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THIS  work  must  be  regarded  as  a  new  edition  rather  than 
as  a  mere  translation  of  my  book,  La  Reazione  idealistica 
contro  la  scienza,  published  in  Italy  in  1912,  .Jince  I 
have  subjected  the  whole  of  it  to  a  process  of  revision 
with  a  view  to  improving  it  and  adapting  it  to 
the  British  public.  In  the  concluding  chapter  I  have 
gathered  together  the  constructive  portions  formerly 
scattered  through  the  whole  book,  so  as  to  give  greater 
prominence  to  my  personal  point  of  view,  which  is  a 
form  of  spiritualistic  realism,  and  to  make  that  view 
clearer.  The  outlines  of  a  spiritualistic  conception  of 
the  world  sketched  therein  have  already  formed  the 
subject-matter  of  three  addresses  given  by  me  in  the 
Philosophical  Library  of  Palermo,  founded  by  Dr. 
Giuseppe  Amato  Pojero,  a  true  apostle  of  philosophy,  the 
study  of  which  he  strives  to  further  by  both  precept  and 
practice.  The  line  of  thought  adopted  by  me — that  of 
the  school  of  Francesco  de  Sarlo  and  his  review,  La  Cul- 
tura  filosofica,  defends  the  rights  of  the  scientific  method 
and  of  natural  reality  against  the  facile  denials  of  the 
neo- Hegelians.  Idealism,  which  came  into  vogue  in 
Italy  after  the  decline  of  positivism,  now  appears  to  be 
on  the  wane,  and  the  abuse  of  the  dialectic  method  has 
resulted  in  such  a  confusion  of  ideas  in  mental  sciences 
that  Croce  himself  recently  lifted  his  voice  in  protest 
against  these  exaggerations.  It  is  now  time  to  return 

vii  6 


to  realism,  and  in  England,  America,  and  Germany 
there  are  already  indications  of  such  a  return,  which 
this  work  of  mine  would  fain  hasten  in  Italy,  where,  if 
absolute  idealism  has  attained  a  large  measure  of  success, 
other  vigorous  and  original  currents  of  thought,  which 
have  disputed  the  victory  with  it,  are  by  no  means 

This  productive  trend  of  thought,  which  merits 
attention  in  other  countries  as  well  as  in  Italy,  is  not 
touched  upon  in  the  present  volume,  because  it  was  not 
included  in  the  general  plan  of  my  work,  which  does 
not  aspire  to  be  a  complete  history  of  contemporary 
philosophy,  but  merely  a  study  of  one  aspect  of  it,  i.e. 
of  the  phenomenon  of  irrationalism  in  its  relations  to 
criticism  of  science.  Irrationalism,  moreover,  in  spite 
of  the  efforts  of  a  few  romantic  minds,  has  not  taken 
root  in  Italy.  I  shall  deal  at  length  with  modern  Italian 
philosophy  in  a  separate  book,  which  will  also  be 
published  in  England  should  the  present  volume  meet 
with  the  favourable  reception  from  English  readers  for 
which  I  venture  to  hope. 




The  reaction  from  intellectualism  in  contemporary  philosophy — In- 
tellectualism  and  anti-intellectualism  in  the  history  of  philosophy — ' 
Causes  of  the  reaction  from  Intellectualism  .  .  .  xv-xxii 







Agnosticism  as  the  consequence  of  the  traditional  mathematical  method 
— The  Ignorabimua  of  Du  Bois-Reymond — Criticism  of  Spencer's 
agnosticism — First  germs  of  the  reaction  from  intellectualism  in  - 
Spencer — The  evolutionary  method  also  leads  to  reaction     .  .3-12 



The  return  to  the  critical  method — Lange — Criticism  of  the  physiological 
interpretation  of  the  a  priori  and  of  the  poetical  intuition  of  the 
Absolute — The  empirical  prejudice  in  Helmholtz — Liebmann  and 
Schultze — Criticism  of  the  neo-Kantian  school — Riehl's  monism — 
Criticism  of  Riehl's  philosophy — Elimination  of  the  thing  in  itself 
and  transition  to  phenomenalistic  monism — Wundt's  critical  ideal- 
ism— Wundt's  uncertain  position — The  return  to  Schopenhauer's 
voluntarism — Von  Hartmann's  philosophy  of  the  unconscious — 




Fouillee's  idle-force — The  endeavour  to  reconcile  pragmatism  and 
intellect  ualism — Ultimate  consequences  of  voluntarism  as  seen  in 
Paulsen  —  Criticism  of  voluntarism  and  the  theory  of  faith  — 
Nietzsche's  individualistic  voluntarism — The  philosophy  of  freedom : 
Ravaisson,  Secretan — Lotze  and  the  primacy  of  practical  reason — 
Psychological  development  of  the  theory  of  the  primacy  of  practical 
reason  in  the  phenomenalism  of  Renouvier — Criticism  of  Renouvier's 
phenomenalism  .  .  .  .  .  .  .  .  13-52 



Old  and  new  positivism — Factors  determining  the  transition  from  one 
form  to  another  and  their  influence  upon  the  thought  of  Mach — Hypo- 
statisation  of  the  sensorial  elements—Science  as  mental  economy — 
Criticism  of  the  traditional  mechanical  theory — Unconscious  meta- 
physic  and  contradictions  in  Mach's  phenomenalism — Petzoldt's 
law  of  univocal  determination — Principle  of  the  minimum  effort,  as 
set  forth  by  Avenarius — Biological  explanation  of  scientific  and 
philosophic  knowledge — Introjection — Criticism  of  the  philosophy 
of  pure  experience — Hodgson's  metaphysic  of  experience — Klein- 
peter's  subjectivism  .......  53-91 



The  two  attempts  at  escape  from  the  agnostic  position — The  eternity  of 
thought,  as  affirmed  by  Green  in  opposition  to  empiricism — Criticism 
of  Green's  pan-logism — lieductio  ad  absurdum  of  pan-logism  in 
Bradley's  philosophy — Criticism  of  Bradley's  dialectic — Mystical 
degeneration  of  English  neo-Hegelianism  :  M'Taggart  .  .92-111 



The  aesthetic  and  moral  conception  of  the  universe :  Secretan, 
Ravaisson — fimile  Boutroux  and  the  contingency  of  natural  laws 
— Criticism  of  the  theory  of  contingency — Milhaud  and  the  limits 
of  logical  certainty — Bergson's  doctrine  of  intuition — Fundamental 
error  of  Bergson's  system — The  two  new  rules  of  invention  pro- 
pounded by  Wilbois — The  will  of  spiritual  activity  in  scientific 
construction  according  to  Le  Roy — The  physical  world  as  an 
instrument  of  moral  life — Ethical  action  as  a  means  of  penetrating 
reality — Criticism  of  intuitionism — Theoretical  value  of  science — 
Criticism  of  Duhem's  arguments  against  the  objective  value  of 
science  .  115-161 





Pragmatism  as  evolutionary  transformation  of  English  empiricism — The 
pragmatism  of  Peirce — Utilitarianism  and  pragmatism — Reasons 
for  the  prevalence  of  pragmatism :  James's  will  to  believe  — 
Differences  between  la  philosophie  nouvelle  and  pragmatism  — 
The  humanism  of  Schiller — Dewey's  instrumental  logic — Prag- 
matical elimination  of  the  duality  of  subject  and  object — Plasticity 
of  experience  according  to  James — Ideas  as  instruments  of  action — 
Criticism  of  pragmatism  ....  .  162-195 




The  philosophy  of  values  and  the  primacy  of  practical  reason — Philo- 
sophy as  the  science  of  universal  values  :  Windelband — Reduction  of 
Being  to  the  Ought — Natural  and  historical  sciences — Criticism  of  * 
the  philosophy  of  values — Historical  knowledge  in  Miinsterberg's 
philosophy  of  values — Attempt  to  deduce  all  values  systematically 
— The  historic  world  of  subjective  wills  and  the  mechanical  world 
of  objects — Criticism  of  Miinsterberg's  philosophy — Miinsterberg's 
super-jEJgro  and  Royce's  absolute  consciousness — Reduction  of  the 
external  meaning  to  the  internal  meaning  of  the  idea — Error — The 
world  of  science  and  the  world  of  valuation — Criticism  of  Royce's 
philosophy — Ward  on  the  realm  of  nature  and  the  realm  of  ends  196-273 




Traditional  geometry  and  the  new  theories  of  Gauss,  Lobatchewsky,  and 
Bolyai — The  empiricism  of  Riemann  and  Helmholtz  and  the  dispute 
with  the  Neo-Kantians — Intuition  and  concept  in  geometry — 
Tannery  on  the  contingency  of  geometrical  truths — The  general 
geometry  of  Calinon  and  Lechalas — Criticism  of  these  theories  :  the 
a  priori  properties  of  space — Vain  attempt  at  an  a  priori  deduction 
of  three-dimensional  space  :  Cohen,  Natorp — Impossibility  of  an 
experimental  proof  of  Euclidean  geometry :  Stallo,  Poincare, 
Couturat — Euclidean  geometry  more  rationally  complete  than  the 
rest 277-305 





Fusion  of  logic  with  mathematics  towards  the  middle  of  the  nineteenth 
century — Peano's  logistic  and  its  application  to  arithmetic  and  the 
geometrical  calculus — Fieri — Whitehead's  universal  algebra — Russell 
on  the  identity  of  logic  and  mathematics — Ordinal  and  cardinal, 
finite  and  infinite  numbers — The  continuum — Geometry  as  a  hypo- 
thetico-deductive  system — The  analytic  character  of  mathematical 
truths  according  to  Couturat — Intuition  in  mathematics — Irre- 
ducibility  of  mathematics  to  logistic — Criticism  of  the  hypothetico- 
deductive  systems — A  priori  synthesis  in  mathematics — Russell  on 
the  philosophical  consequences  of  mathematical  logic — The  new 
realism — Meinong's  theory  of  objects — Criticism  of  Russell's 
theory .  306-345 




Traditional  mechanism — Carnot's  principle — Evolutionary  genesis  of 
chemical  elements — Physical  chemistry — Energetics  in  Rankine  and 
Spencer — Ostwald's  phenomenalistic  programme — Criticism  of  the 
traditional  mechanical  theory — Energy  as  a  universal  substance — 
Reduction  of  matter  to  energy — Energetics  and  vital  psychic 
phenomena — Criticism  of  energetics :  Ostwald  the  phenomenalist, 
and  Ostwald  the  metaphysician — Mechanics  as  the  necessary  basis  of 
energetics  ........  346-373 



Vain  endeavours  to  reduce  all  physical  qualities  to  figure  and  movement 
alone — Duhem's  new  mechanics — The  economic  and  objective  value 
of  scientific  theories — Criticism  of  Duhem's  theory  .  .  374-389 


