have  no  discover- 
able connexion  with  the  causes  which  produce  the 
sensum  in  the  middle  of  my  field  when  I  do  turn.  I  am 
therefore  forced  to  conclude,  either  that  there  is  a  pretty 
continuous  strand  of  very  similar  picture-sensa,  of  which 
I  sense  the  particular  one  which  happens  to  be  occur- 
ring when  I  turn  my  head,  or  at  least  that  there  must 
be  a  pretty  steady  stream  of  similar  physical  events, 
each  of  which  is  sufficient  to  produce  a  sensum  of  the 
required  kind  whenever  my  eye  is  turned  in  the  right 
direction.  Which  of  these  two  alternatives  is  to  be 
accepted  does  not  much  matter  for  the  present  purpose, 
and  the  question  must  be  left  to  the  next  chapter.  On 
either  alternative  we  are  justified  in  concluding  that 
there  is  a  persistent  and  practically  uniform  "picture- 
object,"  slices  of  which  fill  up  the  gaps  between  my 
successive  picture  sensa.  On  the  same  grounds  I  am 
justified  in  supposing  that  there  is  a  persistent  and 
practically  uniform  "door-object,"  slices  of  which  fill 
up  the  gaps  between  my  successive  door-sensa. 

Now   let  us  suppose  that  I   start  by  looking  at  the 
picture,    and  then  turn  my  eyes  several  times  between 


428  SCIENTIFIC  THOUGHT 

the  picture  and  the  door,  ending  up  finally  with  the 
picture.  We  will  suppose  that  I  do  this  at  different 
rates  on  different  occasions,  also  that  I  sometimes  dwell 
for  a  time  on  one  of  the  objects  without  moving".  Let 
us  represent  picture-sensa  by  little  crosses,  door-sensa 
by  little  circles,  and  the  lapse  of  time  by  a  direction  from 
left  to  right.  Then  my  sensible  experience  may  be  re- 
presented by  the  diagram  below. 

X  a  X 

Now  let  us  represent  the  physical  events  which  appear 
as  picture-sensa  by  dots,  and  those  which  appear  as 
door-sensa  by  little  lines.  Then  the  argument  from 
causal  independence,  applied  to  both  objects,  justifies 
me  in  filling  out  my  sensible  experience  as  indicated 
below. 

o  o  o  o _>o  cr 

A  slightly  more  dangerous  argument  would  justify  me 
in  extrapolating  to  some  extent,  i.e.,  in  assuming  that 
the  history  of  the  door  and  that  of  the  picture  extend 
backwards  for  some  distance  before  my  earliest  door- 
and  picture-sensa.  It  would  also  justify  me  in  supposing 
that  the  history  of  the  door  extends  forward  for  some 
distance  after  my  last  door-sensum.  For,  unless  there 
be  sorne  special  reason  to  think  otherwise,  it  is  highly 
improbable  that  I  should  happen  to  have  looked  first 
in  the  door-  or  the  picture-direction  just  when  there  first 
began  to  be  door  or  picture  events.  And  it  is  highly 
improbable  that  door  events  ceased  to  happen  just  when 
I  happened  to  turn  my  head  in  the  picture-direction  for 
the  last  time.  Like  all  extrapolations,  this  argument 
is  weaker  than  an  intrapolation,  and  its  probability  is 
quickly  diminished  as  it  is  extended  further  before  the 
first  sensum  of  one  series  or  after  the  last  sensum  of 
the  other  series. 


SENSIBLE   AND   PHYSICAL   MOTION       429 

The  argument  for  co-existence  is  now  quite  straight, 
forward.  There  is  a  slice  of  picture-history  between 
my  first  and  last  picture-sensum.  And  there  is  a  slice 
of  door-history  between  my  first  and  last  door-sensum. 
But  my  first  door-sensum  is  after  my  first  picture-sensum 
and  my  last  door-sensum  is  before  my  last  picture- 
sensum.  Hence  the  interpolated  picture-history  com- 
pletely overlaps  the  interpolated  door-history,  as  the 
second  diagram  shows.  I  believe  this  to  be  the  truth 
underlying  Kant's  rather  confused  argument  in  the 
Analytic  of  Principles ;  but  that  is  a  purely  historical 
question  in  which  I  take  no  particular  interest. 

There  are,  however,  at  least  two  other  criteria  of 
physical  co-existence  in  face  of  sensible  succession. 
One  of  these  can  be  dealt  with  only  when  we  have 
considered  our  knowledge  of  our  own  bodies.  The 
other  may  be  mentioned  at  once.  I  am  not  obliged  to 
stay  in  one  place.  While  I  sit  in  my  chair  at  the  table 
it  is  true  that  the  picture  and  the  door  can  only  appear 
successively  in  my  sense-history.  But,  if  I  move  back- 
wards to  the  other  side  of  the  room,  I  can  sense  a  single 
field  with  a  picture-sensum  at  the  middle,  and  a  door- 
sensum  to  the  left.  These  sensa  co-exist,  and  they  are 
extremely  like  the  corresponding  sensa  in  my  successive 
fields  when  I  was  nearer  the  wall.  They  are  smaller, 
and  have  greater  depth  ;  otherwise  there  is  very  little 
difference.  As  I  approach  the  wall  on  which  the  picture 
is  hanging,  keeping  my  eye  on  it,  I  first  sense  a  series 
of  fields  with  both  the  door  and  the  picture-sensa  in  each 
of  them.  As  I  go  on,  the  door-sensum  is  more  and 
more  to  the  extreme  left  of  its  field,  and  more  and  more 
distorted.  At  last  there  comes  a  point  where  the  field 
does  not  contain  any  appearance  of  the  door.  The  two 
kinds  of  sensa  can  now  only  be  sensed  successively. 
Now  the  co-existent  sensa  were  presumably  appearances 
of  contemporary  slices  of  two  overlapping  strands  of 
physical  history.  And  the  subsequent  successive  sensa 
are  so  much  like  the  former  simultaneous  ones,  that  it 


430  SCIENTIFIC   THOUGHT 

is  reasonable  to  suppose  that  the  same  pair  of  strands 
of  physical  history  continue,  and  continue  to  overlap  in 
time,  although  contemporary  slices  can  no  longer  appear 
in  my  sense-history. 

Similar  remarks  apply  to  looking  at  a  physical  object 
and  gradually  feeling  its  surface.  It  is  true  that  the 
tactual  sensa  are  successive,  and  yet  that  I  take  them  as 
informing  me  about  the  shape  of  the  physical  object  at 
some  one  moment.  But  we  find  that  we  can  make  the 
tactual  sensa  follow  each  other  in  various  series  at  will, 
provided  we  initiate  suitable  series  of  kinesthetic  sensa- 
tions. And  we  can  repeat  any  of  these  series  as  often 
as  we  like.  Meanwhile,  the  visual  appearances  keep 
constant,  and  we  sense  a  completely  uniform  visual 
sense-object.  In  whatever  order  we  sense  our  tactual 
sensa,  they  are  connected  with  a  part  of  the  visual 
appearance  at  the  time.  It  is  difficult  to  resist  the  con- 
viction that  we  are  dealing  with  a  uniform  strand  of 
physical  history,  and  that  each  of  our  tactual  sensa 
reveals  a  bit  of  some  slice  of  it.  True,  the  slices  revealed 
by  successive  tactual  sensa  are  presumably  successive  ; 
but  then  the  uniformity  of  the  visual  sensa-object 
suggests  that  they  are  all  alike  in  their  spatial  character- 
istics. Hence,  what  we  learn  by  touch  about  different 
parts  of  successive  slices  may  be  put  together  to  tell  us 
about  the  whole  of  any  one  slice.  Here,  again,  there  are 
certain  facts  about  our  experiences  of  our  own  bodies 
which  reinforce  this  interpretation. 

(d)  Single  Observer  Watching  two  Physical  Objects  in 
Relative  Motion.  —  In  the  last  sub-section  we  were  really 
dealing  with  the  case  of  one  observer  who  watches  two 
physical  objects  which  are  at  rest  relatively  to  each 
other  and  to  his  body,  but  which  cannot  both  be  seen 
at  once.  Let  us  now  consider  the  case  of  an  observer 
who  watches  two  physical  objects,  which  are  in  motion 
relatively  to  each  other.  As  we  have  already  seen, 
the  observer  will  always  be  able  to  make  one  of  these 
physical    objects    appear    as    a     uniform     sense-object, 


SENSIBLE   AND   PHYSICAL   MOTION       431 

whose  successive  sensa  are  at  the  centres  of  his  successive 
fields,  provided  he  moves  suitably.  We  can  therefore 
simplify  matters  by  supposing  that  one  of  the  bodies 
appears  in  the  observer's  sense-history  as  a  completely 
uniform  sense-object.  Let  this  body  be  A.  It  may  be 
that  at  first  he  will  sense  a  series  of  fields  in  which 
both  A  and  the  other  body  B  appear  as  sense-objects. 
If  so,  he  will  notice  that  B  does  not  appear  in  the  form 
of  a  uniform  sense-object.  Each  sensum  of  the  sense- 
object  by  which  B  appears,  will  very  likely  have  sensible 
motion  in  its  own  field.  Again,  successive  B-sensa  will 
occupy  more  and  more  eccentric  positions  in  their 
respective  fields  and  will  be  more  and  more  distorted. 
Thus  A  and  B  appear  at  first  as  two  sense-objects  which 
overlap  in  time,  i.e.,  as  two  overlapping  strands  in  the 
observer's  sense-history.  But,  if  we  take  successive 
pairs  of  contemporary  slices  of  the  two  strands,  we  shall 
find  a  progressive  variation  in  their  respective  sensible 
distances  apart.  Sensum  a,,  and  sensum  br  in  the  field  fr 
have  a  certain  sensible  distance  dr.  This  is  slightly  greater 
than  dr_x,  the  sensible  distance  between  ar_x  and  br__x  in 
the  field  fr_x.  And  it  is  slightly  less  than  dr+l,  the 
sensible  distance  between  ar+1  and  br+l  in  the  field  fr+l. 
In  fact,  if  you  take  the  two  sense-objects  together  as 
forming  a  kind  of  composite  sense-object  of  a  higher 
order  in  the  observer's  sense-history,  it  has  the  peculiar 
kind  of  non-uniformity  which  I  have  just  been  describing. 
And  this  kind  of  non-uniformity  is  characteristic  of  the 
relative  motion  of  sense-objects. 

Now  as  time  goes  on  the  sensa  of  the  B-sense-object 
will  occupy  more  and  more  eccentric  positions  in  their 
respective  fields,  till  at  length  no  more  sensa  of  the 
B-kind  appear  in  the  observer's  sense-history.  After  this, 
he  will  still  be  able  to  sense  appearances  of  A  and  of  B, 
provided  he  turns  his  head  ;  but  he  will  no  longer  be 
able  to  sense  them  in  a  single  field  :  they  must  be  sensed 
successively  or  not  at  all.  Let  us  now  compare  and 
contrast  this  with   the  cases  discussed  in  the  last  sub- 


432  SCIENTIFIC   THOUGHT 

section,     (i)  Obviously  the  later  stages  of  this  case  bear 
a   certain   resemblance    to    the    last;  t'.e.,    in    both,    the 
observer  can  only  sense  appearances  of  the  two  physical 
objects  successively.     One  important  difference  is  that 
this  situation  has  developed  out  of  one  in  which  he  could 
sense  appearances  of  both  objects  together.     And  it  has 
developed  independently  of  the  observer  ;  it  is  not  due  to 
any  changes  of  bodily  position  that  he  has  made.     In 
the  previous  case,   if  he  started  by  being  able  to  sense 
appearances  of  the  two  objects  in  the  same  field,  he  went 
on  being  able  to  do  so,  unless  he  deliberately  moved 
nearer  to  the  two  objects.      (2)  It   is  true  that,    in   the 
present  case,  if  the  observer  chooses  to  walk  backwards 
quickly  enough,  he  can  again  sense  fields  in  which  both 
A  and  B  appear.      But,   whereas  in  the  former  case  he 
could  continue  to  sense  the  two  appearances  together  by 
merely  walking  a  certain  distance  backwards  and  stopping 
there,    he  will   now  find  that  he  must  keep  on  walking 
backwards  if  he  wants  to  keep  on  sensing  fields  in  which 
both   the  objects  appear.      It  is  thus  clear  that  in   this 
case  there  is  a  lack  of  reversibility,  due  to  the  operation 
of  some   external    condition,    which    is    not  present    in 
the  former  cases.     The  externally  imposed  condition  is 
evidently  something  of  the  nature  of  a  continuous  process, 
with  a  rate  and  direction  of  its  own,  which,  if  it  is  to  be 
compensated    for   at  all,    must   be  compensated  for  by 
another  appropriate  continuous  process  in  the  observer's 
body.     The  interpretation  of  this  process  as  movement  is 
rendered  almost  inevitable  by  the  fact  that,  so  long  as  A 
and  B  are  appearing  under  the  form  of  two  sense-objects 
with  contemporary  slices  in  each  of  the  successive  fields 
of    a    sense-history,    there    is   sensible    relative    motion 
between    these   sense-objects,    as    described   above.     (3) 
Finally,  the  irreversibility  of  the  present,  as  compared 
with   the   reversibility  of  the    last  case,  shows   itself  in 
another  way.     When  I  dealt  with  two  resting  physical 
objects   which    I    could  see  only   successively,    I   could 
always  pass  from  the  field  containing  an  appearance  of 


SENSIBLE   AND   PHYSICAL   MOTION       433 

A  at  its  centre  to  the  field  containing  an  appearance  of  B 
at  its  centre,  and  back  again,  by  a  mere  reversal  of  my 
rotational  kinesthetic  sensations.  And  the  amount  of 
turning  needed  was  quite  independent  of  the  rate  at 
which  I  turned,  or  the  time  for  which  I  dwelt  on  one 
of  them  before  turning  to  the  other.  With  the  relatively 
moving  physical  objects  this  complete  reversibility  breaks 
down.  The  position  here  is  as  follows  :  If  I  turn  from 
A  to  B  on  one  occasion,  a  reversal  of  the  process  will 
indeed  bring  me  back  to  A.  But,  if  I  now  repeat  the 
process,  the  amount  of  turning  will  always  be  greater 
than  before,  and  it  will  be  greater  the  longer  I  have 
dwelt  on  A.  Again  :  If  I  turn  too  slowly,  I  shall  not  be 
able  to  pick  up  an  appearance  of  B  at  all  ;  and,  if  I  turn 
quickly  enough  to  do  this,  then  the  quicker  I  turn 
the  less  amount  of  turning  will  be  needed.  Lastly,  the 
minimum  quickness  needed  will  be  correlated  with  the 
swiftness  of  the  relative  motion  between  the  sense-objects 
of  A  and  B,  when  both  these  co-exist  in  my  sense- 
history. 

(e)  Rotation. — For  the  sake  of  completeness  I  must 
say  something  about  rotation,  and  for  the  sake  of  brevity 
I  shall  say  but  little.  It  will  be  fairly  easy  for  the 
reader  to  work  out  the  details  for  himself  by  analogy 
with  what  has  already  been  said.  I  have  so  far  assumed 
that  we  were  looking  at  objects  which  either  rested 
altogether  or  moved  with  a  purely  translatory  motion  in 
space.  Let  us  now  consider  the  experiences  of  an 
observer  who  stands  still  and  watches  a  rotating  physical 
object  which  is  translationally  at  rest.  He  will  be  able 
to  keep  its  successive  appearances  in  the  centres  of  his 
successive  fields  without  needing  to  have  either  transla- 
tional  or  rotational  kinesthetic  sensations.  But  the 
sense-object,  which  is  the  appearance  of  the  rotating 
physical  object  in  his  sense-history,  will  be  far  from 
uniform.  In  the  first  place,  each  of  the  sensa  may  have 
sensible  rotation  (a  quite  peculiar  and  characteristic 
sense-quality)  in  its  own  field.     Then,  although  closely 


434  SCIENTIFIC   THOUGHT 

successive  appearances  will  be  very  much  alike,  there 
will  always  be  a  part  of  the  later  to  which  nothing 
corresponds  in  the  earlier,  and  conversely.  In  this 
respect  the  sense-object  which  is  the  appearance  of  a 
rotating  body  bears  some  resemblance  to  the  sense- 
object  by  which  a  moving,  but  non-rotating,  body 
appears  in  the  sense-history  of  an  observer  who  follows 
the  body  with  his  eye  by  turning  his  head. 

There  is,  however,  an  important  difference.  After 
a  time  the  series  of  sensa  will  begin  to  repeat  itself  in 
the  same  order,  and  it  will  do  this  again  and  again. 
We  may  say,  then,  that  a  rotating  body,  which  keeps  in 
the  same  place  and  is  looked  at  by  a  resting  observer, 
appears  in  his  sense-history  as  a  positionally  uniform, 
hut  periodic,  sense-object.  Now  it  is  possible  for  a  non- 
rotating  body  to  appear  as  a  periodic  sense-object,  and 
for  a  rotating  body  to  appear  as  a  non-periodic  sense- 
object.  But  in  each  case  the  observer  will  have  to 
"walk  round"  the  body;  and,  as  he  does  so,  suitably 
turn  his  head  at  each  moment.  "Walking  round"  a 
body  appears  in  the  sense-experience  of  the  observer  as 
a  peculiar  series  of  kinsesthetic  sensations.  If  he  wants 
a  rotating  physical  object  to  appear  in  the  form  of  a 
completely  uniform  sense-object,  he  must  walk  round  at 
a  perfectly  definite  rate,  which  depends  on  circumstances 
over  which  he  has  no  control.  Thus,  again,  we  are 
forced  to  the  conclusion  that  there  are  external  pro- 
cesses of  change,  connected  with  changes  in  our  visual 
sense-histories  ;  and  that  certain  definite  series  of  kin- 
aesthetic  sensations  are  the  signs  of  processes  of  change 
in  our  own  bodies  which  are  "equivalent  to"  these,  in 
the  sense  that  they  compensate  for  them  and  give  a 
uniform  sense-object. 

(/)  Summary  of  Results  of  the  present  Section. — The 
upshot  of  our  discussion  on  the  correlations  between 
visual  motion  and  rest  and  the  kinesthetic  sensations 
of  a  single  observer  seems  to  be  as  follows:  (i)  In 
dealing  with  a  single  physical  object  we  can  generally 


SENSIBLE   AND   PHYSICAL   MOTION       435 

arrange  at  will  whether  it  shall  appear  in  the  form  of 
a  positionally  uniform  or  a  positionally  non-uniform 
(i.e.,  moving)  sense-object.  But  (2)  in  order  to  do  this, 
we  must  sometimes  initiate  series  of  kinaesthetic  sensa- 
tions, and  must  sometimes  refrain  from  doing  so. 
Sometimes  a  physical  object  will  appear  in  my  sense- 
history  as  a  uniform  sense-object,  if  and  only  if  I 
refrain  from  starting  a  series  of  kinesthetic  sensations. 
If  so,  it  will  appear  as  a  non-uniform  sense-object  when 
I  do  initiate  any  such  series.  And  the  nature  of  the 
non-uniformity  will  depend  wholly  on  the  nature  of  the 
series  which  I  choose  to  carry  on.  (3)  Sometimes  a 
physical  object  will  appear  in  my  sense-history  as  a 
uniform  sense-object  if  and  only  if  I  initiate  a  certain 
series  of  kinesthetic  sensations.  If  so,  the  appropriate 
series  is  fixed  for  me.  If  I  do  not  carry  out  one  of  the 
group  of  appropriate  series,  the  physical  object  will 
appear  as  a  non-uniform  sense-object,  whose  particular 
non-uniformity  depends  partly,  and  only  partly,  on  me 
and  my  kinesthetic  sensations.  Having  made  up  my 
mind  whether  I  want  a  physical  object  to  appear  as 
a  uniform  or  a  non-uniform  sense-object,  I  have  to 
conform  to  conditions  which  are  imposed  on  me.  And 
these  conditions  vary  from  one  case  to  another.  (4)  Now 
a  series  of  kinesthetic  sensations  in  me  is  presumably 
an  appearance  of  a  certain  process  of  change  in  my 
body.  I  know  that  this  process  is  one  condition  which 
produces  non-uniformity  of  sense-objects  in  my  sense- 
history  ;  for  in  many  cases  I  do  sense  a  uniform 
sense -object  so  long  as  I  refrain  from  having  kin- 
esthetic sensations,  and  it  becomes  non-uniform  so  soon 
as  I  start  to  have  such  sensations.  Conversely,  I  know 
that  in  many  other  cases  sense-objects  have  the  same 
kind  of  non-uniformity  when  I  have  no  kinesthetic  sensa- 
tions, and  that  this  non-uniformity  can  be  eliminated 
if  I  start  a  suitable  series  of  kinesthetic  sensations.  It 
therefore  seems  reasonable  to  suppose  that  the  other 
set  of  conditions,  to  which  I  have  to  conform,  is  another 


436  SCIENTIFIC   THOUGHT 

process  of  the  same  general  character  as  that  in  my 
own  body  which  is  revealed  to  me  by  my  kinesthetic 
sensations.  In  fact,  it  seems  probable  that  the  positional 
uniformity  or  non -uniformity  of  the  sense-object  by 
which  a  certain  physical  object  appears  to  me,  depends 
in  general  on  the  co-operation  of  two  sets  of  physical 
processes,  one  in  my  body  and  the  other  in  the  physical 
object ;  and  that  the  latter  process  is  of  the  same  general 
character  as  the  former,  which  is  revealed  to  me  by 
my  kinesthetic  sensations.  (5)  Of  course  it  remains  a 
question  whether  these  processes  should  be  regarded  as 
mot ions,  and,  if  so,  in  what  Space  and  what  Time  they 
happen.  For  the  present  all  that  we  can  do  is  to 
make  the  following  tentative  suggestion  :  Two  different 
physical  objects  often  appear  as  two  temporally  over- 
lapping sense-objects  throughout  a  long  tract  of  my 
sense-history.  One  may  be  positionally  uniforrh  and 
the  other  not ;  if  so,  one  of  the  sense-objects  will  be 
in  sensible  relative  motion  to  the  other.  Let  A  be  the 
physical  object  which  appears  as  a  uniform  sense- 
object  a  ;  and  let  B,  the  other  physical  object,  appear 
in  my  sense-history  as  the  non-uniform  sense-object  /3. 
From  what  has  gone  before,  I  conclude  that  the  uni- 
formity of  a  depends  on  certain  processes  (or,  in  the 
limiting  case,  on  the  absence  of  such  processes)  in  my 
body  and  in  A.  Similarly,  the  positional  non-uniformity 
of  /3  depends  jointly  on  certain  processes  in  my  own 
body  and  B.  Since  the  process  in  my  body  is  common 
to  both,  it  seems  certain  that  there  must  be  a  difference 
between  the  A-process  and  the  B-process  ;  for  otherwise 
there  is  no  apparent  reason  why  a  should  be  uniform 
and  /3  non-uniform.  Thus  a  difference  between  the 
processes  in  A  and  B  is  correlated  with  sensible  relative 
motion  between  a  and  /?,  the  two  sense-objects  by  which 
A  and  B  appear  in  this  tract  of  my  sense -history. 
Conversely,  if  A  and  B  had  both  appeared  as  uniform 
sense-objects,  a  similar  argument  would  show  that  there 
is    no    reason    to   assume    that   there    is   any   difference 


SENSIBLE   AND   PHYSICAL   MOTION       437 

between  the  relevant  physical  processes  in  A  and  B. 
Thus  sensible  relative  rest  between  a  and  ,8,  the  sense- 
objects  by  which  A  and  B  appear  in  this  tract  of  my 
sense-history,  is  correlated  with  identity  of  the  processes 
in  A  and  B. 

This,  I  think,  is  about  as  far  as  we  can  go  without 
entering  into  further  detail  about  the  human  body  as 
a  physical  object,  and  our  knowledge  about  it.  When 
we  have  done  this,  we  shall  find  that  the  general  con- 
clusion (4),  and  the  more  special  conclusion  that  the 
physical  processes  on  which  the  uniformity  or  non-uni- 
formity of  visual  sense-objects  depends  are  of  the  nature 
of  motions,  are  greatly  strengthened.  We  will,  there- 
fore, make  this  the  subject  of  our  next  section. 

The  Human  Body  as  a  Physical  Object.  —  Human 
bodies  may  be,  as  we  are  told  that  they  are,  "temples 
of  the  Holy  Ghost"  ;  in  which  case  it  must  be  admitted 
that  the  Third  Person  in  the  Trinity  sometimes  displays 
a  strange  taste  in  temples.  But,  whatever  else  they 
may  be,  they  certainly  are  physical  objects  as  much  as 
chairs  or  tables.  Nevertheless,  they  do  occupy  a  peculiar 
position  among  physical  objects.  In  the  first  place, 
each  is  connected  in  a  perfectly  unique  way  with  an 
observing  mind,  which  looks  out  at  the  rest  of  the  world 
from  its  body.  Secondly,  each  of  these  minds  has  a 
peculiar  knowledge  of  its  own  body,  which  it  does  not 
have  of  any  other  body  in  the  universe.  A  given  mind 
perceives  every  other  body  except  its  own  in  exactly  the 
same  way  as  it  perceives  a  chair  or  a  potato.  It  per- 
ceives its  own  body,  partly  in  this  way,  and  partly  in  a 
quite  different  way,  viz.,  by  organic  sensations.  Lastly, 
the  minds  connected  with  various  human  bodies  can 
and  do  constantly  communicate  with  each  other,  so  that 
observer  A  learns  that  observer  B  perceives  B's  body  in 
the  same  way  in  which  A  perceives  his  own  body.  A 
also  learns  that  B  can  no  more  perceive  A's  body  in 
this  way  than  he  himself  can  perceive  B's  body  in  this 


438  SCIENTIFIC   THOUGHT 

way.  1  believe  that  these  peculiarities  of  human  bodies 
and  of  our  knowledge  about  them  are  essential  factors 
in  founding-  the  common-sense  and  scientific  notions  of 
physical  objects,  and  in  developing  the  concepts  of 
physical  Space,  Time,  and  Motion. 

(<i)  A  Solitary  Observer  s  Perception  of  his  ow)i  Body. — (i) 
I  do  not  know  very  much  about  my  own  body  directly 
by  sight,  but  I  do  know  something.  I  cannot  see  my 
own  head  at  all,  though  by  means  of  a  mirror  I  can  see 
an  incomplete  optical  object  in  a  different  place,  and  I 
now  conclude  on  various  grounds  that  it  is  very  much 
like  the  optical  constituent  of  my  head.  I  can  see  the 
front  of  my  trunk  from  a  little  below  the  chin  ;  can  see 
my  hands  and  feet  often  quite  distinctly  ;  and  can  see 
less  distinctly  the  upper  parts  of  my  arms.  The  greater 
part  of  the  visual  appearance  of  that  fraction  of  my  body 
which  does  appear  in  the  visual  field  is  very  vague  and 
distorted. 

There  are  two  important  points  to  notice  about  the 
visual  appearances  of  my  trunk,  (i)  Although  they  are 
so  fragmentary,  they  are  almost  invariably  present  in 
my  visual  sense-history.  To  sense  a  visual  field  with 
no  such  sensa  in  it,  I  have  to  follow  the  advice  given  to 
the  "  happy  band  of  pilgrims,"  and  "  look  upward  to  the 
skies,"  in  a  most  unnatural  and  uncomfortable  way.  In 
fact,  my  own  trunk  appears  to  me  as  a  highly  uniform 
and  highly  persistent  visual  sense-object.  Whenever  I 
carry  on  a  series  of  translatory  kinesthetic  sensations  the 
greater  part  of  the  contents  of  my  later  fields  bears  no 
resemblance  to  that  of  my  earlier  fields.  But  the  visual 
appearances  of  my  body  are  present  with  little  variation 
throughout.  (ii)  The  other  peculiarity  is  that  all  the 
visual  appearances  of  my  trunk  have  a  very  small  visual 
depth  in  all  the  fields.  They  are  at  the  extreme  "  front " 
of  each  field,  and  the  visual  appearances  of  all  other 
physical  objects  are  "behind"  them  at  various  greater 
depths  in  the  field. 

Now,   with    other   objects  that  appear  in  my  visual 


SENSIBLE   AND   PHYSICAL   MOTION       439 

sense-history,  I  have  to  initiate  a  certain  series  of  trans- 
latory  kinesthetic  sensations  before  I  can  sense  any  corre- 
lated tactual  sensa.  As  this  series  goes  on,  the  visual 
depths  of  the  successive  sensa,  which  together  make  up 
the  sense-object,  steadily  decrease  in  each  successive 
field.  But,  as  I  have  said,  the  visual  appearances  of 
my  own  body  have  a  practically  constant  minimal  depth 
in  all  my  successive  visual  fields.  Thus,  when  I  walk 
up  to  a  resting  physical  object,  there  are  two  sense- 
objects  which  co-exist  throughout  this  tract  of  my  sense- 
history.  One  is  the  sense-object  by  which  the  distant 
physical  object,  to  which  I  am  walking,  appears.  This 
is  positionally  non-uniform,  in  so  far  as  the  successive 
sensa  that  belong  to  it  have  progressively  diminishing 
depths  in  their  respective  fields.  There  are  also  corre- 
lated variations  in  size,  brightness,  etc.  The  other  is 
the  sense-object  by  which  my  own  body  appears  in  my 
sense-history.  This  is  practically  uniform,  since  all  its 
successive  sensa  have  minimal  visual  depth.  Thus, 
successive  pairs  of  contemporary  sensa,  one  from  one 
sense-object  and  the  other  from  the  other,  have  progres- 
sively smaller  visual  distances  apart.  So  the  series  of 
translatory  kinesthetic  sensations,  experienced  in  walk- 
ing up  to  an  external  physical  object,  is  associated  with 
sensible  relative  motion  between  the  sense-object  which 
represents  the  external  body  and  the  sense-object  which 
is  the  appearance  of  my  own  body  in  my  visual  sense- 
history. 

(2)  My  tactual  sensations  of  my  own  body  are 
peculiar,  (i)  As  I  have  said,  most  physical  objects 
which  appear  in  my  visual  sense-history  can  only  be 
touched  after  an  appropriate  series  of  translatory  kin- 
aesthetic  sensations.  If  this  series  be  reversed,  we  soon 
cease  to  be  able  to  sense  any  tactual  sensa  correlated 
with  our  visual  sensa.  But  we  do  not  need  to  walk  in 
order  to  touch  our  own  bodies  ;  and,  having  once 
touched  them,  we  do  not  cease  to  be  able  to  do  so  by 
walking  away.     In  fact,  all  other  tactual   sense-objects 


440  SCIENTIFIC   THOUGHT 

are  rigidly  bound  up  with  series  of  translatory  kin- 
a\sthetic  sensations;  but  the  tactual  sense-object  which 
represents  my  body  is  indifferent  to  all  such  series. 
This  must  be  correlated  with  the  fact  that  translatory 
kinesthetic  sensations  make  no  difference  to  the  depths 
of  successive  visual  appearances  of  our  own  bodies, 
whereas  they  do  make  a  difference  to  the  depths  of  the 
successive  visual  appearances  of  nearly  all  other  physical 
objects.  My  trunk  is  the  only  physical  object  which 
appears  throughout  the  whole  of  my  visual  sense-history 
as  a  positionally  uniform  sense-object  ;  and  it  is  the 
only  physical  object  which  I  can  touch  whenever  I  like, 
i.e.,  which  I  need  not  walk  up  to  and  cannot  walk 
away  from. 

(ii)  The  tactual  sensa  which  I  sense  when  I  touch 
my  own  body  are  characteristically  different  from  those 
which  I  sense  when  I  touch  any  foreign  body.  Suppose 
that  in  each  of  two  successive  visual  fields  of  my  history 
there  is  an  appearance  of  my  hand.  In  the  first,  let  this 
be  in  visual  contact  with  an  appearance  of  my  table, 
and  in  the  second  let  it  be  in  visual  contact  with  an 
appearance  of  my  leg.  Apart  from  minor  qualitative 
differences  there  will  be  the  fundamental  difference  that, 
in  the  second  case,  I  "feel  my  leg  being  touched"  as 
well  as  "feel  my  leg  with  my  finger."  This  peculiar 
experience  of  "  double  contact,"  as  it  is  called,  helps  me 
to  distinguish  the  surface  of  my  own  body  from  those  of 
all  other  physical  objects.  It  also  helps  the  solitary 
observer  to  fill  out  the  very  fragmentary  knowledge  of 
his  own  body  which  he  would  have  if  he  were  confined 
to  visual  appearances  alone.  He  can  feel  a  closed 
surface,  marked  out  by  the  characteristic  of  double 
contact ;  and  can  gradually  explore  its  contours.  Only 
a  very  small  part  of  these  tactual  sensa  will  be  correlated 
with  his  visual  sensa.  But  I  can  start  with  a  visual 
appearance  of  my  hand  visibly  in  contact  with  a  visual 
appearance  of  some  part  of  my  trunk,  and  can  gradually 
move   my  hand  so  that    its    successive    appearances   in 


SENSIBLE   AND   PHYSICAL   MOTION       441 

successive  fields  are  nearer  and  nearer  to  the  extreme 
edge  of  the  appearance  of  my  trunk.  At  length  I  shall 
no  longer  be  able  to  see  my  hand  ;  but  the  character- 
istic tactual  sensa  will  still  be  sensed,  and  they  will  be 
continuous  with  those  earlier  ones  which  were  correlated 
with  the  visual  appearance  of  my  hand  visibly  in  contact 
with  the  visual  appearance  of  part  of  my  trunk. 
Finally,  as  I  go  on  moving  my  hand,  it  may  become 
visible  again  ;  and  its  visual  appearance  will  again  be 
in  visible  contact  with  the  extreme  edge  of  a  visual 
appearance  of  part  of  my  trunk.  My  own  body  is  thus 
known  to  me  by  tactual  exploration  as  a  closed  surface 
which  resists  my  efforts  to  penetrate  it,  like  any  other 
physical  object.  But  it  is  marked  out  from  the  other 
closed  surfaces  that  I  feel  by  the  qualitative  peculiarity 
of  the  tactual  sensa,  and  by  the  fact  that  I  do  not  have 
to  walk  up  to  it  and  cannot  walk  away  from  it. 

(3)  We  come  finally  to  a  most  important  peculiarity 
of  our  sense-experience  of  our  own  bodies.  I  am 
constantly  getting  mild  tactual  sensations  from  the 
whole  surface  of  my  body  without  actively  exploring  it 
with  my  hand.  These  come  from  the  contact  of  my 
clothes,  from  air-currents,  and  so  on.  In  each  Specious 
Present  they  form  a  mass  which  is  the  largest  part  of 
what  I  will  call  the  somatic  field.  These  somatic  fields 
are,  in  the  main,  extremely  alike  over  long  periods  of 
time  ;  they  thus  join  up  with  each  other  to  form  an 
extremely  uniform  somatic  sense-object.  Within  each 
somatic  field  certain  characteristic  sensa  stand  out ;  e.g., 
at  one  time  I  may  itch  in  one  place,  and  at  another  time 
I  may  feel  a  burn  at  another  place,  and  so  on.  Now 
literally  "  inside  "  the  somatic  fields  there  are  from  time 
to  time  outstanding  bodily  feelings,  like  headaches  and 
toothaches  and  stomach-aches,  which  enliven  my  somatic 
history  and  prevent  it  from  being  perfectly  tame  and 
uniform.  Again,  my  kinesthetic  sensations  are  sensible 
events    with    places    in    my    somatic    fields.     Thus    a 

peculiarity  of  my  body  is  that  I  have  sense-perception 

2  F 


442  SCIENTIFIC   THOUGHT 

of  events  which  happen  in  its  inside,  as  well  as  of  events 
on  its  outside.  Of  course,  events  in  the  inside  of  my 
body  appear  to  me  in  a  very  peculiar  way,  viz.,  by  kin- 
aesthetic  sensations,  bodily  pains,  etc.  But  the  insides 
of  other  bodies  do  not  appear  to  me  in  sense-perception 
in  any  way  whatever,  unless,  of  course,  I  cut  them  open 
or  "turn  them  inside  out."  And  if  I  do  this,  I  am  not 
perceiving  their  insides  while  they  are  inside,  but  am 
only  perceiving  new  outsides,  which  for  various  reasons 
I  take  to  be  exactly  similar  to  former  insides. 

(/;)  Several  Intercommunicating  Observers  watching  each 
other  s  Bodies.  —  If  I  were  and  had  always  been  a  com- 
pletely solitary  observer,  these  facts  about  my  body 
would  not  help  me  very  much  to  form  the  concept  of 
physical  objects,  having  insides  as  well  as  outsides, 
occupying  positions  in  physical  Space,  and  moving 
about  in  it  as  physical  Time  elapses.  I  should  rather 
be  inclined  to  stress  the  differences  between  my  own 
body  and  all  other  objects  that  appear  to  me,  and  leave 
the  matter  there.  But  I  am  not  in  this  solitary  situation. 
The  important  fact  is  that  there  are  other  people  like 
myself,  whose  bodies  I  can  see  and  touch,  and  with 
whom  I  can  exchange  notes  by  verbal  communication 
and  gestures.  I  am  convinced  that  this  fact  plays  a 
vitally  important  part  both  in  the  development  of  the 
general  concept  of  physical  objects,  and  in  the  develop- 
ment of  the  connected  concepts  of  physical  Space,  Time, 
and  Motion. 

Any  other  human  body  is  perceived  by  me  in  exactly 
the  same  way  as  I  perceive  a  stone  or  a  chair.  If  I  look 
at  it,  it  appears  as  a  characteristic  visual  sensum  in  the 
middle  of  my  visual  field.  I  can  then  approach  it  and 
sense  correlated  tactual  sensa.  And  there  is  no  essential 
difference  in  the  experiences  which  I  have  in  this  case 
and  in  that  of  an  ordinary  inorganic  object.  Similarly, 
I  perceive  the  motion  or  rest  of  another  human  body 
in  precisely  the  same  way  as  I  perceive  those  of  any 
other  external  object.     But  I  recognise  that  other  human 


SENSIBLE   AND   PHYSICAL   MOTION       443 

bodies  are  connected  with  minds  like  my  own  ;  and, 
although  I  can  only  know  their  bodies  from  the  outside, 
they  tell  me  that  they  know  them  from  the  inside,  and 
that  they  know  mine  only  from  the  outside.  I  under- 
stand what  they  mean,  because  of  my  own  experiences, 
described  in  the  last  sub-section.  I  thus  come  to 
recognise  that  there  are  plenty  of  other  bodies  beside 
my  own,  having  internal  processes  ;  although  I  cannot 
perceive  these  processes  in  any  body  except  my  own. 
So  the  fact  that  I  cannot  perceive  such  processes  else- 
where ceases  to  be  any  reason  for  supposing  that  they 
do  not  exist  elsewhere.  I  know  that  they  happen  in  my 
body,  although  other  people  tell  me  that  they  cannot 
perceive  them  ;  and  I  am  therefore  ready  to  believe  that 
they  happen  in  other  mens  bodies,  though  /  cannot 
perceive  them  ;  since  they  tell  me  that  they  can 
do  so. 