The  two  types  of  ideation  amongst  physicists :  the  abstract  and 
the  concrete— The  nominalist ic  prejudice  of  the  theory  of  models  : 
Hertz — Value  of  concrete  representations  in  physical  theory — The 
model  not  an  indispensable  means  of  discovery — Fertility  of  the 
concept  ........  390-404 





Intuitionism,  pragmatism,  and  intellectualism  as  partial  views — The 
reality  of  concrete  thought — Concrete  thought  as  the  necessary 
organ  of  philosophical  enquiry — The  substantiality  of  the  Ego — The 
sophisms  of  the  idealist — Proof  of  realism — The  truth  of  self-con- 
sciousness— The  knowableness  of  nature — Mind  the  truth  of  nature 
— Natural  monads — The  sense  in  which  the  contents  of  sensation  are 
real — Concept  of  nature — The  vicious  circle  of  empiricism — Irreduci- 
bility  of  thought  to  practical  activity — Inadequacy  of  nominalism — 
Theoretical  value  of  the  scientific  concept — History,  science,  philo- 
sophy— Impossibility  of  a  dialectical  deduction  of  the  categories — 
Ideal  genesis  of  the  scientific  categories — Cause,  substance,  quantity, 
time,  space — Primitive  and  derivative  categories — Ideal  genesis  and 
value  of  the  mechanical  interpretation  of  physical  phenomena — 
Spiritual  meaning  of  science — Epistemological  proof  of  the  existence 
of  God — Faith  in  the  value  of  science  is  faith  in  God — Denial  of 
the  conflict  between  pure  reason  and  practical  reason — Legitimacy 
of  other  types  of  science,  differing  from  mechanics — The  categories 
of  liberty  and  finality — The  accusation  of  anthropomorphism — 
Eternity  of  creation  ......  405-479 

INDEX  481-483 


1.  The  Reaction  from  InteUectualism  in  Contemporary 
Philosophy. — One  of  the  essential  characteristics  of 
contemporary  thought  is  undoubtedly  the  reaction 
from  intellectualism  ID  all  its  forms.  The  mind  of 
man,  which  could  not  rest  content  with  a  simple  trans- 
ference of  results  attained  by  the  methods  of  the  natural 
sciences  to  the  realm  of  philosophy,  and  was  reluctant 
to  stay  its  steps  on  the  threshold  of  the  dim  temple  of 
the  Unknowable,  sought  within  itself  other  and  deeper 
activities  which  should  throw  open  the  portals  of  mystery. 
Art,  moral  lif  e,  and  religious  belief  were  called  upon  to  fill 
the  void  left  by  scientific  knowledge  ;  and  the  reaction 
went  so  far  as  to  extend  to  the  human  intellect  as  a 
whole  a  distrust  which  should  have  been  confined 
to  scientific  naturalism  and  its  claim  to  be  able  to 
comprehend  the  infinite  riches  of  mind  and  nature 
within  a  few  mechanical  formulas.  The  ruined  shrines 
of  the  Goddess  of  Reason,  who  for  so  long  had  tyrannised 
over  the  mind,  were  invaded  by  the  rebel  forces  of 
f  eeling,  will,  imagination,  and  every  obscure  and  primitive 
instinct:  thus  it  came  about  that  Schopenhauer  achieved 
a  posthumous  triumph  over  his  hated  rival  Hegel,  whose 
hearers  he  had  in  his  lifetime  vainly  endeavoured  to 
entice  away,  even  though  he  fixed  his  own  lectures  for 
the  same  hour.  Once  the  blind  power  of  impulse  was 
exalted  and  the  sure  guidance  of  the  intellect  abandoned, 
the  door  was  opened  to  every  kind  of  arbitrary  specula- 
tion ;  hence  the  confusion,  Byzantinism,  and  dabbling 
in  philosophy  which  during  the  last  twenty  years  have 



obscured  thought  and  masqueraded  under  the  fine- 
sounding  name  of  idealism.  0  unhappy  Idealism,  how 
many  intellectual  follies  have  been  committed  in  thy 
name  !  Theosophy,  the  speculations  of  the  Kabala, 
occultism,  magic,  spiritualism,  all  the  mystic  ravings 
of  the  Neo-Platonists  and  Neo-Pythagoreans,  the  most 
antiquated  of  theories,  debris  of  every  kind,  heaped 
haphazard  on  the  foundation  of  the  speculations  of  the 
ages — all  these  have  returned  to  favour  in  defiance  of 
the  dictates  of  logic  and  common  sense.  Balance  and 
the  sense  of  direction  have  to  a  certain  extent  been 
lost,  the  light  of  intelligence  quenched,  and  man  gropes 
in  the  gloom  of  wild  inspirations,  direct  intuitions,  and 
mysterious  miracles  in  the  search  for  some  new  truth 
which  shall  satisfy  the  inmost  needs  of  the  human 

2.  Intettectualism  and  Anti  -  Intellectualism  in  ike 
History  of  Philosophy. — The  reaction  from  pure  intel- 
lectualism, which  reached  its  zenith  towards  the  end 
of  the  last  century,  is  nothing  new  in  the  history  of 
philosophy,  but  a  phenomenon  which  recurs  whenever 
thought  indulges  in  exaggerated  rationali  sm.  In  Greece 
the  splendid  affirmation  of  the  concept  against  the  sub- 
jectivism of  the  Sophists  and  the  intellectualism  which 
had  carried  all  before  it  from  Socrates  to  Aristotle  was 
followed  by  the  sceptical  dissolution  which  ended  in 
the  ravings  of  the  mystics  of  Alexandria ;  while  the 
glow  of  Christian  sentiment  came  to  fill  the  void  left 
by  a  cold  intellectualism  in  minds  confused  by  the 
contradictory  formulas  of  the  various  systems  and 
the  quibbles  of  destructive  dialectic.  All  through 
the  Middle  Ages  we  see  this  antithesis  of  mystic  faith 
and  love,  which  breaks  out  from  time  to  time  with  fresh 
force  in  protest  against  the  excesses  of  rationalism  : 
the  paradoxical  "  Credo  quia  absurdum  "  of  Tertullian 
stands  in  opposition  to  the  bold  assertions  of  the 
gnostics;  the  "Amo  ut  intelligam"  of  S.  Bernard  and  the 
Victorines  marks  the  reaction  of  feeling  from  the  in- 
temperate dialectic  of  Abelard's  "  Intelligo  ut  credam  "  ; 


S.  Thomas  vainly  strives  to  reconcile  these  conflicting 
principles  in  a  higher  synthesis,  defining  clearly  the 
limits  of  faith  and  reason.  The  antithesis  of  feeling" 
lives  on,  although  in  a  more  moderate  form,  in  the 
"  lumen  superius,"  the  "  excessus  mentalis  et  mysticus  " 
of  S.  Bonaventura  who  counsels  his  followers  to  appeal 
for  penetration  into  the  highest  truth :  to  "  gratiam,  non 
doctrinam  "  ;  "  desiderium,  non  intellectum  "  ;  "  cali- 
ginem,  non  claritatem " ;  indeed,  another  antithesis 
is  added  in  the  voluntarism  of  Henry  of  Ghent 
and  John  Duns  Scotus,  which  places  "  Voluntas 
imperans  intellectui  est  causa  superior  respectu  actus 
eius  "  in  opposition  to  the  "  Simpliciter  tamen  intel- 
lectus  est  nobilior  quam  voluntas "  of  S.  Thomas. 
The  exaggerated  subtleties  of  the  scholastics  and  the 
interminable  controversies  between  the  followers  of 
S.  Thomas  and  those  of  Scotus  lead  by  way  of  Ockham's 
scepticism  to  a  re-awakening  of  the  spirit  of  mysticism 
in  Eckhart  and  Gerson.  The  epic  struggle  still  con- 
tinues in  modern  philosophy ;  the  first  triumphs  of 
mathematical  natural  science  encouraged  the  boldness  of 
Cartesianrationalism,  against  which  the  tormenting  doubt  </ 
of  the  mystic  Pascal  struggles  in  vain.  Intellectualism, 
not  content  with  its  theoretical  domain,  would  fain  in 
the  teaching  of  Spinoza  invade  that  of  moral  life  as 
well,  vainly  deceiving  itself  into  the  belief  that  it 
can  interpret  the  action  of  the  passions  more  geometrico, 
and  reaches  its  extreme  in  the  claim  of  Wollaston 
to  be  able  to  express  the  supreme  laws  of  duty  as 
logical  relations,  a  claim  calling  forth  the  just  re- 
action of  the  sentimentalists  from  Shaftesbury  to  Smith. 
The  mind  of  man  is  once  more  irresistibly  drawn  in  the 
opposite  direction  by  the  piercing  analyses  of  Berkeley 
and  Hume  and  the  critical  genius  of  Kant,  which  is 
at  one  and  the  same  time  the  apotheosis  of  the  physico- 
mathematical  method  in  the  order  of  phenomena  and 
the  irrevocable  condemnation  thereof  as  an  organ  of 
speculation.  We  see  the  antithesis  once  more  in  the 
traditional  form  of  feeling  regarded  as  the  direct  revela- 


tion  of  God  in  the  mystical  writings  of  Jacobi,  and  in 
the  form  of  the  primacy  of  practical  reason  in  the  work 

Sof  Kant  and  Fichte,  while  in  the  revolt  of  the  romanti- 
cists, the  Schlegels,  Tieck,  Novalis,  and  Schelling,  it 
takes  on  the  new  aspect  of  poetic  intuition  which 
,  ranks  the  concreteness  of  aesthetic  vision  higher 
i  than  abstract  mathematicism,  the  individual  than 
the  universal,  the  changeful  life  of  history  than  the 
inflexible  formulas  of  mechanical  science.  In  Hegel 
reason  strives  to  break  away  from  the  motionless 
formulas  of  the  old  logic  and  to  comprehend  within 
the  triad  of  a  higher  dialectic  that  concrete  develop- 
ment which  eluded  the  schemes  of  mathematical  intel- 
lectualism,  but  for  all  its  gigantic  efiorts  it  fails  to 
dominate  the  manifold  complexity  of  experience,  or 
to  absorb  into  the  idea  the  productive  wealth  of  intuition 
and  the  vivid  glow  of  feeling ;  and,  while  speculative 
Pan-logism  is  celebrating  the  funeral  rites  of  the 
dead  and  gone  divinities  of  the  romanticists — art  and 
religion,  superseded  now  by  thought — we  behold  the 
gods  arising  once  more  from  the  tombs  to  which  Hegel 
and  his  teaching  had  consigned  them — rising  full  of 
the  ardour  of  youth  in  the  mysticism  of  the  later 
philosophy  of  Schelling,  in  the  feeling  and  religious 
faith  with  which  Schleiermacher  and  Hamilton  sought 
to  supplement  our  poor  intellectual  science  of  the 
finite  and  conditioned,  in  the  belligerent  will  of 
Schopenhauer  who  strives  to  express  his  deep  sense  of 
rhythm  in  music,  beyond  the  realm  of  precise  concepts. 
The  over-depreciation  of  scientific  intellectualism  and 
of  mechanical  and  abstract  mathematicism,  which  is 
characteristic  of  all  idealistic  speculation,  and  its 
claim  to  take  the  place  of  science  and  to  substitute 
for  it  a  fantastic  system  of  natural  philosophy  are 
followed  by  a  fresh  glorification  of  the  physical  mathe- 
matical method,  which  in  its  turn,  in  the  exaggerated 
reaction  which  set  in,  laid  claim  to  the  place  of  philo- 
sophy, thus  invading  the  realm  of  the  mind.  Thus, 
passing  over  the  criticism  of  Kant,  we  return  to  the 


naturalism  of  the  eighteenth  century  with  its  crass 
ignorance  of  the  epistemological  problem.  Scientific 
intellectualism,  however,  after  vainly  striving  to  express 
the  highest  manifestations  of  life  and  consciousness 
by  the  aid  of  its  formulas,  is  forced  to  stop  short  at 
the  limits  already  denned  by  the  genius  of  Kant.  The 
"  Ignorabimus  "  of  Du  Bois-Reymond,  the  Unknowable 
of  the  philosopher  of  First  Principles,  are  the  most 
explicit  confession  of  the  inability  of  that  method  to 
solve  the  problems  of  most  vital  interest  to  the  mind 
of  man. 