The  logical  position  is  therefore  as  follows  :  (i)  I 
know  what  is  meant  by  internal  processes  from  my  own 
sense-experiences  of  pleasures,  pains,  kinesthetic  sensa- 
tions, etc.  (ii)  I  believe  that  there  are  other  instances 
of  bodies  with  such  internal  processes,  from  communica- 
tion with  other  minds  ;  though  I  cannot  myself  perceive 
these  processes  in  the  other  instances.  (iii)  I  then 
extend  this  conception  that  bodies  have  "insides,"  in 
which  all  kinds  of  interesting  events  happen,  from 
human  bodies  to  others,  which,  so  far  as  I  know,  are 
not  connected  with  minds,  (iv)  This  is  reasonable, 
because  they  appear  to  me  in  exactly  the  same  way  as 
do  all  human  bodies  except  my  own  ;  and  I  already 
know,  from  the  instances  of  other  human  bodies,  that 
the  non-appearance  of  internal  processes  to  my  senses 
is  quite  compatible  with  the  fact  that  such  processes  are 
going  on.  I  thus  conceive  that  all  my  sense-objects  are 
appearances  of  physical  objects,  which  have  an  inner 
history  of  their  own,  and  are  seats  of  internal  processes 
in  the  way  in  which  human  bodies  are  the  seats  of  those 
processes  which    appear  to    the   minds  connected   with 


444  SCIENTIFIC  THOUGHT 

them  as  headaches,  toothaches,  (anaesthetic  sensations, 
etc.  How  far  in  detail  the  analogy  is  to  be  pressed  is 
of  course  another  question,  which  can  only  be  gradually 
answered  by  empirical  investigation.  I  propose  now 
to  apply  these  general  considerations,  first  to  the  general 
concept  of  physical  objects,  and  then  to  the  more  special 
concept  of  physical  motion  and  rest. 

(c)  The  Human  Body  as  the  typical  Physical  Object. — 
Intercommunication  with  other  human  minds,  and 
observation  of  the  appearances  of  their  bodies,  fill  out 
the  general  concept  of  physical  objects  in  the  following 
ways : 

(i)  Any  of  the  sense-objects  by  which  other  physical 
objects  appear  to  us  is  liable  to  sudden  interruptions. 
The  visual  sense-object  comes  to  an  end  in  darkness, 
or  when  we  shut  our  eyes  or  turn  our  heads  away. 
And  the  tactual  sense-object  exists  only  when  we  are 
at  or  near  a  certain  place.  But,  in  spite  of  these 
interruptions  in  the  sensible  appearances  of  other  men's 
bodies  in  my  sense-history,  the  minds  connected  with 
these  bodies  tell  me  that  their  somatic  history  has  gone 
on  all  the  time  with  very  little  change.  Thus,  in  the 
case  of  human  bodies,  I  have  reason  to  believe  that 
their  inner  history  is  much  more  permanent  and 
continuous  than  their  appearances  in  my  sense-history. 
I  extend  this  conclusion  by  analogy  to  non-human 
bodies,  which  appear  in  the  same  kind  of  way  in  my 
sense-history.  This  argument  is  strengthened  by  the 
fact  that  I  know  that  my  own  somatic  history  is  going 
on  steadily  at  times  when  other  men  tell  me  that  my 
body  has  ceased  to  appear  in  their  sense-histories. 

(2)  I  know  that  I  can  initiate  noises,  bodily  move- 
ments, etc.,  and  that  when  I  do  so  they  are  preceded 
by  special  series  of  events  in  my  somatic  sense-history. 
Other  people  tell  me  that  they  hear  noises,  see  move- 
ments, and  so  on,  at  the  centre  which  is  the  optical 
place  of  the  visual  appearances  of  my  body.  Similarly, 
when   I  hear  noises  or  see   movements  connected  with. 


SENSIBLE   AND   PHYSICAL   MOTION       445 

the  place  occupied  by  the  optical  constituent  of  another 
man's  body,  he  will  tell  me. that  he  has  been  "  making" 
the  noises  or  movements.  This  means  that  he  produced 
them  by  initiating  an  appropriate  series  of  sensible 
events  in  his  somatic  history.  Thus  we  arrive  at  the 
general  conclusion  that  many  changes  in  the  visual 
appearances  of  A's  body  in  B's  visual  sense-history  are 
connected  with  changes  in  A's  somatic  sense-history. 
Now  the  latter  are  appearances  to  A  of  physical  events 
within  his  own  body.  Thus,  in  the  case  of  a  human 
body,  we  reach  the  notion  that  the  place  which  is  optically 
occupied  by  its  optical  constituent  is  physically  occupied 
by  certain  events  which  produce  changes  in  this  optical 
object,  or  at  any  rate  in  parts  of  it.  This  is  the  crude 
beginning  of  the  notion  of  scientific  events  and  their 
connexion  with  sensible  appearances.  We  extend  this 
result  in  the  usual  way  to  those  places  which  are 
optically  occupied  by  complete  optical  objects  which 
are  constituents  of  non-human  bodies.  That  is,  we 
conclude  that  these  places  are  physically  occupied  by 
certain  events  which  are  responsible  for  the  changes 
that  take  place  from  time  to  time  in  the  complete 
optical  object. 

(3)  The  comparative  constancy  of  my  somatic  sense- 
history,  combined  with  the  fact  that  no  one  can  "see" 
the  whole  surface  of  my  body  at  once,  supports  the 
view  that  successive  visual  sensa  often  justify  a  belief 
in  co-existing-  physical  objects,  or  parts  of  one  physical 
object.  No  one  can  see  my  face  and  the  back  of  my 
head  at  the  same  time,  though  there  may  be  an  appear- 
ance of  each  of  these  in  successive  visual  fields  of  the 
same  observer.  But  I  know  that  my  somatic  history 
includes  "face-feelings"  and  "head-feelings"  in  each 
of  its  successive  fields.  Thus,  although  the  observer's 
visual  sensa  were  successive,  and  presumably  revealed 
non-contemporary  slices  of  my  body-history,  yet  there 
is  reason  to  suppose  that  each  of  these  slices  (and  all 
that  came  between  them)  included  a  part  corresponding 


446  SCIENTIFIC  THOUGHT 

to  the  appearance  of  a  head,  and  a  part  corresponding 
to  the  appearance  of  a  face. 

These  seem    to  be   the   main   factors  which  our  per- 
ception of  our  own  bodies  and  our  intercommunication 
with  other  observers  supply  to  the  concept  of  physical 
objects    in   general.     The   human    body   is   the  physical 
object  par  excellence ;   with  an   "inside"   which   is   con- 
tinually,  if  inadequately,    perceived    by   its   own    mind 
through    bodily    feelings  ;    with    an    outside    which     is 
perceived  on  and  off  by  other  observers  through  their 
visual   and  tactual   sensations  ;    and   with   internal   pro- 
cesses,   which    reveal    themselves    to    its   own    mind    as 
kinesthetic  and  other  bodily  feelings,  and  reveal  them- 
selves to  other  minds  as  movements  and  other  changes  in 
its  visual  and  other  appearances.     Each  observer  reaches 
the  notion  of  human  bodies  as  complete  physical  objects 
by  combining  his  own  experiences  of  the  inside  of  his 
body  with    what  other  observers  tell    him   about  their 
experiences  of  the  outside  of  his  body.     He  then  extends 
the    general    conception,    thus   formed,    to    non-human 
physical  objects,  which  cannot  tell  him  about  their  own 
insides. 

(d)  The  Human  Body  and  the  Concept  of  Physical 
Motion. — In  the  section  on  the  correlations  between 
kinesthetic  sensations  of  a  single  observer  and  the 
motion  or  rest  of  visual  sense-objects  in  his  sense- 
history,  we  made  no  special  assumption  as  to  the  nature 
of  the  physical  objects  which  he  was  watching.  They 
might  be  other  human  bodies,  or  they  might  be 
inorganic  bodies,  like  pennies  or  chairs.  Even  so,  we 
reached  the  following  results,  of  which  I  will  remind 
the  reader :  (i)  That  this  observer  might  reasonably 
conclude  that  the  positional  uniformity  or  non-uniformity 
of  the  visual  sense-object,  by  which  a  certain  physical 
object  appears  in  his  sense-history,  depends  in  general 
on  the  co-operation  of  two  processes,  one  in  his  own 
body  and  the  other  in  the  physical  object  which  he  is 
watching.     The  one  in   his   own  body  appears  to  him 


SENSIBLE   AND   PHYSICAL   MOTION       447 

in  the  form  of  a  series  of  kinesthetic  sensations  in  his 
somatic  sense-history.  And  it  is  reasonable  to  think 
that  the  other  is  of  the  same  general  nature,  (ii)  That 
this  observer  might  reasonably  hold  that  a  certain 
identity  between  such  processes  in  two  physical  objects 
A  and  B  involves  relative  rest  between  them,  and  that 
differences  between  the  two  processes  involve  relative 
motion  between  A  and  B. 

Now  these  conclusions,  which  are  rendered  highly 
plausible  by  the  mere  correlations  between  a  solitary 
observer's  kinesthetic  sensations  and  the  motion  or 
rest  of  his  sense-objects,  are  greatly  strengthened  when 
the  physical  objects  which  he  watches  are  the  bodies 
of  other  observers  who  can  communicate  with  him. 

(1)  Suppose  that  observer  a  watches  B,  the  body  of 
observer  ft,  and  that  at  the  same  time  observer  ft 
watches  A,  the  body  of  observer  a.  The  correlations 
between  the  kinesthetic  sensations  and  the  visual  sense- 
objects  of  each  observer  are  of  exactly  the  same  kind 
as  if  he  were  watching  an  inorganic  body.  But,  in 
the  present  case,  the  observer  and  the  observed  can 
compare  notes  about  their  kinesthetic  sensations  and 
their  visual  sense-objects.  Let  us  first  suppose  that  a 
does  not  have  to  keep  turning  his  head  in  order  to  keep 
his  eye  on  B,  and  that  B  appears  to  him  as  a  completely 
uniform  visual  sense-object.  Then  ft  will  tell  a  that 
he,  too,  does  not  need  to  keep  turning  his  head  in  order 
to  keep  his  eye  on  A,  and  that  A  appears  in  his  sense- 
history  as  a  completely  uniform  visual  sense-object.  If 
they  now  compare  their  translatory  kinesthetic  sensa- 
tions, they  will  find  either  that  they  are  absent  in  both, 
or,  if  present,  are  of  precisely  the  same  character. 

Let  us  next  suppose  that  a  finds  that  he  has  to  keep 
turning  his  head  in  order  to  keep  his  eye  on  B.  B  will 
then  appear  in  a's  sense-history  as  a  partly,  but  only 
partly,  uniform  sense-object.  The  nature  of  its  non- 
uniformity  has  already  been  fully  described.  Now  ft 
will  also  find,  and  will  tell  a  that  he  finds,  that  he  must 


448  SCIENTIFIC   THOUGHT 

keep  turning  his  head  in  order  to  keep  his  eye  on  A, 
and  thai  A  appears  in  his  sensedustory  as  a  partly,  but 
only  partly,  uniform  sense-object  of  the  kind  already 
described.  In  this  case  o  and  (3  will  find,  on  comparing 
notes,  that  they  both  experience  a  series  of  rotational 
kinesthetic  sensations,  and  that  there  is  an  analogy 
between  them.  But,  on  the  other  hand,  they  will 
always  find  that  there  is  a  difference  between  their  trans- 
lators kinesthetic  sensations.  This  will  sometimes  take 
the  form  that  one  and  only  one  of  them  has  such 
sensations  at  all  (I  am  leaving  out  of  account  for  the 
sake  of  simplicity  observers  who  are  carried  about 
without  effort  in  trains  or  motor-cars).  There  is  one 
other  important  point  which  they  will  discover  on 
comparing  their  experiences.  The  appearance  of  a's 
head  in  /3's  sense-history  will  be  a  rotating  visual  sense- 
object,  and  so  will  be  the  appearance  of  /3's  head  in  a's 
sense-history.  Thus  each  will  discover  that,  of  his  two 
kinds  of  kinesthetic  sensation,  one  is  correlated  with  a 
rotationally  non-uniform  sense-object  by  which  his  head 
appears  in  the  sense-history  of  the  other  observer,  and 
the  other  kind  is  correlated  with  a  positionally  non- 
uniform sense-object,  by  which  his  body  appears  in  the 
sense-history  of  the  other  observer. 

(2)  So  far,  we  have  confined  ourselves  to  two  observers 
a  and  /3  respectively  watching  B  and  A,  the  bodies  of 
the  other.  Let  us  now  take  an  observer  y,  who  watches 
the  bodies  A  and  B  of  the  two  observers  a  and  ft,  who 
can  communicate  with  him  and  with  each  other.  As  we 
have  said  before,  if  y  keeps  up  a  suitable  series  of 
kinesthetic  sensations,  he  can  always  make  A  appear  in 
his  sense-history  as  a  completely  uniform  sense-object, 
each  of  whose  successive  constituent  sensa  is  at  the 
middle  of  its  field.  We  will  suppose  that  y  does  this. 
He  may  then  find  either  (i)  that  B  appears  as  a  com- 
pletely uniform  sense-object,  or  (ii)  that  B  appears  as 
a  positionally  non-uniform  sense-object.  Each  of  the 
component  sensa  in  this  may  have  sensible  movement 


SENSIBLE   AND   PHYSICAL   MOTION       449 

in  their  fields.  And,  even  if  they  do  not,  successive 
pairs  of  contemporary  A-  and  B-sensa  will  have  pro- 
gressively different  sensible  distances  in  their  respective 
common  fields  in  y's  visual  sense-history. 

Now,  in  case  (i),  a  and  /3  will  tell  y  that,  on 
comparing  notes  with  each  other,  they  find  no  difference 
in  their  translational  kinesthetic  sensations,  which  may, 
of  course,  in  the  limiting  case  both  be  non-existent.  In 
case  (ii),  a  and  [3  will  tell  y  that,  on  comparing  notes, 
they  do  find  a  difference  in  their  translational  kinesthetic 
sensations.  If  one  of  them  has  no  such  sensations  the 
other  will  have  them.  Moreover,  each  of  them  will  tell 
y  that  the  body  of  the  other  appears  to  himself  as  a  non- 
uniform sense-object.  And  y's  body  C  will  appear  in 
/3's,  though  not  in  a's,  sense-history  as  a  non-uniform 
sense-object. 

Now  these  communicated  experiences  (1)  and  (2) 
leave  no  doubt  at  all  that  the  positional  uniformity  or 
non-uniformity  of  the  sense-object,  by  which  one  human 
body  appears  in  the  sense-history  of  another  observer, 
depends  jointly  on  those  physical  processes  in  the  two 
bodies  which  are  revealed  to  their  respective  minds  in 
the  form  of  kinesthetic  sensations.  Moreover,  they 
show  clearly  that  uniformity  in  the  sense-object  depends 
on  a  certain  identity  of  quality  and  quantity  in  the  two 
processes,  whilst  positional  non-nniformity  in  the  sense- 
object  depends  on  certain  qualitative  and  quantitative 
differences  between  the  two  processes.  Lastly  (2)  shows 
that  relative  motion  of  the  sense-objects  by  which  two 
human  bodies  appear  in  the  sense-history  of  a  third 
observer  depends  on  a  difference  between  these  two 
processes  in  the  two  human  bodies,  whilst  relative  rest 
of  two  such  sense-objects  depends  on  an  identity  of 
character  between  the  two  processes. 

We  now  extend  this  conclusion  in  the  usual  way  to 
physical  objects  which  are  not  connected  with  minds 
that  can  communicate  with  us.  We  assume  that,  in  all 
cases,   the    uniformity  of  a   sense-object   in    the    sense- 


450  SCIENTIFIC   THOUGHT 

history  o\  an  observer  depends  upon  a  certain  identity 
between  that  physical  process  in  his  own  body  which 
appears  to  him  as  a  series  of  kinesthetic  sensations,  and 
another  physical  process  of  the  same  general  type, 
which  happens  in  the  physical  object  of  which  this 
uniform  sense-object  is  the  visual  appearance  in  the 
observer's  sense-history.  And  we  assume  that,  in  all 
cases,  the  positional  non-uniformity  of  a  sense-object  in 
the  sense-history  of  an  observer  depends  on  differences 
between  the  physical  process  in  his  body  which  appears 
to  him  as  a  series  of  kinesthetic  sensations,  and  another 
physical  process  of  the  same  general  type,  which  happens 
in  the  physical  object  of  which  this  non-uniform  sense- 
object  is  the  visual  appearance  in  this  observer's  sense- 
history. 

(e)  Several  Intercommunicating  Observers  watching  the 
same   Physical   Object. — One    more    very    important    fact 
remains  to  be  described.     Suppose  that  two  observers, 
a  and  /?,  are  watching  a  certain   physical  object  O,  and 
that  a  third  observer  y  is  watching  their  bodies,  A  and 
B.      It  may  happen  that  O  appears  in  a's  sense-history 
as  an  uniform  sense-object,  and  that  it  appears  in  /3's 
sense-history  as  a  positionally  non-uniform  sense-object. 
If  this  be  so,  the  observer  y  will  always  notice  that  the 
sense-objects  by  which   A  and  B  appear  in  his  sense- 
history  are  in  relative  motion  to  each  other.     And,  as 
usual  under  these  conditions,  there  will  be  a  difference 
in  the  translational  kinassthetic  sensations  of  a  and  /3. 
If  we  generalise  this  from  human  bodies  to  all  physical 
objects  we  reach  the  following  conclusion  :  It  is  possible 
for  any  physical  object  to  appear  at  once  as  a  uniform 
sense-object  in  the  sense-history  of  one  observer  and  as 
a  non-uniform  sense-object  in  that  of  another  observer. 
But,  if  it  does  so,  it  will  always  be  found  that  there  is 
some  difference  between  those  physical  processes  in  the 
bodies   of  the   two   observers  which  appear  to  them   as 
series  of  their  kinesthetic  sensations. 

This  result,  which  can  actually  be  observed,  might 


SENSIBLE   AND   PHYSICAL   MOTION       451 

also  have  been  deduced  from  what  has  gone  before.  If 
the  physical  object  O  appears  as  a  resting  sense-object 
in  a's  visual  sense-history,  this  implies  a  certain  identity 
of  character  between  the  relevant  physical  processes  in 
A  and  in  O,  according  to  the  argument  of  the  last  sub- 
section. If  O  appears  as  a  moving  sense-object  in  /3's 
sense-history,  this  implies  a  difference  between  the 
relevant  physical  processes  in  B  and  in  O,  on  the  same 
principles.  It  follows  at  once  that,  under  these  circum- 
stances, there  must  be  a  difference  between  the  relevant 
physical  processes  in  A  and  in  B.  And  this  should  appear 
to  a  and  to  j8  as  a  difference  between  their  kinesthetic 
sensations.  That  such  a  difference  is  actually  found 
supports  the  conclusions  of  the  last  sub-section,  since 
they  are  here  used  as  hypothetical  premises  from  which 
it  follows  that  such  a  difference  ought  to  be  found. 

In  the  next  chapter  I  propose  to  apply  the  results  of 
this  one  to  the  notions  of  sensible  and  physical  Space- 
Time,  and  so  to  end  my  treatment  of  the  spatio-temporal 
aspects  of  Nature  and  their  sensible  and  perceptual  basis. 

The  following  additional  works  may  be  consulted 
with  advantage  : 

G.  F.  Stout,  Manual  of  Psychology,  Bk.  III.  Part  II. 
W.  James,  Principles  of  Psychology. 
Kant,  Critique  of  Pare  Reason  {Analytic  of  Principles). 
Schopenhauer,  World  as  Will  and  Idea,  Vol.  I.  Bk.  II. 


CHAPTER    XII 

"  And  nu  bit  and  for  Godcs  naman  halsath  selcne  thara  the 
tlias  boc  raedan  lyste  thaet  he  for  nine  gebidde,  and  him  ne  wite 
gif  he  hit  rihtlicor  ongite  thonne  he  mihte.  Forthsemthe  selc 
mou  sccal  be  his  ondgites  masthe  and  be  his  a^mettan  sprecan 
thaet  he  sprecth  and  don  thset  thaet  he  deth." — King  Alfred, 
Preface  to  his  Translation  of  Basthius. 

Sensible  and  Physical  Space-Time 

We  have  at  length  reached  a  position  where  it  becomes 
possible  to  deal  with  the  concept  of  physical  Space-Time, 
from  which,  as  we  shall  see,  the  concepts  of  physical 
Space  and  of  physical  Time  are  abstractions  of  two 
different  kinds.  We  shall  thus  finally  work  back,  from 
a  wholly  different  starting-point,  to  the  position  which 
we  reached  at  the  end  of  Part  I. 

Let  us  first  take  a  backward  glance  over  the  country 
that  we  have  crossed,  and  see  how  the  universe  looks 
from  our  present  standpoint.  We  shall  then  be  able  to 
see  what  part  of  our  journey  from  crude  sensation  to  the 
refined  concepts  of  mathematical  physics  remains  to 
be  completed  ;  and,  having  done  so,  we  can  try  to 
complete  it. 

(a)  Statement  of  the  Present  Position. — The  situation, 
so  far  as  it  has  now  developed,  is  roughly  as  follows  : 
There  is  a  world  of  physical  objects,  some  of  which, 
like  my  own  body,  are  connected  with  observing  minds 
which  can  communicate  with  each  other.  Others,  so 
far  as  we  know,  are  not  connected  with  minds  ;  but  in 
their  general  character  they  are  very  much  like  those 
which  are.  Correlated  with  each  human  body  there  is 
a  general  sense-history,  which  is  split  up  into  several 
special  sense-histories,  visual,  tactual,  auditory,  somatic, 

452 


SPACE-TIME  453 

and  so  on.  We  can  sense  temporal  relations  between 
sensa  in  our  different  special  sense-histories,  just  as  we 
can  sense  temporal  relations  between  different  sensa  in 
the  same  special  sense-history.  But  we  cannot  sense 
spatial  relations  between  contemporary  sensa  in  our 
different  special  sense-histories,  though  we  can  sense 
such  relations  between  contemporary  sensa  of  the  same 
special  history.  These  spatial  characteristics  are  much 
more  marked  in  the  visual  sense-history  than  in  any  of 
the  others. 

My  somatic  sense-history  contains  sensa  which  are 
appearances  of  internal  states  and  processes  of  my  own 
body.  In  my  other  special  sense-histories  are  various 
sense-objects,  some  uniform  for  a  time,  others  non- 
uniform. There  are  correlations  between  certain  sense- 
objects  in  my  different  special  histories  which  lead  me 
to  regard  them  as  different  kinds  of  appearances  of  the 
same  external  physical  object.  All  these  remarks  about 
me  and  my  sense-histories  apply  equally,  mutatis  mutandis, 
to  other  observers  and  their  sense-histories  ;  as  I  learn 
by  intercommunication. 

Between  sensa  in  the  histories  of  different  observers 
neither  spatial  nor  temporal  relations  can  be  sensed  by 
either  of  the  observers  or  by  any  third  observer  known 
to  us.  But  there  are  correlations  between  certain  sense- 
objects  of  different  observers  which  lead  us  to  say  that 
the  same  physical  object  is  appearing  to  all  of  them. 
When  this  is  so,  there  is  generally  a  certain  external 
place  which  all  these  sensa  maybe  said  to  "occupy" 
in  some  Pickwickian  and  definable  sense,  such  as  optical 
occupation.  Again,  there  are  certain  methods,  discussed 
in  the  last  chapter  but  one,  by  which  some  sensa  of 
different  histories  are  grouped  together  as  "neutrally 
simultaneous,"  and  others  are  grouped  apart  as 
"  neutrally  successive." 

Then  there  are  the  very  elaborate  correlations  between 
the  uniformity  or  non-uniformity  of  sense-objects  in 
the   visual    histories   of   observers,    and    certain    events 


454  SCIENTIFIC   THOUGHT 

in  their  somatic  histories  called  " kinesthetic  sensa- 
tions." We  have  been  studying  these  in  the  last 
chapter.  We  came  to  the  conclusion  that  the  positional 
uniformity  or  non-uniformity  of  the  sense-object  by 
which  a  certain  physical  object  appears  to  an  observer, 
depends  upon  certain  physical  processes  in  the  external 
object  and  the  observer's  body  ;  and  that  these  pro- 
cesses in  one's  own  body  appear  to  oneself  as  kines- 
thetic sensations.  A  more  careful  study  of  these  corre- 
lations revealed  two  further  closely  connected  points. 
One  is  that  the  positional  uniformity  of  a  sense-object 
depends  on  an  identity  of  character  between  these  two 
physical  processes,  and  that  positional  non-uniformity 
is  correlated  with  certain  differences  between  them. 
The  other  is  that  relative  rest  between  two  sense-objects 
in  a  sense-history  depends  on  a  similar  kind  of  identity 
between  two  such  physical  processes  in  the  bodies  which 
appear  as  these  two  sense-objects,  whilst  relative  motion 
between  two  sense-objects  is  correlated  with  similar 
kinds  of  difference  between  two  such  physical  processes 
in  the  bodies  which  appear  as  these  two  sense-objects. 
Sensible  motion  and  rest  are  absolute,  but  they  seem  to 
depend  on  relations  of  identity  and  difference  respectively 
between  physical  processes  in  the  body  which  appears 
and  the  body  of  the  observer  to  whom  it  appears. 

(b)  Statement  of  the  Remaining  Problem. — These,  then, 
are  some  of  the  facts  which  have  so  far  been  elicited, 
and  some  of  the  highly  probable  inferences  which  have 
been  made  from  them.  The  next  thing  is  to  state 
clearly  the  problem  which  still  remains.  The  rest  of 
the  problem  is  to  make,  if  possible,  a  further  synthesis 
by  analogy  with  what  we  already  know.  Can  we  treat 
the  world  of  physical  objects  and  events  as  forming  a 
whole  which  is  analogous  to  a  single  sense-history  ? 
That  is :  Can  we  regard  scientific  objects  as  analogous 
to  sense-objects  ;  can  we  suppose  that  they  have  spatial 
relations  to  each  other,  such  as  we  can  sense  only  between 
sensa  in  a  single  sense-field  ;  and  can  we  suppose  that 


SPACE-TIME  455 

they  endure,  and  have  temporal  relations  to  each  other, 
such  as  we  can  sense  only  between  sensa  within  a  single 
general  sense-history?  Lastly,  can  we  suppose  that 
physical  objects  rest  and  move  in  this  spatio-temporal 
physical  whole,  as  sensa  do  in  their  fields,  and  as  sense- 
objects  do  in  our  sense-histories?  This,  I  think,  is  the 
real  problem  about  physical  Space,  Time,  and  Motion. 
It  is  the  problem  of  constructing  a  single,  neutral, 
public  Space-Time  of  physical  objects  and  events,  on 
the  analogy  of  the  many  personal  private  space-times 
of  the  various  observers'  sense-histories. 

Now  it  is  not,  of  course,  a  question  of  just  making 
such  suppositions  in  the  abstract.  Our  only  possible 
justification  for  supposing  anything  of  the  kind  is  that 
it  provides  a  scheme  which  summarises  all  the  known 
correlations  between  sensa,  and  is,  at  the  same  time, 
familiar  to  us  because  of  its  analogy  to  our  own  sense- 
histories  with  which  we  are  directly  acquainted.  It  is 
theoretically  possible  that  no  such  supposition  would  do 
justice  to  the  actual  correlations  among  sensa.  It  is 
still  more  likely  that  no  supposition  which  made  the 
structure  of  physical  Space-Time  exactly  analogous  to 
that  of  an  individual  sense-history  would  account  for 
the  known  facts.  Again,  if  the  physical  world  can  be 
consistently  regarded  as  a  spatio-temporal  whole  with 
considerable,  though  not  complete,  analogy  of  structure 
to  an  individual  sense-history,  it  is  probable  that  this 
can  be  done  in  a  number  of  alternative  ways,  all  of 
which  will  synthesise  the  known  facts  equally  well. 
Even  if  up  to  a  certain  date  human  beings  had  only 
happened  to  think  of  one  view  of  the  structure  of  physical 
Space-Time,  there  is  no  reason  to  doubt  that,  if  they 
thought  more  carefully  and  paid  less  attention  to  certain 
traditional  points  of  view,  they  would  be  able  to  devise 
dozens  of  alternative  structures  for  physical  Space-Time 
equally  capable  of  doing  justice  to  all  the  known  corre- 
lations among  sensa.  No  doubt  the  physical  world  has 
a  certain  absolute  intrinsic  structure  ;  and  this  structure 


456  SCIENTIFIC   THOUGHT 

exhibits  itself,  in  part  at  least,  in  the  correlations  between 
sensa  of  the  same  and  of  different  observers.  But  we 
have  to  treat  this  structure  piecemeal  in  the  sciences 
of  geometry,  ehronometry,  kinematics,  dynamics,  and 
electro-magnetics,  and  by  making  suitably  correlated 
modifications  in  the  axioms  of  these  various  partial 
sciences  we  can  express  the  same  absolute  structure  in 
innumerable  different  and  equally  satisfactory  ways.  If, 
so  far,  very  few  alternative  schemes  have  been  proposed, 
this  is  due  to  nothing  more  recondite  than  lack  of 
scientific  imagination  and  the  imperfection  of  our  techni- 
cal mathematical  and  logical  apparatus. 

It  is,  nevertheless, an  interesting  and  important  inquiry 
to  see  how  far  we  can  do  justice  to  the  known  facts  by 
supposing  that  the  structure  of  the  physical  world  is 
analogous  to  that  of  our  sense-histories,  and  to  see  what 
is  the  minimum  difference  of  structure  between  the  two 
which  we  must  postulate.  For,  after  all,  our  physical 
concepts  have  their  roots  in  our  sense-histories. 

It  is  evident  that  it  might  be  possible  to  regard  the 
physical  world  as  forming  a  spatio-temporal  whole 
analogous  in  general  outline  to  a  single  sense-history, 
and  yet  that  we  might  have  to  postulate  differences  of 
detail.  I  do  not  mean  by  this  simply  that  the  contents 
of  the  two  might  be  different.  It  is  perfectly  certain 
that  they  will  be.  The  ultimate  contents  of  a  sense- 
history  are  the  sensa  of  the  observer  whose  sense-history 
it  is.  The  ultimate  contents  of  physical  Space-Time 
are  scientific  events.  Even  if  it  should  be  possible  to 
regard  scientific  events  as  composed  of  sensa  (which  is 
far  from  certain),  each  scientific  event  will  be  composed 
of  sensa  from  the  histories  of  many  different  observers, 
and  also  presumably  of  many  more  sensa  which  do  not 
belong  to  the  history  of  any  observer.  Thus,  even  on 
this  hypothesis,  the  ultimate  contents  of  physical  Space- 
Time  will  be  groups  of  correlated  sensa.  But,  beside  this 
difference  which  there  certainly  must  be  between  physical 
Space-Time  and  any  sense-history,  there  may  well  be 


SPACE-TIME  457 

a  difference  of  structure  between  the  two,  e.g.,  the  kind 
of  difference  which  there  is  between  a  Euclidean  and 
a  hyperbolic  space.  A  sense-history  and  the  physical 
world  are  both  four-dimensional  spatio-temporal  wholes, 
and  we  must  therefore  talk  of  their  geo-chronometry  rather 
than  their  geometry.  What  I  am  saying  then  is  that, 
although  a  sense-history  and  the  physical  world  may  be 
so  far  analogous  in  structure  that  we  can  say  that  both 
have  a  geo-chronometry  of  some  kind,  yet  the  geo- 
chronometries  of  the  two  may  differ  in  detail. 

The  reader  must  beware  of  supposing  that  a  Space- 
Time  is  an  entity  which  exists  in  its  own  right,  side  by 
side  with  its  contents.  It  is  often  convenient  to  talk  as 
if  this  were  so,  and  it  does  no  harm,  provided  we 
recognise  that  it  is  always  an  abbreviated  expression, 
and  understand  clearly  what  it  is  an  abbreviation  for. 
Having  got  rid  of  the  absolute  theories  of  Space  and  of 
Time,  we  must  not  introduce  them  again  for  Space- 
Time.  Many  really  eminent  writers  on  the  Theory 
of  Relativity  have  expressed  themselves  in  a  most 
unfortunate  way,  which  suggests  to  innocent  readers 
that  they  think  of  Space-Time  as  a  particular  existent, 
with  properties  of  its  own,  which  acts  on  matter  like 
a  cue  acts  on  a  billiard-ball.  When  we  talk  of  the 
properties  of  physical  Space-Time  we  are  simply 
enumerating  certain  very  general  structural  character- 
istics of  that  spatio-temporal  whole  which  is  the  physical 
world.  The  only  existent  under  discussion  is  this 
whole,  which  is  composed  of  scientific  events  bound 
together  in  a  characteristic  unity  by  spatio-temporal 
relations. 

An  analogy  will  perhaps  make  this  clearer  than 
much  discussion  will  do.  The  French  and  British 
armies  are  two  elaborately  organised  hierarchies.  Their 
contents  are  different ;  since  the  former  is  composed  of 
Frenchmen,  and  the  latter  of  Englishmen  and  Scotsmen 
and  a  few  items  from  the  Celtic  Fringe.  There  is  a 
great  analogy   between   the    organisations   of  the    two, 

2  G 


45^  SCIENTIFIC   THOUGHT 

which  renders  it  reasonable  to  call  them  both  armies. 
But  there  are  also  considerable  differences  in  detail. 
If  a  military  writer  set  (Hit  to  describe  in  general  terms 
the  structure  of  the  French  army  and  that  of  the  British 
army,  he  would  be  studying  something  akin  to  two 
systems  of  geo-chronometry.  He  could  do  this  without 
referring  to  particular  French  and  English  soldiers, 
such  as  Jacques  Bonhomme  and  Tommy  Atkins.  He 
could  even  talk  intelligibly  of  the  "effects"  which  these 
two  types  of  organisation  "produce"  on  French  and 
English  soldiers  of  various  temperaments.  But,  if  this 
led  him  to  suppose  that  the  organisations  whose 
structure  he  is  describing  were  substances  that  existed 
side  by  side  with  the  soldiers,  he  would  be  talking 
nonsense  ;  and  it  would  be  the  same  kind  of  nonsense 
as  is  talked  by  people  who  imagine  Space-Time  to  be 
an  existent  substance  which  pushes  and  pulls  bits  of 
matter  about.  It  must,  therefore,  be  clearly  understood 
that,  when  we  talk  of  the  geo-chronometry  of  Space- 
Time,  we  are  simply  describing  certain  very  general 
and  abstract  structural  features  of  that  whole  which  is 
the  physical  world. 

Since  the  geo-chronometry  which  is  to  be  ascribed 
to  physical  Space-Time  depends  entirely  on  the  cor- 
relations between  our  sensa,  we  must  not  be  surprised 
if  opinions  about  it  alter  with  the  growth  of  scientific 
knowledge.  For  one  view  might  fit  all  the  facts  that 
were  known  up  to  a  certain  date,  and  a  different  view 
might  be  needed  to  fit  both  them  and  certain  new  facts 
which  were  discovered  later.  This  is  exactly  what  has 
happened  in  the  change  from  Newtonian  to  Relativistic 
dynamics  and  kinematics. 

(e)  The  Concept  of  an  Idealised  Sense-history. — If  we 
want  to  see  how  closely  the  geo-chronometry  of  the 
physical  world  can  be  approximated  to  that  of  a  single 
sense-history,  we  must  begin  by  considering  what  is 
the  geo-chronometry  of  a  sense-history.  But,  before 
doing  this,  it  will  be  well  to  remove  in  thought  certain 


SPACE-TIME  459 

limitations,  which  are,  in  fact,  present  in  all  our  sense- 
histories,  but  which  seem  rather  to  depend  on  de  facto 
limitations  of  our  powers  of  sensing  and  remembering 
than  on  anything  characteristic  of  the  structure  of  sense- 
histories  as  such,  (i)  We  can  think  of  a  sense-history 
as  stretching  back  indefinitely  into  the  past,  although 
in  fact  we  can  only  remember  a  certain  distance  back, 
and  although  presumably  the  history  does  not  extend 
backwards  beyond  our  birth.  (2)  We  can  remove  in 
thought  the  limitation  of  a  finite  Specious  Present.  We 
can  regard  the  fact  that  only  a  very  thin  slab  can  ever 
be  sensed  at  once,  and  that  the  whole  history  is  a  series 
of  such  slabs,  as  contingent.  That  is,  we  can  regard 
the  whole  history  as  a  continuous  four-dimensional 
strand.  (3)  We  can  remove  in  thought  those  limita- 
tions which  our  finite  powers  of  seeing,  hearing,  etc., 
impose  on  the  extension  of  each  of  our  actual  sense- 
fields.  We  can,  e.g.,  imagine  the  spatial  limits  of  our 
visual  fields  indefinitely  extended  ;  as  they  would  be 
if  we  could  see  everything,  however  distant  from  our 
bodies.  (4)  We  can  also  remove  the  limitation  which 
is  imposed  by  the  fact  that  we  cannot  see  all  round  us  at 
once.  (5)  So  far  we  have  been  conceptually  extending 
our  sense-histories  by  removing  certain  limits  imposed 
by  sensation  and  memory.  It  now  remains  to  proceed 
in  the  opposite  direction.  We  cannot  sense  fields  of 
no  duration.  But  we  can  sense  events  of  shorter  and 
shorter  duration.  We  can  thus  conceive  any  slab  of 
a  sense-history  as  cut  into  thinner  and  thinner  slabs. 
In  the  end  we  can  conceive  of  slabs  of  no  duration, 
and  can  imagine  the  whole  sense-history  analysed  into 
an  infinite  series  of  such  instantaneous  slices,  just  as 
we  can  conceive  a  cylinder  as  analysed  into  an  in- 
finite series  of  parallel  plane  circular  sections.  Such 
momentary  slices  are  not  of  course  existents,  and  they 
are  not  literally  parts  of  the  sense-history  ;  but  they  can 
be  defined  by  Extensive  Abstraction,  and  a  Pickwickian 
meaning  can  be  given  to  the  statement  that  the  sense- 


460  SCIENTIFIC  THOUGHT 

history  is  composed  of  thorn.  These  momentary  slices 
will  be  purely  spatial,  whereas  the  sense-history  as  a 
whole  and  any  finite  real  part  of  it  are  spatio-temporal. 
We  may  call  each  of  these  momentary  sections  a 
momentary  sense-space  in  the  given  sense-history.  By 
further  applications  of  Extensive  Abstraction  within 
a  single  momentary  sense-space,  we  could  evidently 
define  momentary  sense-planes^  momentary  sense-lines,  and 
;// 1 )  m  e  n  tt  i  ry  sense-poin  ts . 

It  is  pretty  evident  that,  if  the  physical  world  be 
analogous  to  a  sense-history  at  all,  it  will  be  analogous 
to  an  idealised  visual  sense-history,  extended  concep- 
tually in  the  ways  described.  And  I  think  there  is  very 
little  doubt  that  this  is  the  original  of  the  concept  of  the 
physical  world  as  a  whole  in  Space  and  Time.  We 
must  now  consider  more  in  detail  the  geo-chronometry 
of  an  idealised  visual  history.  In  the  section  that 
follows  I  am  more  than  usually  indebted  to  Whitehead, 
and  I  shall  be  contented  if  I  provide  the  reader  with 
"  first  aid  "  to  the  study  of  Whitehead's  two  great  works 
on  the  philosophy  of  Nature. 

The  Geo-chronometry  of  an  Idealised  Visual  History. — 
The  idealised  visual  history  is  a  four-dimensional  spatio- 
temporal  whole,  formed  by  the  continual  addition  of 
successive  slices,  which  are  idealised  fields.  Each  of 
these  slices  has  duration,  and  the  duration  of  the  whole 
history  is  the  sum  of  the  durations  of  the  successive 
slices  up  to  and  including  the  last  that  has  become. 
Now  we  can  regard  all  these  successive  fields  as  normal 
to  a  certain  straight  line  in  the  history,  just  as  successive 
circular  slabs  of  a  cylinder  are  all  normal  to  its  axis. 
This  common  normal  to  all  the  fields  may  be  taken  as 
the  time-axis  of  the  history.  By  Extensive  Abstraction 
we  then  reduce  the  temporal  thickness  of  the  successive 
slabs  to  zero,  and  we  thus  get  a  series  of  momentary 
three-dimensional  spaces,  all  normal  to  the  time-axis  of 
the  history. 

Now   the   geo-chronometry    of    the    history    might, 


SPACE-TIME 


461 


apart  from  all  wilder  alternatives,  be  either  Euclidean 
or  elliptic  or  hyperbolic.  According  to  which  of  these 
alternatives  is  realised,  the  geometry  of  its  momentary 
spaces  will  be  Euclidean  or  elliptic  or  hyperbolic.  On 
either  of  the  two  latter  alternatives  the  successive 
momentary  spaces  will  not  be  parallel  to  each  other. 
In  elliptic  geometry  (which  is  analogous  to  the  geometry 
of  the  surface  of  a  sphere)  there  are  no  parallels,  for  all 
co-planar  straight  lines  intersect  each  other  twice.  In 
hyperbolic  geometry  there  are  parallels  and  there  are 
non-intersecting  co-planar  straight  lines  which  are  not 
parallel.  And  the  common  normals  to  a  given  straight 
line  are  not  parallel  to  each  other,  though  they  do  not 
intersect  each  other.  It  is  only  on  the  Euclidean  alterna- 
tive that  the  momentary  spaces  will  be  parallel.  The 
three  alternatives  may  be  very  roughly  illustrated  in  two 
dimensions  and  on  a  Euclidean  plane  by  the  three 
diagrams  below. 


.t' 


s,  sg 


i)£uc/ideanCase    (it)  £//tpfic  Cose    (//;)  tfypcr6o//e  Case 

(It  must,  of  course,  be  remembered  that  what  appears  in 
these  diagrams  as  lines  normal  to  the  time-axis  represent 
three-dimensional  spaces  in  the  four-dimensional  sense- 
history.  Also  that  the  curves  in  diagrams  (ii)  and  (iii) 
are  attempts  at  representing  non-Euclidean  straight  lines 
on  a  Euclidean  plane.) 

We  may  perhaps  dismiss  the  elliptic  alternative  at 
once.  If  the  geo-chronometry  of  a  sense-history  were  of 
this  type,  its  time-axis,  like  all  other  straight  lines  in  this 
geometry,  would  be  a  closed  curve,  like  a  great  circle 
on  a  sphere.  Whilst  I  see  no  theoretical  impossibility 
in  the  time  of  Nature  being  of  this  kind,  I  think  that 


}<>_>  SCIENTIFIC   THOUGHT 

there  is  no  evidence  to  support  the  suggestion.  If  it 
were  so,  the  course  of  Nature  would  continually  repeat 
itself  in  cycles.  These  might,  of  course,  be  of  enormous 
duration  ;  and  so  the  fact  that  we  have  no  empirical 
evidence  for  this  alternative  cannot  be  counted  as 
evidence  against  it  ;  we  may  make  a  present  of  the 
suggestion  to  the  Dean  of  St  Paul's  and  the  Neo- 
platonists. 

We  will  therefore  confine  ourselves  to  the  Euclidean 
and  the  hyperbolic  alternatives.  On  the  Euclidean 
alternative  there  would  be  an  infinite  number  of  equally 
permissible  time-axes  for  the  sense-history,  and  these 
would  all  be  parallel  to  each  other.  The  line  t'  in  (i) 
is  an  example.  On  the  hyperbolic  alternative,  so  far 
as  my  very  limited  knowledge  of  four- dimensional 
hyperbolic  geometry  may  be  trusted,  I  should  say  that 
there  could  only  be  one  time-axis  for  the  sense-history. 
It  is  true  that  there  are  plenty  of  straight  lines  in  the 
history,  parallel  to  /.  The  line  pp'  in  (iii)  is  an  example. 
But  none  of  them  will  be  normal  to  the  momentary 
spaces  which  are  normal  to  /,  and  therefore  none  of 
them  could  be  taken  as  time-axes.  Again,  there  are 
plenty  of  lines  beside  t  which  are  normal  to  all  the 
momentary  spaces.  The  line  nri  in  (iii)  is  an  example. 
But  none  of  them  are  straight  lines,  and  therefore  none 
of  them  can  be  taken  as  time-axes.  They  are,  in  fact, 
curves  called  horocycles,  and  horocycles  are  to  hyperbolic 
straight  lines  much  as  small  circles  are  to  great  circles 
on  the  surface  of  a  sphere.  I  do  not  think  that  the 
uniqueness  of  the  time-axis  suffices  to  show  that  the 
geo-chronometry  of  an  idealised  sense-history  could  not 
be  hyperbolic  ;  but  we  shall  see  later  that  the  Space- 
Time  of  Nature  could  hardly  be  supposed  to  have  one 
single  unique  time-axis,  even  apart  from  the  Theory 
of  Relativity.  Hence,  we  had  better  work  out  the 
geo-chronometry  of  the  idealised  sense-history  on  the 
Euclidean  hypothesis,  since  we  want  it  only  as  a  basis 
for  the  geo-chronometry  of  physical  Space-Time. 


SPACE-TIME  463 

There  is  a  more  positive  reason  for  rejecting  the 
hyperbolic  alternative  for  the  idealised  sense-history. 
In  the  Euclidean  case,  since  the  normals  to  the  time- 
axis  are  parallel  to  each  other,  and  since  Euclidean 
parallels  are  everywhere  equidistant  from  each  other, 
any  slab  of  the  sense-history,  bounded  by  two  such 
normals,  has  the  same  thickness  throughout  (see  Fig.  (i) 
above).  In  the  hyperbolic  case  the  normals  diverge 
from  each  other  on  both  sides  of  the  common  time-axis. 
The  result  is,  that  it  is  only  on  the  Euclidean  alternative 
that  a  Specious  Present  would  have  one  definite  limited 
duration.  On  the  hyperbolic  alternative  sensa,  far  from 
the  centres  of  a  field,  could  last  for  enormous  stretches 
of  time,  remaining  in  a  single  Specious  Present.  This 
seems  to  be  contrary  to  fact.  So,  on  every  ground, 
it  seems  reasonable  to  take  the  geo-chronometry  of  the 
idealised  sense-field  as  of  the  Euclidean  type. 

We  can  now  advance  to  the  very  important  con- 
ception which  Whitehead  would  call  the  timeless  space 
of  the  idealised  sense-history.  When  we  talk  of  objects 
resting  or  moving  in  a  space,  we  clearly  cannot  be 
thinking  of  a  momentary  space.  For  both  rest  and 
motion  involve  lapse  of  time.  We  must,  in  fact,  be 
thinking  of  some  kind  of  space  which  lasts  for  the 
whole  time  under  consideration,  and  does  not  change 
as  the  time  flows  on.  This  is  what  Whitehead  means 
by  a  timeless  space.  We  have  now  to  define  such  a  space 
for  the  idealised  sense-history. 

Let  us  imagine  a  completely  uniform  sense-object 
which  lasts  throughout  the  whole  of  the  sense-history. 
As  we  slice  the  history  up  into  thinner  and  thinner 
sections  we  shall,  ipso  facto,  be  slicing  this  sense-object 
into  thinner  and  thinner  sections,  all  exactly  alike  and 
all  occupying  precisely  similar  positions  in  these  fields. 
Finally,  by  Extensive  Abstraction,  we  shall  reach  a 
series  of  successive  momentary  spaces,  each  containing 
a  momentary  section  of  the  uniform  sense-object.  All 
these    momentary   sections    will    be    exactly   alike,   and 


464  SCIENTIFIC   THOUGHT 

exactly  similarly  situated  in  their  respective  momentary 
spaces.  If,  now,  we  imagine  the  spatial  dimensions  of 
the  uniform  sense-object  reduced  more  and  more,  so 
that,  finally,  it  is  the  history  of  a  mere  point,  it  is  clear 
that  the  object  reduces  to  a  line  parallel  to  the  time- 
axis  of  the  sense-history.  Each  point  in  this  straight 
line  is  in  one  of  the  momentary  spaces  of  the  history, 
and  each  of  the  momentary  spaces  contains  one  of  the 
points.  And  these  points  are  in  corresponding-  places  in 
their  respective  momentary  spaces.  Thus  any  straight 
line  in  the  sense-history  which  is  parallel  to  the  time- 
axis,  is  the  history  of  a  sense-object  of  punctual  spatial 
dimensions,  which  rests  in  a  single  "place"  through- 
out the  duration  of  the  history. 

We  may  therefore  say  that  every  straight  line,  parallel 
to  the  time-axis  of  a  sense-history,  is  a  pomt  of  the  time- 
less space  of  the  history.  The  timeless  space  of  the 
history  thus  consists  of  the  whole  bundle  of  straight 
lines  in  the  history  which  are  parallel  to  its  time-axis. 

We  have  now  to  define  the  straight  lines  of  the  timeless 
space.  To  do  this,  let  us  imagine  a  sense-object  which 
is  positionally  non  -  uniform  and  of  punctual  spatial 
dimensions.  It  is  evident  that  it  will  consist  of  a  series 
of  points,  one  in  each  of  the  successive  momentary  spaces. 
But  these  points  will  not  occupy  corresponding  positions 
in  their  respective  momentary  spaces,  since  the  object  is 
positionally  non-uniform.  Thus  the  whole  assemblage 
of  them  will  be  a  curve  of  some  kind  in  the  sense-history. 
It  will,  in  general,  be  a  tortuous  curve  ;  and  it  will,  of 
course,  never  be  a  straight  line  parallel  to  the  time-axis, 
for  that  would  be  the  history  of  a  positionally  uniform 
punctual  object.  Again,  it  will,  of  course,  never  be  a 
line  in  any  one  momentary  space,  for  it  would  then  not 
be  the  history  of  any  enduring  object  whatever.  Now, 
through  each  of  the  points  of  this  curve,  there  goes  one 
and  only  one  straight  line  parallel  to  the  time-axis  of 
the  history.  And  each  of  these  lines,  as  we  have  seen, 
is  one  point  in   the  timeless  space    of  the   history.     It 


SPACE-TIME  465 

follows  that  the  assemblage  of  all  these  lines  is  the 
course  traced  by  the  moving  object  in  the  timeless  space. 
Such  an  assemblage  of  parallel  straight  lines  will  form 
a  surface  in  the  sense-history,  which  will  not  in  general 
be  fiat.  But,  if  the  moving  object  happens  to  describe 
a  straight  line  in  the  timeless  space  of  the  history,  this 
surface  will  flatten  out  into  a  plane  parallel  to  the  time- 
axis.  The  easiest  way  to  see  this  is  the  following  :  It 
is  admitted  that  the  points  of  the  timeless  space  of  a 
sense-history  are  straight  lines  in  the  history,  parallel  to 
its  time-axis.  Now  a  straight  line  is  uniquely  determined 
by  two  of  its  points.  Now  the  only  figure  in  the  sense- 
history,  which  is  uniquely  determined  by  two  straight 
lines  parallel  to  the  time-axis,  is  the  plane  which  contains 
them  both,  and  is,  of  course,  itself  parallel  to  this  axis. 
It  is  thus  evident  that  a  straight  line  in  the  timeless  space 
of  a  sense-history  is  a  plane  in  the  sense-history,  parallel 
to  its  time-axis. 

It  remains  to  define  the  planes  of  a  timeless  space. 
A  plane  in  the  timeless  space  will  be  a  figure  uniquely 
determined  by  a  straight  line  in  that  space,  and  a  point 
which  is  in  the  space  but  not  on  the  straight  line.  Now, 
we  have  already  seen  that  a  straight  line  in  the  timeless 
space  is  a  plane  in  the  history,  parallel  to  its  time-axis  ; 
and  that  a  point  in  the  timeless  space  is  a  straight  line 
in  the  history,  parallel  to  its  time-axis.  The  fact  that 
the  point  is  outside  the  line  in  the  timeless  space  is 
identical  with  the  fact  that  the  corresponding  line  is 
outside  the  corresponding  plane  in  the  sense-history. 
It  follows  at  once  that  a  plane  in  the  timeless  space  of  a 
sense-history  is  a  three-dimensional  region  in  the  history, 
uniquely  determined  by  a  plane,  parallel  to  the  time- 
axis,  and  a  straight  line,  also  parallel  to  the  axis  but 
not  contained  in  this  plane.  This  is  an  unlimited  region, 
which  plays  a  corresponding  part  in  a  four-dimensional 
manifold  to  a  plane  in  an  ordinary  three-dimensional 
space. 

We  have  thus  defined  the  points,  straight  lines  and 


466 


SCIFXTIFIC    THOUGHT 


planes  of  the  timeless  space  of  a  given  idealised  sense- 
history  in  terms  of  certain  special  types  of  figures  in  the 
Latter.  These  definitions  are  wholly  due  to  Whitehead. 
It  will  be  noticed  (i)  that  the  timeless  point  is  something 
more  complex  than  the  momentary  point,  since  it  consists 
of  a  whole  series  of  the  latter  ;  (2)  some  straight  lines  in 
the  sense-history  are  also  momentary  straight  lines  in 
one  of  the  momentary  spaces  ;  but  no  straight  line  in 
the  history  is  also  a  straight  line  in  the  timeless  space. 
At  best,  it  can  only  be  a  point  in  the  latter  ;  (3)  a  timeless 
straight  line  is  a  set  of  straight  lines  in  the  sense-history, 
of  a  certain  kind.  Once  the  timeless  concepts  have  been 
defined,  the  geometry  of  the  timeless  space  can  be  worked 
out.  It  will  be  of  the  same  character  as  the  geometry 
of  the  momentary  spaces  of  the  history.  For  there  is  a 
one-to-one  correspondence  (though  never  an  identity) 
between  the  timeless  points,  straight  lines  and  planes, 
as  defined  above,  and  the  momentary  points,  straight 
lines  and  planes  of  any  one  of  the  momentary  spaces. 

As  a  visual  sense-history  is  a  four-dimensional 
whole,  it  is  not  possible  completely  to  illustrate  all  this 
on  paper.  But  we  can  help  the  reader  to  understand 
the  four-dimensional  case  by  imagining  a  sense-history 
which  has  only  three  dimensions,  two  spatial  and  one 
temporal.  The  momentary  spaces  will  then  be  planes 
at  right  angles  to  the  paper,  and  we  can  illustrate  the 
relations  between  sense-history,  momentary  spaces,  and 
timeless  space  in  the  drawing  given  below. 
Y,  Y2 

Q 


>t 


In  this  picture  SL  and  S.,  are  two  momentary  sections 
of  such  a  sense-history.  The  dotted  line  pxq.2  is  the 
straight  line  in  the  sense-history  which  represents  the 


SPACE-TIME  467 

history  of  a  point-object,  moving  along  a  certain  straight 
line  in  the  timeless  space  of  the  history  with  a  certain 
uniform  velocity.  The  first  momentary  section  of  this 
object  is  the  momentary  pointy  in  the  momentary  space 
Sr  The  last  section  of  it  is  the  momentary  point  q2 
in  the  momentary  space  S2.  Intermediate  sections  are 
momentary  points  in  intermediate  momentary  spaces. 

The  dashed  line  pxp2  is  the  point  P  in  the  timeless 
space  of  the  sense-history.  The  dashed  line  qxq2  is  the 
point  Q  in  the  timeless  space  of  the  history.  P  would 
have  represented  the  history  of  the  punctual  sense- 
object  if  the  latter  had  stayed  in  its  original  position. 
Q  would  have  represented  the  history  of  this  object  if 
the  latter  had  always  been  in  the  position  which  it 
finally  occupies.  The  plane  pxqxq.zp»,  which  is  deter- 
mined by  the  two  straight  lines  P  and  Q,  is  the  timeless 
straight  line  in  the  timeless  space  of  the  history  which 
the  moving  punctual  object  traverses.  It  is  uniquely 
correlated  with  the  momentary  straight  lines  pxqx  in  S2 
and  p2q2  in  S2,  which  might  be  called  the  "instantane- 
ous directions  of  motion  of  the  moving  object  at  the  two 
moments  tx  and  £,."  These  are  of  course  similar,  in 
the  present  case,  since  the  object  is  moving  all  the  time 
in  one  direction  in  the  timeless  space. 

The  angle  between  the  dotted  line  pxq2  and  the  dashed 
line  pxp2  depends  on  the  velocity  of  the  moving  point- 
object  in  the  timeless  space.  The  histories  of  all  moving 
points  which  traverse  this  particular  line  in  the  timeless 
space  will  be  straight  lines  in  the  plane pxqxq.±p.z,  but  their 
directions  in  this  plane  will  depend  on  the  velocity  with 
which  the  object  traverses  the  line.  If  the  velocity  be 
non-uniform,  they  will,  of  course,  no  longer  be  straight 
lines  ;  but  they  will  still  be  plane  curves  in  this  plane. 
Naturally  we  cannot  illustrate  timeless  planes  in  our 
diagram  ;  for  we  can  only  get  them  in  connexion  with 
a  four-dimensional  sense-history,  whose  momentary 
sections  are  not  planes,  as  in  the  diagram,  but  three- 
dimensional    spaces.       Also,    there    are    no    momentary 


468  SCIENTIFIC   THOUGHT 

planes  in  our  diagram,  except  the  timeless  spaces 
themselves. 

(</)  Physical  World'lines  and  their  Mutual  Relations. — 
It  is  evident  that  such  an  idealised  sense-history  as  we 
have  just  been  describing  would  be  a  kind  of  "world," 
with  a  time,  a  timeless  space,  and  objects  which  move 
or  rest  in  the  latter  as  the  former  Hows  on.  The  question 
now  is  :  How  far  can  the  world  of  physical  objects  and 
events  be  regarded  as  forming  a  spatio-temporal  whole, 
analogous  in  character  to  an  idealised  sense-history  ?  If 
the  analogy  be  complete,  the  physical  world  will  have  one 
time-direction  (though  many  parallel  time-axes),  and  one 
timeless  Space,  which  will  be  of  the  Euclidean  type. 
In  this  Space  all  physical  objects  will  rest  or  move  as 
the  one  physical  Time  Hows  on. 

We  must  be  prepared  to  recognise  at  once  that  it  is 
by  no  means  obvious  that  any  such  view  of  the  structure 
of  the  physical  world  will  fit  the  known  facts.  After  all, 
why  should  the  physical  events  and  objects  which  are 
connected  with  a  number  of  different  sense-histories 
form  a  spatio-temporal  whole  which  is  exactly  analogous 
in  structure  to  a  single  sense-history?  Even  if  there 
should  be  a  certain  analogy,  we  have  not  the  slightest 
right  to  expect  it  to  extend  to  every  detail  ;  i.e.,  we  have 
no  right  to  be  surprised  if  the  geo-chronometry  of 
physical  Space-Time  should  not  be  exactly  like  that 
of  the  idealised  sense-history.  We  shall  see  in  a  moment 
that  most  of  the  apparent  paradox  of  the  Theory  of 
Relativity  is  due  to  the  fact  that  it  disappoints  our  simple- 
minded  expectation  that  the  geo-chronometry  of  physical 
Space-Time  shall  be  exactly  like  that  of  a  single  ideal- 
ised sense-history.  But,  on  reflection,  we  see  that  this 
expectation  is  absolutely  groundless,  and  that  it  would 
be  rather  a  queer  coincidence  if  the  geo-chronometries 
of  two  such  different  wholes  were  exactly  alike. 

After  these  general  preliminaries,  let  us  see  how  far 
the  analogy  can  be  carried.  A  physical  object  is  a 
succession  of  scientific  events,  just  as  a  sense-object  is 


SPACE-TIME  469 

a  series  of  successive  sensa  in  a  sense  -  history.  A 
punctual  sense-object,  whether  positionally  uniform  or 
non-uniform,  is  a  line  of  some  kind  in  its  sense-history. 
If  it  be  positionally  uniform,  and  therefore  rests  in  the 
timeless  space  of  the  sense-history,  it  is  a  straight  line, 
parallel  to  the  time-axis  ;  if  it  moves,  it  is  a  curve  of 
some  kind  on  a  surface  generated  by  lines  parallel  to  the 
time-axis,  and  so  on.  If  then  a  punctual  physical  object 
can  be  regarded  as  analogous  to  a  sense-object,  we 
must  suppose  that  it  (or  its  history,  if  you  prefer  it)  is  a 
curve  of  some  sort  in  physical  Space-Time.  We  will  call 
such  a  curve  a  "  world-line,"  following  Minkowski.  All 
other  material  particles  must  equally  be  regarded  as 
curves  in  physical  Space-Time.  We  must  next  consider 
the  intrinsic  characters  and  mutual  relations  of  world- 
lines,  for  the  whole  question  of  whether  it  is  worth  while 
to  talk  of  a  physical  Space-Time  at  all  depends  on  the 
nature  of  these. 

Suppose  that  B,  the  body  of  observer  /3,  appears  as 
a  resting  sense-object  in  the  visual  sense-history  of 
another  observer  a.  We  know  that  A,  the  body  of  a, 
will  appear  as  a  resting  sense-object  in  the  visual  sense- 
history  of  /3,  provided  that  a's  and  /3's  kinesthetic 
sensations  are  alike.  The  complete  symmetry  between 
a's  experiences  in  connexion  with  B,  and  /3's  experiences 
in  connexion  with  A,  suggests  that  there  is  some  great 
similarity  in  the  world-lines  of  A  and  B.  (Or  rather  in 
the  world-lines  which  would  represent  their  histories  if 
they  were  reduced  to  punctual  spatial  dimensions.)  It 
seems  reasonable  to  suppose  that,  in  such  cases,  we  are 
dealing  with  pairs  of  intrinsically  similar  and  similarly 
situated  world-lines  in  physical  Space-Time.  We  can 
conceive  of  groups  of  observers  whose  bodies  form  sets  of 
similar  and  similarly  situated  world-lines.  We  will  call 
these  sets  of  relatively  resting  physical  objects.  We  know 
that,  if  a  certain  body  appears  as  a  sense-object  which 
moves  in  the  timeless  space  of  any  one  member  of  the 
set,  it  will  appear  as  a  sense-object  which  moves  in  the 


470  SCIENTIFIC   THOUGHT 

timeless  space  of  each  member  of  the  set.  If  it  happens 
to  be  the  body  of  an  observer,  we  know  further  that  his 
translatory  kinesthetic  sensations  will  differ  from  those  of 
all  members  of  the  set.  Moreover,  all  the  bodies  of  the 
set  will  appear  to  this  observer  as  sense-objects  which 
move  absolutely,  but  rest  relatively  to  each  other,  in 
the  timeless  space  of  his  sense-history.  It  seems  reason- 
able to  suppose  that  the  world-line  of  this  observer's 
body  is  in  some  way  different  from  those  of  the  set  in 
question.  There  might  be  an  intrinsic  difference  in  the 
nature  of  the  curve,  or  some  kind  of  difference  in  its 
situation  or  direction  in  physical  Space-Time.  A  geo- 
metrical illustration  of  the  first  kind  of  difference  would 
be  given  by  a  straight  line  and  a  hyperbola  ;  an 
illustration  of  the  second  kind  of  difference  would  be 
given  by  two  non-coplanar  straight  lines,  or  by  two 
coplanar  straight  lines  at  an  angle  to  each  other. 

We  can  now  extend  these  suggestions  in  the  usual 
way  from  the  bodies  of  observers  to  physical  objects 
in  general.  We  can  suppose  that  a  set  of  relatively 
resting  particles  is  a  set  of  similar  and  similarly  situated 
world-lines,  and  that  any  particle  which  moves  relatively 
to  this  set  is  a  world-line  which  differs,  either  intrinsic- 
ally or  in  its  situation  in  physical  Space-Time,  from 
the  members  of  this  set. 

{e)  Straight  and  Tortuous  World-lines. — World-lines 
might  be  curves  of  many  different  kinds  ;  some  might 
be  intrinsically  very  complex  (like  highly  tortuous 
curves  in  ordinary  space)  ;  others  might  be  intrinsically 
very  simple  (like  ordinary  straight  lines).  It  will  be 
remembered  that  a  punctual  sense-object,  which  rests 
in  the  timeless  space  of  its  sense-history,  is  a  straight 
line  parallel  to  the  time-axis  of  the  history.  Punctual 
sense-objects,  which  move  in  the  timeless  space  of  the 
sense-history,  may  be  straight  lines  (though  they  need 
not  be)  ;  but  they  are  never  parallel  to  the  time-axis. 
We  must  see  how  far  there  is  analogy  to  this  in  physical 
Space-Time. 


SPACE-TIME  471 

If  any  analogy  at  all  can  be  drawn  between  a  sense- 
history  and  the  physical  world,  we  must  assume  (1)  that 
at  least  some  particles  are  straight  world-lines  ;  (2)  that 
at  least  some  of  these  straight  world-lines  are  per- 
missible directions  for  time-axes  for  physical  Space- 
Time  ;  and  (3)  that,  by  taking  certain  particles  as  having 
the  characteristics  (1)  and  (2),  and  by  using  suitable 
criteria  of  simultaneity,  we  can  account  for  all  the  known 
general  rules  of  spatio-temporal  correlation  among 
physical  events.  We  will  now  see  how  far  the  analogy 
can  be  carried  on  this  assumption. 

A  straight  world-line  which  is  a  permissible  time- 
axis  for  physical  Space-Time  will  be  analogous  to  the 
time-direction  of  a  sense-history.  If  the  whole  physical 
world  is  to  be  analogous  to  a  single  sense-history,  every 
momentary  physical  event  must  have  one  and  only  one 
straight  world-line  passing  through  it,  parallel  to  the 
given  time-direction.  The  whole  of  such  a  bundle  of 
parallel  world-lines  may  be  called  a  physical  reference 
frame.  From  what  has  been  said  in  the  last  section  it 
is  clear  that  every  line  of  such  a  bundle  is  a  point  in  the 
timeless  space  of  the  frame,  and  conversely.  Each  line 
of  the  bundle  is,  in  fact,  the  history  of  a  hypothetical 
particle,  which  rests  at  a  certain  place  in  the  timeless 
space  of  the  frame  as  the  time  of  the  frame  flows  on. 
The  place  of  any  momentary  point-event  in  the  timeless 
space  of  the  frame  will  be  the  particular  line  of  the 
bundle  which  passes  through  this  point-event.  The 
date  of  this  event  in  the  frame  will  be  its  particular 
position  on  this  line. 

Particles  which  move  uniformly  in  straight  lines  in 
the  timeless  space  of  this  frame  will  be  world-lines 
which  (1)  are  straight,  and  (2)  are  contained  in  a  certain 
plane  parallel  to  the  time-axis,  but  (3)  are  not  themselves 
parallel  to  it.  Particles  which  move  non-uniformly  but 
rectilinearly  in  the  timeless  space  of  the  frame  will  be 
world-lines  which  (1)  are  not  straight,  but  (2)  are 
contained  in  some  plane  parallel  to  the  time-axis.     This 


472  SCIENTIFIC   THOUGHT 

plane  in  Space-Time  is,  of  course,  the  straight  line  in  the 

timeless  spaee  of  the  frame  along-  which  the  particle 
moves.  Particles  which  move  non-uniformly  and  non- 
rectilinearly  in  the  timeless  space  of  the  frame  will  be 
lines  which  (i)are  not  straight,  (2)  are  not  plane,  but 
(3)  are  confined  to  a  surface  generated  by  straight  lines 
parallel  to  the  time-axis  of  the  frame.  Finally,  the 
momentary  spaces  of  the  given  frame  will  be  sections 
of  physical  Space-Time,  normal  to  the  time-axis  of  the 
frame.  Momentary  events  in  the  same  momentary  space 
will  be  contemporary  with  respect  to  the  frame. 

(/)  The  Point  of  Separation  between  the  Traditional 
View  and  the  Special  Theory  of  Relativity. — There  is  thus 
a  complete  analogy  between  a  physical  reference  frame 
and  an  idealised  sense-history,  on  the  assumptions 
which  we  are  at  present  making.  On  these  assumptions 
every  event  in  Nature  has  its  place  and  date  in  such  a 
frame.  But  now  there  arises  a  question  to  which  there 
is  nothing  analogous  in  a  sense-history.  The  question 
is  this  :  Are  all  straight  world-lines  permissible  time- 
axes  for  physical  Space-Time,  or  are  some  of  them 
permissible  and  others  not?  And,  if  the  latter  be  true, 
what  distinguishes  those  which  are,  from  those  which 
are  not  permissible? 

In  a  given  sense-history  there  is  one  and  only  one 
Ume-direetion.  This  is  because  the  simultaneity  or 
successiveness  of  sensa  in  the  same  sense-history  is 
actually  sensed,  and  we  have  therefore  no  choice  as  to 
which  we  shall  group  together  as  simultaneous,  and 
which  we  shall  group  apart  as  successive.  The  succes- 
sive slabs  of  the  sense-history  are  given  to  us  in  the  form 
of  sense-fields,  and  the  only  possible  time-direction  is 
that  of  their  common  normal.  The  only  choice  allowed 
to  us  is  that  we  could  take  any  straight  line  in  the  sense- 
history,  parallel  to  the  time-direction,  as  a  permissible 
time-axis,  assuming  that  the  geo-chronometry  of  the 
sense-history  is  Euclidean. 

If  there  were   an    exact   analogy    between    physical 


SPACE-TIME  473 

Space-Time  and  an  idealised  sense-history,  there  would 
be  one  and  only  one  direction  in  physical  Space-Time 
which  could  be  taken  as  the  time-direction.  If  this  were 
so,  there  would  be  one  and  only  one  frame  of  reference 
in  which  all  the  events  of  Nature  could  be  consistently 
placed  and  dated.  The  only  latitude  allowed  us  would 
be  that  any  frame  which  rested  in  the  timeless  space  of 
the  first  would  itself  be  a  permissible  frame.  For  this 
would  merely  amount  to  taking  another  world -line, 
parallel  to  the  original  one,  as  our  new  time-axis. 

Now  this  is  exactly  the  assumption  which  the 
classical  mathematical  physics  did  make.  It  assumed 
that  there  was  one  and  only  one  fundamental  frame  of 
reference  in  which  all  the  events  of  Nature  could  be 
consistently  placed  and  dated.  The  timeless  space  of 
this  is  the  ''stagnant  ether,"  and  the  one  permissible 
time-direction  is  the  history  of  any  particle  of  the  ether 
or  of  any  particle  that  rests  in  it.  No  straight  line  which 
makes  an  angle  with  the  one  outstanding  time-direction 
will  be  a  possible  time-axis  ;  the  sections  of  physical 
Space-Time  normal  to  such  a  line  will  not  be  momentary 
spaces,  and  the  whole  bundle  of  lines  parallel  to  such 
a  line  will  not  form  the  points  of  a  timeless  space. 

Now  there  is  nothing  antecedently  absurd  in  such 
a  view.  Temporal  and  spatial  characteristics  are 
different,  for  all  observers  ;  and  therefore  it  might  well 
be  that  there  is  one  and  only  one  outstanding  direction 
in  Space-Time  which  can  be  taken  as  a  time-direction. 
Moreover,  it  is  certain  that  the  assumption  is  not  far 
wrong ;  since  it  is  the  assumption  of  the  traditional 
physics,  and  this  has  proved  capable  of  dealing  with 
all  the  more  obvious  spatio-temporal  correlations  of 
physical  events  in  a  single  spatio-temporal  scheme. 
We  can,  in  fact,  at  once  reject  the  opposite  extreme 
view,  viz.,  that  all  straight  world-lines  are  equally  per- 
missible as  time-axes.  For  this  would  be  inconsistent 
with  the  admitted  difference  between  spatial  and  tem- 
poral   characteristics   for    all    observers,    and   with   the 

2  H 


474  SCIENTIFIC   THOUGHT 

very  great  measure  of  success  which  has  attended  the 
diametrically  opposite  assumption,  that  there  is  only 
one  direction  in  Space-Time  which  can  be  taken  as  a 
time-axis. 

(g)  7  he  Hypothesis  of  a  UmitedRange  of  'lime-directions. — 
The  only  alternative  worth  discussing  is  that  all  straight 
world-lines  whose  directions  lie  within  certain  limits, 
and  only  these,  are  permissible  time-directions.  The 
traditional  physics  makes  physical  Space-Time  exactly 
analogous  in  structure  to  a  single  idealised  sense-history. 
The  present  suggestion  makes  it  considerably  different 
in  principle,  though  not  necessarily  very  different  in 
practice.  Nothing  but  the  observable  correlations 
between  physical  events,  as  betrayed  by  correlations 
between  sensible  events  in  various  sense-histories,  can 
decide  between  these  alternatives. 

A  little  reflection  shows  that  there  is  a  certain 
incoherence  in  the  traditional  view,  as  regards  mechanical 
phenomena.  It  is  admitted  that  axes  which  move  uni- 
formly in  straight  lines  in  the  timeless  space  of  the 
supposed  fundamental  frame  will  do  equally  well  for 
placing  events  for  mechanical  purposes.  And  such 
axes  will  be  represented  by  straight  world-lines  which 
make  an  angle  with  those  which  represent  the  funda- 
mental frame.  If  there  were  only  mechanical  phenomena 
to  be  considered,  it  would  be  natural  to  suppose  that 
all  such  world-lines  would  do  equally  well  as  time-axes, 
and  that  all  the  corresponding  frames  would  do  equally 
well  for  placing  and  dating  physical  events.  The  only 
reason  for  thinking  that  there  must  be  one  fundamental 
frame  connected  with  a  certain  unique  direction  in 
Space-Time,  was  the  notion  that  any  pair  of  events  must 
be  either  simultaneous  or  successive,  and  that  they  could 
never  be  both.  It  was  thought  that  the  phenomena  of 
light,  electricity  and  magnetism,  would  show  us  the 
one  fundamental  frame,  which  was  merely  concealed  in 
mechanical  phenomena  by  the  particular  form  which  the 
laws  of  motion  happen  to  have.    Thus  the  traditional  view 


SPACE-TIME  475 

holds  that  there  is  only  one  permissible  time-direction, 
which  can  and  must  be  used  for  dating  all  physical 
phenomena.  But  it  allows  you  to  place  mechanical 
phenomena  by  reference  to  any  axes  which  move 
uniformly  and  rectilinearly  in  the  timeless  space  of 
the  fundamental  frame. 

Now  the  experiments  on  which  the  Special  Theory 
of  Relativity  is  based,  show  that  this  supposed  difference 
between  mechanical  and  electro-magnetic  phenomena 
is  a  pure  myth.  Electro-magnetic  phenomena  fail  to 
reveal  any  unique  fundamental  frame.  Their  laws 
remain  of  exactly  the  same  form  if  you  refer  the  events 
to  axes  which  move  uniformly  and  rectilinearly  in  the 
space  of  one  fundamental  frame,  provided  that  you  take 
the  straight  world-line  which  represents  these  moving 
axes  as  a  permissible  time-direction,  and  use  it  for  dating 
your  electro-magnetic  events. 

The  Special  Theory  of  Relativity  may,  in  fact, 
be  summed  up  in  the  following  statement:  There  is  a 
whole  set  of  different  directions  in  Space-Time,  equally 
permissible  as  time-directions  for  dating  physical  events. 
But  all  the  permissible  time-directions  are  confined 
within  certain  limits.  Corresponding  to  any  one  of 
these  will  be  a  timeless  space,  whose  points  are  the 
world-lines  parallel  to  it.  Every  physical  event  has 
a  unique  place  and  date  in  any  one  such  frame.  Its 
place  in  the  timeless  space  of  any  frame  is  determined 
by  the  line,  parallel  to  the  time-direction  of  the  frame, 
which  passes  through  it.  Its  date  in  the  frame  is  deter- 
mined by  its  position  on  this  line.  The  laws  of  all 
physical  phenomena  have  precisely  the  same  form,  no 
matter  which  of  these  frames  is  used  for  placing  and 
dating  them. 

All  the  characteristic  features  of  the  Special  Theory 
of  Relativity  follow  at  once  from  this  supposition  as  to 
the  geo-chronometry  of  physical  Space-Time,  as  I  will 
now  show  in  brief  outline. 

(i)  There  is  nothing  that  can  be  called  the  timeless 


47^ 


SCIENTIFIC   THOUGHT 


Space  of  Nature.  There  will  be  as  many  different 
timeless  spaces  as  there  are  different  permissible  time- 
directions. 

(2)  Two  events  which  are  contemporary  in  one  frame 
will  not  be  contemporary  in  another,  unless  they  happen 
to  occupy  the  same  place  in  the  timeless  space  of  the  first 
frame.     The  figure  below  will  make  this  clear. 

M\fz 


rnz 


X 


t, 


m, 


/> 


^ 


•&.- 


+*, 


5fy 

Call  the  two  frames  Fx  and  F2.  Since  they  differ,  they 
will  consist  of  two  bundles  of  parallel  world-lines, 
inclined  to  each  other.  Since  the  two  events  are  not  to 
be  at  the  same  place  in  the  timeless  space  of  F1(  they 
will  be  on  two  different  world-lines  of  the  bundle,  say 
lx  and  mv  Since  they  are  to  be  contemporary  in  F1} 
they  must  both  be  in  some  one  momentary  space  of  Fx. 
This  will  be  a  section  of  Space-Time,  normal  to  the  time- 
direction  of  Fr  Call  this  momentary  space  S\/x.  Then 
the  points  A  and  /*,  in  which  the  lines  lx  and  mx  cut  S\u, 
will  represent  our  two  events,  which  are  simultaneous 
in  the  frame  Fx,  but  spatially  separated  in  its  timeless 
space.  Now  let  X  lie  on  the  line  /2  of  the  frame  F2,  and 
let  p.  lie  on  the  line  ;«2  of  the  frame  F2.  In  this  frame, 
instead  of  being  in  a  single  momentary  space  S\u,  they 
are  in  the  two  successive  momentary  spaces  S\  and  SM. 
They  are  therefore  successive  in  F2,  though  simultaneous 
in  Fr  Moreover,  their  distances  apart  in  the  two  time- 
less spaces  are  not  the  same.  In  the  former,  it  is  the 
distance  between  lx  and  mx  ;  in  the  latter,  it  is  the  smaller 
distance  between  1.2  and  ni2. 

(3)  Conversely,   two   events  which  are  in  the  same 
place  in  the  timeless  space  of  Fx  will  not  be  in  the  same 


SPACE-TIME 


477 


place  in  the  timeless  space  of  F2,  unless  they  happen  to 
be  also  contemporary  in  Fr  The  diagram  below  will 
show  this. 