3.  Causes  of  the  Reaction  from  Intellectualism. — 
Could  thought  rest  easy  in  this  complacent  agnosticism  ? 
Could  it  silence  the  ever  -  questioning  voice  within  ? 
There  were  two  ways  of  escaping  this  intolerable  situa- 
tion :  either  to  turn  to  the  other  functions  of  the^mind 
jojJ^e'g5m^ion~oTthe  problem  which  had  baffled  the  in- 
teSeCT7or~to  elimmate_the_i)roblem  altogether,  by  proving 
jt-4iO  be  due_tp^Jaulty^  per^ectiy^and  to  a  false_con- 
cieption  of  science  andjoi-the  value  ci_scieiitinc_theories. 
Both  'ways  ~have  been  tried ;  on  the  one  hand,  by  a 
return  to  the  moralism  of  Fichte  and  the  aestheticism 
of  the  romanticists,  into  which  the  rebellious  genius 
of  Nietzsche  had  breathed  new  life,  the  will,  as  the 
creative  source  of  all  values  and  of  unfettered  aesthetic^ 
intuition,  is  exalted  above  the  intelligence ;  while,  on 
the  other,  the  bases  of  the  mechanical  conception  and 
of  its  chief  instruments  —  geometrical  intuition  and 
mathematical  calculation — are  subjected  to  a  searching 
examination.  This  analysis,  to  which  men  of  science 
themselves  were  impelled  by  the  discovery  of  the  new 
principles  of  energy,  and  by  meta-geometrical  con- 
ceptions, resulted  in  stress  being  laid  upon  the  active  <* 
work  of  the  mind  in  the  construction  of  scientific  laws 
and  theories,  and  has  therefore  contributed  to  the 
triumph  of  that  line  of  philosophic  thought  which 
holds  that  the  fullest  revelation  of  reality  is  to  be  found 
in  the  aesthetic  point  of  view,  and  in  the  practical 
functions  of  consciousness.  In  this  way  speculative 


criticism,  determined  by  imperious  demands  of  the  mind 
which  positivism  failed  to  satisfy,  came  into  contact 
with  the  new  criticism  which  the  new  theories  called 
into  being  in  the  realm  of  science  itself,  thus  shaking 
dogmatic  belief  in  the  old  geometry  and  in  traditional 
mechanical  science.  This  valid  co-operation  of  physi- 
cists and  mathematicians  distinguishes  the  struggle 
against  intellectualism  of  the  closing  years  of  the 
nineteenth  century  from  the  analogous  movement 
of  the  beginning  of  the  present  century ;  it  is  also 
more  intense  and  more  extensive,  especially  as  regards 
its  critical  aspect.  The  scientific  method  which  Kant 
and  the  idealists  had  declared  to  be  inadequate  in 
the  domain  of  the  absolute  had  successfully  resisted 
all  attacks,  entrenching  itself  within  the  citadel  of  the 
phenomenon  which  Kant  himself  had  fortified  so 
strongly  with  his  vigorous  criticism,  but  towards  the 
end  of  the  century  the  reaction  spread  to  this  sphere 
also,  and  science  was  not  only  divested  of  its  speculative 
office,  but  its  theoretical  value  was  denied  as  well. 

The  prevalence  of  Darwinism  and  of  the  theory  of 
evolution  in  general  contributed  not  a  little  to  this 
radical  change  in  the  concept  of  science.  From  this 
standpoint  consciousness  too  appeared  to  be  a  complex 
of  functions,  whose  meaning  could  not  differ  from  that 
of  the  other  organic  functions  :  it  was  but  an  additional 
weapon  in  the  struggle  for  existence,  a  means  of  adapta- 
tion. The  theoretical  function  could  not  be  regarded 
as  an  exception  to  this  utilitarian  value — a  value,  that 
is  to  say,  of  an  essentially  practical  order — of  psychic 
life  as  a  whole,  and  the  forms  of  thought,  like  the  other 
types  of  the  biological  world,  could  not  therefore  be 
considered  as  being  immutable  and  eternal,  but  rather 
as  being  subject  to  a  continuous  process  of  formation 
by  means  of  successive  adaptations  to  new  conditions 
of  life.1  Science  is  no  longer  the  standard  by  which 
every  form  of  knowledge  is  gauged,  as  was  the  case  in 
the  days  of  the  old  positivism  ;  it  is  no  longer  the  eternal 
mould  into  which  human  consciousness  must  be  forced 


if  it  would  attain  to  certainty ;  it  too  is  an  organism 
capable  of  that  development,  renewal,  and  change  of 
structure  which  enable  it  better  to  fulfil  its  biological 
function.  That  very  theory  of  evolution  which  had 
at  first  sight  appeared  to  prove  the  mechanical  method 
afresh,  and  to  give  it  a  new  weapon  wherewith  to  subdue 
the  rebel  world  of  life,  helped  rather  to  depreciate  its 
value  and  to  shake  its  foundations.  Regarded  in  the 
light  of  evolution,  was  the  world  what  the  mechanical 
theory  had  held  it  to  be,  an  eternal  persistence  of  un- 
changeable substances,  an  eternal  repetition  of  necessary 
movements  subject  to  unchangeable  laws  ;  or  was  it 
rather  a  perennial  becoming,  an  incessant  renewal  of 
forms  which  cannot  be  foreseen,  and  which  cannot 
therefore  be  subject  to  the  rigid  necessity  of  determinism? 
i  Is  not  variability,  that  is  to  say,  the  possibility  of  the 
;  new,  presupposed  in  all  evolution  ?  Can  the  new  be 
confined  within  the  limits  of  any  mathematical  formula  ? 
How  can  mechanics,  the  science  of  eternal  types,  mirror 
the  transient  life  of  the  real  ?  It  is  not  to  the  motionless 
ideas  of  reason  that  we  must  turn  if»we  would  sound 
the  depths  of  being  and  grasp  it  in  the  productive 
moment  of  its  generation,  but  rather  to  the  free  creations 
of  imagination  and  energy.  Not  sub  specie  aeternitatis, 
but  sub  specie  generations  is  the  motto  of  modern 

The  researches  of  psycho  -  physiology  and  more 
especially  the  analyses  of  perception,  which  proved 
the  subjective  character  of  those  sensory  elements 
which  the  mechanical  theory  had  raised  to  the  rank  of 
ultimate  reality,  contributed  largely  to  the  change  in 
the  conception  of  science  and  of  knowledge  in  general. 
Are  not  resistance,  space,  and  time  presentations  no 
less  dependent  on  the  special  physiological  structure 
than  sounds,  colours,  tastes,  and  smells  ?  What  right 
have  we  to  regard  the  one  class  as  objective  and  primary, 
the  other  as  subjective  and  secondary  ?  Helmholtz 
considers  that  the  only  distinction  which  can  fairly 
be  drawn  between  these  elements  is  of  a  practical  kind, 


in  as  much  as  some  of  them  are  of  more  assistance  to 
us  than  others  as  guides  to  reality,  awakening  in  us,  as 
they  do,  expectations  which  are  habitually  verified. 

In  the  first  glow  of  enthusiasm  to  which  these  re- 
searches gave  birth,  the  possibility  of  discovering  the 
psychological  origin  of  these  presentations  and  of 
resolving  them  into  their  elements  seemed  to  be  a  clear 
proof  of  the  empirical  nature  of  geometrical  truths  and 
therefore,  also,  of  mechanics  ;  thus  from  this  point  of 
view  also  doubt  was  cast  upon  the  apodeictic  value  of 
science  more  geometrico  demonstrate,. 

The  reaction  irom  intellectualism,  which  is,  in  my 
opinion,  the  predominant  characteristic  of  contemporary 
philosophy,  will  act  as  our  guide  in  the  study  of  the 
prevailing  tone  of  present-day  thought  touching  the 
theory  of  knowledge.  By  the  general  term  "  intel- 
lectualism,"  taken  in  the  widest  sense  of  the  word,  we 
shall  understand  those  epistemological  systems  which 
assign  an  autonomous  value  to  the  cognitive  function,3 
and  we  shall  therefore  regard  as  forms  of  reaction  all 
those  currents  of  thought  which  make  the  value  of 
science  and  of  knowledge  in  general  depend  upon  the 
ends  of  other  functions  of  the  mind  and  rank  will  and 
imagination  above  intellect. 


1  Sergi,  I!  Origine  dei  fenomeni  psichici  e  la  loro  significazione  biologica 
(Milan,  1885),  p.  72. 

2  Dewey,  "  Does  Reality  possess  Practical  Character  ?  "  Essays  Philo- 
sophical and  Psychological  in  Honour  of  W.  James  (London,  1908). 

*  Intellectualism  in  the  strict  sense  of  the  word  is  the  reduction  of  all 
the  functions  of  the  mind  to  intellectual  processes.  The  pragmatists  and 
intuitionists,  however,  in  their  polemic  against  the  intellectualists,  apply 
the  term  also  to  those  who,  though  not  going  so  far,  yet  look  upon  the 
intelligence  as  a  theoretic  function  of  intrinsic  value,  and  do  not  consider 
it  as  identical  with  or  subordinate  to  practical  activity.  It  would  be 
waste  of  time  to  enter  upon  a  discussion  of  the  justifiability  of  using  the 
word  in  this  sense  ;  the  essential  thing  is  that  we  should  clearly  understand 
what  concepts  we  attach  to  the  word. 