The  two  events  are  on  a  certain  line  lv  parallel  to  tXi 
since  they  are  in  the  same  place  in  the  timeless  space 
of  Fj.  Since  they  are  not  to  be  contemporary  in  Fx,  they 
must  be  in  different  momentary  spaces  S\  and  Sx'  of  Fr 
The  two  events  will  be  represented  by  the  two  points 
X  and  X',  in  which  the  line  lx  cuts  these  two  momentary 
spaces  respectively.  In  F2  the  two  events  X  and  X'  are 
necessarily  on  two  different  lines,  /2  and  /'2,  parallel  to 
t2,  the  time-direction  of  F2.  They  are  therefore  at 
different  places  in  the  timeless  space  of  F2.  Moreover, 
their  temporal  separation  is  different  in  the  two  frames. 
In  Fj  it  is  represented  by  the  line  XX',  in  F2  by  the  shorter 
line  between  the  two  dotted  normals  to  %,  which  represent 
the  momentary  spaces  of  F2,  in  which  the  two  events  are 
respectively  situated. 

(4)  We  have  still  to  consider  some  implications  of 
the  fact  that  not  all  straight  world-lines  are  permissible 
time-axes,  but  only  those  whose  directions  lie  within  a 
certain  limited  range  in  physical  Space-Time.  Take 
any  straight  world-line  t,  which  is  a  permissible  time- 
axis,  and  consider  any  other  non-parallel  straight  world- 
line/'.  There  will  be  one  and  only  one  plane  in  Space- 
Time  which  is  parallel  to  t  and  contains  p.  In  this 
plane  take  a  line  t' ,  parallel  to  /.  Then  /  and  t'  will 
cut  each  other  at  an  angle.  This  plane  will  be  a  straight 
line  in  the  timeless  space  of  the  frame  of  which  t  is  the 
time-axis.     The  line  p  will  represent  a  particle  moving 


478  SCIENTIFIC  THOUGHT 

along  this  straight  line  in  the  timeless  space  with  a 
uniform  velocity.  As  we  saw  in  the  last  section,  the 
greater  the  velocity  of  this  particle  the  greater  will  be 
the  angle  between/  and  /'.  Now  we  know  that,  if  the 
angle  between  p  and  t'  exceed  a  certain  size,/  will  not 
be  a  permissible  time-axis.  This  would  imply  that  there 
is  no  frame  in  whose  timeless  space  the  particle,  whose 
history  is  the  line/,  rests.  This  would  be  contrary  to 
the  complete  relativity  of  physical  rest  and  motion. 
There  is  thus  a  certain  maximum  possible  relative 
velocity,  whose  magnitude  is  determined  by  the  size 
of  the  angle  in  Space-Time  within  which  all  permis- 
sible time-directions  lie.  If  a  straight  world-line  make 
a  greater  angle  than  this  with  any  permissible  time- 
direction,  it  cannot  be  the  history  of  an  actual  particle 
or  physical  process.  Such  a  world-line  will,  of  course, 
cut  each  momentary  space  of  any  one  frame  at  a  point ; 
but  you  cannot  take  these  successive  momentary  points 
as  sections  of  the  history  of  any  one  object,  though  of 
course  each  may  be  a  section  of  the  history  of  a  different 
object.  Now  this  notion  of  a  certain  maximum  relative 
velocity  is  characteristic  of  the  Special  Theory  of  Rela- 
tivity, which,  on  empirical  grounds,  identifies  this 
velocity  with  that  of  light  in  vacuo. 

(5)  We  cannot,  so  far  as  I  can  see,  determine  any- 
thing about  the  actual  magnitude  of  the  angle  of  the 
four-dimensional  cone  in  physical  Space-Time,  within 
which  all  permissible  time-directions  lie.  The  tangent 
of  its  half-angle  will  indeed  be  the  velocity  of  light. 
But  we  must  beware  of  supposing  that,  because  c,  the 
velocity  of  light  in  centimetres  per  second,  is  a  very 
large  number,  therefore  the  half-angle  of  the  funda- 
mental cone  must  be  very  nearly  a  right  angle,  and 
therefore  that  there  is  a  very  wide  range  of  possible 
time-directions.  For  the  numerical  value  of  the  velocity 
of  light  obviously  depends  entirely  on  the  units  that 
we  choose  for  measuring  distance  and  duration.  The 
largeness   of  c   may  simply   mean   that  the  centimetre 


SPACE-TIME 


479 


is  a  very  small  space-unit,  or  that  the  second  is  a  very- 
large  time-unit ;  it  tells  us  nothing  about  the  size  of 
the  ansfle  of  the  fundamental  cone. 

(6)  It  follows  at  once  from  what  has  just  been  said 
that,  whilst  all  the  points  in  any  timeless  space  are 
straight  world-lines,  there  are  many  straight  world- 
lines  which  are  not  points  in  any  timeless  space.  It 
follows  also  that  some  pairs  of  momentary  point-events 
are  intrinsically  separated  spatially,  i.e.,  occupy  different 
positions  in  all  timeless  spaces,  whilst  others  are  not, 
i.e. ,  they  occupy  the  same  place  in  some  timeless  space. 
The  diagram  below  will  make  this  clear  : 


X  X' 


P 


-I 


■  m 


e, 


■**, 


Let  X  and  X'  be  two  momentary  point-events  at  the 
same  point  /  of  the  timeless  space  of  the  frame  Fr 
Let  hi  be  another  momentary  point-event  at  the  point  m 
of  the  same  frame,  and  let  X,  X',  and  /u,  all  have  different 
dates  in  this  frame.  Draw  the  straight  world-lines  X/x 
and  XV«  ^  both  fall  within  the  fundamental  cone,  both 
are  permissible  time-directions.  If  so,  X  and^u  will  occupy 
the  same  place  in  the  timeless  space  of  the  frame  corre- 
sponding to  X/x,  and  X'  and  p.  will  occupy  the  same  place 
in  the  timeless  space  of  the  frame  corresponding  to  XV- 
But  it  may  happen  that  XV  falls  inside  the  cone,  whilst 
X/x  falls  outside  it.  If  so,  X/x  is  not  parallel  to  a  possible 
time-axis,  and  therefore  is  not  a  point  in  any  timeless 
space.  Hence  the  momentary  point-events  X  and  /x  will 
have  an  intrinsic  spatial  separation.  It  will  be  noticed 
that  the  question  whether  two  momentary  point-events, 
which  occupy  different  places  in  the  timeless  space  of  a 
certain  frame,  are  intrinsically  separated  in  space  or  not, 
depends  on  whether  their  dates  in  the  frame  are  much 
or  little  separated.       X  and  /x,  which    are    intrinsically 


480  SCIENTIFIC   THOUGHT 

separated  in  space,  are  much  nearer  together  in  date 
than  V  and  p,  which  are  not  spatially  separated  in  all 
timeless  spaces. 

(7)  Almost  exactly  similar  remarks  apply,  mutatis 
mutandis^  to  temporal  separation.  This  is  sometimes 
intrinsic  and  sometimes  not.  The  diagram  below  will 
explain  how  this  happens. 


,"3  ■'"& 


X 


-// 


■m>  \  /v 


S&L », 


-*-/, 


X  and  jjL  are  two  momentary  point-events,  which  are 
simultaneous  in  the  frame  Fx,  and  occupy  the  two  points 
/j  and  iii1  respectively  in  the  timeless  space  of  this 
frame,  v  is  a  third  point-event,  which  differs  both  in 
place  and  in  date  from  both  X  and  /x  in  the  frame  Fx. 
Join  \y  and  fxv  by  straight  world-lines.  Draw  the 
straight  world-lines  n2  and  n3,  normal  to  \v  and  jxv 
respectively.  If  both  u2  and  nz  be  permissible  time- 
directions,  \v  and  fxv  will  both  represent  momentary 
spaces,  one  in  the  frame  corresponding  to  ;/2,  and  the 
other  in  the  frame  corresponding  to  nz.  If  so,  X  and 
v  will  be  contemporary  in  one  of  these  frames,  and  fx 
and  v  will  be  contemporary  in  the  other.  Their  tem- 
poral separation  is  therefore  non-intrinsic.  But  it  may 
happen  that,  whilst  ;/2  falls  inside  the  fundamental  cone, 
and  is  therefore  a  permissible  time-direction,  ;/3  falls 
outside  it,  and  therefore  is  not  a  permissible  time- 
direction.  If  so,  Xv  will  be  a  momentary  space,  and 
ixv  will  not.  It  will  follow  that  fx  and  v  are  intrinsically 
separated  in  time,  i.e.,  that  there  is  no  frame  in  which 
they  are  simultaneous.  Here,  again,  the  difference 
depends  on  the  fact  that  X  and  v  are  further  apart  in 
the  timeless  space  of  Ft  than  are  fx  and  v.  Hence,  two 
point-events,  which  are   successive   in  a  certain  frame, 


SPACE-TIME  481 

are  intrinsically  successive  if  they  be  near  enough 
together  in  the  timeless  space  of  the  frame.  If  they 
be  far  enough  apart  in  the  timeless  space,  they  will 
not  be  intrinsically  successive,  i.e.,  it  will  be  possible 
to  find  a  frame  in  which  they  are  simultaneous. 

All  these  seven  consequences  of  the  view  that  more 
than  one,  but  not  all,  directions  in  physical  Space- 
Time  are  permissible  time-directions,  are  characteristic 
results  of  the  Special  Theory  of  Relativity  ;  and,  as 
this  certainly  fits  the  facts  better  than  the  traditional 
views,  we  may  assume  that  physical  Space-Time  has 
this  particular  kind  of  structure,  at  least  to  a  very  high 
degree  of  approximation.  Thus  the  physical  world  as 
a  whole  is  not  completely  analogous  to  a  single  idealised 
sense-history,  since  the  latter  has  only  one  possible 
time-direction,  whilst  the  former  has  several.  Instead 
of  being  surprised  at  this  difference,  we  ought  rather 
to  be  impressed  by  the  remarkable  amount  of  similarity 
which  exists  between  the  structures  of  two  such  wholes. 

(h)  The  Facts  imderlying  the  above  Theory  of  the  Geo- 
chronometry  of  Physical  Space-Time. — If  the  above  view 
of  the  structure  of  physical  Space-Time  is  to  be  verifi- 
able, as  it  is  to  a  high  degree  of  approximation,  we 
must  have  some  empirical  means  of  (i)  distinguishing 
straight  from  tortuous  world-lines,  and  (ii)  distinguish- 
ing those  straight  world-lines  which  are  permissible 
time-directions  from  those  which  are  not.  We  find 
that  we  can  unify  the  facts  by  assuming  that  the  history 
of  any  particle  which  rests  relatively  to  the  fixed  stars 
is  a  straight-world  line,  and  that  the  history  of  any 
particle  which  moves  in  a  straight  line  with  respect  to 
the  fixed  stars,  and  with  uniform  velocity  as  judged 
by  clocks  set  by  the  method  of  light-signals  described 
in  Part  I,  Chapter  IV,  is  another  straight  world-line 
inclined  to  the  first.  And  the  history  of  a  wave  of  light 
is  the  limiting  kind  of  straight  world-line  which  we  can 
take  as  a  permissible  time-direction.  It  is  important 
to  notice  that,  although  any  one  permissible  reference- 


482  SCIENTIFIC  THOUGHT 

frame  for  physical  Space-Time  is  strictly  analogous,  on 
the  present  theory,  to  an  idealised  sense-history,  yet 
we  have  to  treat  the  two  from  rather  different  stand- 
points. The  temporal  relations  between  events  in  the 
sense-history  are  cognised  directly  by  sense  and 
memory.  Certain  events  are  given  simultaneously  and 
others  are  given  in  succession.  Moreover,  the  sense- 
history  has  an  intrinsic  unit  of  duration  in  the  constant 
sensible  duration  of  all  the  successive  Specious  Presents. 
In  dealing  with  the  physical  world  we  have  to  set  up 
c?iteria  for  the  simultaneity  or  succession  of  physical 
events  ;  and  it  is  not  until  we  have  done  this  that  we 
can  say  which  physical  events  are  to  be  put  into  the 
same  momentary  space  and  which  into  different 
momentary  spaces  of  a  given  frame.  Moreover,  there 
is  no  intrinsic  standard  of  equality  of  physical  duration, 
and  so  we  have  to  set  up  some  criterion  for  equality 
of  time-lapse.  Until  we  have  done  this,  we  cannot 
decide  whether  the  motion  of  a  certain  particle  in  the 
timeless  space  of  a  certain  frame  is  uniform  or  not. 
And,  until  this  has  been  decided,  we  cannot  say  whether 
the  history  of  this  particle  is  or  is  not  to  be  regarded  as 
a  straight  world-line,  inclined  to  the  time-direction  of 
the  frame  in  question. 

(/)  The  Difference  between  the  Special  and  General 
Tlieories  of  Relativity. — The  traditional  physics  and  the 
special  Theory  of  Relativity  agree  in  making  the  geo- 
chronometry  of  physical  Space-Time  Euclidean.  Or, 
to  put  it  more  accurately,  the  geo-chronometry  of  the 
one  permissible  frame  on  the  traditional  theory  is 
Euclidean,  and  that  of  each  of  the  many  permissible 
frames  on  the  special  Theory  of  Relativity  is  also 
Euclidean.  This  amounts  to  saying  that,  on  both 
views,  all  straight  world-lines  are  Euclidean  straight 
lines.  This  implies  that  the  geometry  of  the  one 
timeless  space  of  the  traditional  theory  and  of  the 
many  timeless  spaces  of  the  special  Theory  of  Relativity 
is  Euclidean. 


SPACE-TIME  483 

Now  in  both  theories  we  have  taken  the  history  of 
a  particle  which  rests  or  moves  relatively  to  the  fixed 
stars  with  a  uniform  rectilinear  velocity,  as  judged  by 
properly  adjusted  clocks,  to  be  a  straight  world-line. 
Similarly,  on  both  theories,  we  have  taken  the  history 
of  a  wave  of  light  to  be  a  straight  world-line.  But, 
even  on  the  traditional  theory,  it  would  have  to  be 
admitted  that  the  universality  of  gravitation  prevents 
the  history  of  any  actual  particle  from  being  an  exactly 
straight  world-line,  on  this  definition,  if  the  geo- 
chronometry  of  physical  Space-Time  be  Euclidean. 
For,  however  far  a  particle  may  be  from  the  fixed  stars 
and  from  all  other  bodies,  it  is,  even  on  traditional 
views,  subject  to  gravitational  forces,  though  these  may 
be  practically  negligible.  We  have  now  to  add  to  this 
the  newly  discovered  fact  that  light,  and  all  other  forms 
of  radiant  energy,  are  themselves  affected  by  gravita- 
tional fields.  Thus  it  turns  out  that,  if  the  geo- 
chronometry  of  physical  Space-Time  be  Euclidean,  it 
must  be  admitted  that  the  history  of  no  particle  or 
process  that  we  could  possibly  meet  with  is,  in  fact,  a 
straight  world-line.  Thus  both  the  traditional  physics 
and  the  Special  Theory  of  Relativity  are  in  the  odd 
position  of  holding  that  the  geo-chronometry  of  physical 
Space-Time  is  Euclidean,  and  that  therefore  all  straight 
world-lines  are  Euclidean  straight  lines,  and  then 
admitting  that  the  history  of  no  actual  particle  or 
process  is  a  Euclidean  straight  line.  The  universal 
force  of  gravitation  thus  appears  as  a  hypothesis  to 
account  for  this  universal  divergence.  It  must  be 
admitted  that  this  hardly  inspires  confidence. 

Now  the  Euclidean  hypothesis  is  only  one  of  three 
possibilities  ;  the  other  two  being  the  hyperbolic  and 
the  elliptic,  as  described  earlier  in  this  chapter.  These 
three  types  of  hypothesis  agree  in  the  important  respect 
that  anv  manifold  which  has  either  of  these  three 
structures  is  homaloidal.  This  means  roughly  that  the 
structure  of  any  finite   region   of  the  manifold  will   be 


484  SCIENTIFIC   THOUGHT 

the  same  as  that  of  any  other,  no  matter  where  that 
region  be  situated  within  the  whole.  It  is  only  on  these 
three  hypotheses  that  this  is  true.  Obviously  then,  the 
next  step  would  be  to  suppose  that  the  geo-chronometry 
of  physical  Space-Time  is  not  Euclidean,  but  is,  never- 
theless, homaloidal.  We  might  then  suppose  that  the 
histories  of  actual  particles  and  processes  in  gravi- 
tational fields  are  straight  world-lines,  though  these 
are  not  Euclidean,  but  hyperbolic  or  elliptic,  straight 
lines.  If  this  view  of  the  structure  of  physical  Space- 
Time  would  account  for  all  gravitational  phenomena, 
without  our  having  to  introduce  gravitation  ad  hoc  as 
a  special  but  universal  force,  it  would  obviously  be 
reasonable  to  adopt  it. 

Now  we  can  deal  with  gravitational  fields  on  such 
a  hypothesis,  so  long  as  we  confine  ourselves  to 
regions  of  physical  Space-Time  which  are  not  occupied 
by  physical  events.  For  here  we  are  concerned  with 
regions  for  which  the  analogy  to  Laplace's  equation 

Wv     d*v     <^  =  0 

dx2     d/2     ds* 

holds.  This  analogy,  as  we  saw  in  Part  I,  is  the 
vanishing  of  the  Modified  Riemann-Christoffel  Tensor 
throughout  the  region.  But,  when  we  are  concerned 
with  regions  occupied  by  physical  events,  we  require 
an  analogy,  not  to  Laplace's,  but  to  Poisson's  equation 

d2v     d'2v     d2v  _ 

where  p  is  the  density  of  the  "  filling  "  of  the  region. 

Now  the  analogy  to  this  is  not  the  vanishing  of  the 
Modified  Tensor,  but  the  equating  of  it  to  another 
tensor,  which  expresses  the  "  filling  "  of  the  region  under 
discussion.  And  we  must  remember  that,  under  the 
heading  of  "  occupied  regions"  of  physical  Space-Time 
we  have  to  include  not  merely  those  which  contain 
matter  in  the  ordinary  sense  of  the  word,  but  also  those 


SPACE-TIME  485 

which  contain  only  radiant  energy  of  any  kind,  since 
this  also  gravitates. 

It  is  evident  then,  that  if  we  want  to  explain  gravi- 
tational phenomena  by  reference  to  the  spatio-temporal 
structure  of  Nature,  we  cannot  do  this  by  ascribing  a 
homaloidal  structure  to  physical  Space-Time.  We  must 
assign  different  values  to  the  Modified  Tensor  for 
different  regions  ;  since  some  regions  are  physically 
occupied  and  others  are  not,  whilst  of  those  which  are 
physically  occupied,  some  are  more  densely  filled  than 
others.  The  vanishing  of  the  Unmodified  Tensor,  every- 
where and  everywhen,  would  imply  that  physical  Space- 
Time  is  homaloidal  and  Euclidean  ;  the  vanishing  of 
the  Modified  Tensor  only,  everywhere  and  everywhen, 
would  imply  that  physical  Space-Time  is  homaloidal, 
though  not  Euclidean  ;  but,  since  it  is  certain  that 
neither  of  these  alternatives  is  compatible  with  explain- 
ing gravitational  phenomena  in  terms  of  the  structure 
of  physical  Space-Time,  any  such  theory  must  assume  a 
non-homaloidal  structure  for  physical  Space-Time.  The 
only  property  which  remains  common  to  all  regions  of 
physical  Space-Time  is  that  the  square  of  the  spatio- 
temporal  separation  of  any  pair  of  adjacent  events  is  a 
homogeneous  quadratic  function  of  the  differences 
between  the  values  of  their  four  corresponding  co- 
ordinates in  any  frame. 

Now  it  does  seem  to  me  immensely  important  that 
we  should  not  slur  over  this  last  transition.  The 
passage  from  one  to  another  view  of  the  structure  of 
physical  Space-Time,  so  long  as  this  structure  is  assumed 
still  to  be  homaloidal,  is  of  no  particular  philosophical 
importance.  But  the  jump  from  a  homaloidal  to  a 
non-homaloidal  structure  ought  not  to  be  taken  lightly. 
It  does  involve,  so  far  as  I  can  see,  the  definite  abandon- 
ment of  a  certain  concept  of  Nature,  which  has  so  far 
been  universally  held.  This  is,  roughly  speaking, 
the  concept  of  Space  and  Time  as  inert  indifferent 
"containers,"  distinguishable  from  the  material  which 


,S..  SCIENTIFIC   THOUGHT 

happens  to  occupy  them.  This  view  appears  in  a  very 
crude  form  in  the  Absolute  theories  of  Space  and  Time. 
But  it  survives,  and  can  be  restated,  in  the  Relational 
theories  and  in  the  Special  Theory  of  Relativity.  The 
cash  value  of  the  distinction  between  physical  Space- 
Time  and  its  contents  is  that  the  sum  total  of  physical 
events  has  a  certain  spatio-temporal  structure  which  is 
the  same  always  and  everywhere,  and  is  independent 
of  qualitative  differences  between  events.  One  region 
of  Space-Time  is  differentiated  from  another  only  by 
qualitative  differences  in  the  filling  of  the  two  regions. 
Now  any  such  view  vanishes  altogether  on  the  General 
Theory  of  Relativity.  It  has  been  said  that  the  Special 
Theory  broke  down  the  distinction  between  Space  and 
Time,  and  that  the  General  Theory  broke  down  the 
distinction  between  both  and  Matter.  The  first  part  of 
the  statement  seems  to  me  very  loose,  since  the  distinc- 
tion between  spatial  and  temporal  isolation  remains 
for  every  observer.  The  Special  Theory  breaks  down, 
not  the  distinction,  but  the  isolation  of  space  and  time. 
But,  in  a  very  real  sense,  the  general  theory  does  break 
down  the  distinction  between  Space-Time  and  events. 

Now  I  do  not  make  this  an  objection  to  the  General 
Theory.  All  theories  are  but  ways  of  unifying  the 
observable  facts  under  concepts  ;  and  any  theory  that 
succeeds  in  doing  this  is  permissible.  I  only  want  the 
reader  to  be  quite  clear  that  there  is  here  a  radically 
new  way  of  looking  at  Nature.  I  think  it  will  always 
be  possible  to  unify  the  same  facts  by  the  more  usual 
scheme  of  a  homaloidal  Space-Time  and  suitable  fields 
of  force.  In  so  far  as  this  fits  in  better  with  our 
traditional  way  of  looking  at  things,  this  is  to  be 
preferred.  But  I  should  suppose  that  its  advantages 
are  only  temporary  ;  thai  they  will  vanish  as  we  become 
more  familiar  with  alternative  concepts  ;  and  that  our 
preference  for  homaloidal  Space-Time,//^  material  and 
fields  of  force,  has  no  greater  ultimate  significance  than 
our  preference  for  beginning  dinner  with  hors  d'ceuvres 


SPACE-TIME  487 

and  ending  it  with  coffee  over  taking  it  in  the  opposite 
order. 

The  following  additional  works    may  be    consulted 
with  advantage  : 

A.    N.    Whitehead,    Principles   of    Natural    Knowledge, 

Chaps.  IX.  to  XIII. 
,,  Concept  of  Nature,  Chaps.  V.  to  IX. 

,,  Mathematical   Concepts  of  the  Material 

World.     (Proc.  Roy.  Soc,  vol.  205.) 
,,  ,,  The  Principle  of  Relativity.* 

H.  Minkowski,  Raum  und  Zeit. 
H.  Weyl,  Space,  Time,  and  Matter. 

A.    S.    Eddington,    Report   on    the    Relativity    Theory    of 

Gravitation. 
,,  ,,  Space,  Time,  and  Gravitation. 

A.  A.  Robb,  A   Theory  of  Time  and  Space. 

,,  ,,      Absolute  Relations  of  Time  and  Space. 

S.  Alexander,  Space,  Time,  and  Deity,  Bk.  I. 

B.  Riemann,  Ueber  die  Hypothesen  welche  der  Geometrie  zu 

Grunde  liegen. 

D.  M.  Y.  Sommerville,  Non-Euclidean  Geometry. 

E.  H.  Neville,  The  Fourth  Dimension. 


*  This  most  important  work  appeared  while  the  present  book  was  in  the 
press.  Whitehead  argues  that  Space-Time  must  be  homaloidal ;  and  he 
deduces  the  characteristic  results  of  the  General  Theory  of  Relativity  from 
a  modification  of  the  traditional  law  of  gravitation,  and  not  from  supposed 
variations  in  the  structure  of  different  regions  of  Space-Time. 


CHAPTER    XIII 

"  .   .   .   .  quam  scdcm  Somnia  vulgo 
Vana  tcncrc  fcrunt,  foliisque  sub  omnibus  hacrent. 
Multaque  praeterea  variarum  monstra  ferarum, 
Centauri  in  foribus  stabulant,  Scyllaeque  biformes, 
Et  centumgeminus  Briareus,  ac  bellua  Lernac 
Horrendum  stridens,  flammisque  armata  Chimaera. 

•  ••■••  •  * 

Et  ni  docta  comes  tenues  sine  corpore  vitas 
Admonuit  volitare  cava  sub  imagine  formae, 
Trruat,  et  frustra  ferro  diverberet  umbras." 

(Virgil,  Mneid,  VI.) 

The  Physiological  Conditions  of  Sensations,  and  the 
Ontological  Status  of  Sensa 

At  the  end  of  Chapter  VIII  we  said  that  the  Critical 
Scientific  Theory  of  physical  objects  and  our  perception 
of  them  left  two  main  problems  on  hand.  One  was  to 
clear  up  the  meanings  of  physical  place,  shape,  size,  date, 
diiration,  etc.,  and  to  establish  their  cash  value  in  terms 
of  those  corresponding  characteristics  of  our  sensa,  on 
which  they  must  ultimately  be  founded.  This  task  I 
have  performed  to  the  best  of  my  ability  in  the  last 
four  chapters.  The  other  problem  was  to  elucidate  the 
very  obscure  statement  that  external  physical  objects 
and  our  own  bodies  "jointly  produce  in  us  the  sensa 
by  which  these  external  bodies  appear  to  us."  Probably 
any  solution  of  this  problem  will  be  found  to  favour 
(if  not  actually  to  require)  some  particular  view  as  to 
the  nature  of  sensa  and  their  ontological  status  in  the 
universe.  So  this  book  will  fitly  end  with  an  attempt 
to  define  the  meaning  and  estimate  the  truth  of  the 
above  statement. 

488 


CONDITIONS   AND   STATUS   OF   SENSA     489 

Almost  every  phrase  in  this  statement  bristles  with 
ambiguities.  (1)  The  notion  of  "joint"  production 
will  be  found  to  be  far  from  clear,  and  its  possible 
alternative  meanings  will  have  to  be  analysed.  (2)  We 
shall  have  to  raise  the  question  whether  the  conditions 
jointly  produce  sensations,  or  sensa,  or  both.  (3)  The 
word  "production"  is  highly  ambiguous,  even  when 
we  have  settled  what  we  mean  by  "joint  production." 
It  may  mean  a  kind  of  creation  out  of  nothing,  or  a 
process  of  ordinary  causation,  or  a  process  of  selection 
out  of  a  mass  of  pre-existing  material. 

These  questions  are  not,  of  course,  independent  of 
each  other.  It  is  pretty  certain  that  any  answer  that  is 
given  to  one  of  them  will  cut  out  certain  answers  to  the 
rest,  and  will  favour  certain  other  answers  to  them. 
But  we  must  start  by  treating  each  question  separately, 
and  then  try  to  view  the  results  of  our  separate  discus- 
sions as  a  whole. 

Without  prejudice  to  the  conclusions  that  we  may 
reach  when  we  discuss  question  (2),  we  shall  find  it 
best  to  start  by  saying  that  processes  in  external  bodies 
and  in  our  own  jointly  condition  sensations,  rather  than 
that  they  jointly  condition  sensa.  On  our  view  a 
sensation  is  a  complex  whole,  in  which  an  objective 
factor  (the  sensum)  and  a  subjective  factor  (the  act  of 
sensing)  can  be  distinguished.  Whether  either  of  these 
can  exist  apart  from  the  other  we  do  not  at  present 
either  assert  or  deny.  But  this  at  least  is  certain  ;  all 
the  sensa  of  whose  existence  I  am  directly  aware  are 
constituents  of  my  sensations,  and  all  the  sensa  of  whose 
existence  other  observers  tell  me  are  constituents  of 
their  sensations.  Hence  any  evidence  that  I  may  think 
I  have  that  certain  physical  and  physiological  processes 
are  necessary  and  sufficient  to  produce  sensa  is  prima 
facie  evidence  that  they  are  necessary  and  sufficient  to 
produce  sensations.  It  may  be  that  they  can  only  pro- 
duce sensations  by  producing  sensa,  but  this  question 

must  be  left  aside  for  the  present.     So,  to  start  with, 

2  1 


490  SCIENTIFIC   THOUGHT 

we  shall  talk  about  the  production  of  sensations,  and 
shall  leave  it  an  open  question  whether  this  involves 
the  production  of  sensa. 

The  Notion  of  Joint  Production. — I   think  that  the 
view  of  educated  common-sense  is  that  there  are  certain 
events,    very  definitely  localised    in   Time   and   Space, 
which  happen  in  my  brain  and  are  the  necessary  and 
sufficient  conditions   of   the  occurrence  of  each  of  my 
sensations.     If  I  sense  a  practically  uniform  sense-object, 
it  is  thought  that  there  is  a  practically  uniform  process 
in  some  part  of  my  brain,   which  lasts  as  long  as  the 
sensation,  and  is  its  necessary  and  sufficient  condition. 
Some,  but  not  all,  of  these  brain-events  are  supposed  to 
be  due  to  external  physical  events,  such  as  the  striking 
of    bells,    the    lighting   of    matches,    etc.     Others    are 
supposed  to  be  due  to  internal  causes.     It  is  held  that, 
even  when  a  sensation  is  due  to  some  external  cause, 
such  as  the  striking  of  a  bell,  this  is  never  a  sufficient 
condition.     Something  must   be  transmitted    from   the 
external  object  to  the  sense-organ,  and  something  must 
be    transmitted    from    the   sense-organ    to   the    brain. 
Otherwise  the  brain-event,  which  is  supposed  to  be  the 
necessary  and  sufficient  condition  of  the  occurrence  of 
the  sensation,   will   not  happen,  and  so  the  sensation 
will  not  be  produced.      I  propose  first  to  introduce  some 
necessary  technical  terms  for  stating  the  common-sense 
view ;    then    to    clear    up    certain    ambiguities    in    the 
notion    of    necessary    and    sufficient    conditions ;     and 
then   to  ask  in  what  sense,  if  any,  there   is   reason  to 
believe  that  certain  definitely  localised  brain-events  are 
the   necessary  and  sufficient  conditions  of  each  of  my 
sensations. 

(a)  Originative,  Transmissive  and  Productive  Conditions. 
— On  the  ordinary  view,  the  production  of  a  sensation 
by  an  external  physical  event  requires  the  fulfilment  of 
at  least  three  types  of  condition.  Let  us  take  the  case 
of  hearing  a  certain  stroke  of  a  certain  bell,     (i)  The 


CONDITIONS   AND   STATUS   OF   SENSA     491 

bell  must  be  struck,  or  I  shall  not  hear  any  sound 
characteristic  of  it  at  the  time.  This  may  be  called  the 
originative  condition.  (2)  Unless  there  be  air  or  some 
other  material  medium  between  my  body  and  the  bell 
I  shall  hear  nothing,  even  though  the  bell  be  struck. 
There  are  excellent  reasons,  some  of  which  have  been 
mentioned  in  Chapter  X,  for  holding  that  something 
travels  with  a  finite  velocity  from  where  the  bell  is, 
through  the  medium,  to  my  body.  This  may  be  called 
an  external  transmissive  condition  for  my  sensation  of 
sound.  (3)  We  have  reason  to  think  that,  even  though 
the  originative  and  the  external  transmissive  conditions 
for  the  occurrence  of  a  sensation  be  fulfilled,  no  sensa- 
tion will  happen  unless  a  certain  nerve  be  intact, 
leading  from  the  sense-organ  to  the  brain.  And  it  is 
generally  held  that  the  process  in  the  nerve  is  trans- 
missive in  character.  The  evidence  for  this  is  fairly 
good,  (a)  If  the  nerve  be  cut  at  any  point,  no  sensation 
of  the  kind  will  henceforth  be  experienced.  Its  integrity 
is  therefore  a  necessary  condition.  (/3)  It  is  possible  to 
note  the  time  when  an  external  stimulus  acts  on  a  sense- 
organ,  and  to  get  the  patient  to  press  a  button  as  soon 
as  he  can  after  getting  the  sensation.  If  this  button 
stops  a  clock,  and  the  clock  be  delicate  enough,  there 
will  always  be  a  lapse  of  time  between  the  two  events. 
This,  of  course,  does  not  conclusively  prove  that  there  is 
any  lapse  of  time  between  the  reception  of  the  stimulus 
and  the  occurrence  of  the  sensation,  since  the  observed 
lapse  might  simply  be  the  time  between  having  the 
sensation  and  pressing  the  button.  We  have  direct 
experimental  evidence  that  a  process,  which  takes  time, 
travels  along  motor-nerves  to  muscles.  So  far  as  I  am 
aware,  we  have  no  direct  experimental  evidence  that 
a  process  which  takes  time  travels  up  a  sensory  nerve 
from  the  stimulated  organ  to  the  brain.  Still,  it  is 
reasonable  to  suppose  that  this  is  so,  and  it  is  in  fact 
always  assumed.  On  this  assumption,  we  may  say 
that  there  is  an  internal  transmissive  conditio)i  which   is 


492  SCIENTIFIC  THOUGHT 

necessary  if  I  am  to  have  here  and  now  a  sensation  of 
the  sound  characteristic  of  this  bell. 

A  transmissive  condition  might  be  defined  as  follows  : 
It  is  a  process  which  is  practically  uniform  in  character, 
and  is  immanent.  This  means  that  it  is  divisible  into 
successive  slices  which  are  qualitatively  very  much 
alike.  They  differ  only  in  date  and  place,  and  the 
nearer  they  are  together  in  date  the  nearer  they  are 
together  in  place.  And  the  character  of  each  slice  is 
the  necessary  and  sufficient  condition  of  the  character 
of  the  next  slice. 

(4)  Now,  at  a  certain  stage,  viz.,  when  the  process 
has  reached  a  certain  part  of  the  brain,  it  is  supposed 
that  a  transeunt  causal  relation  supervenes.  This  means 
that  there  is  a  certain  brain-event,  which  is  continuous 
with  the  immanent  process,  and  is  the  necessary  and 
sufficient  condition  of  an  event  of  an  entirely  different 
kind,  belonging  to  a  different  "substance"  or  strand  of 
history.  This  event  is  a  sensation,  which  is,  of  course, 
an  event  belonging  to  that  substance  or  strand  of 
history  which  we  call  the  observer's  mind.  Even  if 
the  transmissive  process  in  the  body  should  continue 
beyond  the  point  at  which  the  sensation  occurs  (as  it  no 
doubt  does  when  the  sensation  is  followed  by  a  motor- 
reaction),  we  should  say  that  the  sensation  belonged  to 
an  entirely  different  series  from  the  later  events  in  the 
transmissive  process  in  the  body.  If  the  internal  trans- 
missive process  ends  up  in  the  brain,  we  say  that  a 
certain  slice,  which  ends  it,  is  the  productive  condition  of 
the  sensation.  If  the  internal  transmissive  process 
continues  after  the  sensation  has  been  produced,  we 
must  say  that  the  productive  condition  of  the  sensation 
is  a  certain  intermediate  slice  of  this  process. 

It  seems  to  be  commonly  supposed  that  the  slice  of 
the  internal  transmissive  process  which  is  the  productive 
condition  of  the  sensation  must  be  extremely  thin  in  time, 
i.e.,  that  it  cannot  stretch  back  from  the  date  at  which 
the  sensation  begins  for  any  appreciable  time.     We  shall 


CONDITIONS   AND   STATUS   OF   SENSA     493 

see  in  the  next  sub-section  that  this  belief  is  based  on 
tacit  assumptions,  which  are  far  from  self-evident  and 
cannot  be  proved. 

It  is  held  that  all  sensations  have  originative  and 
productive  conditions,  even  though  the  sensation  be 
"hallucinatory."  If  I  "see  stars,"  this  sensation  is 
presumably  due  to  a  certain  brain-event,  which  is  its 
productive  condition.  If  this  event  can  be  traced  to 
changes  of  blood-pressure  in  my  eyes  or  to  something 
happening  in  my  liver,  these  would  count  as  originative 
conditions.  Whether  all  sensations  have  transmissive 
conditions  is  uncertain.  It  is  certain  that  most  of  them 
have,  and  probably  the  difference  between  those  which 
obviously  do,  and  those  which  apparently  do  not,  is  a 
difference  of  degree  rather  than  one  of  kind.  It  is 
perfectly  obvious  that  an  ordinary  sensation  of  light  or 
of  sound  has  a  long  train  of  transmissive  conditions, 
both  external  and  internal.  It  is  fairly  clear  that  a 
sensation  of  itching  in  the  finger,  or  of  stomach-ache, 
has  internal,  though  not  external,  transmissive  condi- 
tions. But,  if  an  auditory  or  visual  experience  were 
started  by  a  change  of  blood-pressure  in  a  part  of  the 
brain  immediately  adjacent  to  that  in  which  the  pro- 
ductive conditions  of  such  experiences  are  localised, 
the  transmissive  process  would  be  so  short  as  to  be 
evanescent.  Still,  we  are  probably  justified  in  saying 
that  the  vast  majority  of  sensations  have  originative, 
transmissive,  and  productive  conditions. 

We  must  next  notice  (a)  that  some  kinds  of  sensa- 
tions have  only  internal  originative  (and  therefore  internal 
transmissive)  conditions.  These  are  the  sensations  con- 
nected with  our  somatic  sense-histories,  such  as  feelings 
of  headache,  stomach-ache,  etc.,  and  kinesthetic  sensa- 
tions. It  is  a  well-known  fact  that  the  places  of  somatic 
sensa  in  their  fields  are  not  always  a  safe  guide  to  the 
places  of  their  originative  conditions  in  physical  space. 
A  toothache  occupies  a  certain  sensible  place  in  the 
total  somatic  field  of  the   moment,   and   it  may  go  on 


494  SCIENTIFIC   THOUGHT 

occupying  similar  places  in  successive  somatic  fields. 
These  somatic  places  will  be  correlated,  through  past 
experience,  with  certain  places  in  the  movement-con- 
tinuum, which  are  optically  occupied  by  the  visual 
appearances  of  my  tooth  and  physically  occupied  by 
certain  scientific  events  which  dentists  profess  to  know 
about.  As  a  general  rule  the  part  of  my  body  which 
thus  corresponds  to  a  given  sensible  place  in  my  somatic 
fields  is  the  seat  of  those  scientific  events  which  originate 
the  somatic  sensum  which  occupies  this  sensible  place. 
E.g. ,  if  a  feeling-  of  toothache  be  located  in  a  certain 
sensible  place  in  my  somatic  field,  my  dentist  will 
generally  find  something  wrong  with  the  particular  tooth 
which  I  point  out  to  him  as  occupying  the  physical  place 
correlated  with  this  sensible  place.  Sometimes,  how- 
ever, he  will  find  that  nothing  relevant  is  happening  in 
this  tooth,  but  that  the  originative  conditions  of  my 
toothache  are  located  in  a  part  of  physical  space  which 
is  correlated  with  a  quite  different  part  of  my  somatic 
field  from  that  in  which  the  feeling  of  toothache  is 
located. 