1.  Agnosticism  as  the  Consequence  of  the  Traditional 
Mathematical  Method. — Agnosticism  was  the  logical 
outcome  of  a  prejudice  which  had  become  more  and 
more  deeply  rooted  in  thought  from  the  time  of  the 
Renaissance  on :  a  prejudice  which  affirms  that  there 
is  no  other  form  of  knowledge  save  that  of  which  we 
have  the  perfect  model  in  mathematical  physics.  The 
rich  results  yielded  by  the  quantitative  method  of 
studying  natural  phenomena  which  modern  science 
had  opposed  to  the  fruitless  multiplication  of  hypo- 
thetical qualities  led  to  over -estimation  of  this  type 
of  knowledge  :  everything  which  could  not  be  com- 
prised in  this  scheme,  everything  which  from  its  very 
nature  could  not  be  comprehended  within  the  narrow 
limits  of  a  precise  formula,  was  for  ever  banned  from 
the /domain  of  knowledge.  Even  Kant  could  not 
wholly  shake  off  this  prejudice ;  for  although  the 
intuition  of  genius  taught  him  to  discern  beyond  the 
realm  of  mathematics  and  physics  that  of  Aesthetics 
and. .jnoxal  -values,  he  yet  considered  them  as  being 
beyond  the  pale  of  true  knowledge,  and  as  belonging 
to  the  domain  of  feeling,  contemplation,  and  faith. 
Positivism  with  its  apotheosis  of  the  scientific 
method,  with  its  claim  to  give  a  comprehensive  explana- 
tion not  merely  of  natural  reality,  but  also  of  ethics 
and  aesthetics,  by  constructing  the  whole  sphere  of 
philosophy  on  scientific  principles,  carried  this  prejudice 


FT.  I 

to  its  extreme  consequences,  declaring  those  problems 
for  which,  from  its  one-sided,  restricted  point  of  view, 
it  could  find  no  adequate  solution  to  be  insoluble, 
and  was  thus  led  by  faulty  perspective  to  attribute 
to  the  nature  of  human  knowledge  that  inadequacy 
which  was  due  rather  to  its  own  method  and  system. 

P  2.  The  Ignorabimus  of  Du  Bois-Reymond. — Du  Bois- 
Reymond  x  lays  down  the  dogma  that  the  one  and  only 
true  exact  science  is  mechanics ;  all  points  of  view 
based  on  teleological,  aesthetic,  and  qualitative  principles 
are  but  anthropomorphic  conceptions,  from  which 
we  must  free  ourselves  that  we  may  consider  nothing 
in  the  world  but  the  quantitative  aspects  of  the  move- 

ynent  of  material  masses.  What,  then,  is  the  essence 
and  source  of  matter,  force,  motion,  and  of  their  dis- 
tribution ?  A  mystery  which  baffles  human  know- 
ledge !  How  does  the  qualitative  complexity  of  sensa- 
tion and  consciousness  issue  from  this  world  of  purely 
homogeneous  magnitudes  ?  Yet  another  mystery  ! 
How  about  the  source  of  life,  the  finality  of  organisms, 
the  highest  functions  of  the  mind  and  free  will  ?  These 
too  are  inscrutable  enigmas,  otherwise  we  might  well 
ask  ourselves  :  Are  these  bounds  really  the  Pillars  of 
Hercules  of  human  knowledge  ?  Do  they  not  rather 
mark  the  limits  of  your  partial  and  fragmentary  con- 
ception ?  Du  Bois-Reymond,  taking  as  his  starting- 
point  the  old  prejudice  that  knowledge  is  but  the  power 
of  formulating  mechanically,  unhesitatingly  choeses 
the  first  alternative,  and  cries,  "  Ignorabimus  !  "  But 
the  mind  of  man  with  its  higher  ideals  refused  to 
submit  to  this  "  Ignorabimus,"  and,  since  science  had 
declared  herself  unable  to  satisfy  its  loftiest  moral 
aspirations  and  attributed  her  failure  to  the  congenital 
defects  of  our  reason,  what  more  natural  than  that 
it  should  seek  to  meet  the  requirements  of  life  in  some 
other  way  ?  Scientific  intellectualism  with  its  sceptical 
conclusions  prepared  the  soil  for  the  various  forms  of 
reaction;  indeed  it  went  farther,  and  sowed  the  seed, 
leaving,  as  did  Spencer,  the  revelation  of  the  Absolute 

SEC.  I 


to  religious  belief,  and  to  a  vague  indefinite  consciousness 
incapable  of  being  expressed  in  precise  concepts. 

3.  Criticism  of  Spencer's  Agnosticism. — The  philo- 
sopher of  First  Principles  goes  even  farther  than 
Du  Bois  -  Reymond,  striving  as  he  does  to  prove 
that  the  ultimate  essence  of  things  eludes  not  only 
scientific  knowledge,  but^  also  speculative  reason,  and 
tEat  because  human  knowledge  can  of  necessity  be 
but  relative.  Agnostic  positivism,  using  as  its  weapons 
the  transcendentalism  of  Kant,  which  Hamilton  2  and 
Mansel 3  had  pressed  into  the  service  of  faith,  is  forced 
back  on  its  negative  side,  on  the  ancient  forms  of 
traditional  mysticism,  which,  though  latent,  had  never 
really  perished,  and  was  ever  ready  to  rise  again  to  do 
battle  with  the  theological  rationalism  of  the  extreme 
school.  In  the  theory  of  the  Unknowable  we  see  the 
reappearance  of  the  mystical  tendency,  finding  expres- 
sion not  in  the  moderate  formula  "  Credo  ut  intelligam," 
but  rather  in  the  blind  aberration  involved  in  "  Credo 
quia  absurdum,"  since  the  absurd  unknowable  is  in  its 
ultimate  analysis  but  the  confession  of  the  powerless- 
ness  of  that  rationalism  which  is  supposed  to  reconcile 
the  conflicting  claims  of  science  and  theology.  But,  we 
may  ask,  must  thought  inevitably  lead  to  such  an  absurd 
conclusion  ?  If  we  examine  the  Unknowable  closely,  we 
shall  find  that  it  is  simply  something  which  we  think  or  at 
least  vaguely  feel  to  be  actual,  but  which  we  affirm  that 
we  cannot  know.  We  must  here  make  sure  that  we  clearly 
understand  in  exactly  what  sensewe  use  the  word  "know," 
since  it  is  just  the  arbitrary  limitation  of  its  meaning 
which  has  given  rise  to  certain  alleged  antinomies. 

Spencer  admits  no  other  knowledge  than  that  which 
subjects  fact  to  law,  classifying  it,  resolving  it  into  its 
abstract  relations,  determining  in  what  respects  it 
resembles  other  facts  or  differs  from  them ;  but  side 
by  side  with  this  form  of  mediate  knowledge  which 
seeks  the  intelligible  element  in  the  phenomenon  brought 
to  its  notice,  there  exists  that  immediate  knowledge 
which  consists  in  the  direct  life  of  conscious  reality 


as  manifested  in  its  individual  physiognomy.  Any 
form  of  consciousness,  however  embryonic  and  rudi- 
mentary, is  already  a  knowing  of  the  content  which  is 
manifested  in  it.  The  pain  which  I  feel  at  a  given 
moment  is  an  actual  fact,  known  by  me  to  be  such, 
though  I  may  not  be  able  to  subject  it  to  law,  classify  it 
in  a  system  of  concepts,  or  explain  it  scientifically  ;  real 
too  is  the  world  of  colour,  sound,  and  form  in  its  un- 
ending variety.  The  error  of  abstract  rationalism, 
in  its  scientific  and  speculative  forms  alike,  lies  in  its 
claim  to  be  able  to  reduce  reality  in  its  entirety  to  a 
system  of  relations,  since  there  exists  an  individual 
aspect  of  things  which  cannot  be  expressed  in  its  con- 
creteness  by  means  of  abstract  relations.  It  is  for 
this  reason  that  we  find  ourselves  confronted  by  in- 
soluble antinomies  when  we  attempt  to  realise  this 
pure  system  of  relations,  that  we  vainly  endeavour 
to  find  a  fixed  point  in  the  process  of  reasoning  which 
leads  us  from  one  relation  to  another,  a  goal  which 
cannot  be  in  its  turn  a  relation  unless  we  are  prepared 
to  continue  the  process  indefinitely.  Thought,  whose 
function  is  the  establishment  of  relations,  cannot  reach 
this  absolute  goal,  but  our  consciousness  is  not  forced 
to  seek  it  beyond  the  indefinite  series  of  relations, 
since  it  is  found  within  itself  as  an  original  possession 
in  immediately  experienced  facts.  Knowledge  founded 
on  pure  logic  is  thus  doomed  to  grope  in  the  empty 
darkness  of  its  own  contradictions,  unless  it  will  take 
refuge  in  the  luminous  atmosphere  of  concrete  conscious- 
ness. If_by  "  knowing "  we  understand  simply  the 
reduction~oi  phenomena  to  law  and  their  dissolution 
into  abstract  elements,  then  the  unknowable  will  be 
found,  not  beyond  the  bounds  of  experience,  but  in 
the  facts  themselves  in  as  much  as  they  possess  a  concrete 
physiognomy  which  cannot  be  translated  into  abstract 
relations,  and  even  our  own  individuality,  as  presented 
to  us  by  experience,  will  be  unknown  to  us  !  If,  on  the 
other  hand,  we  understand  by  the  term  "  knowledge  " 
not  merely  logical  reflection,  but  also  the  immediate 


life  of  the  real,  nothing  is  unknowable,  since  everything 
which  we  regard  as  real  becomes  a  content  of  our 
consciousness  the  very  moment  we  recognise  its  reality. 
Try  as  it  may,  thought  cannot  call  its  own  objective 
value  in  question,  and,  while  endeavouring  to  prove  its 
own  relativity,  posits  as  the  absolute  term  of  reference 
something  made  of  like  substance  with  itself !  This 
is  proved  by  Spencer's  Unknowable,  which  in  the 
doctrine  of  transfigured  realism  is  conceived  of  as  the 
cause  of  phenomena,  as  being  at  once  single  and  the 
manifold,  in  its  variations  which  correspond  to  empirical 
changes  ;  as  a  substance  possessed  of  persistent  modes 
connected  by  an  indissoluble  relation  with  their 
conditioned  effects — space,  time,  motion,  and  force. 
And  yet  it  is  alleged  that  we  know  nothing  about  it ! 
Moreover,  we  are  supposed  to  have  found  an  absolute 
model  of  reality  face  to  face  with  which  thought  must 
perforce  own  its  impotence,  as  if  this  model  were  not 
just  as  much  a  thought !  Logical  activity  will  brook 
no  limits,  since  in  the  very  act  of  denning  these  limits 
it  comprehends  and  transcends  them  in  its  universal 
concepts.  A  reality^  absolutely  eluding  thought  is  an 
epistemological  absurdity ;  how  can  we  affirm  that  it 
\  exists  without  thinking  of  it  in  some  way  ? 