(/3)  Another  important  fact  is  that,  although  experi- 
ences of  a  certain  kind  may  generally  have  external 
originative  (and  therefore  partly  external  transmissive) 
conditions,  yet  experiences  of  the  same  general  character 
may  sometimes  be  originated  by  purely  internal  condi- 
tions. This  is  best  illustrated  by  experiences  of  the 
visual  type.  Generally  these  are  originated  by  some 
external  luminous  body,  which  starts  waves  that  travel 
to  the  eye  and  there  set  up  a  disturbance  which  travels 
up  the  optic  nerve  to  the  brain.  But  in  dreams  we  have 
perfectly  distinct  visual  experiences,  very  much  like 
those  of  waking  life,  although  our  eyes  are  shut  and 
we  may  be  in  a  perfectly  dark  room.  Again,  visual 
images  are  rather  like  visual  sensa ;  and  we  can 
apprehend  them  best  in  the  dark  and  with  our  eyes  shut. 
Thus  it  is  evident  that  the  originative  conditions  for 
experiences  of  the  visual  type  need  not  be  external  to 


CONDITIONS   AND   STATUS   OF   SENSA     495 

the  body  in  every  case.  It  is  worth  noticing  that  here 
presumably  the  internal  originative  conditions  are  ex- 
tremely unlike  the  normal  external  originative  condi- 
tions. The  inside  of  the  body  is  quite  dark  ;  so  that, 
whatever  be  the  internal  conditions  which  originate  the 
visual  experiences  of  dreams,  they  must  be  extremely 
different  from  the  luminous  events  which  are  the  origi- 
native conditions  of  normal  visual  sensations. 

I  think  that  visual  experiences  provide  the  only 
perfectly  clear  case  where  very  similar  experiences  are 
originated  sometimes  from  without  and  sometimes  from 
within,  and  where  the  two  kinds  of  originative  condition 
are  extremely  different  in  character.  If  we  take  auditory 
experiences,  the  facts  are  much  less  certain.  It  is  quite 
true  that  I  have  auditory  experiences  in  dreams,  and 
that  these  are  very  much  like  those  of  waking  life, 
which  are  originated  by  events  outside  my  body.  It 
is  also  true  that  many  people  can  apprehend  auditory 
images,  and  that  these  are  a  good  deal  like  auditory 
sensa.  So  far,  the  facts  about  auditory  experiences 
resemble  those  mentioned  above  about  visual  experi- 
ences. But  now  we  have  to  notice  two  important 
differences  :  (i)  It  is  much  harder  to  be  sure  that  the 
auditory  experiences  of  dreams  are  not  originated 
externally  than  to  be  sure  that  the  visual  experiences 
of  dreams  are  not  thus  originated.  Rooms  are  dark 
and  our  eyes  are  shut  when  we  are  asleep.  But  we 
cannot  shut  our  ears,  and  few  rooms  are  wholly  free 
from  those  physical  events  which  would  suffice  to 
originate  auditory  experiences  in  a  waking  man.  It  is 
therefore  uncertain  whether  the  auditory  experiences 
of  dreams  be  not  originated  externally. 

(ii)  As  I  have  said  above,  our  bodies  are  dark  inside, 
i.e.,  there  are  no  physical  events  in  them  of  a  kind  which 
would  suffice  to  originate  normal  visual  sensations  in  a 
waking  man.  But  it  cannot  be  said  that  our  bodies  are 
silent  inside.  All  sorts  of  processes  are  going  on  in  them, 
which  would  be  quite  capable  of  producing,  in  a  mild 


496  SCIENTIFIC  THOUGHT 

form,  vibrations  of  the  kind  which  strike  a  waking  man's 
ears   when    he    hears   an    externally    originated   sound. 
Moreover,  our  bones  are  capable  of  transmitting  sound- 
waves just  as  well  as  air  or  any  other  material  medium. 
Thus,  even  if  there  be  auditory  experiences  which  are 
originated  internally,  it  cannot  be  confidently  asserted 
that  their  originating  conditions  are  different  in  kind 
from  those  of  externally  originated  auditory  sensations. 
E.g.,  "  head-noises  "  may  quite  well  be  noises  of  perfectly 
normal  origin,  which  are  heard  by  the  sufferer  and  not 
by  others,  simply  because  his  brain    is   nearer  to  and 
better  connected  with  their  originative  conditions  than 
the  brain  of  anyone  else  can  be.     Thus  we  are  reduced 
to  the  apprehension  of  auditory  images,  as  the  one  clear 
example  of  auditory  experiences  whose  originative  con- 
ditions are  almost  certainly  internal  and  almost  certainly 
different  in  character  from  the  external  originative  con- 
ditions of    normal    auditory    sensations.      I    am    indeed 
prepared  to  believe  that  some  of  the  auditory  experiences 
of  dreams  and  disease  probably  do  originate  internally, 
and   trom  events  which  are    not   like   ordinary  sound- 
vibrations  ;  but  I  take  this  view,  rather  on  the  ground 
of  analogy  with  visual  experiences,  than  on  account  of 
any  purely  auditory  phenomena  known  to  me. 

(y)  The  question  might  be  raised  whether  there  be 
any  type  of  sensible  experience  which  is  always  originated 
by  external  conditions.  I  should  not  care  to  assert 
anything  so  sweeping  ;  but  I  think  it  may  be  said  that 
tactual  experiences  have  a  fair  claim  to  this  position. 
Tactual  experiences  are  far  less  common  in  dreams  than 
are  visual  or  auditory  experiences.  Tactual  images  are 
extremely  rare.  If  they  exist  at  all,  I  certainly  do  not 
apprehend  them  myself,  and  I  have  not  met  anyone  else 
who  admitted  doing  so.  Moreover,  it  is  quite  impossible 
to  prove  that  such  "hallucinatory"  tactual  experiences 
as  there  are,  do  not  originate  through  actual  contact 
between  the  skin  and  other  bodies.  For  it  is  certain 
that  throughout  the  whole  of  our  waking  and  sleeping 


CONDITIONS   AND   STATUS   OF   SENSA     497 

life  parts  of  our  skin  are  in  contact  with  other  bodies. 
Again,  there  must  always  be  contact  between  various 
parts  of  our  internal  organs  ;  and  between  some  of  these 
and  the  blood,  undigested  food,  and  so  on.  Thus,  I 
think  it  would  be  very  difficult  to  show  even  that  any 
tactual  experience  was  not  originated  by  contact  with 
external  objects,  and  impossible  to  show  that  such 
experiences  are  ever  originated  except  by  contact  of 
some  kind,  either  internal  or  external.  This  is  doubtless 
why  most  of  us  agree  with  the  Apostle  Thomas,  who 
thought  that  touch  was  the  best  test  for  distinguishing 
normal  from  hallucinatory  perceptions. 

The  theoretical  importance  of  the  points  which  we 
have  just  been  raising  will  be  seen  in  a  later  sub- 
section, where  we  shall  consider  how  far  we  are  justified 
in  holding  that  certain  brain-events  are  sufficient  con- 
ditions of  every  sensation.  Before  ending  the  present 
sub-section  we  must  discuss  one  point  about  originative 
and  transmissive  conditions.  It  is  fairly  obvious  what 
part  of  the  whole  process  is  to  be  taken  as  the  productive 
condition  of  a  sensation.  At  least  it  is  obvious  where 
it  ends  ;  for  it  ends  where  the  sensation  begins.  Exactly 
how  far  back  it  stretches  from  this  date  is  less  de- 
terminate, and  will  need  further  discussion  later  on. 
But  it  is  much  less  clear  what  stage  in  the  long  process, 
which  ends  up  with  a  certain  sensation,  ought  to  be 
taken  as  the  originative  condition  of  that  sensation.  Let 
us  return  for  a  moment  to  the  example  of  the  striking 
bell.  We  took  the  stroke  of  the  bell  as  the  originative 
condition  of  the  auditory  sensation.  But  it  mi-ght  fairly 
be  asked  whether  we  should  not  have  had  just  as  good 
reasons  for  taking  an  earlier  or  a  later  stage  in  the  total 
process  as  the  originative  condition.  Whenever  the 
process  passes  from  one  substance  to  another  of  a 
different  kind,  and  changes  sharply  in  character,  there 
is  an  outstanding  slice  of  it  which  might  plausibly  be 
taken  as  the  originative  condition.  Now  one  such  point 
is  where  and  when  the  transmissive  process  of  sound- 


4<)8  SCIENTIFIC   THOUGHT 

waves  in  the  air  ends  and  the  transmissive  process  of 
nervous  disturbance  in  the  auditory  nerve  begins.  Why 
should  we  not  take  a  terminal  slice  of  the  external 
transmissive  process  as  the  originative  condition  of  the 
sensation?  Again,  the  process,  of  which  one  stage  is 
the  stroke  of  the  bell,  does  not  begin  at  that  stage. 
Probably  a  man  struck  the  bell  ;  a  contraction  in  his 
muscles  caused  the  blow  ;  a  nervous  current  in  a  motor- 
nerve  caused  the  contraction  ;  and  so  on  to  infinity. 
Why  should  we  not  take  one  of  the  innumerable  stages 
which  precede  the  stroke  as  the  originative  condition 
of  the  sensation  ? 

To  these  questions  I  answer  (i)  that  we  do  recognise 
the  last  stage  of  the  external  transmissive  process  as 
important,  and  do  mark  it  out  by  the  special  name  of 
stimulus.  For  the  physiologist  and  the  physiological 
psychologist  this  is  the  earliest  outstanding  part  of  the 
total  process  which  is  of  special  importance.  (2)  The 
importance  of  the  stage  which  immediately  precedes 
the  external  transmissive  process  arises  from  its  common 
relation  to  a  number  of  different  observers.  If  there  be 
a  number  of  observers  listening  to  the  same  bell,  there 
are  as  many  different  external  and  internal  transmissive 
conditions,  stimuli,  and  productive  conditions,  as  there 
are  observers.  But  all  these  different  processes  diverge 
from  a  common  centre  in  Space-Time,  and  at  this  centre 
is  located  the  physical  event  which  is  taken  to  be  the 
common  originative  condition  of  all  these  very  similar 
auditory  sensations.  (3)  We  can  see  how  closely  the 
notion  of  originative  conditions  is  bound  up  with  the 
fact  of  common  optical  and  other  centres  for  the  corre- 
sponding sensa  of  different  observers,  by  noting  how 
difficult  it  becomes  to  apply  this  notion  where  the  sensa 
of  different  observers  are  not  correlated  in  this  way. 
For  instance,  when  we  see  a  mirror-image  we  are 
doubtful  what  we  ought  to  regard  as  the  originative 
conditions  of  our  visual  sensations.  The  mirror-image 
is  a  partial  optical  object,  and  there  is  a  certain  place 


CONDITIONS   AND   STATUS   OF   SENSA     499 

behind    the    mirror   which    is    optically   occupied    from 
many,  though  not  from  all,  directions  by  sensa  belong- 
ing to  this  object.     A  child  or  a  cat  might  be  inclined 
to  suppose  that  this   place   is    physically  occupied    by 
those  events    which    are    the  common  originative  con- 
ditions of  all  the  sensations  whose  sensa  together  make 
up  the  optical  object.     But  the  incompleteness  of  such 
optical  objects   prevents  a   grown  man,    even   if  he   be 
ignorant  of  physics,  from  locating  the  originative  con- 
ditions  of  his  sensation    in    the  optical  place  of  these 
objects.     We  are  left  with  the  choice  of  events  in  the 
mirror  or  events  in  the  reflected  physical  object,  as  the 
originative  conditions  of  such  sensations  ;  and,  which- 
ever choice  we  make,  we  have  to  admit  that  the  place 
which  is  optically  occupied  by  our  visual  sensa  and  the 
place  which  is   physically  occupied  by  the  originative 
conditions  of  our  sensations  are  widely  separated.     If 
we  say  that  the  events  in  the    mirror  are  the  originative 
conditions  of  our  sensation,   we    must  remember   that 
they  will  not  originate  similar  sensations  in  observers 
in   all  directions,  as  the   normal   originative  conditions 
of  visual  sensa  do.     If  we  say  that  the  events  in   the 
reflected  physical   object  are  the  originative  conditions 
of  our  sensation,  we  must  remember  that,  unless  men- 
tion be  made  of  the  mirror  as  well,  we  cannot  account 
either  for  the  peculiar  optical  place  or  for  the  peculiar 
"  inversion  "  of  the  image-sensa. 

(fr)  Dependently  and  Independently  Necessary  Conditions. 
— As  I  have  said,  it  is  commonly  held  that  certain 
brain-events  are  the  necessary  and  sufficient  conditions 
of  the  occurrence  of  all  our  different  sensations.  We 
have  now  to  clear  up  the  notion  of  "necessary  and 
sufficient  conditions,"  and  to  see  in  what  sense,  if  any, 
it  is  true  that  brain-events  are  the  necessary  and 
sufficient  conditions  of  all  our  sensations.  A  number 
of  conditions  a,  b,  and  c,  are  said  to  be  severally 
necessary  and  jointly  sufficient  to  produce  an  event  x, 
if  (1)  whenever  they  are  all  present  .r  happens,  and  (2) 


500  SCIENTIFIC  THOUGHT 

whenever  they  are  not  all  present  x  does  not  happen. 
It  is  obviously  much  easier  to  be  sure  that  a,  b,  and  care 
severally  necessary  than  that  they  are  jointly  sufficient 
to  produce  x.  If  we  can  omit  in  turn  a,  b,  and  c,  and 
find  that  x  does  not  happen,  we  can  be  sure  that  each  of 
these  conditions  is  necessary.  But  it  is  far  from  safe 
to  assume  that,  because  abc  has  always  been  followed 
in  our  experience  by  x,  therefore  these  conditions  are 
jointly  sufficient  to  produce  x.  It  is  never  really 
possible  to  get  abc  in  complete  isolation  from  the  rest 
of  the  world,  and  there  may  have  been  some  fourth 
factor  d,  which  was,  in  fact,  present  in  all  the  cases  that 
fell  under  our  notice  and  was  necessary  for  the  pro- 
duction of  x.  Statements  that  such  and  such  conditions 
are  jointly  sufficient  to  produce  a  certain  result  should 
therefore  always  be  viewed  with  suspicion. 

If  abc  be  sufficient  to  produce  x,  it  follows  that  no 
other  factor  (unless  it  be  simply  a  constituent  of  one  of 
the  factors  a,  b,  or  c,  or  a  combination  of  them,  such  as 
ab),  can  strictly  be  necessary  to  produce  x.  For  to  say 
that  abc  is  sufficient  to  produce  ,r,  is  to  say  that  whenever 
abc  happens  x  follows.  Hence  both  abed  and  abed  will 
be  followed  by  x,  whatever  d  may  be.*  And  if  x  follows 
in  the  absence  of  d,  as  it  does  in  the  case  abed,  d  cannot 
be  necessary  for  the  occurrence  of  x.  If  then  a  certain 
brain-event  be  really  sufficient  to  produce  a  certain 
sensation  (say  that  of  the  sound  characteristic  of  a 
certain  bell),  the  existence  of  the  bell  and  the  air,  and 
the  occurrence  of  a  stroke  on  the  bell,  and  so  on,  cannot 
be  strictly  necessary  to  produce  this  sensation.  Yet  we 
should  commonly  say  that  the  striking  of  the  bell,  and 
the  other  conditions  which  we  have  enumerated,  are 
necessary,  if  that  particular  noise  is  to  be  sensed  at 
that  particular  time.  Our  ground  for  this  statement  is 
that  we  believe  that  no  such  sensation  would  have 
happened  then,  if  no  bell  had  existed,  and  if  it  had  not 
been  struck  shortly  before. 

*  Here  "  d"  simply  stands  for  "  the  absence  of  d." 


CONDITIONS   AND   STATUS   OF   SENSA     501 

It  is  clear  from  this  that  we  use  the  word  "  necessary  " 
in  two  different  senses.  In  one  of  them,  nothing  can 
be  necessary  to  produce  an  event  unless  it  be  contained 
in  the  smallest  set  of  conditions  which  will  jointly 
suffice  to  produce  the  event.  In  the  other,  many  factors 
which  are  not  contained  in  the  smallest  set  of  conditions 
which  will  jointly  suffice  to  produce  an  event  are  yet 
said  to  be  necessary  for  its  production.  We  must,  in 
fact,  distinguish  between  independently  and  dependently 
necessary  conditions.  If  a  certain  brain-event  be  really 
sufficient  to  produce  the  sensation  of  the  sound  of  a 
certain  bell,  then  the  striking  of  the  bell,  the  disturbance 
of  the  air,  and  so  on,  are  only  dependently  necessary 
to  the  production  of  this  sensation.  That  is,  they  are 
necessary  to  produce  the  sensation  only  in  so  far  as 
they  are  necessary  to  produce  the  whole,  or  some  part 
of,  that  brain-event  which  is  sufficient  to  produce  the 
sensation.  We  may  say  in  general  that  a  is  a  depend- 
ently necessary  condition  of  the  event  jt,  if  a  be  necessary 
to  produce  the  whole,  or  some  part  of,  the  conditions 
which  are  independently  necessary  and  jointly  sufficient 
to  produce  x. 

Now  a  very  important  question  at  once  arises. 
Can  a  certain  event  a  be  both  dependently  and  independ- 
ently necessary  to  produce  x?  I  think  that  this  would 
commonly  be  denied  ;  but  we  shall  see  in  a  moment 
that  it  can  only  be  denied  on  the  basis  of  certain 
assumptions  about  causation,  which  have  very  little 
plausibility  when  they  are  explicitly  stated.  What 
would  it  mean  to  say  that  a  is  both  dependently  and 
independently  necessary  to  produce  x?  It  would  mean 
that  a,  b,  and  c  (say)  were  all  needed  to  produce  x,  and 
that  they  are  all  that  is  needed,  but  that  a  plays  two 
parts.  It  produces  b  (say).  And  it  co-operates  with  b  and 
c  to  produce  x.  Supposing  it  to  be  possible  that  a  should 
play  both  parts,  and  supposing  it  to  be  certain  that  a  is 
dependently  necessary,  then  it  would  always  be  impossible 
to  know  that  a  is   not  also  independently   necessary  to 


502  SCIENTIFIC   THOUGHT 

produce  x.  For,  if  a  be  dependently  necessary  to 
produce  x,  there  is  some  factor  b  in  the  necessary  and 
sufficient  conditions  of  x,  which  cannot  occur  unless  a 
has  preceded.  Since  b  never  does  occur  without  a 
preceding,  we  cannot,  possibly  know  whether  /;  does  not 
need  the  co-operation  of  a  in  order  to  produce  x,  unless 
we  have  some  positive  reason  for  holding  that  a 
dependently  necessary  condition  of  an  event  cannot 
also  be  an  independently  necessary  condition  of  it. 

Let  us  apply  this  abstract  logical  argument  to  the 
concrete  case  of  the  auditory  sensation  of  the  noise  of  a 
i^rD*1       bell.     If  the  brain-event  which   produces  this  sensation 
fr'*^        could  not  occur  unless  the  bell  had  rung  a  little  earlier, 
*k  we  cannot  be  sure   that   the    brain-event    is  by  itself  a 

sufficient  condition  of  this  sensation,  unless  we  are  sure 
that  a  dependently  necessary  condition  cannot  also  be 
an  independently  necessary  condition  of  the  same  event. 
If  the  brain-event  never  happens  without  the  bell-event 
preceding,  we  cannot  possibly  know  that  the  brain- 
event,  without  the  co-operation  of  the  bell-event,  would 
suffice  to  produce  the  auditory  sensation,  unless  we 
have  some  a  priori  ground  for  this  belief.  For  the  only 
conclusive  empirical  ground  for  such  a  belief  would  be 
to  get  the  brain-event  without  the  bell-event,  and  to 
find  that  the  sensation  still  followed.  But,  ex  hypothesis 
we  cannot  get  just  this  kind  of  brain-event  without  a 
bell-event  preceding,  and  therefore  this  empirical  argu- 
ment cannot  be  used.  Conversely,  of  course,  we  cannot 
be  sure  that  the  bell-event  is  independently  as  well 
as  dependently  necessary  for  the  production  of  the 
sensation. 

Now,  is  there  any  a  priori  argument  against  the 
possibility  of  a  certain  condition  a  being  at  once 
dependently  and  independently  necessary  to  produce  a 
certain  event  x?  I  know  of  one  and  only  one  way  in 
which  such  a  possibility  could  be  refuted.  If  it  be  held 
that  all  the  independently  necessary  conditions  of  an 
event  must  be   contemporary  with    each   other,   it  will 


CONDITIONS   AND   STATUS   OF   SENSA     503 

follow  that  the  same  factor  cannot  be  both  independently 
and  dependently  necessary  to  produce  a  certain  event. 
For  the  dependently  necessary  condition  will  precede 
that  one  of  the  independently  necessary  conditions 
Which  it  produces.  Consequently  it  could  not  itself  be 
an  independently  necessary  condition,  if  these  have  all 
to  be  simultaneous  with  each  other. 

But  I  cannot  accept  the  premise  of  this  argument. 
(1)  It  does  not  seem  to  me  to  have  the  slightest  trace 
of  self-evidence.  I  think  there  is  something  to  be  said 
for  the  proposition  that  cause  and  effect  must  be 
continuous  with  each  other  in  time,  and  that  the 
complete  cause  must  itself  be  a  continuous  process  in 
time.  This,  however,  is  quite  compatible  with  a  and 
b  being  successive,  and  yet  both  of  them  being  inde- 
pendently necessary  conditions  of  x.  Suppose  that  the 
end  of  b  is  simultaneous  with  the  beginning  of  x,  and 
that  the  end  of  a  is  separated  by  a  lapse  of  time  from  the 
beginning  of  b.  Then  the  principle  of  the  temporal 
continuity  of  causation  would  only  show  that  the  com- 
plete cause  of  x  consists,  not  merely  of  a  and  b,  but  also 
of  some  process  which  bridges  the  gap  between  the 
.wo.  It  has  no  tendency  to  show  that  b  is  the  complete 
cause  of  x,  and  that  a  is  only  dependently  necessary. 

(2)  Apart  from  the  lack  of  self-evidence  in  the 
principle  that  all  the  independently  necessary  conditions 
of  an  event  must  be  simultaneous,  there  is  a  serious 
positive  objection  to  it.  We  have  seen  that  no  two 
events  are  intrinsically  simultaneous,  unless  they  also 
have  no  spatial  separation.  Events  which  are  separated 
in  the  timeless  space  of  one  permissible  frame,  and 
are  simultaneous  with  respect  to  that  frame,  will  be 
temporally  separated  with  respect  to  any  other  frame 
which  moves  in  the  timeless  space  of  the  first.  Thus 
the  principle  would  presumably  have  to  be  stated  in 
the  much  milder  form  that  the  independently  necessary 
conditions  of  an  event  must  not  be  intrinsically  separated 
in  time,  i.e.,  that  there  is  at  least  one  permissible  frame 


5o4  SCIENTIFIC  THOUGHT 

with  respect  to  which  they  are  all  simultaneous.  But, 
when  it  thus  loses  its  original  sweet  simplicity,  it  seems 
to  lose  any  trace  of  self-evidence  which  it  may  have 
had  before. 

(3)  Lastly,  it  seems  to  me  almost  certain  that  the 
sufficient  productive  conditions  of  many  sensations  could 
not  be  momentary,  and,  therefore,  must  include  non- 
simultaneous  factors.  I  do  not  merely  mean  by  this 
that  "  momentary  "  conditions  are  not  existent  facts  and 
can  only  be  defined  by  Extensive  Abstraction.  I  mean 
that,  if  you  tried  to  apply  Extensive  Abstraction  to  the 
conditions  of  many  sensations  you  would  find  that  these 
do  not  converge  to  a  set  of  contemporary  momentary 
states.  It  is  practically  certain,  e.g.,  that  the  external 
originative  and  transmissive  conditions  of  sensations 
of  light  and  sound  are  periodic,  and  it  is  reasonable  to 
suppose  that  the  subsequent  internal  processes  in  nerves 
and  brain  are  periodic  too.  There  is  a  very  accurate 
correlation  between  the  colour  or  pitch  of  the  sensum  and 
the  period  of  the  external  originative  and  transmissive 
events.  Now  it  is  impossible  that  the  characteristic 
periodicity  of  red  light,  or  of  a  certain  note  on  the  piano, 
should  be  carried  by  a  purely  momentary  brain-event. 
Presumably  the  brain-event,  which  is  the  productive 
condition  of  even  the  shortest  sensation  of  red,  must  last, 
at  least  as  long  as  one  complete  vibration  of  red  light. 
Or,  if  we  prefer  to  express  ourselves  more  guardedly, 
we  must,  at  least,  hold  that  the  productive  conditions  of 
the  shortest  possible  sensations  of  (say)  red  and  blue 
must  both  have  characteristic  finite  durations,  and  that 
these  durations  must  have  to  each  other  the  same  ratio 
as  the  periods  of  a  complete  vibration  of  red  light,  and 
a  complete  vibration  of  blue  light.  If  the  productive 
conditions  have  durations,  they  must  have  non-simul- 
taneous parts.  And,  if  the  whole  finite  event  be  the 
least  that  is  sufficient  to  produce  the  sensation,  all  its 
successive  parts  must  be  independently  necessary  to 
produce  the  sensation.     If,  further,  the  event  in  question 


CONDITIONS   AND   STATUS   OF   SENSA     505 

be  transmissive  in  character  (if,  e.g.,  it  be  the  passage  of 
some  kind  of  disturbance  through  a  finite  tract  of  brain 
and  nerve)  the  earlier  parts  of  it  will  also  be  dependently 
necessary  conditions  of  the  sensation,  since  the  later 
parts  will  not  happen  unless  the  earlier  ones  happen  and 
produce  them. 

The  upshot  of  this  discussion  seems  to  be  that  we 
cannot  prove  by  any  direct  empirical  argument  that  any 
condition  which  is  dependently  necessary  to  produce 
a  sensation  is  not  also  an  independently  necessary 
condition  of  it.  And  we  cannot  prove  a  priori  that 
dependently  necessary  conditions  cannot  also  be  inde- 
pendently necessary,  except  from  a  premise  which  is 
not  self-evident,  is  of  very  uncertain  meaning  when  the 
relativity  of  physical  simultaneity  is  considered,  and  is 
almost  certainly  false  as  applied  to  the  productive  con- 
ditions of  some  of  our  most  important  sensations.  It 
follows  that  it  is  rash  in  the  extreme  to  expect  to  be 
able,  even  in  theory,  to  isolate  a  momentary  event  at 
a  definite  place  in  the  brain,  and  to  say  :  "This  is  the 
necessary  and  sufficient  condition  of  such  and  such  a 
sensation."  We  cannot  be  absolutely  certain  that  even 
such  remote  dependently  necessary  conditions  as  the 
stroke  of  the  bell  are  not  also  independently  necessary 
conditions  of  our  sensation  of  the  sound  which  is 
characteristic  of  the  bell.  And  we  can  feel  fairly 
confident  that  at  least  the  later  stages  of  the  internal 
transmissive  conditions  of  a  sensation  are  independ- 
ently as  well  as  dependently  necessary  conditions 
of  its  occurrence.  To  put  it  shortly  :  The  productive 
conditions  of  a  sensation  almost  certainly  include  the 
later  stages  of  its  internal  transmissive  conditions  ;  and, 
for  all  that  we  can  certainly  know,  they  might  include 
the  external  transmissive  and  the  originative  conditions 
as  independently  necessary  factors. 

I  think  it  is  possible  to  produce  a  more  or  less 
plausible  indirect  empirical  argument,  which  renders  it 
probable  that  the  independently  necessary  conditions  of 

2  K 


506  SCIENTIFIC  THOUGHT 

some  at  least  of  our  sensations  do  not  extend  so  far 
back  as  the  external  transmissive  or  the  originative 
conditions.  But  it  is  only  an  argument  from  analogy, 
and,  as  we  shall  see,  the  analogy  is  none  too  good. 
The  argument  would  run  as  follows :  Although  the 
particular  sensation  s  would  not  have  arisen  when  it 
did,  unless  certain  external  originative  and  transmissive 
conditions  had  been  fulfilled,  there  are  sensible  experi- 
ences s',  very  much  like  s,  which  happen  {e.g.,  in 
dreams)  when  there  is  good  reason  to  believe  that  no 
such  external  originative  or  transmissive  processes  are 
operating.  If  so,  internal  conditions  are  sufficient  to 
produce  /.  And  the  analogy  between  s'  and  s  may 
suggest  that  purely  internal  conditions  are  sufficient 
to  produce  s,  though  these  cannot,  in  fact,  arise  unless 
certain  external  conditions  be  first  fulfilled.  If  this 
be  so,  the  external  conditions  are  only  dependently 
necessary  for  the  production  of  s.  To  take  a  concrete 
example.  Although  I  should  not  have  sensed  a  certain 
flash  at  a  certain  moment  unless  someone  had  struck 
a  match  very  shortly  before  in  my  neighbourhood,  yet 
I  do  have  visual  experiences  very  much  like  this  sensa- 
tion in  dreams.  The  latter  must  have  been  produced 
by  purely  internal  conditions.  Hence  purely  internal 
conditions  are  sufficient  to  produce  experiences  very 
much  like  this  particular  sensation.  Therefore  probably 
the  sufficient  conditions  of  all  visual  experiences  are 
internal ;  and  the  external  conditions,  which  are  necessary 
for  the  production  of  many  such  sensations,  are  only 
dependently  necessary.  That  is,  the  striking  of  the 
match  is  necessary  only  for  producing  the  internal 
process  which  is  the  sufficient  condition  for  the  sensation 
of  the  flash  ;  it  is  not  also  necessary  as  a  condition  which 
co-operates  with  the  later  stages  of  this  process. 

It  is  evident  that  such  an  argument  could  never 
establish  more  than  a  probability  that  external  events 
are  not  independently  necessary  conditions  of  those 
sensations    to  which    they   are   dependently   necessary. 


CONDITIONS  AND   STATUS   OF   SENSA     507 

The  strength  of  the  argument  in  any  particular  case 
will  depend  on  two  factors,  viz.:  (1)  the  degree  of  analogy 
between  the  experiences  /,  which  are  alleged  to  be 
originated  wholly  from  within  the  body,  and  the 
sensations  s,  which  are  externally  originated  ;  and  (2) 
the  degree  of  certainty  with  which  it  can  be  asserted 
that  the  experiences  s'  are  originated  altogether  inter- 
nally. When  the  experiences  s'  are  apprehensions  of  so- 
called  "  mental  "  images  I  should  not  deem  the  analogy 
strong  enough  to  bear  any  great  weight  of  argument. 
For,  although  visual  and  auditory  images  are  a  good 
deal  like  visual  and  auditory  sensa  respectively,  yet 
there  are  such  marked  differences  between  them  that 
we  hardly  ever  mistake  one  for  the  other  in  normal 
waking  life.  I  should  be  inclined  to  say  that  only  the 
experiences  of  dreams,  and  other  forms  of  hallucination, 
bear  enough  likeness  to  auditory  and  visual  sensations 
to  support  an  argument  such  as  I  have  outlined  above. 
Now,  in  the  last  sub-section  we  saw  that  it  is  by  no 
means  certain  that  auditory  experiences  (other  than 
images)  are  ever  originated  save  by  external  physical 
events  or  by  internal  events  of  precisely  the  same 
character.  It  is  therefore  doubtful  whether  there  be 
any  facts  about  auditory  experiences  which  the  present 
argument  could  use  as  premises.  With  tactual  ex- 
periences, as  we  saw,  the  position  is  still  less  favourable. 
In  fact,  it  is  only  with  visual  experiences  that  there  is 
really  good  evidence  that  something  very  much  like 
normal  sensations  can  be  originated  by  events  which 
are  wholly  internal  and  are  quite  unlike  the  external 
originative  conditions  of  the  normal  sensations.  Thus 
Ave  can  argue  with  a  fairly  high  degree  of  probability 
that  the  sufficient  conditions  of  visual  sensations  are 
internal,  and  that  the  external  originative  and  trans- 
missive  conditions  are  only  dependently  necessary  ;  but, 
for  auditory  and  tactual  sensations,  a  similar  argument 
leads  to  only  a  weak  probability. 

It  must  be  remembered,  on  the  other  hand,  that  it 


5o8  SCIENTIFIC   THOUGHT 

is  equally  impossible  to  prove  (what  the  nai'ver  Realists 
would  like  to  believe)  that  the  external  originative  con- 
ditions of  our  sensations  are  independently,  as  well  as 
dependently,  necessary  conditions  for  the  occurrence  of 
these  sensations.  Thus,  so  far  as  I  can  see,  empirical 
facts  and  a  priori  principles  about  causation  justify  little 
more  than  complete  agnosticism  on  this  subject.  There 
is,  therefore,  an  almost  open  field  for  different  hypotheses, 
each  carrying  the  independently  necessary  conditions 
backwards  in  Time  and  Space  by  different  amounts. 
Each  will  lead  to  a  somewhat  different  theory  as  to 
what  is  involved  in  the  perception  of  external  physical 
objects  and  events,  and  the  hypothesis  which  leads  to 
the  theory  of  perception  which  best  unifies  all  the 
known  facts  is  the  one  to  be  preferred. 

Within  the  body  I  know  of  no  means  of  setting  even 
probable  limits  to  the  distance  backwards  in  Space  and 
Time  to  which  the  independently  necessary  conditions 
of  a  sensation  may  stretch.  It  may  be  that  the  events 
in  the  brain  are  sufficient,  and  that  the  process  in  the 
sensory  nerve  is  merely  transmissive.  On  the  other 
hand,  it  is  equally  likely,  so  far  as  I  can  see,  that  the 
process  in  the  nerve  is  an  independently  necessary,  as 
well  as  a  transmissive  condition,  for  the  occurrence  of 
the  sensation.  The  former  alternative  appears  to  be 
unhesitatingly  taken  by  physiologists,  and  accepted,  on 
their  authority,  by  the  general  public.  But  this  con- 
viction rests  on  no  stronger  basis  than  a  failure  to  draw 
certain  distinctions  among  "  necessary  conditions,"  and 
a  simple  faith  in  certain  dogmas  about  causation  which 
will  not  bear  the  light  of  common  day. 

I  will  end  this  sub-section  by  considering  a  rather 
confused  semi-popular  argument,  which  tries  to  raise 
doubts  about  the  existence  of  external  objects  and  events, 
on  the  ground  of  physiological  theories  about  the 
conditions  of  our  sensations.  I  will  call  this  position 
Physiological  Scepticism.  The  argument  would  run  some- 
what as  follows.     "  My  only  ground  for  believing  in 


CONDITIONS   AND   STATUS   OF   SENSA     509 

the  existence  of  external  physical  objects  is  the  occur- 
rence of  certain  sensations  which  I  ascribe  to  them.  But 
physiology  proves  that  states  of  my  body  are  siifficient 
conditions  of  all  my  sensations.  Hence  I  have  no  right 
to  conclude  from  the  occurrence  of  sensations  to  the 
existence  of  external  physical  objects  and  processes,  as 
their  originative  conditions."  To  this  we  may  answer  : 
(1)  That,  even  if  internal  processes  be  sufficient  condi- 
tions of  our  sensations,  we  do  not  know  and  have  no 
reason  to  believe,  that  these  internal  processes  would 
take  place  unless  certain  external  events  were  happening 
and  affecting  our  bodies.  Thus  we  may  still  argue  to 
the  existence  of  such  external  objects,  as,  at  least,  the 
dependently  necessary  conditions  of  many  of  our  sensa- 
tions. Moreover,  the  resemblance  between  many  of  the 
sensa  which  I  sense  and  those  which  are  sensed  by 
other  observers,  the  fact  that  visual  sensa  from  different 
observers'  sense-histories  are  in  the  same  optical  place, 
and  the  somewhat  similar  facts  about  auditory  sensa, 
suggest  strongly  that  there  is  often  a  remote  external 
physical  event,  which  is  located  in  this  place,  and  is 
a  common  dependently  necessary  condition  of  all  these 
correlated  sensations.  (2)  We  have  seen  that  it  is  im- 
possible to  be  sure  that  these  dependently  necessary 
external  conditions  are  not  also  independently  necessary. 
It  is,  therefore,  quite  uncertain  whether  internal  pro- 
cesses ai'e  sufficient  conditions  of  all  my  sensations.  If 
this  be  held  at  all,  it  can  only  validly  be  held  as  a 
probability  based  on  certain  partial  analogies.  (3)  It 
is  perhaps  worth  while  to  point  out  that  Physiological 
Scepticism  cannot  consistently  stop  at  the  stage  of 
doubting  the  existence  of  external  physical  objects.  If 
such  arguments  be  valid  at  all,  they  must  finally  be 
applied  to  one's  own  body  and  its  supposed  internal 
structure.  All  that  anyone  knows  about  the  physiology 
and  internal  anatomy  of  his  own  body  he  has  learnt  by 
studying  and  dissecting  other  organised  bodies.  Now, 
for  each  observer,  these   are  simply  external  physical 


510  SCIENTIFIC  THOUGHT 

objects,  of  whose  existence  and  inner  structure  he  learns 
by  sensations  of  sight  and  touch.  If  then  he  is  forced  to 
be  wholly  sceptical  about  external  physical  objects,  he 
ought,  if  he  wants  to  be  consistent,  to  be  equally  sceptical 
about  all  statements  which  imply  the  existence  of  a  per- 
manent inner  structure  and  variable  states  of  his  own 
body.  The  conclusion  of  Physiological  Scepticism  blows 
up  its  own  premises,  and  the  only  consistent  result  is 
complete  scepticism  about  all  physical  objects  and  pro- 
cesses, including  those  with  which  physiology  professes 
to  deal.  Physiologists  with  a  tendency  to  philosophical 
speculation  are  liable  to  combine  Naive  Realism  about 
the  purely  hypothetical  states  of  their  brains  with  Sub- 
jective Idealism  about  all  other  physical  objects,  includ- 
ing those  which  they  have  had  to  study  in  order  to  learn 
about  their  own  brains.  To  parody  Mr  Gibbon's  re- 
mark about  the  Jews  :  "  In  contradiction  to  every  known 
principle  of  the  human  mind  this  singular  people  seems 
to  have  yielded  a  stronger  and  more  ready  assent  to" 
the  hypothetical  entities  of  their  science  "than  to  the 
evidence  of  their  own  senses." 

(c)  Occurrent  and  Continuant  Conditions. — In  the  last 
sub-section  I  brought  forward  certain  abstract  logical 
considerations  to  show  that  it  is  impossible  to  tell  how 
far  the  series  of  independently  necessary  conditions  of 
a  sensation  must  be  carried  in  Space  and  Time.  But, 
quite  apart  from  these  considerations,  it  is  practically 
certain  that  no  event  in  the  brain  is  a  completely  sufficient 
condition  for  the  occurrence  of  any  sensation.  Every 
event  depends  on  two  kinds  of  conditions,  which 
we  may  call  occurrent  and  continuant,  borrowing  two 
useful  names  from  Mr  W.  E.  Johnson.  We  are 
always  very  liable  to  notice  the  occurrent  and  to 
ignore  the  continuant  conditions,  and  then  to  think 
that  the  former  are  sufficient  to  produce  the  event. 
It  would  commonly  be  said  that  the  stroke  of  a  bell  is 
a  necessary  and  sufficient  condition  of  the  occurrence 
of  certain  vibrations  in  the  surrounding  medium.     So  it 


CONDITIONS   AND   STATUS   OF   SENSA     511 

is, provided that  there  is  a  material  medium  in  contact  with 
the  bell,  and  that  it  is  capable  of  being  set  in  vibration 
by  a  disturbance  of  this  particular  period.  It  is  evident 
that  the  latter  condition  is  as  necessary  for  the  setting 
up  of  vibrations  as  the  former.  But  the  striking  of  the 
bell  is  a  short  outstanding  event  in  that  long  and  fairly 
uniform  strand  of  history  which  is  the  bell  ;  whilst  the 
medium  and  its  structure  existed  before  the  bell  was 
struck,  and  will  exist  with  very  little  change  for  long 
afterwards.  Moreover,  in  our  experience,  bells  are  much 
more  often  than  not  surrounded  with  such  a  medium. 
The  medium  is  thus  such  an  unexciting  and  such  a 
usual  piece  of  physical  history  that  we  hardly  think  it 
worth  mentioning.  Now  I  should  call  the  striking  of 
the  bell  an  occurrent  condition,  and  the  existence  of  a 
surrounding  medium  of  suitable  structure  a  continuant 
condition,  of  the  setting  up  of  the  vibrations.  Both  are 
necessary,  and  neither  by  itself  is  sufficient.  Together 
they  are  sufficient.  We  can,  if  we  like,  call  the  striking 
of  the  bell  the  necessary  and  sufficient  occurrent  condition  of 
the  vibrations,  but  we  must  on  no  account  call  it  the 
necessary  and  sufficient  condition  without  qualification. 

I  do  not  pretend  that  an  absolutely  hard  and  fast 
line  can  be  drawn  between  occurrent  and  continuant 
conditions.  An  occurrent  condition  is  a  short  out- 
standing slice  in  some  long  strand  of  physical  history, 
which  is  fairly  uniform  up  to  this  slice  and  again  shows 
uniformity,  often  of  the  same  kind  as  before,  after  the 
slice.  A  continuant  condition  is  a  long  and  practically 
uniform  strand,  which  stretches  out  with  little  varia- 
tion before,  during,  and  after  the  occurrent  condition. 
Obviously  terms  like  "short,"  "outstanding,"  "uni- 
form," etc.,  are  relative.  But,  for  our  purpose,  all 
that  we  need  to  notice  is  that  some  of  the  conditions 
of  an  event  are  always  of  the  continuant  type,  and  that 
the  more  a  condition  is  of  the  continuant  type  the  more 
likely  it  is  to  be  overlooked. 

Let  us   now  apply  these  general    considerations  to 


512  SCIENTIFIC  THOUGHT 

the  necessary  and  sufficient  conditions  of  our  sensations. 
When  a  stimulus,   which   normally  produces  a  certain 
kind   of  sensation,  acts  on  a  sense-organ,  such   as  the 
eye  or  ear,    no  sensation   will  be   produced   unless   the 
nerve   be   intact  and  the  general  structure  of  the  brain 
be  not  disintegrated  beyond  a  certain  very  small  degree. 
Again,  the  structure  of  the  sense-organ,  sensory  nerve, 
and  brain  may  (so  far  as  we  know)  be  intact,  and  yet 
no  sensation  will  be  produced  if  the  man  be  dead.      If 
he    be   alive,    but  asleep    or  in   a  swoon   or  under  the 
influence  of  a  drug,  the  stimulus  may  also  fail  to  produce 
a  sensation  in  his  mind.     Again,  there  are  such  pheno- 
mena  as    "  psychic"    blindness,   deafness,    etc.,    which 
happen  spontaneously  in  hysteria,  and  can  be  induced 
artificially  by  hypnosis.    Here  there  is  no  reason  whatever 
to  suppose  that  there  is  any  defect  in  the  structure  of 
sense-organs,  nerves,  or  brain  —indeed  there  is  evidence 
to  the  contrary— and  yet  the  external   stimulus  is  not 
followed   by  any  correlated  sensation  in  the  conscious 
mind  of  the  patient.      Lastly,  we  have  seen  in  an  earlier 
chapter  that  similar  external  stimuli  will  often  produce 
in  different  observers  sensations  whose  sensa  are  partly 
different  in  quality,   and   that  these  differences  can   be 
correlated  with   differences   in  the  past  histories  of  the 
observers. 

It  is  evident  then  that  one  general  continuant  con- 
dition for  the  production  of  sensations  is  that  the  sense- 
organ  and  the  nerve  which  are  specially  concerned, 
and  at  least  a  considerable  part  of  the  brain,  shall  be 
structurally  intact.  Given  this  condition,  it  is  also 
necessary  that  the  body  shall  be  "alive."  This  is 
probably  a  distinct  condition  from  the  one  just  men- 
tioned. Although  the  structure  of  the  brain  and  nervous 
system  does  not  remain  intact  for  very  long  after  the 
death  of  the  body,  it  would  be  rash  to  say  that  it  dis- 
integrates profoundly  immediately  after  death.  Motor 
nerves  can  certainly  be  kept  alive  for  some  considerable 
time  after  the  death  of  the  body.      I  should  suppose  that 


CONDITIONS   AND   STATUS   OF   SENSA     513 

"being  alive"  involves  at  least  the  maintenance  of  a 
certain  moving  equilibrium  among  bodily  changes.  We 
might  therefore  call  it  the  general  somatic  occurrent  con- 
dition of  sensations.  I  suppose  that  "being  awake" 
or  "  being  conscious  "  involves  at  least  a  certain  moving 
equilibrium  among  processes  in  the  brain.  This  might 
therefore  be  called  the  general  cerebral  occurrent  condition 
of  sensations.  Since  a  man  can  be  alive  without  being 
awake,  though  he  cannot  be  awake  without  being  alive, 
there  is  a  partial  dependence  and  partial  independence 
between  these  two  sets  of  conditions. 

The  bodily  conditions  on  which  psychic  blindness  or 
deafness  depend,  if  such  there  be,  are  quite  unknown  to 
us.  It  seems  to  me  theoretically  possible  that  the 
conditions  of  such  phenomena  are  wholly  psychic,  and 
have  no  bodily  correlates  at  all.  Whatever  view  we 
may  take  on  this  point,  we  can  at  least  say  that  they 
are  special,  and  not  simply  general  conditions,  such  as  we 
have  so  far  been  describing.  A  patient  is  not,  as  a  rule, 
psychically  blind  to  all  lights  or  psychically  deaf  to  all 
noises.  Most  usually  he  is  blind  or  deaf  only  to  those 
which  have  some  special  association  for  him,  or  to  those 
about  which  suitable  suggestions  have  been  made  to 
him  by  himself  or  by  others.  We  may  reasonably 
suppose  that  psychic  blindness  or  deafness,  if  it  have  a 
bodily  correlate  at  all,  depends  on  certain  disconnexions 
between  the  particular  nervous  process  which  would 
normally  give  rise  to  the  sensation,  and  the  rest  of  the 
brain.  Thus  the  condition  that  we  shall  not  be  psychi- 
cally blind  or  deaf  when  a  certain  stimulus  acts  on  us 
may  be  called  a  special  connective  condition  for  the  occur- 
rence of  the  sensation.  As  it  is  a  condition  which 
usually  holds,  unless  there  be  special  causes  to  disturb 
it,  it  should  presumably  be  counted  as  continuant  rather 
than  occurrent.  Lastly,  when  the  quality  of  the  sensum 
partly  depends  on  the  past  experiences  of  the  observer, 
we  may  say  (borrowing  a  useful  expression  from  Mr 
Russell)  that  the  sensation  has  mnemic  conditions.     (By 


514  SCIENTIFIC   THOUGHT 

using  this  phrase  I  do  not  imply  either  the  acceptance 
or  the  rejection  of  that  peculiar  kind  of  causation  which 
Mr  Russell  calls  "  mnemic  causation.")  On  the  ordinary 
view  that  past  experiences  leave  traces  which  persist, 
and  that  it  is  these  which  condition  our  present  sensa- 
tions, I  suppose  that  mnemic  conditions  would  be  partly 
continuant  and  partly  occurrent.  The  trace,  having 
become  part  of  the  permanent  structure  of  the  nervous 
system,  would  be  a  continuant  condition.  The  con- 
nexions between  this  trace  and  other  parts  of  the  brain, 
which  have  been  formed  by  association,  will  also  be 
continuant  connective  conditions.  But  the  excitement 
of  this  particular  trace,  when  a  certain  part  of  the  brain 
is  excited  by  some  external  stimulus,  is  a  special 
occurrent  condition. 

All  the  conditions  which  I  have  just  been  enumerating 
must  be  fulfilled  if  a  certain  stimulus  is  to  be  followed 
by  a  characteristic  sensation  at  a  given  moment.  The 
mnemic  conditions  may,  in  a  sense,  be  called  "less 
necessary  "  than  the  others,  since  (a)  there  are  probably 
some  sensations  in  whose  production  they  play  little 
if  any  part ;  and  (/3)  even  if  they  be  necessary  to  produce 
a  certain  sensation  at  a  certain  moment,  it  is  probable 
that  a  rather  similar  sensation  would  be  produced  with- 
out them,  provided  that  all  the  other  conditions  were 
fulfilled.  On  the  other  hand,  if  any  of  the  other  con- 
ditions be  not  fulfilled,  no  sensation  at  all  will  be 
produced  in  the  conscious  mind  *  of  the  observer. 

The  question  can  now  be  raised  as  to  which  of  these 
conditions  are  only  dependently  necessary,  and  which 
are  also  independently  necessary,  for  the  production  of 
a  sensation.     The  structural  integrity  of  a  special  nerve, 

*  I  use  the  expression  "conscious  mind"  here,  because  I  think  that  it  is 
theoretically  possible  that  sensations  may  be  produced  in  connexion  with  a 
certain  brain  and  nervous  system,  which  do  not  form  parts  of  that  mind  which 
normally  manifests  itself  through  this  organism.  Such  sensations  (if  they 
exist  at  all)  might  not  form  parts  of  anything  that  deserves  to  be  called  a 
mind  ;  or  again,  they  might  form  parts  of  a  mind  which  seldom  or  never 
manifests  itself. 


CONDITIONS   AND   STATUS   OF   SENSA     515 

and  its  "being  alive,"  are  presumably  dependently 
necessary  conditions  ;  since,  unless  they  be  fulfilled,  no 
disturbance  will  be  produced  in  the  brain.  Whether 
they  be  or  be  not  also  independently  necessary  it  seems 
impossible  to  tell,  for  the  reasons  given  in  the  last  sub- 
section. But  I  should  suppose  that,  on  any  view,  the 
substantial  structural  integrity  of  the  brain  as  a  whole, 
in  addition  to  that  of  the  particular  part  that  is  imme- 
diately connected  with  a  special  sensory  nerve,  is  an 
independently  necessary  condition  for  the  production 
of  a  sensation.  In  addition  to  this,  I  should  suppose 
that  the  general  balance  ot  cerebral  processes,  which  is 
involved  in  the  statement  that  the  observer  is  "awake," 
is  an  independently  necessary  condition.  The  special 
connective  conditions,  which  are  needed  for  the  absence 
of  psychic  blindness  or  deafness,  are  also  independently 
necessary.  And,  if  the  sensation  has  mnemic  conditions, 
these  are  independently  necessary  for  the  production  of 
just  this  sensation,  though  a  sensation  a  good  deal  like 
it  might  be  produced  in  their  absence. 

We  see  now  how  loose  it  is  to  talk  of  a  certain  brain- 
event,  very  definitely  localised  in  time  and  place,  as 
the  sufficient  condition  for  the  occurrence  of  a  sensation. 
Apart  altogether  from  the  fact,  elicited  in  the  last  sub- 
section, that  we  do  not  know  how  many  of  the  dependently 
necessary  conditions  are  also  independently  necessary, 
we  see  that  such  assertions  ignore  many  conditions, 
some  occurrent  and  some  continuant,  which  are  inde- 
pendently necessary.  At  the  utmost  we  can  call  a 
certain  brain-event,  fairly  definitely  localised  in  Time  and 
Space,  the  necessary  and  sufficient  special  non-mnemic 
occurrent  condition  of  a  sensation.  In  addition  to  this, 
every  sensation  needs  at  least  the  following  conditions  : 
(1)  the  general  continuant  cerebral  condition  of  structural 
integrity  of  the  brain  as  a  whole  ;  (2)  the  general  occur- 
rent cerebral  condition  of  "wakefulness";  and  (3)  a 
special  continuant  connective  condition  to  prevent 
psychic    blindness,     deafness,     etc.       Moreover,     many 


516  SCIENTIFIC  THOUGHT 

sensations  require  further  (4)  mnemic  conditions,  which 
are  partly  OCCiirrent  and  partly  continuant;  (5)  and  all 
sensations  require,  as  at  least  dependency  necessary 
conditions,  that  the  body  as  a  whole,  and  especially  the 
sensory  nerve,  shall  be  structurally  intact  (a  continuant 
condition),  and  that  the  body  shall  be  "alive"  (a  general 
occurrent  condition).  Beside  all  these,  there  may  well 
be  purely  psychic  conditions,  having  no  bodily  correlates, 
which  must  also  be  fulfilled  if  sensations  are  to  arise  in  the 
mind.  I  am  going  to  assume,  for  the  sake  of  simplicity, 
in  this  book  that  there  is  such  a  complete  parallelism 
between  mind  and  body  that  it  is  enough  to  mention 
bodily  conditions,  because  every  psychic  condition  has 
its  bodily  correlate.  I  am  very  far  from  believing  that 
this  is  true,  and  am  not  even  sure  that  it  has  any  very 
definite  meaning  which  would  survive  analysis ;  so  I 
assume  it  here  simply  as  an  excuse  for  avoiding 
additional  complications  which  are  hardly  relevant  to 
our  present  purpose. 

Sensations,  Sensa  and  Acts  of  Sensing. — For  reasons 
given  at  the  beginning  of  this  chapter  we  have  so  far 
spoken  of  physiological  and  physical  conditions  as  pro- 
ducing sensations.  We  have  now  to  ask  whether  this 
involves  the  production  of  sensa,  or  of  acts  of  sensing, 
or  of  both.  Before  we  can  hope  to  answer  this,  we  must 
try  to  clear  up  the  notion  of  a  sensation  a  little  more 
fully  than  we  have  yet  had  occasion  to  do. 

(a)  The  General  Process  of  Sensing. — A  sensation,  on 
our  view,  is  a  complex  in  which  an  objective  factor  (the 
sensum)  and  a  subjective  factor  (the  act  of  sensing)  can 
be  distinguished.  Whether  either  of  these  can  exist 
without  the  other  is  a  matter  which  has  so  far  been  left 
in  decent  obscurity.  It  is  obviously  logically  possible, 
and  indeed  quite  plausible,  that  there  might  be  unsensed 
sensa.  It  is  very  much  harder  to  believe  that  there 
could  be  acts  of  sensing  which  did  not  sense  anything, 
because   an    act   of  sensing  would    seem   to  involve    a 


CONDITIONS   AND   STATUS   OF   SENSA     517 

special  relation  between  a  sensum  (which  is  thereby 
sensed)  and  something  else.  Let  us  begin  by  asking 
whether  every  different  sensation  involves  a  different 
act  of  sensing. 

It  seems  clear  to  me  that  we  distinguish  different 
sensations  by  means  of  the  different  sensa  which  are 
their  objects.  If  two  sensa  be  in  different  fields  of  the 
same  sense-history  we  should  say  that  the  observer  had 
two  different  sensations.  If  two  sensa  were  in  the  same 
field,  and  completely  overlapped  in  time,  we  should  say 
that  the  observer  had  two  sensations,  provided  the  two 
sensa  were  separated  spatially  in  the  field  by  a  back- 
ground which  differed  qualitatively  from  both  of  them. 
I  think  it  would  be  reasonable  to  say  that  sensa  in 
successive  fields  are  sensed  by  different  acts,  which  are 
themselves  successive.  But  I  see  no  reason  to  postulate 
different  acts  of  sensing  for  different  sensa  in  the  same 
field.  When  we  remember  that  sensa  do  not  exist  in 
isolation,  but  are  simply  outstanding  features  in  sense- 
fields,  any  such  view  seems  far  from  plausible.  It 
seems  more  reasonable  to  suppose  that  the  same  act 
of  sensing  grasps  a  whole  sense-field.  We  can  then 
distinguish  as  many  sensations  as  there  are  outstanding 
sensa  in  the  field  ;  but  there  seems  no  need  whatever  to 
assume  a  special  act  of  sensing  for  each  of  these  sensa. 
To  say:  "I  have  two  contemporary  sensations,  one  of 
x  and  the  other  of  y"  would  seem  to  mean  simply  :  "I 
sense  a  field  /,  in  which  x  and  y  are  two  outstanding 
parts,  which  may  overlap  in  time  but  are  separated  in 
space."  Thus,  although  every  sensation  involves  an 
act  of  sensing,  it  does  not  follow  that  the  production  of 
every  sensation  involves  the  production  of  a  special  act 
of  sensing. 

So  far,  we  have  been  considering  sensa  which  are  in 
the  same  special  field,  e.g.,  in  some  one  visual  field. 
But  my  general  sense-history  consists  of  a  number  of 
parallel  special  sense-histories,  e.g. ,  visual,  tactual, 
auditory,    etc.        My    general    sense-history    goes    on 


518  SCIENTIFIC   THOUGHT 

throughout  the  whole  of  my  waking  life  at  any  rate, 
though  there  may  be  gaps  in  any  one  of  my  special 
sense-histories.  Now  I  do  not  see  any  reason  to 
suppose  that  there  are  as  many  contemporary  acts  of 
sensing  as  there  are  contemporary  special  sense-fields. 
The  various  special  fields  are  joined  up  with  each  other 
by  sensible  temporal  relations  to  give  a  general  sense- 
field.  If  I  am  aware  at  once  of  a  visual  and  a  tactual 
field,  I  see  no  more  ground  for  postulating  two  acts  of 
sensing,  one  visual  and  the  other  tactual,  than  for 
postulating  two  acts  of  sensing  for  grasping  a  red  patch 
and  a  blue  patch  in  the  same  visual  field.  I  would 
rather  say  that  there  is  a  single  general  act  of  sensing, 
which  happens  to  be  supplied  with  both  a  visual  and  a 
tactual  field  for  its  objects.  Certainly  a  tactual  sensation 
is  very  different  from  a  visual  sensation.  But  so,  too, 
is  a  sensation  of  a  round  red  patch  from  a  sensation  of 
a  square  blue  patch.  The  difference  in  the  objects 
seems  to  be  enough  to  account  for  the  difference  between 
the  sensations  in  both  cases,  and  it  is  needlessly  multi- 
plying entities  to  postulate  different  acts  of  sensing  as 
well,  unless  there  be  some  special  positive  reason  for 
doing  so.7^ 

I  am  therefore  inclined  to  think  that  at  any  moment 
in  our  lives,  while  we  are  awake  at  any  rate,  there  is 
a  general  act  of  sensing  ;  and  that  these  successive 
general  acts  join  up  to  give  a  single  general  process  of 
sensing,  forming  the  subjective  correlate  to  our  general 
sense-history  which  is  its  object.  Some  slices  of  this 
general  object  consist  of  more,  and  some  of  fewer, 
special  sense-fields.  Consequently,  we  have  sometimes 
more,  and  sometimes  fewer,  kinds  of  sensations. 
Again,  one  jfield  of  some  special  sense-history  may  be 
more  differentiated  into  outstanding  sensa  than  another. 
Consequently",  we  have  sometimes  more,  and  sometimes 
fewer,  sensations  of  the  same  kind.  But,  if  I  am  right, 
this  makes  no  difference  to  the  number  of  our  acts  of 
sensing.      I   do  not  deny  for  a  moment  that  there  may 


CONDITIONS   AND   STATUS   OF   SENSA     519 

be,  from  time  to  time,  special  mental  acts  directed  on 
to  special  sensa.  Sometimes  one  sensum  particularly 
interests  me,  either  because  of  its  intrinsic  character  or 
because  of  its  associations.  If  so,  I  may  specially 
attend  to  it.  In  so  far  as  this  involves  more  than 
merely  adjusting  my  body,  so  that  I  sense  a  new  field 
in  whose  centre  there  is  a  larger  and  more  distinct 
sensum  correlated  with  the  old  one  that  first  attracted 
my  attention,  it  no  doubt  involves  the  directing  of  a 
special  mental  act  on  to  a  certain  sensum.  But  specially 
to  attend  to  a  sensum  is  something  more  than  merely 
to  sense  it,  and  therefore  the  fact  just  admitted  is  quite 
consistent  with  our  earlier  statement  that  there  is  no 
need  to  assume  a  distinct  act  of  sensing  for  each  distinct 
sensation. 

(b)  Conditions  of  Sensing  and  Conditions  of  Sensa. — 
Let  us  now  apply  some  of  the  conclusions  which  we 
reached  in  the  last  section  about  the  various  conditions 
which  are  necessary  for  the  production  of  sensations. 
We  have  just  seen  that  not  every  special  sensation 
involves  a  special  act  of  sensing,  though  every  sensation 
does  involve  an  act  of  sensing.  In  the  last  section  we 
distinguished  between  the  special  occurrent  conditions 
of  a  sensation  and  certain  equally  and  independently 
necessary  general  conditions,  some  occurrent  and  some 
continuant.  Now  it  seems  to  me  probable  that  the 
general  process  of  sensing  is  kept  up  by  the  continuant 
and  occurrent  general  cerebral  conditions,  which  are 
involved  in  being  "awake"  and  conscious.  And  it 
seems  to  me  that  the  function  of  the  special  occurrent 
conditions  is,  not  to  produce  acts  of  sensing,  but  to 
produce  outstanding  sensa  in  our  special  sense-histories, 
and  thus  to  supply  the  general  process  of  sensing  with 
various  objects.  If  the  special  occurrent  conditions  be 
fulfilled  without  the  general  cerebral  conditions,  it  is 
conceivable  that  sensa  may  still  be  produced,  but  it  is 
certain  that  they  will  not  be  sensed.  And  we  know, 
from    such    facts   as   psychic    blindness   and    deafness, 


520  SCIENTIFIC  THOUGHT 

that,  even  when  both  sets  of  conditions  are  fulfilled,  no 
sensum  will  be  consciously  sensed  by  the  observer 
unless  certain  special  continuant  connective  conditions 
be  also  fulfilled.  In  such  cases  it  seems  still  more 
likely  that  sensa  may  be  produced  without  being 
sensed.  But  these  abstract  possibilities  of  the  pro- 
duction of  unsensed  sensa  cannot  be  properly  estimated 
until  we  have  cleared  up  the  notion  of  "production," 
which  we  shall  try  to  do  in  the  next  section. 

Now  it  might  be  said:  "If  you  think  it  possible 
that  the  special  occurrent  conditions  might  produce 
unsensed  sensa  in  the  absence  of  the  general  cerebral 
conditions,  do  you  think  that  the  general  cerebral  con- 
ditions might  produce  a  general  process  of  sensing, 
with  nothing  to  sense,  in  the  absence  of  special 
occurrent  conditions?"  To  this  I  answer  :  (a)  Probably 
not ;  because  I  find  it  difficult  to  know  what,  if  anything, 
would  be  meant  by  a  process  of  sensing  with  no  objects 
to  sense,  and  am  therefore  doubtful  whether  anything 
of  the  kind  be  possible  at  all.  I  do  not  feel  any  similar 
difficulty  about  the  possibility  of  unsensed  sensa.  And 
(j3)  in  any  case  the  question  cannot  be  tested  empirically, 
for  the  following  reason.  The  cerebral  conditions  which 
keep  up  the  general  process  of  sensing  are  themselves 
dependent  on  more  general  somatic  conditions.  We 
cannot  be  conscious  without  beings  alive  :  though,  if 
there  be  ever  completely  dreamless  sleep  or  complete 
anaesthesia  through  drugs  or  disease  or  accident,  we 
may  sometimes  be  alive  without  being  conscious. 
Thus,  whenever  the  cerebral  conditions  for  sensing  are 
fulfilled,  there  is  a  rough  balance  of  physiological 
processes  in  the  body  as  a  whole.  These  somatic 
conditions  supply  the  general  process  of  sensing  with 
a  continual  series  of  internal  sensa  as  objects.  Thus, 
in  practice,  the  general  process  of  sensing  never  could 
lack  at  least  a  somatic  sense-field  to  sense,  for  the 
dependently  necessary  conditions  of  the  former  are  the 
originative  conditions  of  the  latter.     Once  the  general 


CONDITIONS   AND   STATUS   OF   SENSA     521 

process  of  sensing  is  started  and  supplied  with  a  somatic 
sense-history  to  sense,  external  stimuli  acting  on  the 
organs  will  supply  the  process  with  sense-fields  of  other 
kinds,  such  as  the  visual  and  the  auditory.  The  one 
process  of  sensing,  which  is  permanently  provided 
with  a  somatic  sense-history  for  the  reasons  given 
above,  grasps  the  other  kinds  of  sense-field  in  its  stride, 
as  they  are  supplied  to  it  from  time  to  time  by  special 
occurrent  conditions. 

Here  we  might  perhaps  leave  the  matter;  but  there 
is  a  further  speculation  on  this  subject  which  it  seems 
worth  while  to  mention.  I  do  not  wish  to  stake  too 
much  on  it,  but  it  does  seem  to  me  to  be  hopeful,  and 
not  without  plausibility.  My  suggestion  is  as  follows  : 
We  have  never  attempted,  so  far,  to  analyse  what  is 
meant  by  an  act  of  sensing.  We  have  assumed  that, 
when  a  sensum  is  sensed,  it  stands  in  some  special 
relation  to  something  else,  and  that  it  would  not  stand 
in  precisely  this  relation  to  this  something  if  it  were 
not  being  sensed.  But  we  have  never  attempted  to 
state  what  this  something  is,  nor  to  describe  the  relation. 
Now  one  result,  which  seems  relevant  for  the  present 
purpose,  did  emerge  from  our  discussions  in  Chapter 
VIII  on  the  question  whether  sensa  are  in  any  way 
mental.  We  saw  there  that  the  need  of  distinguishing 
between  the  sensum  and  the  act  of  sensing  was  most 
obvious  in  the  case  of  visual  and  auditory  sensations, 
and  that  it  was  least  evident  for  bodily  sensations.  In 
fact,  we  suggested  that  it  was  possible  that  bodily 
"sensations"  are  not  true  sensations  at  all,  but  are  of 
the  nature  of  presentations.  This  would  mean  that 
they  are  unitary  experiences,  in  which  there  really  is 
no  possibility  of  distinguishing  act  and  object.  We 
have  also  just  seen  that,  even  if  the  distinction  between 
act  and  object  is  to  be  drawn  for  bodily  "sensations," 
the  general  cerebral  conditions  of  the  process  of  sensing 
cannot,  in  fact,  arise  apart  from  those  general  somatic 
conditions  which  supply  this  process  with  somatic  sensa 

2  L 


5-  SCIENTIFIC   THOUGHT 

as  objects.  If  we  combine  the  latter  result  with  the 
suggestion  that  bodily  "sensations"  are  really  not 
distinguishable  into  act  of  sensing-  and  sensum,  we 
reach  the  following  tentative  conclusion  :  The  general 
cerebral  and  the  general  somatic  conditions  co-operate 
to  give  a  continuous  series  of  unitary  bodily  feelings, 
in  which  no  distinction  between  act  of  sensing  and 
sensum  can  be  drawn.  This  constitutes  the  somatic 
sense-history  ;  and  it  is  broken  during  life  only,  if  at 
all,  in  dreamless  sleep  and  other  states  of  complete 
unconsciousness.  Granted  that  these  general  condi- 
tions are  in  operation,  suitable  stimuli  on  the  special 
organs  of  sense  cause  special  sensa,  visual,  auditory, 
etc.,  to  unite  with  the  somatic  sense-history  and  thus 
to  form  the  general  sense-history.  Now  I  suggest,  very 
tentatively,  that  "getting  sensed"  may  just  mean 
"coming-  into  such  relations  with  the  somatic  sense- 
history  as  to  form  with  it  a  general  sense-history."  On 
this  view  a  sensation  of  a  red  patch  would  be  a  red 
sensum,  so  related  to  a  somatic  field  that  they  form 
together  a  general  field  in  a  certain  sense-history.  A 
contemporary  auditory  sensation  would  consist  of  a 
noise-sensum,  related  in  the  same  kind  of  way  to  the 
same  somatic  field.  The  somatic  field  itself  would 
consist  of  feelings  or  presentations,  which  are  not 
objects  of  acts  of  sensing,  but  are  unanalysable  mental 
states.  It  will  thus  form  the  subjective  factor  in  all 
true  sensations.  If  we  ask:  "What  is  the  relation 
which  a  special  sensum  must  have  to  a  somatic  field 
in  order  to  be  sensed?"  the  answer  seems  to  be  that 
the  sensum  must  stand  in  the  relation  of  sensible  simul- 
taneity to  some  part  of  the  somatic  field,  i.e.,  that  the 
two  must  fall  into  a  single  Specious  Present.  For  this 
is  certainly  the  only  known  relation  which  binds  various 
special  sense-fields  together  into  a  single  general  sense- 
field.  Of  course,  it  may  well  be  that  something  further 
than  this  is  needed,  but  at  any  rate  this  seems  to  be  the 
most  noticeable    feature    in    the  relation.     If  this  sug- 


CONDITIONS   AND   STATUS   OF   SENSA     523 

gestion  be  right,  what  we  have  formerly  called  the 
"general  process  of  sensing"  is  just  the  somatic  sense- 
history,  and  what  we  have  called  "getting  sensed  by 
the  general  process  of  sensing"  is  just  coming  into  the 
relation  of  sensible  simultaneity  with  some  part  of  the 
somatic  sense-history. 

What  is  meant  by  the  "  Production  "  of  Sensa. — We 
have  agreed  that,  in  some  meaning  of  the  word,  sensa 
are  "produced."  The  production  of  a  sensation  con- 
sists in  supplying  the  general  process  of  sensing  with 
a  certain  sensum  at  a  certain  time  as  an  object.  And, 
if  the  suggestion  made  at  the  end  of  the  last  section  be 
accepted,  this  means  causing  a  certain  sensum  to  be 
sensibly  simultaneous  with  a  certain  part  of  the  somatic 
sense-history.  Even  so,  the  notion  of  "production" 
remains  highly  ambiguous,  and  we  must  start  by  clear- 
ing up  its  various  possible  meanings. 

(a)  Selection  and  Generation. — Dr  Johnson  is  reported 
to  have  described  his  one  meeting  with  Mr  David 
Hume  in  the  following  terms:  "On  the  sole  occasion, 
Sir,  on  which  I  entered  into  the  intimacy  of  a  familiar 
conversation  with  that  notorious  Sceptic,  his  contribu- 
tion to  the  mutual  conviviality  was  to  produce  a.  drawing, 
so  unutterably  gross  in  its  conception  as  to  merit  a 
murmur  of  disapprobation  even  within  the  walls  of  a 
brothel  !  ''  Now  Dr  Johnson's  statement  leaves  us  in 
doubt  as  to  exactly  what  happened  at  this  memorable 
meeting,  and  the  doubt  is  due  to  a  characteristic  ambig- 
uity in  the  word  "produce."  Did  Mr  Hume  select  for 
Dr  Johnson's  inspection  one  of  a  number  of  objection- 
able pictures  which  (like  too  many  of  his  countrymen) 
he  was  carrying  in  his  pocket?  Or  did  he  take  a  pencil 
and  pollute  a  previously  virginal  sheet  of  paper  by 
generating  such  a  picture  upon  it?  We  may  compare 
Dr  Johnson  to  the  general  process  of  sensing,  Mr  Hume 
to  the  productive  conditions  of  a  sensation,  and  the 
picture  to  the  sensum  itself.     And   we    may    raise   the 


524  SCIENTIFIC  THOUGHT 

question  whether,  when  a  sensation  is  produced,  the 
special  occurrent  conditions  simply  pick  out  a  certain 
sensum  from  a  mass  of  already  existing"  sensa,  and  con- 
nect it  up  with  the  general  process  of  sensing- ;  or 
whether  they  have  to  generate  the  sensum  which  is 
sensed.  Of  course,  it  may  well  be  that  sensa  are 
subject  to  both  kinds  of  production.  P'ven  if  the  pro- 
duction of  a  sensation  only  needs  the  selection  of  a 
certain  sensum  from  a  mass  of  already  existing  sensa, 
it  is  hardly  likely  that  these  sensa  have  existed  for  ever. 
If  they  have  not,  they  must  at  some  time  have  been 
generated.  Conversely,  if  the  production  of  a  sensation 
involves  the  generation  of  its  sensum,  it  does  not  follow 
that  this  is  sufficient  to  produce  the  sensation.  No 
sensation  will  be  produced  unless  the  sensum  which  is 
generated  gets  properly  connected  with  a  general  pro- 
cess of  sensing  ;  and  it  is  not  obvious  that  a  sensum 
could  not  be  generated  without  ipso  facto  becoming  con- 
nected with  a  general  process  of  sensing. 

We  may  say  then,  in  general,  that  production  must 
be  differentiated  into  selection  and  generation.  Now 
selection  may  be  either  positive  or  negative.  We  may 
select  a  card  from  a  mass  of  other  cards,  either  by 
picking  it  up  and  leaving  the  rest  on  the  table,  or  by 
leaving  it  on  the  table  and  sweeping  all  the  others  on 
to  the  floor.  I  should  call  the  first  process  positive,  and 
the  second  negative,  selection.  In  general,  to  select  x 
from  a  group  g  implies  the  following  facts:  (i)  All  the 
members  of  g  originally  stand  in  like  relations  to  the 
selector  s.  (2)  A  particular  member,  a;  of  the  group 
g  is  made  to  stand  in  a  different  relation  from  all  the 
rest  to  s.  This  result  can  be  reached  either  by  leaving 
the  rest  of  the  group  in  their  old  relations  to  s  and 
changing  the  relation  of  .r,  or  by  leaving  x  in  its  old 
relation  to  s,  and  changing  the  relations  of  all  the  other 
members  of  the  group  to  s.  The  former  is  positive  and 
the  latter  is  negative  selection. 

Both  forms  of  selection  imply  that  a  mass  of  sensa 


CONDITIONS   AND   STATUS   OF   SENSA     525 

already  exists  for  us  to  select  from.  It  will  first  be 
necessary  to  see  what  precisely  this  means.  A  sensum, 
which  I  sense,  is  an  event  with  a  certain  short  duration. 
If  I  say  that  it  existed  before  I  began  to  sense  it,  and 
that  it  will  exist  after  I  cease  to  sense  it,  I  cannot 
literally  mean  that  precisely  and  numerically  the  same 
event  as  that  which  I  sensed  exists  before  and  after  my 
sensing  of  it.  What  I  must  mean  is  that  this  sensum, 
which  I  sense,  is  a  short  slice  of  a  longer  strand  which 
stretches  out  before  the  beginning  and  after  the  end  of 
my  sensum.  This  strand  must  be  qualitatively  alike 
in  all  its  sections  if  it  is  to  be  true,  even  in  a  Pickwickian 
manner,  that  my  sensum  "existed  before  and  after  I 
sensed  it."  The  strand,  as  a  whole,  is  not  contained 
in  my  sense-history  ;  but  I  can  understand  what  is 
meant  by  such  a  strand,  since  there  are  plenty  of  sense- 
objects  which  are  contained  in  my  sense-history.  The 
physiological  and  other  conditions  must  be  supposed  to 
pick  out  a  short  slice  of  such  a  strand,  and  to  connect 
it  up  with  my  general  process  of  sensing,  so  that  it 
becomes  one  of  my  sensa.  So  the  selective  theory 
would  seem  to  imply  that  all  sensa  are  short  slices  of 
longer  and  practically  uniform  strands,  even  when  these 
strands  are  not,  as  wholes,  sensed  by  us,  and  therefore 
are  not  sense-objects  in  our  histories. 

On  such  a  view  I  take  it  that  the  selective  process 
would  have  two  different  parts  to  play.  (1)  It  would 
select  one  or  more  out  of  a  much  larger  number  of  such 
strands  ;  and  (2)  out  of  each  selected  strand  it  would 
further  choose  the  particular  slice,  long  or  short,  which 
is  to  be  connected  with  my  general  process  of  sensing. 
Suppose,  e.g. ,  that  a  certain  source  were  to  send  out.  a 
flash  of  red  light  and  a  flash  of  ultra-violet  light.  On 
the  present  view  these  would  both  be  sense-objects. 
The  former  would  consist  of  a  successive  series  of  very 
similar  red  sensa.  The  latter  would  consist  of  a  succes- 
sive series  of  sensa  with  a  different  sensible  quality 
from  the  former.     The  structure  of  our  eyes,  or  optic 


526  SCIENTIFIC  THOUGHT 

nerves,  or  brains,  would  completely  prevent  us  from 
sensing  any  part  of  the  latter  sense-object.  This  would 
be  an  example  of  negative  selection.  Again,  we  should 
not  be  able  to  sense  more  than  a  short  slice  of  the 
former  sense-object.  The  position  of  my  body  and  the 
relevant  events  in  my  brain  and  nervous  system  pre- 
sumably select  this  particular  short  slice  out  of  the 
whole  red  sense-object  to  be  a  sensum  in  my  history. 

Now,  of  course,  there  is  no  doubt  that  our  bodies  do 
act  selectively.  If  we  turn  in  one  direction,  we  auto- 
matically cut  out  the  appearances  of  objects  in  many 
other  directions.  Again,  it  is  presumably  the  structure 
of  our  bodies  which  determines  the  comparatively  small 
range  of  ethereal  vibrations  to  which  sensations  of 
colour  correspond,  and  so  on.  But  the  question  is  : 
Do  our  bodies  select  sensa,  and  are  they  only  selective  in 
their  action?  Or  are  they  also  generative?  I  take  it 
that  the  ordinary  view  of  educated  common-sense  is 
that  they  do  not  select  sensa,  and  that  they  do  generate 
sensa.  The  ordinary  view  would  be  that  our  special 
sense-organs  and  sensory  nerves  select  vibrations  of 
certain  wave-lengths,  and  transmit  corresponding  dis- 
turbances to  the  brain  ;  magnetic  vibrations,  light- 
waves of  too  high  or  too  low  frequency,  and  so  on,  are 
automatically  cut  out,  and  fail  to  disturb  the  brain. 
The  selection,  so  far,  is  made  out  of  a  number  of 
physical  vibrations,  not  out  of  a  number  of  different  sense- 
objects.  Again,  it  is  commonly  supposed  that  if,  and 
only  if,  a  disturbance  reaches  the  brain,  a  sensum  is 
generated. 