4.  First  Germs  of  the  Reaction  from  Intellectualism 
in  Spencer. — If  Kant,  Hamilton,  and  Mansel  pronounce 
the  Absolute  to  be  unknowable,  it  is  because  they 
wrongly  restrict  the  circle  of  knowledge  to  abstract 
intelligibility  ;  yet  at  bottom  they  too  grant  the  possi- 
bility of  a  revelation  of  this  reality  in  the  mind  of  man. 
Hamilton  writes  : 

By  virtue  of  a  wonderful  revelation  we  are  thus,  in  the  con- 
sciousness of  our  inability  to  conceive  anything  but  the  relative 
and  the  finite,  inspired  to  believe  in  the  existence  of  something 
unconditioned  beyond  the  sphere  of  comprehensible  reality. 

And  Spencer  explicitly  recognises  that  the  so-called 
Unknowable  does  not  absolutely  elude  consciousness, 
but  is  rather  presented  thereto  in  a  form  differing 
from  precise  and  determined  thought : 


Besides  that  definite  consciousness  of  which  logic  formulates 
the  laws,  there  is  also  an  indefinite  consciousness  which  cannot  be 
formulated.  Besides  complete  thoughts,  besides  the  thoughts 
which,  though  incomplete,  admit  of  completion,  there  are  thoughts 
which  it  is  impossible  to  complete  and  yet  which  are  still  real 
in  the  sense  that  they  are  normal  affections  of  the  intellect.  .  .  . 
The  error  fallen  into  by  philosophers  intent  on  demonstrating 
the  limits  and  conditions  of  consciousness  consists  in  assuming 
that  consciousness  contains  nothing  but  limits,  conditions,  to 
the  entire  neglect  of  that  which  is  limited  and  conditioned.  It 
is  forgotten  that  there  is  something  which  alike  forms  the  raw 
material  of  definite  thought  and  remains  after  the  definiteness 
which  thinking  gave  to  it  has  been  destroyed.4 

Does  not  this  sound  like  the  voice  of  Bergson  ? 

.  .  .  Autour  de  la  pensee  conceptuelle  subsiste  une  frange 
indistincte  qui  en  rappelle  l'origine.5 

The  indefinite  consciousness  of  which  Spencer  speaks 
becomes  the  fundamental  organ  of  philosophy  in 
"  infoifovft  gsfom.  If  it  be  this  indefinite 

consciousness  surrounding  logical  thought  which  presents 
I  to  us  the  absolute,  the  culminating  point  of  every  reality, 
according  to  the  opponents  of  intellectualism,  has  it 
not  a  cognitive  value  far  beyond  the  limited,  phenomenal 
consciousness  of  the  intellect  ?  But  Spencer  is  still 
too  much  under  the  influence  of  the  old  mathematical 
prejudice  to  draw  these  bold  conclusions  from  his  own 
premisses  ;  he  therefore  persists  in  designating  as  un- 
knowable that  aspect  of  reality  which  cannot  be  classified 
and  ordered  by  the  scientific  method  ;  he  makes  a 
tremendous  effort  to  apply  a  single  mathematical  formula 
to  the  perennial  evolution  of  mind  and  nature,  to  subject 
the  concrete  reality  of  becoming  to  a  law  of  persistency, 
to  a  system  of  intelligible  relations  which  is  outside 
the  limits  of  time.  It  is  an  endeavour  which  is  doomed 
to  failure,  and  will  cause  the  final  crash  of  the  structure 
of  scientific  intellectualism,  a  structure  whose  founda- 
tions are  already  undermined  by  its  own  confession 
of  impotence,  by  proving  its  inadequacy  in  the  realm 
of  phenomena  as  well. 

SEC.  I 


5.  The  Evolutionary  Method  also  leads  to  Reaction. — 
The  law  of  preservation  from  which  Spencer  is  deceived 
into  deducing  the  necessity  of  the  evolutionary  process 
only  applies  to  the  quantitative  relations  of  the  forces 
at  work  in  the  system ;  hence  it  can  give  us  no 
information  as  to  the  direction  the  changes  will  take. 
The  qualitative  transformation  of  forces,  on  the  other 
hand,  is  subject  to  the  law  of  degradation,6  according  to 
which  the  imperceptible  differences,  and  more  especially 
the  inequalities  existing  in  the  redistribution  of  energy 
in  respect  to  masses,  constantly  tend  to  diminish,  so 
that  the  natural  course  taken  by  physical  phenomena 
makes  for  the  greater  homogeneity  of  the  system,  though 
this  is  diametrically  opposed  to  Spencer's  assertion. 
As  far  as  the  principle  of  conservation  is  concerned, 
it  is  a  matter  of  indifference  whether  we  pass  from  the 
homogeneous  form  of  heat  to  differing  forms  of  'energy, 
or  whether  the  process  be  reversed,  since  in  either  case 
it  remains  unchanged  in  its  totality. 

As  Lalande  7  has  well  said,  this  permanency  would 
be  equally  true  even  if  the  progress  of  the  world  were 
suddenly  to  be  reversed,  supposing,  that  is  to  say, 
trees  were  to  grow  smaller  instead  of  taller,  till  they 
returned  to  the  germs  from  which  they  had  developed, 
and  mankind  were  to  grow  towards  youth  instead  of 
age,  reaching  the  embryonic  stage  at  the  end  of  life 
instead  of  at  the  beginning.  Nor  is  this  hypothesis 
purely  fantastical !  There  are  many  biological  instances 
of  retrogression  or  involution  of  organs,8  yet  the  law  of 
the  persistence  of  force  is  in  no  way  affected  thereby. 
For  that  matter,  does  not  Spencer  himself  deduce  from 
the  law  of  conservation  the  necessary  dissolution  of 
the  system  when  its  cycle  has  been  accomplished  ? 
How  marvellous  is  this  law,  from  which  we  may  deduce 
on  the  one  hand,  when  it  suits  us  so  to  do,  the  necessity 
of  passing  to  the  heterogeneous,  and  on  the  other  with 
equal  facility  the  no  less  necessary  return  to  primitive 
homogeneity  ! 

The  evolutionary  process  cannot  be  deduced  from  a 


system  of  mathematical  laws.  To  the  physicist,  who 
would  seek  in  the  development  of  natural  phenomena 
the  permanent  and  universal  relations  of  co-existence 
and  succession,  the  world  is  ever  the  same  in  its  totality 
and  unchangeable  in  its  inexorable  mechanical  laws. 
From  this  point  of  view  the  individual  aspects  of  things 
must  be  considered  as  illusions  of  the  senses  ;  we  are 
under  the  impression  that  we  see  an  inexhaustible 
multiplicity  of  forms  where  objectively  there  merely 
exists  a  continual  repetition  of  one  and  the  same  form, 
the  same  mechanism,  a  uniform  play  of  forces  whose 
action  can  be  calculated  and  foreseen  to  a  nicety  by 
mathematical  means.  Since,  then,  the  evolutionary 
process  disappears  when  we  exclude  the  possibility  of 
the  genesis  of  new  forms,  of  the  production  of  new 
characteristics,  are  we  not  perhaps  justified  in  concluding 
that  the  mechanical  theory  of  the  universe,  interpreted 
strictly,  must  also  regard  the  evolutionary  transforma- 
"  tion  of  species  as  an  illusory  appearance  ?  Meghanism 
and  evolution  are  two  concepts  which  cannot  be  derived 
from  one  another,  since  they  correspond  to  two  different 
aspects  of  nature  :  one  is  quantitative  permanence  and 
absolute  determinism  of  mathematical  law ;  the  other 
qualitative  transformation  and  fruitful  genesis  of 
individual  forms,  which  no  set  of  abstract  formulas 
comprehends  in  the  fulness  of  its  living  reality.  The 
evolutionary  conception  of  things  could  never  be  made 
to  fit  the  Procrustean  bed  of  the  traditional  mathematical 
method  ;  it  was  inevitable  that  it  should  (if  I  may  so 
say)  insinuate  the  poison  of  dissolution  into  the  veins 
l_of  intellectualism.  The  living  spirit  of  history,  which 
Tiad  animated  the  idealistic  speculation  of  the  beginning 
of  the  century,  finding  its  way  with  Darwinism  into 
the  domain  of  positive  research,  whilst  thus  endeavour- 
ing to  find  itself  a  place  in  the  schemes  of  science, 
breaks  down  their  mechanical  rigidity,  and  exposes 
the  tremendous  gaps  left  by  empty  formulas  in  the 
sphere  of  experience.  The  scientific  method  is  thus 
proved  to  be  inadequate  not  only  in  the  field  of  specula- 


tion,  but  also  in  that  of  phenomena  itself.  The  theory 
of  evolution,  whilst  thus  calling  attention  to  the  new 
forms  and  new  concrete  aspects  assumed  by  reality 
in  the  process  of  development,  to  the  irreversible 
direction  of  development  in  time,  and  to  the  hierarchical 
order  of  the  beings  which  rise  little  by  little  to  higher 
forms  of  life,  reveals  a  world  beyond  and  above  abstract 
mechanism  and  indifferent  to  every  temporal  and 
hierarchical  order — the  world  of  valuation  and  history, 
of  which  Kant  caught  a  glimpse  in  his  Kritik  der 
Urteilskraft,  and  which  achieves  its  triumph  over  intel- 
lectualism  in  the  philosophy  of  Windelband,  Rickert, 
Miinsterberg,  and  Royce.  It  is,  however,  specially  in 
another  direction  that  Spencerian  evolution  prepares  the 
ground  for  reaction,  i.e.  in  its  psychology  which  main- 
tains that  the  explanation  of  all  conscious  life  is  to  be 
found  in  the  requirements  of  biological  adaptation. 
The  cognitive  function  thus  becomes  but  a  means  for 
the  preservation  of  the  species,  consciousness  a  weapon 
of  defence  against  natural  forces,  valuable  only  for  its 
utility  in  foreseeing  facts,  an  instrument  for  the  main- 
tenance of  organic  equilibrium  against  the  influence 
of  perturbing  actions  in  an  ever-wider  sphere,  which 
is  subject,  like  every  other  organ,  to  transformations 

corresponding  to  the  altered  conditions  of  the  environ- 

ment.9  Science  is  not  then  based  on  an  eternal,  uni- 
versal model,  as  was  asserted  by  traditional  rationalism ; 
scientific  theories  are  born  into  the  world  just  as  are 
organic  species,  and  like  them  they  perish  when  they  can 
no  longer  resist  the  shock  of  new  experiences.  Science, 
too,  has  its  history,  and  if  we  would  know  the  meaning 
of  that  history  we  must  seek  it,  not  in  the  tendency  of 
speculation  to  grasp  the  absolute  truth  of  the  rational 
order  which  is  immanent  in  things,  but  rather  in  the_j 
needs  of  life  and  action.  This  biological  conception  of 
knowledge  will  pass  through  the  writings  of  Avenarius 
and  Mach  into  almost  every  form  of  reaction  from  intel- 
lectualism,  and  will  act  more  especially  as  the  motive 
power  of  pragmatism.  Spencer's  system  with  its  theory 


of   the   Unknowable   appealing  to   a   belief,  a   feeling 
beyond  conception,  with  its  doctrine  of  the  evolutionary 
intuition  of  the  universe,  discrediting,  as  it  does,  the 
traditional  mathematical  attitude,  and  putting  science 
at  the   service   of  biological  adaptation,   is  not  only 
>regnant  with  the  crisis  of  scientific    intellectualism, 
ut  enfolds  the  first  germs  of  that  reaction  whose  develop- 
ent  we  shall  follow  as  it  strives  in  various  ways  to 
Escape  from  the  difficult  position  in  which  agnosticism 
has  placed  it. 


1  Reden,  two  volumes  (Leipzig,  1886-87),  containing  the  two  famous 
addresses:    "  Uber  die  Grenzen  des  Naturkennens "    (1873)  and    "Die 
sieben  Weltratsel "  (1880). 

2  Discussions  on  Philosophy  and  Literature,  Education  and  University 
Reform  (London,  1853) ;   Lectures  on  Metaphysics  and  Logic  (Edinburgh, 

3  The  Limits  of  Religious  TJiought  (London,  1858). 

4  First  Principles  (chap.  iv.  section  26). 

5  L'Evolution  creatrice  (Paris,  1907),  p.  210. 
'  Cp.  on  this  point  Chapter  III.  Part  II. 

7  La  Dissolution  opposie  a  FEvolution  (Paris,  1899),  p.  47. 

8  Demoor,  Massart  et  Vandervelde  :  U  Evolution  regressive  en  BMogie 
et  en  Sociologie  (Paris,  1897). 

8  Principles  of  Psychology,  voL  i.  pt.  iii.  chap.  xi.  p.  383  ff.     (Third 



1 .  The  Return  to  the  Critical  Method. — The  first  indication 
of  the  awakening  of  the  mind  from  the  extremely  negative 
attitude  of  the  materialists  may  be  seen  in  the  return 
to  the  teaching  of  Kant ;  the  activity  of  the  subject  in 
the  elaboration  of  science,  which  had  been  for  long 
ignored,  and  had  been  thrust  into  the  background 
by  the  triumphs  so  easily  achieved  by  the  mechanical 
method,  asserts  its  rights  once  more  and  inaugurates 
the  fruitful  work  of  salutary  criticism.  Scientific 
intellectualism,  having  experienced  for  itself  in  the 
failure  of  its  bold  attempts  to  exhaust  the  totality  of 
things  the  limitations  already  defined  by  Kant,  finds 
itself  in  the  self -same  position,  face  to  face  with  the  self- 
same problems  which,  baffled  the  thought  of  the  philo- 
sophy of  Konigsberg.  It  is  natural  that  the  solution  of 
these  difficulties  should  be  looked  upon  as  the  necessary 
starting-point  of  the  new  criticism  of  value  and  the 
limits  of  human  science  ;  but  at  the  same  time  the 
need  is  seen  of  modifying  it  to  a  certain  extent  in  order 

•\to  bring  it  into  harmony  with  the  results  of  the  theory 
of  evolution  and  of  psycho-physiological  research,  and 

-  it  is  therefore  incumbent  upon  us  to  define  more  clearly 
the  meaning  of  the  a  priori  element,  and  to  assign 
limits  thereto. 

2.  Lange.  —  Albrecht    Lange    recognises,    as    does 
materialism,  the  necessity  of  finding  a  mechanical  ex- 


planation  for  physical  phenomena  and  for  the  physio- 
logical processes  of  the  brain,  seeing  that  we  are 
organically  so  constituted  as  to  be  unable  to  intuit  and 
conceive  the  world  of  phenomena  in  any  other  way. 
There  is,  however,  something  which  eludes  all  and  every 
explanation,  and  this  something  is  the  origin  of  our 
physiological  constitution ;  thought,  no  matter  what 
efforts  it  may  make,  will  always  be  brought  up  short 
by  the  limiting  concept  of  the  thing  in  itself ,  a  difficulty 
which  it  utterly  fails  to  surmount.  It  cannot  even 
ascertain  whether  it  actually  corresponds  to  anything 
real  or  is  not  rather  an  illusion  born  of  our  special 
organisation.  May  not  the  dualism  of  phenomenon  and 
noumenon  be  due  to  faulty  perspective  ? 

This  doubt  cannot  be  dispelled  by  the  intellect ; 
poetic  imagination  alone  can  guide  us  beyond  the  limits 
of  experience.  One  thing  only  is  certain :  that  man 
feels  the  need  of  supplementing  reality  by  an  ideal  world 
of  his  own  creation,  and  this  creative  work  brings  into 
play  the  loftiest  and  noblest  functions  of  his  intelligence.1 
Speculation  must  not  claim  to  be  rational  and  demon- 
strative J  ^he  more  theoretical  it  is,  the  more  it  would 
compete  with  science  in  certainty,  the  less  important 
will  be  its  part  in  life  ;  if,  on  the  other  hand,  it  is  content 
to  bring  the  world  of  actualities  into  relationship  with 
the  world  of  values,  and  rises  in  its  conception  of  phe- 
nomena to  a  moral  action,  mastering  matter  by  means 
of  form  without  doing  violence  to  facts,  it  will  raise  a 
temple  built  up  of  its  ideas  meet  for  the  worship  of  the 
eternal  and  divine.2  Peace  will  never  be  attained,  the 
conflict  between  science  and  the  highest  human  aspira- 
tions will  never  cease,  until  the  transient  character 
of  all  that  is  fictitious  in  art,  religion,  and  philosophy 
be  recognised.3 

3.  Criticism  of  the  Physiological  Interpretation  of  the 
a  priori  and  of  the  Poetic  Intuition  of  the  Absolute. — To  i 
Lange  belongs  the  credit  of  having  asserted  loudly  the  I 
rights   of   mind   as   opposed   to   vulgar   materialism ;  I 
but  by  thus  relegating  to  the  domain  of  poetry  the 


solution  of  those  problems  which  are  of  greatest  interest 
to  the  human  consciousness,  he  opens  the  door  to  every 
kind  of  fantastic  and  arbitrary  speculation,  under- 
mining at  the  same  time  the  most  stable  foundations 
of  moral  life.  His  physiological  interpretation  of  the 
a  priori  of  Kant  deprives  science  of  all  essential  and 
universal  value,  narrowing  it  down  to  a  sceptical  sub- 
jectivity, and  merely  sets  the  problem  without  solving 
it.  Our  physiological  constitution  is  undoubtedly  a 
part  of  the  world  of  experience,  and  therefore  the  a  priori 
conditions  of  its  possibility  demand  investigation. 
Lange  is  not  aware  that  he  is  moving  in  a  vicious  circle  : 
the  basis  of  mechanical  explanation  is  to  be  found 
in  our  organic  structure,  but  this  structure  in  its  turn 
demands  a  mechanical  explanation.  It  is  impossible 
to  conceive  of  the  physiological  organism  without  making 
use  of  those  intuitive  forms  and  categories  which  are 
supposed  to  be  deduced  therefrom,  and  it  therefore 
presumes  the  laws  of  thought  and  the  activity  of  the 
knowing  subject.  With  Lange  begins  that  confusion  Jy 
between  epistemological,  psychological,  and  physio-) 
logical  problems  which  serves  later  as  the  basis  of 
empirio-criticism  and  pragmatism.  Thus,  then,  the  doubt 
as  to  the  reality  of  the  thing  in  itself  to  which  it  gives 
expression  is  but  the  first  step  to  phenomenalism  which 
calls  upon  psychology  and  physiology  to  explain  the 
illusion  of  the  two  opposing  terms.  On  the  other  hand, 
if  intelligence  be  unable  to  discover  the  sources  of  our 
organisation  which  are  also  the  sources  of  thought, 
and  if  feeling  and  poetic  insight  succeed  where 
intelligence  failed,  is  not  creative  intuition  anterior 
and  superior  to  the  intellect  ?  How  else,  Bergson 
would  ask,  can  we  reach  the  inmost  heart  of  things  ? 
We  have  seen  that  the  philosophical  system  of  Lange 
is  vitiated  by  his  incurable  habit  of  begging  the  question  ; 
it  is  nevertheless  of  great  historic  value  in  as  much  as  , 
it  strives  to  overcome  sordid  materialism,  but  un- 
fortunately he  fails  to  free  himself  wholly  from  its  toils, 
and  to  place  intellectual  knowledge  on  a  sure  foundation. 


4.  The  Empirical  Prejudice  in  Helmholtz. — The  same 
empirical  prejudice  recurs  in  Helmholtz,4  who  admits 
causality  as  the  one  and  only  a  priori  form,  but  treats 
it  as  a  species  of  instinct  or  impulsive  tendency,  a  purely 
subjective  affair  of   whose   necessity  and  universality 
there  can  in  consequence  be  no  guarantee.     It  is  evident 
that  this  view  of  the  a  priori  more  nearly  approaches 
the  mental  attitude  of  the  English  empiricists  than  the 
category  of  Kant  as  a  condition  essential  to  the  in- 
telligibility of  the  real ;   it  is  a  law  of  our  nature  from 
which  there  is  no  escape,  and  which  for  that  very  reason 
must  ever  be  to  us  an  obscure  and  mysterious  power 
for  which   we    can  in  no  wise  account.    How  can  a 
principle  which  is  blind  and  incomprehensible  in  itself 
help  us  to  interpret  experience  ?     Above  all,  what  value 
has  the  science  to  which  this  need  gives  birth  unless  it 
be  that  of  a  contingent  and  subjective  construction  ? 
The  results  of  the  researches  of  Helmholtz,  which  seemed 
to  him  to  contradict  Kant's 5  theories  on  certain  points, 
inclined  him  to  adopt  the  views  of  Stuart  Mill,  and  even 
those  expressed  earlier  by  Hume  and  Berkeley.    Intuition 
a  priori,  the  universal  necessity  of  mathematical  truths, 
is  excluded  by  the  fact  that  perception  of  space  is  not 
inborn  but  acquired  in  the  course  of  a  slow  process  of 
experience,  and  more  especially  by  the  fact  that  it  is 
possible  to  conceive  of  a  space  other  than  that  of  which 
Euclid  treats  in  his  geometry.6    We  will  leave  to  the 
second  part  of  this  book  the  discussion  of  the  value  of 
the  new  geometrical  speculations  and  the  alleged  proof 
that  the  empiricists  have  deduced  therefrom  in  support 
of  their  teaching ;   for  the  present  we  will  content  our- 
selves with  pointing  out  that  Helmholtz  clearly  fails  to 
distinguish  between  the  epistemological  and  the  psycho- 
physiological  a  prioriy  with  the  result  that  his  analyses 
of  perception  prepare  the  way  for  the  phenomenalism 
of  Mach  and  Avenarius. 