Now  I  do  not  think  that  there  is  any  direct  way 
of  deciding  between  purely  selective  and  generative 
theories.  All  that  we  can  do  at  present  is  to  point  out 
the  main  merits  and  defects  of  theories  of  the  selective 
type.  On  the  face  of  it  their  chief  merit  is  that  they 
make  the  ontological  status  of  sensa  in  the  world  easier 
to  understand  than  do  generative  theories.  With  the 
latter   there    is    a   sharp   distinction    between    scientific 


CONDITIONS   AND   STATUS   OF   SENSA     527 

objects  and  events,  on  the  one  hand,  and  the  sensa, 
which,  under  certain  peculiar  circumstances,  they 
generate,  on  the  other.  The  very  notion  of  generation 
is  not  easy  to  understand,  whilst  that  of  selection  is 
fairly  intelligible.  And  the  status  of  sensa,  when 
generated,  in  a  world  which  consists  almost  wholly  of 
scientific  events  and  objects,  is  certainly  most  peculiar. 
Finally,  we  are  directly  acquainted  with  many  sensa, 
and  therefore  do  know  that  there  are  such  things  and 
what  kind  of  things  they  are.  Now  the  natural  com- 
plement of  a  selective  theory  of  the  production  of  sensa 
is  a  theory  that  physical  events  and  objects  are  com- 
posed of  sensa,  some  few  of  which  are  sensed  and  the 
great  majority  of  which  are  unsensed.  It  might  reason- 
ably be  said  that  the  hypothetical  entities  of  such  a 
theory  are  less  hypothetical  than  those  of  the  generative 
theory,  which  makes  physical  events  and  objects  to 
differ  in  kind  from  sensa  and  sense-objects.  On  the 
view  of  physical  objects  and  events  which  corresponds 
to  the  selective  theory  of  the  production  of  sensa,  all 
that  we  need  to  postulate  is  unsensed  sensa  and  unsensed 
sense-objects.  That  is,  we  only  need  to  assume  more 
entities  of  the  same  kind  as  we  meet  with  in  our  sense- 
histories. 

Thus  we  may  fairly  say  that,  if  a  purely  selective 
theory  can  be  made  to  work,  and  if  it  can  be  accompanied 
by  a  satisfactory  theory  of  physical  objects  as  composed 
wholly  of  sensa,  it  will  have  the  double  merit  of  avoiding 
the  difficult  notion  of  generation  and  of  giving  sensa 
a  less  ambiguous  status  in  the  universe  than  any 
generative  theory  is  likely  to  do.  I  will  now  point  out 
certain  difficulties  in  theories  of  the  selective  type,  and 
in  the  view  of  the  nature  and  status  of  sensa  which 
generally  accompanies  such  theories. 

(1)  It  is  difficult  to  work  a  purely  selective  theory 
without  postulating  a  perfectly  enormous  number  of 
unsensed  sensa.  I  am  not  now  alluding  to  the  sensa 
which   have   to  be    put    in    places  where   there   are    no 


528  SCIENTIFIC   THOUGHT 

observers.  After  all,  any  theory  has  to  put  something 
(e.g.)  light-waves,  etc.)  into  such  places  and  times;  so 
that  the  selective  theory  is  here  no  worse  off  than  the 
generative  theory.  For  similar  reasons  I  do  not  make 
it  an  objection  that  there  will  have  to  be  many  kinds  of 
sensa  {e.g.,  magnetic,  ultra-violet,  and  so  on)  which  no 
one  ever  senses.  What  I  am  thinking  of  is  the  following 
fact.  At  a  place,  where  the  physicist  would  say  that 
a  single  physical  process  is  going  on,  it  is  possible 
for  all  sorts  of  qualitatively  different  sensa  to  be  sensed 
by  putting  in  different  observers  or  by  altering  the 
internal  states  of  a  single  observer.  If  physiological 
processes  be  purely  selective,  we  shall  have  to  postulate 
as  many  different  kinds  of  sensa  co-existing  at  a  given 
place  and  time  as  any  observer,  however  abnormal  his 
bodily  condition,  can  sense  if  put  there  at  that  time. 
I  say  co-existing,  although  we  cannot  literally  have  the 
same  observer  in  two  different  states  at  once,  or  two 
different  observers  in  the  same  place  at  once.  For  we 
do  find  characteristic  changes  in  the  sensa  which  are 
sensed  from  a  place  whenever  we  suitably  alter  the 
internal  state  of  the  observer  there  or  introduce  a 
suitably  abnormal  observer  into  his  place.  If  you  hold 
that  the  internal  states  of  the  observers'  bodies  are 
causally  independent  of  the  sensa  which  they  sense, 
and  that  they  act  merely  selectively,  you  must  conclude, 
in  accordance  with  the  argument  of  Chapter  XI,  that 
sensa  like  all  those  which  the  various  observers  sense 
co-exist,  although  the  sensa  which  are  achtally  sensed 
are  successive.     {Cf.  pp.  422  to  429.) 

I  will  take  one  very  simple  example  to  illustrate  my 
meaning.  An  observer  stands  in  a  certain  place  and 
senses  a  certain  sense-object.  He  pushes  his  eye  aside 
with  his  finger,  and  begins  to  sense  two  similar  sense- 
objects  which  are  sensibly  separated.  This  happens 
whenever  he  chooses  to  push  his  eye  aside.  If  bodily 
conditions  be  purely  selective,  there  must  have  been 
two    separate    and    similar   sense-objects   all    the    time, 


CONDITIONS   AND   STATUS   OF   SENSA     529 

one  of  which  remains  unsensed  except  when  he  pushes 
his  eye  aside.  I  find  this  very  difficult  to  swallow  ;  and 
a  supporter  of  a  purely  selective  theory  will  have  to 
swallow  a  large  number  of  equally  unpalatable  doses. 
If  the  sensa  which  an  abnormal  observer,  or  a  normal 
observer  in  a  temporarily  abnormal  state,  senses  from  a 
certain  place  were  absolutely  unlike  those  which  normal 
observers  sense  from  that  place,  a  purely  selective 
theory  would  be  more  plausible.  The  difficulty  is  that 
the  abnormal  sensa  are  a  great  deal  like  the  normal 
ones,  and  yet  distinctly  different.  It  is  very  difficult, 
under  these  conditions,  to  resist  the  conviction  that 
both  the  abnormal  and  the  normal  sensa  are  generated 
by  two  sets  of  conditions,  one  common  to  both,  and 
one  varying  from  observer  to  observer.  The  former 
accounts  for  the  likeness,  and  the  latter  for  the 
difference,  between  the  sensa. 

The  only  purely  selective  theories  that  I  know  of  are 
M.  Bergson's  in  Matter  and  Memory and  Prof.  Alexander's 
in  Space,  Time,  and  Deity.  M.  Bergson  holds,  so  far 
as  I  can  understand,  that  physiological  conditions  are 
purely  selective,  and  that  the  selection  is  negative. 
Our  minds  would  normally  be  in  similar  cognitive 
relations  to  every  event  in  Nature,  and  the  whole 
function  of  our  bodies  in  perception  and  memory  is  to 
shut  out  the  vast  majority  of  these  events  from  our 
cognisance.  Unfortunately,  M.  Bergson  does  not 
condescend  to  enter  into  detail,  and  the  only  possible 
way  to  decide  for  or  against  selective  theories  is  to 
work  them  out  in  detail  and  to  see  whether  they 
can  be  made  to  fit  the  known  facts.  Prof.  Alexander 
is  not  open  to  this  objection.  He  has  made  the  most 
heroic  efforts  to  work  out  a  purely  selective  theory,  and 
he  accompanies  it  with  a  definite  and  extremely  interest- 
ing view  as  to  the  nature  of  sensa  and  their  status  in  the 
universe.  He  takes  physical  objects  to  be  four-dimen- 
sional strands  of  history  ;  and  here  he  is  undoubtedly 
right.     He  then  supposes  sensa  to  be  "  sections  "  across 


530  SCIENTIFIC   THOUGHT 

such  strands.  Sensa  are  thus  "contained  in"  physical 
objects,  as  the  various  sections  which  could  be  got  by 
slicing  an  ordinary  cylinder  in  various  directions  are 
"contained  in'  the  cylinder.  The  position  of  the 
observer's  body  selects  the  particular  physical  objects, 
and  the  particular  sections  of  each  of  these,  which  his 
mind  can  "  contemplate  "  there  and  then.  The  function 
of  the  physiological  processes  in  brain  and  nervous 
system  is  to  keep  up  that  process  of  "enjoyment" 
which  is  the  contemplating  of  such  sections.  Such  a 
theory  has  many  advantages,  if  it  could  be  made  to 
work.  It  accords  with  common-sense  in  making  sensa 
fragmentary  and  dependent,  as  compared  with  physical 
objects.  And  yet  it  makes  all  sensa,  whether  sensed 
or  not,  exist  as  "parts"  of  physical  objects,  in  a 
perfectly  definite  and  intelligible  way.  They  exist  in 
physical  objects,  as  the  various  possible  sections  of  a  geo- 
metrical solid  figure  exist  in  it.  Some  are  momentary, 
and  may  be  compared  to  the  various  circular  sections 
of  a  cylinder,  if  we  compare  the  axis  of  an  ordinary 
cylinder  to  the  time-direction  of  a  strand  of  physical 
history.  Others  consist  of  a  set  of  momentary  events 
of  various  dates,  all  falling  within  a  certain  short 
duration  ;  these  might  be  compared  to  oblique  sections 
of  an  ordinary  cylinder. 

Unfortunately,  it  seems  very  difficult  to  uphold  such 
a  theory  in  face  of  all  the  facts.  If  we  never  dreamed, 
and  if  we  always  saw  objects  through  a  perfectly  homo- 
geneous medium,  without  mirrors,  lenses,  etc.,  and 
if  people  and  things  never  moved  about,  it  would 
be  more  plausible.  I  cannot,  of  course,  attempt  any 
adequate  criticism  of  it  here,  but  I  will  raise  one  point : 
When  I  see  an  image  of  a  pin  in  a  mirror,  of  what 
physical  object  precisely  are  my  visual  sensa  sections? 
If  they  be  sections  of  the  pin's  history,  why  are  they 
optically  present  at  a  place  quite  remote  from  that 
which  is  occupied  by  the  pin  ?  And  how  can  the  image- 
sensa  and    those  which  1  sense  when    I    look   directly 


CONDITIONS   AND   STATUS   OF   SENSA     531 

at  the  pin  be  sections  of  the  same  strand  of  physical 
history?  If  the  image-sensa  be  not  sections  of  the 
history  of  the  pin,  are  they  sections  of  some  strand  of 
physical  history  which  is  located  at  their  optical  place? 
Surely  not  ;  for  it  is  well  known  that  no  relevant 
physical  process  is  going  on  there.  Are  they  then 
sections  of  some  strand  of  physical  history  located  at 
the  surface  of  the  mirror?  If  so,  why  is  their  optical 
place  at  some  distance  beJiind  the  surface  of  the  mirror 
instead  of  upon  it?  Prof.  Alexander  has  tried  his 
hardest  to  deal  with  such  difficulties,  and  in  the  course 
of  his  discussion  much  of  value  has  emerged  ;  but  he 
has  provided  no  answer  which  I  can  fully  understand 
or  accept. 

(2)  If,  in  face  of  difficulties  of  this  kind,  we  add  the 
smallest  trace  of  generation  to  a  purely  selective  theory, 
the  latter  at  once  loses  many  of  its  advantages.  I  will 
take  Mr  Russell's  theory,  as  expounded  in  his  Lowell 
Lectures  and  his  Analysis  of  Mind,  as  an  example  of  a 
predominantly  selective  theory  with  a  small  trace  of 
generation  in  it.  He  regards  a  physical  object  as  a 
group  of  connected  sensa,  with  members  in  all  parts 
of  physical  Space-Time.  The  vast  majority  of  these 
are  unsensed.  If  the  body  of  a  living  observer  be  at  a 
certain  place  at  a  certain  time,  he  will  sense  one  sensum 
from  each  such  group,  and  one  only  ;  though  he  will, 
of  course,  be  sensing  sensa  from  many  different  groups 
at  once.  So  far  the  theory  is  purely  selective.  But  I 
understand  Mr  Russell  to  hold  that  those  sensa,  belong- 
ing to  a  given  physical  object,  which  occupy  regions 
of  physical  Space-Time  where  there  is  no  living 
organised  body,  are  systematically  different  in  quality 
from  sensa  of  the  same  group  which  occupy  regions 
of  Space-Time  where  such  a  body  is  present.  This 
would  seem  to  suggest  that  the  observer's  body  and 
its  internal  processes  are  generative,  as  well  as  selective, 
in  their  action,  and  that  they  at  least  modify  quali- 
tatively those  sensa  of  any  group  which  are   in  their 


532  SCIENTIFIC  THOUGHT 

neighbourhood.  Mr  Russell  seems  generally  to  regard 
organised  bodies  as  analogous  to  distorting  media,  like 
coloured  glass.  I  take  it  that  Mr  Russell's  theory,  in 
its  present  form,  is  admittedly  transitional  ;  it  is  only 
a  first  step  in  the  direction  which  he  wishes  to  follow. 
This  makes  it  a  very  delightful  "  Aunt  Sally"  for  the 
numerous  philosophers  who  are  more  anxious  to  score 
neat  verbal  hits  than  to  help  in  unravelling  the  com- 
plexities of  Nature.  I  propose  to  state  some  of  the  main 
difficulties  which  strike  me  in  the  theory,  as  presented  ; 
without  imagining  for  a  moment  that  they  are  fatal 
objections  to  this  type  of  theory,  or  that  Mr  Russell  is 
not  quite  as  well  aware  of  them  as  I  am. 

(i)  A  purely  selective  theory,  if  it  could  be  worked 
out,  would  have  two  advantages,  one  ontological,  and 
the  other  epistemological.  The  ontological  advantage 
is  that  sensa  would  be  given  a  definite  and  intelligible 
status,  as,  in  some  sense,  "  parts"  of  physical  objects  ; 
whereas,  in  theories  of  the  generative  type,  it  is  hard 
to  see  how  they  exist  side  by  side  with  the  physical 
events  and  objects  which  generate  them.  The  episte- 
mological advantage  is  that  the  hypothetical  entities, 
which  every  theory  needs  in  order  to  fill  the  gaps 
between  our  sensations,  are  here  of  the  same  kind  as 
the  sensa  which  we  sense.  We  are  therefore  only 
postulating  more  entities  of  a  kind  which  we  already 
know  to  exist. 

Now  it  does  seem  to  me  that  a  theory  like  Russell's, 
however  successful  it  might  be  on  the  ontological  side, 
sacrifices  most  of  the  epistemological  advantages  of  a 
purely  selective  theory.  If  our  brains  and  nervous 
systems  be  a  kind  of  "medium,"  they  are  media  from 
which  even  the  "Free  Man"  cannot  get  free.  And  it 
is  admitted  that  they  "colour"  to  an  unknown  extent 
all  the  sensa  with  which  we  can  possibly  become 
acquainted.  We  therefore  do  not  really  know  that 
sensa  can  exist  at  all  apart  from  brains  and  nervous 
systems.     And,  even  if  we  decide  to  postulate  sensa  of 


CONDITIONS   AND   STATUS   OF   SENSA     533 

some  kind  in  places  and  times  where  there  are  no  brains 
and  nervous  systems,  we  cannot  have  the  slightest  idea 
what  intrinsic  sensible  qualities  such  sensa  will  have. 
We  really  know  just  as  much  and  just  as  little  about 
them  as  we  do  about  the  hypothetical  scientific  events 
and  objects  of  the  Critical  Scientific  Theory.  To  call 
them  sensa,  under  these  circumstances,  seems  rather 
misleading  ;  for  it  is  liable  to  disguise  the  purely  hypo- 
thetical character  of  these  events,  and  to  suggest  that 
we  know  a  good  deal  about  their  intrinsic  qualities. 
Really  we  know  nothing  about  the  events  which  happen 
at  intermediate  times  and  places  between  the  opening 
of  a  shutter  and  our  sensing  of  a  flash,  except  that  they 
obey  Maxwell's  Equations. 

(ii)  In  Chapters  IX  and  X  I  pointed  out  that  per- 
ceptual physical  objects  are  composita,  made  up  of  various 
correlated  constituent  objects,  optical,  tactual,  etc.  Now, 
Mr  Russell's  theory  seems  to  have  been  built  up  wholly 
by  considering  the  optical  constituents  of  perceptual 
physical  objects.  It  is  a  theory  of  complete  optical  objects, 
and,  so  far,  of  nothing  else.  It  cannot  even  be  said 
that  he  has  yet  dealt  with  partial  optical  objects,  like 
mirror-images,  or  with  the  still  worse  complications 
of  non-homogeneous  transmitting  media.  When  Mr 
Russell  tells  us  that  he  can  easily  deal  with  Nature 
by  regarding  it  as  a  six-dimensional  spatial  whole,  in 
which  all  sensa  have  their  places,  and  by  regarding 
physical  objects  as  groups  of  sensa  which  form  three- 
dimensional  spatial  wholes,  I  cannot  help  suspecting 
that  he  is  thinking  only  of  visual  sensa  and  of  complete 
optical  objects.  At  least,  I  can  understand  more  or 
less  what  he  means,  on  this  interpretation,  but  not  at 
all  if  he  expects  to  work  all  kinds  of  sensa  and  all  the 
various  components  of  perceptual  physical  objects  into 
such  a  scheme. 

(iii)  Closely  connected  with  this  is  the  fact  that 
Mr  Russell  has  not  yet  treated  the  observer's  body 
in  terms  of  his  general  theory  of  physical  objects.     The 


534  SCIENTIFIC  THOUGHT 

body  is  a  physical  object  ;  and,  regarded  as  a  per- 
ceptual object,  it  has  all  the  components  which  an 
ordinary  piece  of  matter  has,  together  with  a  special 
component,  viz.,  the  somatic  history.  If  Mr  Russell's 
general  theory  be  right,  my  body  must  consist  of  a 
set  of  correlated  groups,  each  composed  of  correlated 
sensa  of  a  certain  kind  ;  and  it  must  be  this  composite 
set  which  selects  and  "colours  "  the  sensa  of  the  other 
physical  groups  which  we  sense.  I  am  not  sure  that 
his  theory  does  not  at  present  owe  some  of  its  plausibility 
to  the  fact  that,  while  we  read  his  exposition,  we  think 
of  our  own  bodies  (and  perhaps  of  other  media,  like 
mirrors  and  coloured  glass)  as  physical  objects  in  the 
non-Russellian  sense,  and  of  all  other  pieces  of  matter 
as  physical  objects  in  the  Russellian  sense. 

(iv)  It  might,  perhaps,  be  objected  that  Russell's 
theory  makes  sensa  too  substantial  and  self-subsistent, 
whilst  it  makes  physical  objects  too  ghostly.  Certainly 
Alexander's  theory  is,  in  this  respect,  more  in  accord- 
ance with  common-sense.  But  I  am  not  inclined  to 
attach  much  weight  to  this  objection  myself.  After 
all,  on  Russell's  theory,  unsensed  sensa  do  not  as  a 
rule  exist  in  isolation.  They  are  members  of  physical 
groups,  connected  together  by  qualitative  similarity  and 
regular  rules  of  spatio-temporal  correlation.  And  the 
alleged  substantiality  of  physical  objects,  as  compared 
with  sensa,  may  well  rest  on  nothing  but  our  special 
practical  interest  in  those  groups  of  sensa  which  happen 
to  be  pretty  stable,  and  our  practical  ignoring  of  isolated 
sensa,  or  of  abnormal  and  less  permanent  groups,  such 
as  mirror-images. 

The  upshot  of  the  discussion  seems  to  be  that  selective 
theories  are  at  present  rather  in  the  position  of  demo- 
cratic government.  There  is  no  positive  argument  for 
them  ;  the  only  arguments  for  them  are  the  objections 
against  their  alternatives.  And  the  analogy  may  be 
carried  further,  in  so  far  as  there  are  serious  positive 
objections  to  all  selective  theories  that  have  yet  been 


CONDITIONS   AND   STATUS   OF   SENSA     535 

suggested.  If,  to  avoid  these,  we  introduce  a  certain 
amount  of  generation,  we  may  keep  many  of  the  onto- 
logical  advantages  of  selective  theories,  but  we  lose 
most  of  their  epistemological  benefits  and  we  introduce 
the  new  and  difficult  conception  of  generation. 

(b)  Causation  and  Creation. — It  remains  to  consider 
the  form  of  production  which  we  have  called  generation. 
This  is  itself  an  ambiguous  term  ;  and  generation  must 
be  distinguished  into  causation  and  creation.  We  shall 
see  that  the  distinction  between  creative  and  causal 
theories  does  not  rest  on  an  absolute  difference  of  kind  ; 
still  it  is  important,  and  it  must  be  firmly  grasped 
before  we  can  criticise  generative  theories  of  the  pro- 
duction of  sensa. 

When  I  say  that  the  friction  of  two  bodies  ' '  generates  " 
heat,  I  am  using  "generation"  in  the  causal,  and  not 
in  the  creative,  sense  of  the  word.  I  mean  that  a 
certain  process  in  two  pre-existing  bodies  {e.g.,  the 
rubbing  together  of  a  drill  and  a  piece  of  iron)  is 
followed  by  a  change  of  quality  (or  rather,  by  a  change 
of  intensity  in  an  already  existing  quality)  in  both  of 
them.  All  ordinary  generation  is  of  this  type.  It  pre- 
supposes one  or  more  already  existing  substances,  as 
continuant  conditions  ;  and  it  asserts  that  one  specific 
kind  of  change  in  their  qualities  or  relations  is  followed, 
according  to  a  general  rule,  by  another  specific  kind 
of  change  in  their  qualities  or  relations.  Creation,  on 
the  other  hand,  would  mean  that  certain  occurrent 
conditions  in  a  pre-existing  substance  or  substances 
are  followed  by  the  springing  into  existence  of  a  new 
substance  of  some  specific  kind.  The  difference  may  be 
stated  shortly,  in  terms  of  occurrent  and  continuant 
conditions.  Both  causation  and  creation  involve  these 
two  kinds  of  condition.  In  ordinary  causation,  the 
event  which  is  determined  by  them  joins  up  with  one 
or  other  of  the  continuant  conditions,  and  becomes  a 
part  of  its  history.  In  creation,  the  event  which  is 
determined  does  not  join  up  with  any  of  its  continuant 


536  SCIENTIFIC   THOUGHT 

conditions  to  form  a  further  stage  in  their  history  ;  it 
either  remains  isolated  or  is  the  beginning  of  an 
altogether  new  strand  of  history. 

Now,  in  real  life,  there  are  no  examples  of  pure 
creation.  However  isolated  an  event  may  be  when  it 
is  generated,  it  has  some  place  and  date  in  Nature,  and 
thus  joins  up  with  and  continues  the  history  of  Nature 
<rs  a  -whole,  if  not  the  history  of  some  particular  pre- 
existing object in  Nature.  Moreover,  if  it  be  determined 
bv  events  in  pre-existing  substances,  its  place,  date, 
and  specific  qualities  will  be  fixed  by  those  of  its 
determining  conditions.  So  it  is,  at  least,  joined  on 
by  causal  connexions  to  one  or  more  special  pre-existing 
parts  of  Nature ;  although  it  lacks  that  qualitative 
similarity  and  spatial  continuity  with  any  of  these  parts, 
which  would  be  needed  before  we  could  say  that  it 
actually  joins  up  with  and  continues  the  history  of  some 
particular  pre-existing  substance.  Thus,  we  may  speak 
of  one  generative  process  as  being  "more  of  the  creative 
type,"  and  of  another  as  being  "more  of  the  causal 
type";  but  we  can  hardly  speak  of  any  process  as 
"purely  creative."  In  proportion  as  a  generative 
process  is  more  of  the  creative  type,  it  is  less  intelligible 
to  us  ;  and  one  difficulty  about  generative  theories  of 
the  production  of  sensa  is  that,  at  first  sight  at  any 
rate,  the  generation  of  sensa  by  physical  and  physio- 
logical processes  seems  to  be  predominantly  of  the 
creative  type.      Let  us  see  how  far  this  is  true. 

If  processes  in  our  own  bodies  be  sufficient  con- 
ditions for  generating  sensa,  it  cannot  be  said,  as  a 
rule,  that  the  sensa  which  they  generate  join  up  with 
and  continue  the  history  of  the  conditions  which 
generate  them.  If  a  change  in  my  optic  nerve  or  my 
brain  generates  a  red  sensum,  there  is  no  obvious  way 
in  which  this  sensum  can  be  said  to  join  up  with  and 
continue  the  history  of  my  brain  or  optic  nerve.  If 
sensa  and  sense-objects  differ  in  kind  from  scientific 
events   and   objects,    it    is   clear   that   there   cannot    be 


CONDITIONS   AND   STATUS   OF   SENSA     537 

much  literal   continuity  of  quality  or  position   between 
a  sensum  and  its  generative  conditions.     The  only  con- 
tinuity is  temporal   and  causal.      Even   if  we  suppose 
that  physical  objects,  including  our  brains  and  nerves, 
are   groups   of  sensa,    some  of  which    are   sensed  and 
most  of  which   are   not,    there  is    still    very  little   con- 
tinuity   between  most  of  our   special    sensa   and    their 
somatic  conditions.      For,  on  such  a  view,  my  body  is 
presumably   a    large    group    of  somatic   sensa,    out   of 
which  I  sense  a  certain  small  selection  which  forms  my 
somatic   sense-history.      The    physiological    conditions 
which  generate  other  sensa  would   therefore  be  some- 
where in  this  mass  of  somatic  sensa.      Now,  visual  and 
auditory  sensa  are  not  in  the  least  like  somatic  sensa  ; 
they  fall  into  different  special  sense-histories,  and   not 
into   the   somatic    sense-history.       Hence,    even    if  our 
brains  and  nervous  systems  be  simply  groups  of  somatic 
sensa,    it  cannot  be  said   that  the  visual  and  auditory 
sensa,  of  which  they  are  the  continuant  generative  con- 
ditions, join  up  with  them   and  continue  their  history 
in  any  plain  and  straightforward  way.      (Of  course,  these 
remarks  do  not  apply  to  the  generation  of  somatic  sensa 
themselves  ;  for  they  do  join  up  with  the  somatic  sense- 
history,  and  the  latter  simply  is  a  selection  out  of  that 
whole    mass   of  somatic  sensa  which  would  constitute 
my  body  on  the  hypothesis  under  discussion.)      Thus 
we  may  say  that,  on  no  view  of  the  nature  of  physical 
events  and  objects,  can   visual   and  auditory  sensa  be 
said  to  join   up   with  and  continue  the  history  of  their 
generative  conditions,  if  the  latter  be  processes  in  our 
brains  and  nervous  systems.     Thus,   if  such  sensa   be 
generated  at  all  by  physiological  processes,  it  must  be 
admitted  that  the   generation   is   rather  of  the  creative 
than  of  the  causal  type. 

On  the  other  hand,  we  must  not  exaggerate  the 
isolation  of  visual  and  auditory  sensa.  (1)  All  those 
that  we  sense  are  at  any  rate  events  in  our  general  sense- 
history,    and   are    thus    related    at    least    by    sensible 

2  M 


5/.S  SCIENTIFIC   THOUGHT 

temporal  relations  to  parts  of  our  somatic  sense-history. 
(2)   Again,  it   is  very  rare  for  a  visual  sensum  to  occur 
apart  from  other  visual  sensa.     This  does  happen  indeed 
if  we  sense  a  single  flash  on  a  dark  night.     But  usually 
a  visual  sensum  is  an  outstanding  part  of  a  much  larger 
visual  field,  and   this    visual  field  is    itself  a  slice  of  a 
visual    sense-history,    which    stretches   out    before   and 
after  it.     So,  in  the  vast  majority  of  cases,  visual  sensa 
when  they  occur,  do  join  up  with  a  special  pre-existing 
continuant,    viz.,    the    observer's   visual    sense-history. 
This  is  less  frequently  true  of  auditory  sensa,  though  it 
is  often  true  of  them  too.     (3)  Often  a  visual  sensum 
does    not    merely  continue  the  visual    sense-history    in 
general,   but  continues  the  history  of  some   particular 
sense-object  within  it.     This  is  true  of  most  of  the  out- 
standing sensa  in  our  visual  fields,  if  we  look  steadily 
in  any  one  direction.     (4)  Even   when  a  sensum  is  a 
quite  isolated  event    in  my  general    sense-history,  and 
not  part  of  any  sense-object  in  one  of  my  special  sense- 
histories  {e.g.,  when  it  is  a  single  flash  sensed  on  a  dark 
night),  it  may  have  specially  close  correlations  with  sensa 
in  the  histories  of  other  observers.     It  may  be  a  member 
of  a   group   of  very   similar   sensa,    which    constitutes 
a  complete  or  partial   optical  object  and  has  members 
in   various   observers'   histories.      And   the   sensum    in 
another  observer's  history,  which  is  thus  correlated  with 
an  isolated  sensum  in  mine,  may  not  itself  be  isolated. 
It  may  be  a  slice  of  a  long  sense-object.     For  instance, 
another  man  may  be  gazing  at  a  lighted  candle,  and 
between  it  and  my  body  there  may  be  an  opaque  object 
with  a  shutter.     If  this  shutter  be  suddenly  opened  and 
immediately  afterwards   closed  again,  I  shall  sense  an 
isolated  visual  sensum.     But  it  will  be  correlated  with 
a  very  similar  sensum  in  the  other  man's  history,  and 
this  other  sensum  will  be  a  short  slice  of  a  long  sense- 
object.     So   that,    indirectly,    my   isolated    sensum    will 
be  correlated  with  a  certain  special  sense-object,  although 
this  sense-object  is  not  in  my  history. 


CONDITIONS   AND   STATUS   OF   SENSA     539 

Thus  it  is  far  from  being  true  in  general  that  sensa 
are  perfectly  isolated  occurrents,  and  that  they  do  not 
join  up  with  the  history  of  pre-existing  continuants. 
What  we  must  say  is  that  sometimes  they  seem  to  be 
extremely  isolated  ;  that  often  their  connexion  with  pre- 
existing continuants  is  rather  remote  and  indirect;  and 
that  apparently  they  never  join  up  with  the  history  of 
that  particular  continuant  (viz.,  the  brain)  which  is  the 
seat  of  their  most  immediate  special  occurrent  conditions. 
These  facts  show  that  the  generation  of  sensa  by 
physical  and  physiological  processes  must  be  consider- 
ably different  from  the  causation  of  a  change  in  one 
physical  object  by  a  change  in  another.  But  they  do 
not  suggest  that  the  generation  of  sensa,  if  it  take  place 
at  all,  is  a  perfectly  unintelligible  process  of  creation. 

(c)  Physical  Causation  and  Causation  of  Sensa. — We 
have  seen  that  there  is  no  radical  distinction  between 
causation  and  creation,  but  that  the  generation  of 
physical  events  is  more  of  the  causal  type,  and  that  of 
sensa  more  of  the  creative  type.  We  ought  therefore 
to  be  able  to  give  a  definition  of  generation,  which  shall 
cover  both  cases,  and  then  to  point  out  what  dis- 
tinguishes the  generation  of  sensa  from  that  of  physical 
events. 

In  order  to  do  this,  we  must  enter  a  little  more  deeply 
into  the  nature  of  events.  An  event  is  a  particular 
existent,  and  therefore  the  generation  of  any  event  is 
the  generation  of  a  new  particular  existent.  By  this 
I  simply  mean  that  precisely  and  numerically  the  same 
event  cannot  possibly  recur,  although,  of  course,  quali- 
tatively similar  events  can  occur  at  many  different  times 
and  places.  Next,  we  must  distinguish  between  de- 
terminateness  and  particularity .  A  perfectly  definite  shade 
of  red  is  determinate,  but  is  not  particular.  The  differ- 
ence between  determinateness  and  particularity  will 
best  be  seen  by  an  example.  Let  us  take  (1)  redness 
in  general,  (2)  a  perfectly  definite  shade  of  red,  and 
(3)  a  certain  sensum  which  has  this  shade  of  red.     The 


540  SCIENTIFIC  THOUGHT 

relation  of  (3)  to  (2)  is  quite  different  from  that  of  (2) 
to  (1),  though  this  is  often  disguised  by  the  statement 
that  (2)  is  an  instance  of  (1)  and  (3)  is  an  instance  of  (2). 
The  difference  is  that  the  sensum  cannot  recur,  though 
other  sensa  of  exactly  the  same  shade  may  occur  at 
other  times  and  places.  On  the  other  hand,  the  definite 
shade  of  red  is  still  a  universal  ;  since  any  number 
of  sensa  may  have  precisely  this  shade  of  red.  It  is 
therefore  best  to  say  that  the  definite  shade  of  red  is 
a  loivest  determinate  under  the  determinable  of  redness  (to 
adopt  Mr  W.  E.  Johnson's  phraseology),  and  that  the 
sensum  is  a  particular  instance  of  this  determinate.  The 
analogies  and  differences  between  being  a  determinate 
under  a  determinable,  and  being  an  instance  of  a  de- 
terminate, are  the  following:  (1)  Determinables  have 
a  plurality  of  determinates,  and  determinates  have  a 
plurality  of  instances.  But  (2)  the  number  of  determi- 
nates under  a  given  determinable  is  a  necessary  conse- 
quence of  the  nature  of  the  determinable,  whilst  the 
number  of  instances  of  a  given  determinate  is  purely 
contingent.  It  is  of  the  nature  of  redness  that  there 
should  be  just  such  and  such  shades  of  red,  but  the 
number  of  instances  of  any  shade  of  red  depends  on  the 
make-up  of  the  existent  world.  And  (3)  the  instances 
of  determinates  are  always  particulars,  whilst  the  de- 
terminates under  determinables  are  always  universals. 

Now  an  event  is  fully  described  i.e.,  is  marked  off 
from  all  other  events,  if  we  know  (1)  its  place  and  date 
in  some  Space-Time  ;  (2)  its  extension  and  duration  ; 
and  (3)  the  determinates  of  which  it  is  an  instance. 
For  example,  a  certain  visual  sensum  is  completely 
described  if  we  know  where  and  when  it  occurs  in 
an  observer's  sense-history,  what  shape  it  has,  how 
long  it  lasts,  and  what  precise  shade  of  what  precise 
colour  it  has.  Thus,  the  occurrence  of  any  event  con- 
sists in  the  "occupation"  of  a  certain  definite  region 
of  some  Space-Time  by  one  or  more  determinates  under 
one  or   more   determinables.      Now  the    nature   of  the 


CONDITIONS   AND   STATUS   OF   SENSA     541 

"  filling"  of  one  or  more  regions  may  fix,  according  to 
general  rules,  the  nature  of  the  "filling"  of  a  certain 
other  region.  If  so,  we  say  that  the  events  which  con- 
sist in  the  former  regions  being  "filled"  with  such  and 
such  determinates  generate  the  event  which  consists 
in  the  latter  region  being  "filled"  with  such  and  such 
other  determinates. 

We  can  now  give  a  definition  of  generation  in 
general.  The  widest  form  of  causal  law  would  seem 
to  be  of  the  following  kind  :  If  any  determinate  c  of  the 
determinable  C  inheres  in  a  region  r  of  the  Space-Time 
S,  then  a  certain  correlated  determinate  y  of  a  certain 
correlated  determinable  T  inheres  in  a  certain  correlated 
region  p  of  a  certain  correlated  Space-time  2.  (Of 
course,  the  antecedent  may  involve  more  than  one 
determinable,  and  more  than  one  region  ;  but  there  is 
no  need  to  complicate  matters  further  for  our  present 
purpose.) 

Now  I  take  it  that  ordinary  physical  causation  is 
distinguished  by  a  very  great  simplification  of  this 
most  general  type  of  law.  (1)  All  the  events  under 
consideration  are  in  the  same  Space-Time  (viz.,  physical 
Space-Time)  so  that  S  =  2.  This  is  true,  in  spite  of  the 
fact  that  physical  Space-Time  can  be  split  up  in  many 
different  ways  into  time-axes  and  timeless  spaces.  (2) 
Very  often  in  physical  causation  we  have  only  to  deal 
with  a  single  determinable,  e.g.,  physical  motion.  This 
would  be  true  if,  e.g., we  were  considering  how  the  motion 
of  one  billiard-ball  generates  that  of  another.  In  such 
cases  C  =  F.  (3)  The  determinables  are  generally  such 
that  their  determinates  can  be  fixed  by  giving  a  particular 
numerical  value  to  some  quantitative  variable.  If  so, 
c  and  y  will  be  connected  by  a  mathematical  formula, 
such  as  y  =  0  (e).  Lastly  (4),  since  we  are  dealing  here 
with  a  single  Space-Time,  we  may  be  able  to  assign 
a  single  system  of  co-ordinates  to  the  whole  of  it.  The 
regions  r  and  p  will  then  have  co-ordinates  in  the  same 
frame,  and  the  correlation  between  them  will  be  expres- 


542  SCIENTIFIC   THOUGHT 

sible   in  an   equation  or   set   of  equations  of  the   form 

Now  the  peculiarity  of  the  causation  of  sensa  may  be 
that  these  special  simplifying  conditions  are  not  fulfilled 
here.     Take,  e.g.,  the   production   of  a  red  sensum  by 
processes  in  the  optic  nerve  and  brain,  supposing-  that 
these  are  sufficient  occurrent  conditions,     (i)  The  brain- 
events  consist  in  the  tilling  of  a  certain  region  of  physical 
Space-Time  with  certain   physical  determinates.      The 
sensum  consists  of  the  filling  of  a  region  in  the  observer's 
visual    Space-Time   with  a   determinate   shade  of  red. 
Thus  two  different  Space-Times  are  involved.     (2)   In 
-consequence  of  this,    the  correlation    between    r  and  p 
will  be  of  a  much  more  complicated  type  than  it  would 
be  if  r  and  p  were  just  two  regions  in  the  same  Space- 
Time.   (3)  We  are  here  concerned  with  two  quite  different 
determinates,  viz.,  physical  motion   (say)  and  redness. 
Thus  we  cannot  put  C  =  T.     (4)  The  determinates  under 
redness,  i.e.,  the  definite  shades  of  red,  cannot  be  ex- 
pressed simply  by  different  values  of  the  same  numerical 
variable,  since  they  differ  qualitatively.     Thus  we  cannot 
put  y  =  <p  (c),  where  this  is  an  ordinary  algebraic  equa- 
tion or  set  of  equations. 