5.  Liebmann    and   SchuUze. — The   philosophers    of 
the  neo-Kantian  school  were  not,  however,  all  thus 
led  astray.    Liebmann  draws  a  sharp  distinction  between 


the  norms  of  thought,  considered  as  categorical  pre- 
scriptions which  act  as  our  guides  in  the  search  for  truth, 
and  the  natural  laws  of  psychology,  in  accordance  with 
which  objects  are  presented  to  the  mind,  thoughts 
change  and  pass  away,  and  the  empirical  content  of  the 
consciousness  is  transformed  :  the  a  priori  must  not  be 
regarded  as  an  innate  idea,  but  rather  as  the  basis  of 
sensible  experience  and  of  the  world  of  speculation.7 
Schultze,8  another  adherent  of  the  neo-Kantian  school, 
observes  that  the  psycho-genetic  theory  does  not  in 
the  least  advance  the  critical  problem,  i.e.  the  analysis 
of  the  conditions  essential  to  knowledge  at  the  present 
stage  of  our  thought.  Both  Liebmann 9  and  Schultze,10 
however,  agree  with  Lange  in  the  doubt  he  expresses 
of  the  existence  of  the  thing  in  itself,  leaning,  as  they 
do,  towards  phenomenalistic  idealism,  and  viewing  the 
noumenon  as  a  mere  product  of  feeling,  a  poetical 
creation  of  the  mind. 

6.  Criticism  of  the  Neo-Kantian  School. — The  theories 
of  the  neo-Kantians,  whilst  thus  striving  to  overcome 
the  difficulties  arising  from  the  conception  of  the  thing 
in  itself,  and  from  its  relations  to  phenomena,  do  but 
increase  those  difficulties.  We  cannot  possibly  under- 
stand how  that  which  is  absolutely  outside  consciousness 
can  stand  in  any  sort  of  relation  to  feeling  and  im- 
agination, the  most  intimate  and  subjective  functions 
of  the  mind  of  man.  The  thing  in  itself,  problematic 
as  it  may  be,  is  ever  present,  like  some  mysterious 
deity,  behind  sensible  appearances,  and  our  absolute 
ignorance  of  its  function  forbids  us  to  take  for  granted 
that  the  stream  of  phenomena  of  which  it  is  the  source 
will  always  be  content  to  flow  in  the  channel  of  forms 
and  intellectual  categories.  Our  mental  organism  may 
subject  phenomena  to  law,  but  the  Absolute  is  com- 
pletely beyond  its  jurisdiction,  and  might  at  any  moment 
reveal  an  aspect  of  itself  antagonistic  to  our  nature,  and 
by  so  doing  imperil  the  universal  character  of  science. 
Are  the  sensations  imparted  to  us  by  the  unknowable 
object  purely  plastic  and  amorphous  ?  If  so,  it  is 



difficult  to  understand  why  one  form  of  classification 
should  be  more  applicable  than  another,  and  we  end 
at  the  same  time  in  reducing  knowledge  to  nothing  more 
than  a  creation  of  the  subject  totally  devoid  of  any  objec- 
tive meaning.  Or  must  we  admit  data  to  be  possessed 
of  characteristics  and  a  physiognomy  of  their  own  which 
act  as  a  stimulus  to  the  activity  of  thought  in  certain 
directions  ?  If  this  be  granted,  we  cannot  explain  how 
these  stimuli  which  have  their  source  in  the  impenetrable 
heart  of  things  can,  by  some  happy  accident,  be  moulded 
without  any  difficulty  by  the  human  intellect.  This 
uncertain  equivocal  position  of  neo-Kantian  philosophy 
left  a  painful  sense  of  doubt  in  the  mind  which  no  flight 
of  imagination,  even  though  inspired  by  genius,  and 
no  feehng,  however  lofty  and  poetical,  could  entirely 

7.  Riehl's  Monism. — Biehl,  while  retaining  the 
unknowable  residuum  of  the  thing  in  itself,  has 
endeavoured  to  invest  science  with  objective  validity 
by  substituting  a  monistic  conception  for  the  sub- 
jectivism of  the  neo-Kantists.  The  harmony  between 
the  activity  of  thought  and  the  processes  of  the  real, 
which  could  not  be  explained  by  Kantism  pure  and 
simple  unless  the  sensible  objects  were  to  be  regarded 
as  a  creation  of  the  mind,  thus  returning  to  the  theories 
of  romantic  idealism,  is,  according  to  Kiehl,  accounted 
for  by  the  identity  of  the  unknowable  source,  in  which 
the  streams  of  thought  and  objective  reality  both  take 
their  rise,  and  from  which  they  pursue  their  course  along 
parallel  lines.  The  unifying  activity  of  the  human  mind, 
the  one  and  only  true  a  priori,  is  not  purely  formal,  but 
has  its  objective  correlative  in  the  unity  of  nature,  the 
ruling  idea  of  scientific  research.  The  intuitive  forms 
and  the  categories  are  not  a  priori,  but  are  constructed 
by  the  synthetic  activity  of  thought,  which  is  ever 
striving  to  reduce  the  changeful  world  of  individual 
perceptions  to  a  reality  possessed  of  social  value  ;  they 
express  necessary  conditions,  because  experience  in  its 
manifold  forms  acquires  characteristics  of  universal 


and  objective  knowledge.  Kant  considers  intuitive 
forms  to  be  a  priori,  because  he  confuses  mathematical 
space  and  time,  which  are  concepts,  with  sensible  space 
and  time  ;  whereas  they  contain  a  material  element 
irreducible  to  pure  formal  and  mathematical  relations.11 
This  must  not  be  taken  to  mean  that  either  geometry 
or  mechanics,  taking,  as  they  do,  sensible  data  as  the 
basis  of  their  concepts,  are  of  purely  empirical  and 
contingent  value.  The  activity  of  thought  elaborates 
the  impressions  of  the  senses  in  accordance  with  its 
own  laws,  and  thus  transforms  and  completes  them 
till  they  correspond  to  its  need  of  unity  and  univers- 
ality ;  and  this  logical  reconstruction  is  neither  arbitrary 
nor  violent,  but  answers  to  their  nature,  whose  source, 
as  we  have  already  pointed  out,  is  identical  with  that 
of  thought. 

8.  Criticism  of  Riehl's  Philosophy. — There  can  be  no 
question  that  Riehl's  conception  more  nearly  succeeds  in 
placing  science  on  a  firm  basis  than  does  neo-Kantism ; 
but  it  has  the  serious  drawback  of  being  founded,  just 
as  is  the  transfigured  realism  of  Spencer,  upon  a  meta- 
physical doctrine  against  which  human  thought  rebels, 
i.e.  on  the  hypothesis  of  that  unknowable  entity  which 
nothing  but  a  miracle  could  bring  within  the  range  of 
thought.  Eiehl  not  only  admits  its  reality,  but  credits 
it  with  being  the  common  cause  of  the  two  series, 
that  is  to  say,  with  standing  in  certain  functional 
relations  thereto,  thus  implicitly  assuming  it  not  to  be 
beyond  the  forms  of  our  thought.  How  indeed  could  it 
be  so  without  losing  the  character  of  reality  ?  Can  we 
conceive  of  anything  real  which  cannot  be  translated 
more  or  less  definitely  into  terms  of  thought  ?  Eiehl 
rightly  insists  upon  the  necessity  of  admitting  the 
existence  of  a  cause  producing  our  sensations,  but 
differing  from  them,  since  between  the  stimulus  and  the 
fact  of  consciousness  there  is  a  series  of  processes  which 
physiology  has  described  to  us  in  all  its  stages  ; 12  but 
the  fact  that  we  conceive  this  cause  proves  it  to  be  already 
known  to  a  certain  extent.  Monism  based  upon  the 


PT.  I 

unknowable  is  a  castle  in  the  air  :  how  can  we  affirm 
that  to  be  one  of  which  we  can  know  nothing  ?  If  it 
be  really  unknowable,  we  cannot  possibly  apply  the 
category  of  number  to  it.  This  obscure  basis  can  only 
afford  an  explanation  of  the  harmony  of  the  two  worlds 
if  we  assume  it  to  be  possessed  of  a  certain  rationality  ; 
otherwise  it  might  be  revealed  now  in  one  way,  now  in 
another,  the  latter  contradicting  the  former,  and  the 
thought-series  might  consequently  develop  along  lines 
directly  opposed  to  objective  processes.  Riehl  may 
apparently  succeed  in  proving  the  value  of  scientific 
concepts,  but  this  is  simply  because  he  unconsciously 
transforms  his  unknowable  into  an  essentially  logical 
activity,  to  which  he  transfers  the  synthetic  unity 
proper  to  our  consciousness,  and  which  he  regards  as  a 
kind  of  potential  thought. 

9.  Elimination  of  the  Thing  in  Itself  and  Transition 
to  Phenomenalistic  Monism. — In  its  final  stage  of  develop- 
ment critical  philosophy,  in  order  to  shake  off  the  fetters 
of  absurd  agnosticism,  has  striven  to  eliminate  the  thing 
in  itself,  and  has  turned  towards  that  form  of  monism 
prevalent  in  contemporary  philosophy.  The  older  form 
of  monism  always  took  as  its  starting-point  the  duality 
of  subject  and  object,  of  internal  and  external  experience, 
and  of  the  psychic  and  physical  world,  assuming  it  as 
an  undeniable  fact,  and  then  trying  to  reconcile  the 
opposition  of  the  two  regarded  as  originary  empirical  data, 
by  resorting  to  metaphysical  speculation;  it  imagines, 
that  is  to  say,  the  existence  over  and  above  these  two 
orders  of  phenomena  of  a  substance  sustaining  them  both, 
an  entity  which  might  be  material  or  spiritual  as  best 
suited  the  exigencies  of  the  individual  case,  or  which 
might  even,  should  it  seem  undesirable  to  define  it  too 
sharply,  be  regarded  as  a  tertium  quid,  neither  matter 
not  spirit,  unknowable  in  its  essence  and  hence  admirably 
adapted  to  run  with  the  hare  and  hunt  with  the  hounds, 
or  act  the  part  of  a  buffer  state  situated  between  two 
Belligerent  powers.  The  new  monism,  on  the  contrary, 
maintains  the  unity  of  the  two  orders  of  phenomena 