All  this  complication  is  doubtless  troublesome,  but 
it  does  not  really  render  the  causation  of  sensa  different 
in  kind  from  the  causation  of  one  physical  event  by 
another.  The  scientist  has  simply  banished  nearly  all 
qualitative  differences  from  his  world,  and  has  contented 
himself  with  the  residuum.  But  the  whole  mass  of 
sensible  appearances,  from  the  most  impressive  to  the 
most  trivial,  and  from  the  most  normal  to  the  most 
outlandish,  forms  part  of  the  total  content  of  the  existent 
world.  We  have  no  right  then  to  feel  surprised  if  the 
structure  and  laws  of  the  existent  world  as  a  whole  fail 
to  show  that  sweet  simplicity  which  distinguishes  the 
particular  part  of  it  to  which  natural  scientists  have 
confined  themselves.  Science  has  been  able  to  make 
the    great   strides  which    it   has    made   by   deliberately 


CONDITIONS   AND   STATUS   OF   SENSA     543 

ignoring  one  side  of  reality.  The  end  has  justified  the 
means,  for  the  world  is  so  complex  that  it  can  only  be 
understood  bit  by  bit.  Moreover,  the  success  of  this 
abstraction  does  show  that  reality  as  a  whole  has  less 
unity  than  certain  departments  of  it.  The  physical  part 
of  reality  and  the  sensible  part  do  not  indeed  form  water- 
tight compartments,  but  it  does  seem  as  if  there  were 
characteristic  forms  of  unity  in  each  which  do  not  stretch 
across  from  one  to  the  other.  From  the  philosophic 
point  of  view,  the  procedure  of  natural  science  has  rather 
resembled  that  of  those  diplomatic  Conferences  which 
have  done  so  much  to  brighten  European  life  since  the 
Allies  inaugurated  the  New  Jerusalem  in  191 8.  The 
most  edifying  unity  has  been  secured  on  each  occasion 
by  turning  a  blind  eye  to  all  the  less  convenient  facts, 
and  referring  them  to  a  future  Conference  for  further 
discussion.  In  philosophy,  as  in  economics,  facts  do  not 
cease  to  be  real  by  being  ignored  ;  and  the  philosopher 
becomes  the  residuary  legatee  of  all  those  aspects  of 
reality  which  the  physicist  (quite  rightly,  for  his  own 
purpose)  has  decided  to  leave  out  of  account.  The 
analogy  only  breaks  down  when  we  contrast  the  relative 
success  of  the  scientists  and  of  the  politicians  in  their 
respective  fields. 

The  difficulty  which  we  feel  about  the  ontological 
status  of  sensa  may  be  put  as  follows  :  We  feel  that 
anything  which  can  successfully  claim  to  be  "  real," 
must  be  somewhere  and  somew/ien.  And  we  are  so 
much  accustomed  to  physical  Space-Time,  and  to  the 
way  in  which  physical  events  and  objects  occupy  regions 
in  it,  that  we  think  that  an  event  cannot  be  "real" 
unless  it  occupies  some  region  of  physical  Space-Time 
in  the  way  in  which  a  physical  event  does  so.  Now, 
it  seems  clear  that  either  (1)  sensible  determinates  (such 
as  some  particular  shade  of  red)  do  not  inhere  in  regions 
of  physical  Space-Time,  but  in  regions  of  some  other 
Space-Time  ;  or  (2)  that,  if  they  do  inhere  in  regions 
of  physical  Space-Time,  they  must  inhere  in  the  latter 


544  SCIENTIFIC   THOUGHT 

in  some  different  way  from  that  in  which  physical  deter- 
minates (like  physical  motion)  do  so.  Either  there  is  one 
sense  of  "  inherence"  and  many  different  Space-Times, 
or  there  is  one  Space-Time  and  many  different  senses 
of  "  inherence."  On  either  alternative  the  world  as  a 
whole  is  less  simple  than  we  should  like  to  believe  ; 
and,  if  we  have  come  to  think  that  there  is  only  one 
possible  Space-Time  and  only  one  possible  kind  of 
inherence,  we  shall  be  inclined  to  suppose  that  sensa 
are  nowhere  and  nowhen.and  therefore  are  mere  fictions. 
Since  this  is  plainly  contrary  to  fact,  unless  the  whole 
way  of  treating  sensible  appearance  which  is  developed 
in  this  book  be  wrong,  we  must  accept  one  of  the  two 
alternatives  just  mentioned. 

Now,  it  seems  to  me  that  these  two  alternatives  are 
not  mutually  exclusive,  but  are  complementary.  We 
have  long  ago  dropped  the  notion  that  a  Space-Time  is 
a  kind  of  empty  warehouse,  with  various  cellars  ready 
to  receive  different  materials  ;  although  it  remains  con- 
venient to  talk  as  if  this  were  so.  Our  view  is  that  a 
Space-Time  is  a  characteristic  form  of  relational  unity 
which  pervades  a  whole  set  of  entities,  and  binds  them 
together  into  a  peculiar  kind  of  complex  whole,  whose 
fundamental  structure  is  summed  up  in  the  geo-chrono- 
metry  of  the  Space-Time  in  question.  When  we  say 
that  a  determinate  "  inheres  in  a  certain  rep-ion  of  a 
certain  Space-Time,"  we  only  mean  that  an  instance 
of  it  enters  into  certain  relations  with  other  instances 
of  the  same  and  of  other  determinates,  and  that  the 
relations  which  it  has  to  them  are  of  the  same  type 
as  those  which  they  have  to  each  other.  I  think 
that  my  view  of  the  structure  of  Nature  as  a  whole, 
with  its  peculiar  mixture  of  unity  and  disunity,  can  be 
more  clearly  explained  by  a  familiar  analogy  than  by 
a  great  deal  of  formal  exposition. 

Let  us  compare  a  Space-Time  to  a  family  of 
brothers  and  sisters.  Then,  coming  to  occupy  a  region 
of  this  Space-Time  will   be   like    being   born    into   this 


CONDITIONS  AND   STATUS   OF   SENSA      545 

family.  Let  us  take  such  a  family,  and  suppose  that  all 
its  members  are  children  of  the  same  husband  and  wife. 
This  fundamental  family  Fx  shall  be  taken  as  analogous 
to  the  physical  world,  and  the  simple  relation  of  brother 
or  sister  within  it  shall  be  analogous  to  the  structure  of 
physical  Space-Time.  Now  we  can  suppose  that  some 
of  the  members  of  Fx  have  children,  and  that  others  do 
not.  Those  who  do  may  be  compared  to  organised 
bodies,  and  those  who  do  not  to  unorganised  bodies. 
I  am  going  to  take  the  children  as  analogous  to  sensa. 
Now  consider  the  families  of  two  members  of  Fr  Let 
these  two  members  be  A  and  B,  and  let  us  call  their 
families  respectively  FA  and  FB.  Then  we  notice  the 
following  facts:  (1)  Each  of  these  families  forms  a 
group  analogous  to  Fr  This  corresponds  to  the  fact 
that  the  sensa  of  each  individual  (provided  they  are  of 
the  same  sort)  form  a  spatio-temporal  whole.  (2)  FA 
and  FB  do  not  together  form  one  family,  in  the  sense 
defined.  This  corresponds  to  the  fact  that  the  sense- 
histories  of  different  observers  form  different  Space- 
Times.  (3)  Neither  FA  nor  FB  forms  with  F,  a  single 
family,  in  the  sense  defined.  This  corresponds  to  the  fact 
that  sensa  are  not  literally  in  physical  Space-Time,  and 
that  physical  events  are  not  literally  in  any  sensible 
Space-Time.  (4)  In  spite  of  this,  there  are  relations 
between  members  of  FA  and  members  of  FB,  viz.,  the 
relation  of  cousinship.  Similarly,  there  are  relations 
between  members  of  FA  or  FB  and  those  of  Fx,  viz., 
the  relations  of  child-and-parent  or  of  nephew-and- 
uncle.  Thus,  although  the  whole  set  of  individuals 
of  the  two  generations  does  not  constitute  one  family, 
in  the  sense  of  one  set  of  brothers  and  sisters,  yet  it  does 
constitute  a  set  of  interrelated  terms,  which  may  be 
called  a  "family"  in  a  wider  sense.  In  precisely  the 
same  way,  I  take  it,  the  physical  world  and  the  various 
sense-histories  form  one  interrelated  whole,  although 
the  relations  which  stretch  across  from  one  sense- 
history  to  another  or  from  a  sense-history  to  the  physical 


546  SCIENTIFIC  THOUGHT 

world  arc  more  complex  than  those  which  interconnect 
physical  events  or  interconnect  sensa  in  the  same  sense- 
history.  (5)  Lastly,  we  might  suppose  that  some  of 
the  members  of  F,  had  married  twice  in  succession,  and 
had  thus  had  two  families.  Or,  again,  some  of  them 
might  have  embraced  Mormonism  and  a  plurality  of 
contemporary  wives.  We  should  thus  get  a  peculiar 
relation,  viz.,  that  of  half-brother,  to  which  there  is 
nothing  exactly  analogous  in  the  family  Fx.  The  whole 
family  of  M,  the  Mormon  member  of  Fx,  would  split  up 
into  two  or  more  families.  The  relation  between  a 
member  of  one  of  these  families  and  a  member  of  another 
of  them  would  be  more  intimate  than  that  of  cousinship 
and  less  intimate  than  that  of  complete  brotherhood. 
This  is  analogous  to  the  fact  that  the  general  sense- 
history  of  an  observer  splits  up  into  a  number  of  special 
sense-histories,  such  that  sensible  temporal  relations  do, 
and  sensible  spatial  relations  do  not,  stretch  across  from 
one  to  the  other. 

Now,  if  we  had  taken  the  original  family  F1  as 
fundamental,  and  had  "placed"  all  the  members  of 
the  second  generation  by  stating  their  various  relations, 
such  as  child,  nephew,  etc.,  to  various  members  of  Fx, 
this  would  be  analogous  to  taking  physical  Space-Time 
as  fundamental  and  saying  that  sensible  determinates 
of  different  kinds  inhere  in  different  ways  in  regions 
of  this  one  Space-Time.  If,  on  the  other  hand,  we 
take  the  notion  of  families,  in  the  strict  sense,  as  funda- 
mental, this  will  be  analogous  to  saying  that  there  is 
a  plurality  of  different,  though  correlated,  Space-Times, 
and  that  sensible  determinates  inhere  in  their  own 
Space-Times  in  the  same  way  as  physical  determinates 
inhere  in  physical  Space-Time.  It  is  obvious  that 
these  are  only  two  different  ways  of  treating  the  same 
set  of  interrelated  facts.  Logically  the  two  methods 
are  equivalent  to  each  other. 

I  have  taken  this  elementary  example  to  illustrate  in 
rough  outline  how  we  can  combine  sensa  and  physical 


CONDITIONS   AND   STATUS   OF   SENSA     547 

events  into  one  universe,  in  spite  of  their  many  important 
differences.  The  exact  details  of  this  must  be  left  to 
the  symbolic  logician  ;  but  the  complexities  which  arise 
even  in  the  simple  example  of  family  relationships  will 
show  the  reader  that  the  complication  of  Nature  as  a 
whole  is  compatible  with  the  ultimate  relations  between 
its  elements  being  comparatively  few  and  simple.  The 
mistake  is  to  try  to  force  Nature  as  a  whole  into  the 
mould  which  fits  one  important  part  of  it ;  and  then  to 
suppose  that,  because  this  attempt  breaks  down,  Nature 
as  a  whole  has  no  structure  at  all,  but  falls  into  com- 
pletely isolated  and  incoherent  fragments.  There  are, 
I  believe,  two  different  levels  of  "simplicity,"  and 
between  them  there  is  a  region  of  "complexity." 
There  is  the  lower  kind  of  simplicity,  which  we  find 
when  we  isolate  one  fragment  of  Nature  from  the  rest, 
and  ignore  all  the  awkward  facts  that  refuse  to  fit  into 
the  scheme  which  applies  to  this  fragment.  There  is, 
or  there  well  may  be,  a  higher  kind  of  simplicity,  where 
we  have  recognised  the  fundamental  structure  of  Nature 
as  a  whole,  and  have  seen  how  the  structure  of  special 
regions  of  Nature  is  just  a  special  case  of  these  funda- 
mental relations.  But,  in  order  to  pass  from  the  lower 
to  the  higher  kind  of  simplicity,  we  must  traverse 
an  intermediate  stage  of  confusion  and  complexity, 
in  which  we  confront  the  lower  simplicity  with  all  the 
awkward  facts  which  it  has  ignored.  This  is  a  task 
in  which  we  can  all  help,  if  we  keep  our  heads  clear 
and  refuse  to  be  put  off  with  cheap  and  easy  explana- 
tions. The  final  stage,  that  of  finding  the  simple  plan 
on  which  all  this  complexity  is  constructed,  can  only 
be  accomplished  by  men  who  combine  the  insight  of 
genius  with  technical  mathematical  ability  of  the  highest 
order.  To  this  combination  of  gifts  few  of  us  can  lay 
claim,  and  the  present  writer  is  certainly  not  one  of 
those  who  can.  In  our  day  one  man,  Einstein,  has 
shown  what  such  a  combination  can  accomplish  within 
the    region  of  physics.     We  still  await    the  man  who 


54$  SCIENTIFIC   THOUGHT 

will  show  us  in  detail  how  the  world  of  physics  and  the 
world  of  sensible  appearance  are  united  into  the  one 
whole  of  Nature.  The  utmost  that  we  can  claim  to  have 
done  here  is  to  have  stated  some  of  the  facts  which  he 
will  have  to  take  into  account  and  to  unify. 

The    following-   additional  works  may  be   consulted 
with  advantage  : 

A.  \.  Whitehead,  The  Principles  of  Natural  Knowledge^  Parts 

II.  and  IV. 
The    Concept    of   Nature,     Chaps.     I.,     II. 
and   VII. 

The  Principle  of  Relativity,  Chaps.  II.  and 

IV. 

B.  A.    \V.    Russell,    Our  Knowledge  of  the  External   World, 

Lects.  III.  and  IV. 
The  Analysis  of  Mind,  Lects.  V.  and  VII. 
S.  Alexander,  Space,  Time,  and  Deity,  Bk.  III. 
H.  BEKGSON,  Matter  and  Memory. 
G.  E.  Moore,  Philosophical  Studies. 
G.  F.  Stout,  Mind,  Vol.  XXXI.  No.  124. 


INDEX 


"  How  index-learning  turns  no  student  pale 
Yet  holds  the  eel  of  Science  by  the  tail." 

(Pope,  The  DunciaJ.) 


Aberration,    and    Theory    of    Rela- 
tivity, 124 

■ and  Velocity  of  Light,  380 

Absolute  Structure  of  Nature,   186, 
194 

alternative  views  of,  203 

and  gravitation,  206,  etc. 

Absolute  Theory,  of  Time,  88,  etc. 

of  Space,  92,  etc. 

of  Motion,  96,  etc. 

Acts,  mental,  251 

of  sensing,  253,  521,  etc. 

Alexander,    Prof.    S.,    on    External 

World,  14 

on  Bodily  Feelings,  250 

on  Sensa,  529,  etc. 


etc. 


on  Russell's  Theory,  534 


Anne,  Queen,  her  death,  79,  etc. 
Appearance,  definition  of,  234 
two  theories  of,  237 

Sensum  Theory  of,  240,  etc. 

Appearing,   Multiple  Relation  The- 
ory of,  237 

Asquith,  Ri.  Hon.  H.  H.,  139 
"  At,"  temporal,  89 

spatial,  93 

Athanasian  Creed,  156,  215 
Axes  of  Reference,  105,  etc.,  no 

Newtonian     and     non-New- 
tonian, 173,  etc. 


Becoming,  67,  etc. 

Bergson,  Prof.  H.,  on  sense-percep- 
tion, 529 

Berkeley,  Bishop,  on  External 
World,  14,  232 

on  Esse  and  Per  dpi,  251 

on    Primary   and    Secondary 

Qualities,  274,  279 

on  Visual  Distance,  295 


Brace,  135,  n. 

Bradley,  Mr  F.  H.,  165 

Bucket  Experiment,  99,  etc. 

Relational  theory  of,  101,  etc. 


Cantor,  G.,  and  continuity,  17 
Carlisle,   Very  Rev.  The  Dean  of,  on 

Time,  84 
Causal  Generation,  535,  etc. 
Causation,  mnemic,  289 

immanent  and  transeunt,  492 

and  Creation,  535,  etc. 

physical,  539 

Centres  of  Discontinuity,  307 
Cerebral  Conditions,  513 
Chamberlain,  Rt.  Hon.  J.,  29 
Change,  of  things,  63 

of  events,  63,  etc. 

of   relational   properties,    65, 


Body,  human,   as  Physical  Object, 

437,  etc.,  444,  etc. 
and    Physical    Motion,    446, 


etc. 


etc. 


from  present  to  past,  67 
from   future   to   present, 


67, 


Bolingbroke,  Viscount,  82,  83 


sensible,  351,  etc. 

general  remarks  on,  405,  etc. 

Christ,  J.,  Body  and  Blood  of,  93 
Clifford,    Prof.    W.    A'.,    and    non- 

homaloidal  Spaces,  32 
Clocks,  setting  of,  128,  etc. 

Newtonian     and      non-New- 
tonian, 175,  etc. 

Co-existence,    physical,    criteria    of, 

422,  etc. 
Colour,  and  Wave-Theory  of  Light, 

280 
Columbus,  C,  51 
Compass,  gyrostatic,  103 
Compresence,  visual,  304,  etc.,  363, 

etc. 
"  Concealed  Masses,"  176 
Concordance  with  Fact,  71,  etc. 
Conditions,     originative,     transmis- 

sive,  and  productive,  490,  etc. 

necessary  and  sufficient,  499, 

etc. 


549 


55° 


INDEX 


Conditions,     occurrenl     and     con- 
tinuant, iin,  etc, 

mnemic,   cerebral,   and    con- 
nective, 51 3,  etc 

psychic,  516 

of  sensa  and  of  sensing,  519, 

etc. 
Connective  Conditions,  513 
Conscious  Mind,  514,  ;;. 
Conservation,   of  Momentum,   etc., 

on  Special  Theory  of  Relativity, 

180,  etc. 
Constituents    of    Physical    Objects, 

33o,  342 

tangible,  340 
optical,  341 
Constitutive  Properties  of  Physical 

Objects,  267 
Contact,  double,  440 
Containing  Volumes,  47 
Continuants,  510 
Continuous  and  Discrete  Aspects  of 

Nature,  310,  etc. 
Convergence,  46 
Co-ordinates,    Cartesian,    186,    191, 

193 

polar,  191 

on  surface  of  sphere,  192,  etc. 
Co- variance,  of  Laws  of  Nature,  151, 

etc. 
Creative  Generation,  535,  etc. 
Critical  Philosophy,  18,  etc. 
Critical  Scientific  Theory,  statement 

of,  272,  etc. 
• difficulties  of,  282 

final  treatment  of,  533,  etc. 

Cycloid,  51 


Ballon,].,  13 

Depth,  visual,  298,  etc. 

Descartes,  R.,  and  Mechanics,  87 

and  Secondary  Qualities,  279, 
282 
Determinables     and     determinates, 

54° 

Discordance  with  Fact,  71,  etc. 

Distance,    on    Absolute    and    Rela- 
tional Theories,  94,  etc. 

direct  and  indirect  measures 

of,  144 

connected     with    time-lapse, 


147,  etc. 

Doyle,  Sir  A.  Conan,  and  fairies,  71 

Dreams,  495 

Duration,  and  extension,  54 

sensible,  353 

of  perceptible  events,  388 
of     physical     objects,      393, 


etc. 


from  a  place,  397 


Easy,  Midshipman,  38 

Edward  I'//,   King,  233 
Edward  the  Confessor,  78,  89 
Einstein,    Prof.  A.,  and   non-homa- 
loidal  Spaces,  32 

on    peculiarities    of    gravita- 
tion, 175 

his  achievements,  547 

Electrodynamics,       and       Absolute 

Motion,   1  1  4,  etc. 
Empirical     Properties    of    Physical 

Objects,  267 
Energy,  Conservation  of,  182 

and  gravitation,  485 
Ether,  and  Absolute  Space,  31,  115 

stagnant,  120,  473 
Ethics,  and  Philosophy,  23 
Eucharist,  93 
Euclid,  28 

Euclidean  Hypothesis,  483 
Events,  finite,  54 

momentary,  56 

perceptible,  386 

dates  of,  387 

scientific,  389 

Excluded  Middle,  Law  of,  and  the 

future,  73,  etc. 
Extensive  Abstraction,  Principle  of, 
applied  to  Space,  41,  etc. 

applied  to  Time,  55,  etc. 
applied   to   Sense-fields,    350, 


etc. 


applied  to  Space-Time,   469, 

463 
External  World,  Reality  of,  14,  267, 
etc. 


Facts,  negative,  71 
Faraday,  M.,  13 

Feelings,     bodily,     and     sensations, 
255,  etc.,  521,  etc. 

and  sensa,  261 

Fields,  of  force,  176 

visual,  285,  etc. 

physical,  382 

tactual,  339 

somatic,  441 

First  Law  of  Motion,  155,  etc. 
Fixed   Stars  as  frame  of  reference, 
102,  etc.,  483 

hypothetical  annihilation  of, 

107,  etc. 

Fizean,   and  velocity  of  light,  377, 

etc. 
Force,  descriptive  theory  of,  162 
sensational  basis  of,  163 
measurement  of,  165 

in  what  sense  unimportant  to 

Mechanics,  166,  etc. 

one  aspect  of  stress,  171 


INDEX 


551 


Force,  Newtonian  and  non-New- 
tonian, 175,  etc. 

Foucault's  Pendulum,  103 

Frames  of  Reference,  Newtonian 
and  non-Newtonian,  173,  etc. 

- —        and  laws  of  Nature,  185,  etc. 

and  General  Theory  of  Rela- 
tivity, 196,  etc. 

Future,  non-existence  of,  66,  etc. 

alleged  knowledge  of,  78,  etc. 


Galileo,  G.,  13,  87,  96,  in 
Generation,  526,  541 

causal  and  creative,  535,  etc. 

Geo-chronometry,  457 
Geometry,  applied,  49 

and  Mechanics,  57 

elliptic  and  hyperbolic,   461, 

etc. 
George,  Rt.  Hon.  D.  LI.,  139 
George  V,  H.M.  King,  233 
Ghost,  the  Holy,  and  human  bodies, 

437 
Gibbon,   Mr   E.,   on   Jewish  beliefs, 

5io 

God,  his  knowledge  of  Nature,  217 

Berkelev's  view  of  his  rela- 


tion to  the  External  World,  232 
Gravitation,      and     non-Newtonian 
forces,  175,  206,  etc. 

peculiarities  of,  177 

Relativistic  Theory   of,    293, 
etc.,  482,  etc. 

and  radiant  energy,  212,  485 


Gravitational  Mass,  170,  etc. 

and  radiant  energy,  212,  485 


Hastings,  Battle  of,  78,  89 

Head-noises,  496 

"  Hearing,"  ambiguity  of,  248 

Heat,  radiant,  309 

"  Here,"  58,  etc. 

"  Hereness,"  59 

Hicks,  Prof.  G.  Dawes,  his  theory  of 

appearance,  237 
History,  strands  of,  406 

as  four-dimensional,  409 

Homogeneous    and    non-homogene- 
ous objects,  402 

Hume,  Mr  D.,  523 

Huyghens,  C. ,  37 


Images,  mental,  and  sensa,  263,  507 

in  mirrors,  317,  etc. 

tactual,  496 

Induction,  403 
Inertial  Mass,  169,  etc. 

and  energy,  182,  213 


"  Inherence,"     different    senses    of, 

544,  etc. 
Internal  Origination  of  Sensations, 

494 
Internal  Processes,  443 
Irrationals,  39,  etc. 
Isochrony,  157,  etc. 


Johnson,  Dr  S.,  and  Mr  Pope,  51 

and  Mr  Hume,  523 
Johnson,  Mr  W.  E.,  on  Ties,  75 

on  Occurrents  and  Continu- 
ants, 510 

on  Determinables  and  Deter- 


minates, 540 

Joint  Production,  490,  etc. 

Judgments,    existential,    character- 
ising, and  genetic,  68,  etc. 

about  the  future,  70,  etc. 

and  sentences,  74 

perceptual,  247 

Jupiter,  eclipses  of  its  moons,   378, 
etc. 

Kant,  I.,  13 

on     objective     simultaneity, 
423,  429 
Kekule,    and    constitution    of   Ben- 
zene, 13 
Keynes,  Mr  J.  M.,  on  Induction,  403 
Kinesthetic  Sensations,  and  concept 
of  Space,  300,  315 

translational  and  rotational, 
413,  etc. 

and  motion,  413,  etc. 


Kinematics,    of    Special    Theory    of 

Relativity,  136,  etc. 
Kinetics,  of  Special  Theory,  179,  etc. 


Laird,   Prof.  J.,  on  bodily  feelings 

256 
Laplace's  Equation,  210,  484 
Law  of  Gravitation,  peculiarities  of, 

177,  etc.,  206,  etc. 

and  structure  of  Nature,  204, 

etc. 

Laws,  of  Logic,  83,  etc. 

of  Motion,  no,  155,  etc.,  177, 

etc.,  195,  etc. 

of    Nature,    and    Theory    of 


Relativity,  153,  etc.,  185,  etc 
League  of  Nations,  186 
Leibniz,  G.,  and  Mechanics,  87 
Liberal  Theologians,  242 
Light,  aberration  of,  124,  380,  etc. 
■ ■     velocity    of,    118,    etc.,    376, 

etc.,  478,  etc. 

rectilinear     propagation     of, 


184,  etc. 


552 


INDKX 


Light,    gravitational    deflection    of, 

21  2,  etc. 
Light  signals,  129 

1  imits,    1  1  .  etc. 

Lines,  definition  by  Extensive  Ab- 
stention, 48 

Local  Time,  125,  etc.,  143,  etc. 

Locke,    Mr    J.,    on    Primary    and 
Secondary  Qualities,  279,  282 

Logic,  and  Philosophy,  23 
and  Time,  83,  etc. 

London,  lit.  Rev.  The  Bishop  of,  and 
birth-control,  66 

Lorentz,  and  the  Ether,  31 

Lorentz- Fitzgerald  Contraction,  125, 
etc. 

not  a  physical  change,  135 
relational  view  of,  149,  etc. 


Mack,    E.,  and  Absolute  Rotation, 

197,  etc. 
M'Taggart,     Dr     J.     M.     E.,     and 

Time,  79,  etc. 
Mass,  gravitational  and  inertial,  169, 

etc.,  212,  etc. 

conservation  of,  170,  182 

and  energy,  182 

Matter,  traditional  concept  of,  229, 


etc. 
Maxwell's  Equations,  150, 
co-variance  of,  153 


533 

57 


Mechanics,  and  geometry, 

classical,  Chap.  V 

relativistic,  Chap.  VI 

Media,  transmissive,  317,  etc. 
Meinong,     Prof.  A.,    on    Sein 


and 


Sosein,  68 
Memory,  403 

Mercury,  perihelion  of,  212 
Micawber,  Mr  and  Mrs,  31 
Michelson-Morlcy   Experiment,   119, 

etc. 

physical  explanations  of,  123, 

etc. 

absolutist  theory  of,  125 

relationist    theory    of,-    135, 

etc. 
Mind,  states  of,  252 

involves  memory,  403 

Mind-dependence,  definition  of,  250 

existential    and    qualitative, 

251,  etc. 

Minkowski,  and  Space-Time,  469 
Mirror-images,  317 
Mnemic  Conditions,  513 
Momentum,  168 

conservation  of,  153,  180 

•    rate  of  change  of,  and  force, 

162,  etc. 
Mookerjee,  Mr,  109 


Moore,  Dr  C.  E.,  on  "  Pickwickian 
senses,"  233 

on  Multiple  Relation  Theory 

of  Appearance,  237 

Motion,  Absolute  Theory  of,  97,  etc. 

Relational  Theory  of,  98,  etc. 

Laws  of,  no,  etc.,  Chap.  V, 

Chap.  VI 

visual,  286,  410,  etc. 

sensible,  238,  405,  etc. 

of  sense-objects,  411,  etc. 
and    kinesthetic    sensations, 


413,  etc. 

and  the  human  body,  446 
absolute,    sensible    basis    of, 


412 
Movement-Continuum,      314,      333, 

etc.,  341 
Multiple     Relations,     and     sensible 

appearance,  237  to  243,  369 

examples  of,  325 

■ and  neutral  simultaneity,  369 

Munro,  Mr  ('  Saki'),  242 

Necessary  Conditions,  dependent 
and  independent,  499,  etc. 

Neoplatonists,  and  World-Cycles, 
462 

Newman,    His    Eminence    Cardinal, 

369 
New  Realists,  offensive  self-satisfac- 
tion of,  266 

their  view  of  bodily  feelings, 

250 

Newton,  Sir  I.,  87 

and   Absolute   Rotation,   99, 

etc. 

his  Laws  of  Motion,  Chap.  V 

Newtonian  Clocks,  175 
Newtonian  Frames,  173 

and  Special  Theory  of  Rela- 
tivity, 183,  etc. 

and  the  structure  of  Nature, 


194,  etc.,  482 
Non-Newtonian  Forces,  174,  etc. 

and  gravitation,  175,  etc. 

and  Third  Law  of  Motion,  176 

and  General  Theory  of  Rela- 
tivity, 196,  etc. 

"  Now,"  58,  etc. 

Objects,  sensible,  347,  etc. 

optical,  329,  etc.,  397,  etc. 

perceptible,     330,     389..    393, 

etc. 

scientific,  331,  400,  etc. 

uniform     and     non-uniform, 

402,  etc. 

and  strands  of  history,  406, 


etc. 


INDEX 


553 


Object  Theory  of  Appearance,  237 
Occupation,  optical,  313,  321,  etc. 

tactual,  340 

Occurrent  Conditions,  510,  etc. 
Ontological  Argument,  69 
Optical  Compresence,  313 
Optical  Filling,  313 

Optical  Objects,  complete  and  par- 
tial, 329,  etc. 

duration  of,  from  a  place,  397 

total  duration  of,  397 

persistent,  397,  533 

■ non-persistent,  398 

Optical  occupation,  313,  321 

■ is  a  triadic  relation,  325 

Optics,  geometrical,  320 
Order,  and  Sense,  57 
Oxford,  University  of,  139 

Tutors  of,  30,  154 


Part  and  Whole,  48,  etc.,  55,  etc. 
Past,  reality  of,  66 
Perception,  and  Sensation,  243 

of  one's  own  body,  438 

Perceptual  Objects,  330 

unperceived    parts    of,    390, 

etc. 

Philosophy,    alleged   unprogressive- 

ness  of,  13,  etc. 
■ Critical,  18,  etc. 

Speculative,  20,  etc. 

Method  of,  19 

and      Psychology,     21,      24, 

etc. 


and  Logic,  23 

■     and  Ethics,  23 

Physical  World,  existence  of,  267 

not  an  inference  from  sensa, 

268 

■ spatial  character  of,  270 

"  Pickwickian  Sense,"  233 

Place,  sensible,  303 

■     optical,  321 

physical,  328 

■ of  somatic  sensa,  493 

Plato,  13 

Points,  defined  by  Extensive 
Abstraction,  48,  etc. 

Poisson's  Equation,  484 

Pope,  Mr  A.,  51 

Potentials,  197,  202,  210,  etc. 

Presentations,  251 

Present,  Specious,  348,  etc.,  482 

Production,  selective  and  genera- 
tive, 523,  etc. 

Productive  Conditions,  492,  etc. 

Psychic  Conditions,  516 

Psychology,  and  Philosophy,  22,  24, 
etc. 

Puck,  71 


0 


Qualities,   Primary  and  Secondary, 
279,  etc. 

Rayleigh,  Lord,  135,  n. 

"  Reality,"  ambiguity  of,  242 

Relational  Theory,  of  Time,  88,  etc. 

of  Space,  92,  etc. 

of  Motion,  98,  etc. 

Relativity,  90 

■ Special  Theory  of,   114,  etc., 

183,  472,  475,  etc. 

Physical    Principle    of,     149, 

etc. 

General  Theory  of,  138,  171, 

etc.,  482,  486 

Representative    Ideas,    Theory    of, 

238 
Riemann- Christoffel     Tensor,     194, 

298,  484 

Modified,  209,  etc.,  485 

Romer,  and  Velocity  of  Light,  378 
Rotation,  absolute  and  relative,  99, 

etc. 

sensible    and    physical,    433, 

etc. 

Russell,  Hon.  B.   A.  W .,  on  logical 
constructions,  51 

on    "  publicity  "    of   Matter, 


230 


513 


his  Lowell  Lectures,  238 

his  analysis  of  sensations,  264 

on    mnemic    causation,    289, 

on  physical  objects,  531,  etc. 


St  Paul's,    Very  Rev.   The  Dean  of, 

and  World-cycles,  462 
Scepticism,  physiological,  508 
Scientific  Objects,  331 

different  orders  of,  400,  etc. 

Secondary  Qualities,  279 

Second  Law  of  Motion,  161,  etc. 
"  Seeing,"  ambiguity  of,  248 
"  Sein  "  and  "  Sosein,"  68 
Selection,    positive    and    negative, 

523,  etc. 
Selective   Theories,    advantages   of, 

527.  532 

examples  of,  529 

difficulties  of,  530 

Sensa,  defined,  240 

and  physical  objects,  241,  266 

and  perception,  243 

mistakes     about    their    pro- 
perties, 244 

as  signs  of  physical  objects, 


247 


258 


probably   not   presentations, 
privacy  and   dependence  on 


the  human  body,  259 


2  N 


554 


INDEX 


Sensa,  how  fax  mind-dependent,  261  ; 

and  mental  images,  263 

status  of,  270,  523,  ad  fin. 

spatial       characteristics       of, 
Chap.  IX 

temporal    characteristics    of, 


Chap.  X 
Sensations,  243,  249 

analysis  of,  249,  489,  516,  etc. 

and  bodily  feelings,  254,  etc. 

and  presentations,  257 

Sense,  intrinsic,  of  Time-series,  57 
Sense-fields,  momentary,  349 

duration  of,  354 
general  and  special,  360 
Sense-histories,  362 

and  Scientific  Time,  392 

idealised,  458 

• somatic,  521 

Sense-objects,  346 

—  somatic,  441 
Sense-spaces,  460 

Sensing,  Acts  of,  253,  etc.,  521 
■ momentary,  350 

temporal    characteristics    of, 

344,  etc. 

Sensing,  general  process  of,  516,  etc. 
Series,  Time,  57,  etc. 

of  rationals,  40 

■ of  volumes,  44,  etc. 

■ of  visual  sensa,  305,  etc. 

Shape,  and  secondary  qualities,  280 

and  Time,  335 

—  sensible,  335 

optical,  336 

■ physical,  339 

Simplicity,  two  stages  of,  547 

Simultaneity,  sensible,  360 

■ tests  for  and  definitions  of, 

364 

neutral,  370,  etc. 

multiple   relation   theory   of, 

and  sound,  366,  etc. 
and  light,  374,  etc. 

relativity  of,  476 

Solidity,  visual,  290,  etc. 

Sound,  spatial  characteristics  of,  309 
Space,  traditional  view  of,  26,  etc. 

different  kinds  of,  27,  etc. 

and  Ether,  31 

Absolute      and       Relational 

Theories  of,  92,  etc. 

momentary,  96,  460 

timeless,  96,  463,  etc. 
of  a  sense-history,  411 


369 


Space-Time,  physical,  454,  etc.,  543, 

etc. 
• homaloidal    and    non-homa- 

loidal,  483 
compared  with  a  family,  544 


Spatial  Separation,  188,  479 
Spatio-temporal     Separation,     188, 

etc. 
Speculative  Philosophy,  20,  etc. 
Spheres,  converging  scries  of,  44,  47 

—  •  and  planes,  193 
Staircase  Figure,  260 
Standard    Processes,    correction   of, 

158,  etc. 
Stationary  Courses,  199,  etc. 
Stimulus,  498 
Stout,  Prof.  G.  F.,  on  presentations, 

250,  etc. 
Strain,   feeling  of,   and  Force,   162, 

etc. 
Stress,  171 
Structure,  intrinsic,  of  Nature,  186, 

etc.,  455 
Stumpf's  Argument,  244,  etc. 
Surfaces,  intrinsically  different,  193, 

208,  etc. 
Swift,  Dean,  on  Irish  Bishops,  204 


Tactual  Occupation,  316 
Temporal    relations,    between    acts 
and  sensa,  358 

within  a  sense-field,  359 

— within  a  sense-history,  362 

neutral,  362,  etc. 

between  perceiving  and  per- 
ceived object,  388 

Temporal  Separation,  intrinsic  and 

non-intrinsic,  480,  503 
Tennant,    Dr    F.     R.,    his    alleged 

paltering  with  Sin,  234 
Things,  393 
Third  Law  of  Motion,  171,  etc. 

indefiniteness  of,  172 

and  Newtonian  Frames,  173 

and    non-Newtonian    forces, 

176 

Thomas,     The  Apostle,    uses    touch 

as  test  for  physical  reality,  497 
Ties,  logical,  75 
Time,  traditional  view  of,  54 

analogies  to  Space,  54,  etc. 

intrinsic  sense  of,  57,  etc. 

M'Taggart's     criticisms     on, 

79,  etc. 

and  Laws  of  Logic,  83,  etc. 

Absolute      and       Relational 


Theories  of,  88,  etc. 
Scientific,  392 


Time-directions,  468 

plurality  of  possible,  472 

limited  range  of,  474 

Time-lapse,      direct     and     indirect 

measures  of,  145 

and  spatial  separation,    147, 


etc. 


INDEX 


555 


Timeless  Space,  96,  463,  etc. 

its  points,  464 

its  straight  lines  and  planes, 

465 
Touch,  active  and  passive,  340 
Traces,    hypothetical   character 

261,  etc. 

and  sensible  movement, 

and  visual  solidity,  294 

and  visual  distance,  297 

and  mnemic  causation,  514 

Transformation-equations,      deduc 

tion  of,  136,  etc. 

evidence  for,  139,  etc. 


of, 

288 


Transmissive  Conditions,  491 
Trinity,    the    Blessed,   its    internal 

structure,  156,  215 
its  College  at  Cambridge,  286, 

etc. 


Uniform  and  non-uniform  Strands  of 

History,  408 
Uniformity,  standard  of,  156,  etc. 


Universe  of  Discourse,  and  Becom- 
ing, 83,  etc. 

Variations,  Calculus  of,  196 
Velocity  of  Light,  118,  etc.,  478 
Volumes,   series  of  converging,   44, 
etc. 

Containing,  47 

Waterloo,  Battle  of,  89 
Westminster  Bridge,  52 
Whitehead,    Prof.  A.   N.,   and    Ex- 
tensive Abstraction,  38,  etc. 

and  Timeless  Space,  96,  463, 

etc. 

and  Scientific  Objects,  331 

and  Scientific  Events,  389 

and    non  -  homogeneous    ob- 
jects, 402 

Whole  and  Part,  48,  etc.,  55,  etc. 
Wiener,    Dr    N.,   and   definition  of 

moments,  55 
William  III,  King,  80 
World-lines,  469,  etc. 


PRINTED   IN   GREAT   BRITAIN    BY 
THE   EDINBURGH    PRESS,    q   AND   II    YOUNG  STREET,    EDINBURGH 


Brotdy   Ctrrlie  Dunbar 
175  Scientific  thought, 

B79 


PfcA  Sci. 


PLEASE  DO  NOT  REMOVE 
CARDS  OR  SLIPS  FROM  THIS  POCKET 

UNIVERSITY  OF  TORONTO  LIBRARY