to  be  a  primitive  and  original  datum,  the  opposition  1 
and  irreducibility  of  the  two  terms  to  be  due  to  faulty  ] 
perspective,  and  to  be  the  outcome  of  an  unconscious 
metaphysic  ;  it  further  maintains  that  as  soon  as  this 
illusory  superstructure  is  removed,  and  a  return  made 
to  the  pure  sources  of  immediate  experience,  which  are  . 
still  unsullied  by  philosophical  reflection,  we  shall  be 
able  to  grasp  the  undivided  unity  of  the  real  without 
going  beyond  the  limits  of  the  phenomenal.  The  unity 
of  the  two  worlds,  the  physical  and  the  psychical,  is  a 
presentation,  not  a  structure  raised  by  thought ;  it 
is  the  starting-point,  not  the  goal,  of  philosophical 
speculation.  There  are  various  degrees  of  this  new 
form  of  monism — which  may  be  designated  empirical  as 
distinguished  from  the  older  metaphysical  monism— 
which  spread  rapidly  during  the  last  quarter  of  the 
nineteenth  century,  and  is  prevalent  at  the  present 
day.  We  shall  see  that  in  its  most  advanced  form  it 
has  the  adherence  of  the  critics  of  the  empirical  school, 
of  the  French  mtuitionists,  and  the  pragmatists,  all  of 
whom  agree  in  denying  to  original  experience  the  dis-  . 
tinction  between  subject  and  object,  which  they  regard 
as  a  product  of  posterior  reflection,  determined  by^ 
motives  of  a  practical  order.  A  more  moderate  form 
of  empirical  monism  is  that  supported  by  the  philosophers 
of  immanence,  who  are  at  one  with  the  radical  empiricists 
in  maintaining  that  subject  and  object  are  but  two 
abstract  aspects  of  the  phenomenon,  or  of  the  content 
of  concrete  consciousness,  but  who  assert  on  the  other 
hand  that  it  is  impossible  to  conceive  of  conscious 
reality  without  making  such  a  distinction,  and  that  the 
two  terms,  subject  and  object,  although  neither  can 
exist  independently  of  the  other,  are  nevertheless  real, 
in  so  far  as  they  are  distinct  though  not  separate  aspects 
of  experience.13  In  short,  whilst  empirical  monism  in 
its  earlier  form  asserts  duality  to  be  illusory  or  at  most 
of  purely  practical  value,  the  later  form  views  it  as  the 
fundamental  characteristic  of  consciousness,  and  hence 
also  of  reality,  which  without  the  two  terms  would  be 


inconceivable  :  when  the  attempt  is  made  to  do  away 
with  this  distinction,  the  cognitive  relation  disappears, 
and  with  it  every  form  of  real  life.  This  last  form  of 
monism  is  undoubtedly  of  greater  value  than  the  older 
type,  which  merely  moves  in  a  vicious  circle  while 
claiming  to  deduce  from  a  vague  neutral  experience 
the  opposition  of  the  two  terms,  which  is  already  pre- 
sumed by  the  mere  fact  that  the  philosopher  thinks  this 
empirical  content,  that  is  to  say,  that  he  places  it  before 
his  own  Ego  as  something  extra-subjective.  It  is  child's 
play  for  the  philosopher  to  argue  the  duality  of  subject 
and  object  from  non-differentiated  experience,  when,  try 
as  he  may  to  eliminate  all  subjectivity,  and  however 
sure  he  may  be  that  he  has  succeeded  in  so  doing,  his 
Ego  is  still  acting  as  subject,  even  though  he  himself 
may  be  quite  unaware  of  the  fact,  and  may  be  under  the 
impression  that  he  is  constructing  it,  whereas  it  has 
always  been  the  unseen  watcher  of  his  psycho-genetical 
researches.  The  critical  idealism  of  Wundt  approaches 
very  closely  to  this  first  form ;  the  neo-criticism  of 
Renouvier  more  nearly  to  the  second. 

10.  WundCs  Critical  Idealism. — According  to  Wundt,14 
our  presentations  are  originally  identical  with  the 
object :  they  are  at  the  same  time  thinker  and  thought. 
No  object  exists  independently  of  representative  activity; 
we  may  admit  that  objects  exist  which  are  not  present 
to  us  at  this  moment,  and  which  are  possibly  not 
present  to  any  consciousness,  but  we  must  attribute  to 
these  objects  the  property  of  being  presentable.  If 
thought  and  being,  the  presentation  and  the  thing, 
be  postulated  as  two  distinct  realities,  the  cognitive 
relation  becomes  inexplicable,  since  it  is  incompre- 
hensible how  one  can  be  related  to  the  other.  The 
subject  is  not  anterior  to  the  object — both  come  into 
being  as  the  result  of  a  simultaneous  process  of  abstrac- 
tion from  the  indivisible  object  of  the  primitive  presenta- 
tion the  moment  thought  begins  to  reflect  on  the 
different  aspects  of  the  object  in  question.  The  distinc- 
tion between  the  two  orders  of  facts  should  be  preserved 


when  it  is  a  question  of  formulating  the  data  of  our 
experience  with  the  aid  of  concepts,  but  we  must  bear 
in  mind  that  its  value  is  merely  that  of  a  distinction 
between  two  stages  found  in  every  act  of  cognition. 
Subject  and  object  are  two  logical  determinations  of|\ 
one  and  the  same  real  fact,  not  two  different  facts.  The 
starting-point  of  the  cognitive  process  is  neither  pure 
thought  nor  subjective  presentation,  but  a  presentation 
in  which  the  character  of  objectivity  is  immanent. 
The  fact  that  in  common  thought,  and  still  more  in 
the  scientific  elaboration  of  reality,  certain  elements 
break  away  from  the  objective  presentation  and  adhere 
to  the  subjective  nucleus,  should  not  lead  us  to  con- 
found by  means  of  real  separation  that  which  is 
merely  a  distinction  necessary  to  enable  science  to  reach 
its  goal,  and  we  must  above  all  beware  of  regarding 
the  concrete  presentation  as  an  illusory  appearance 
by  substituting  for  it  an  abstract  conceptual  fiction, 
which,  even  though  it  may  enable  us  to  order  experience 
in  a  higher  synthesis,  can  never  take  its  place  as  true 
reality.15  Why  is  it  that  thought  does  not  stop  short 
at  the  immediate  presentation,  the  fact  as  experienced 
in  the  indivisible  complex  of  its  three  aspects — active, 
affective,  representative — instead  of  rising  gradually 
to  generic  conceptions  until  it  attains  the  most  abstract 
concepts  of  science  and  the  ultimate  notions  of  meta- 
physic  ?  The  latent  contradictions  contained  in 
primitive  experience  act  as  a  stimulus  to  the  thought  of 
man ;  reason,  which  is,  according  to  Wundt,  the  only 
a  priori,  strives  to  purge  the  presentations  of  the  senses 
in  such  a  way  as  to  fulfil  its  own  most  intimate  require- 
ments and  conform  to  its  supreme  laws.  We  may 
distinguish  three  stages  in  this  process  of  refinement, 
stages  corresponding  not  to  three  different  forms  of 
cognition,  but  rather  to  three  gradations  of  one  and  the 
same  process  of  refinement  of  experience  :  common  or 
perceptive  knowledge,  intellectual  or  scientific  know- 
ledge, rational  or  philosophic  knowledge.  Thought 
works  spontaneously  and  unconsciously  in  the  construe- 


tion  of  the  practical  world,  which  therefore  appears  to  us 
to  be  presented  from  without,  but  which  is  in  reality 
our  own  work,  and  bears  the  stamp  of  our  reason  on 
the  complex  of  its  relations.  This  explains  why  the  every- 
day world  is  adapted  to  the  successive  logical  elabora- 
tions of  science.  In  the  first  stage  of  knowledge  we 
construct  things  with  their  temporal  and  spatial  relations. 
Time  and  space  are  not  a  priori  forms,  as  Kant  con- 
sidered them  to  be,  but  elements  forming  part  of  the 
complex  of  concrete  perception,  which  are  only  re- 
garded separately  to  suit  the  requirements  of  logic  and 
epistemology.  Abstract  division  is,  however,  possible 
in  so  far  as  the  form  permits  of  variation  independently 
of  the  matter,  and  vice  versa  ;  hence  the  sensorial  content 
may  be  heterogeneous,  whilst  the  spatial  properties 
remain  constant  and  uniform.16  Thought,  in  order  that 
it  may  the  more  readily  eliminate  the  contradictions 
inherent  in  the  practical  world,  separates  certain  elements 
from  the  perceptions,  and  attributes  them  to  the  subject ; 
but,  after  what  has  already  been  said,  it  is  clear  that 
this  distinction  can  only  be  of  a  heuretic  nature,  and  that 
it  does  not  correspond  to  anything  real.17  Thus  it 
follows  that  the  world,  though  it  may  when  reduced 
to  purely  mathematical  terms,  as  science  conceives  of 
it,  answer  more  nearly  to  the  requirements  of  reason, 
in  as  much  as  it  eliminates  a  large  number  of  contradic- 
tions along  with  the  qualitative  content  of  common 
reality,  is  nevertheless  not  possessed  of  a  higher  degree  of 
objectivity  than  is  the  primitive  and  still  unpurified 

The  hypothetical  concepts  to  which  science  has 
recourse  in  its  efforts  to  classify  the  complex  of  experi- 
ence coherently  are  valueless  in  the  field  of  real  know- 
ledge, although  useful  in  so  far  as  they  enable  us  to 
comprehend  a  large  number  of  objects  in  a  single  act 
of  thought,  and  to  transfer  the  same  logical  considera- 
tions from  one  object  to  another  belonging  to  the  same 
class.  Our  cognitive  activity  has  the  individual,  not  the 
general,  as  its  goal ;  hence  the  concepts  of  real  cognitive 


value  are  not  general  but  individual,  generic  presenta- 
tions, that  is  to  say,  of  particular  objects.  Thus,  then, 
the  supreme  ideas  which  satisfy  the  demand  of  reason, 
that  the  totality  of  experience  which  has  never  been 
presented  in  its  completeness  should  be  comprised  in 
a  coherent  whole,  cannot  be  assumed  as  principles  of 
real  knowledge ;  nevertheless  we  cannot  agree  with 
Kant  that  the  effort  to  complete  the  series  must  confront 
us  with  insoluble  antinomies  or  force  us  to  posit  a  tran- 
scendent and  unknowable  reality  beyond  the  realm  of 
phenomena.  The  aim  of  ideas  is  not  to  comprehend 
the  thing  in  itself,  but  merely  to  embrace  all  experi- 
ence in  a  harmonious  system  which  shall  satisfy  the 
exigencies  of  reason  and  sentiment  alike. 

11.  Wundt's  Undecided  Position. — While  the  older 
speculative  idealism  took  the  subject  as  its  starting- 
point,  deducing  the  object  therefrom  by  means  of 
dialectic,  Wundt  reverses  the  process,  starting  from 
the  objective  presentation  and  endeavouring  to  recon- 
struct the  knowing  subject  by  essentially  psychological 
means.  In  this  method  lies  the  fundamental  error  of 
his  theory.  From  the  psychological  point  of  view  it 
is  impossible  to  deny  that  self-consciousness  is  not  a 
primitive  fact,  but  rather  something  which  is  slowly 
acquired  by  means  of  an  evolutionary  process  of  which 
the  phases  can  be  described,  so  that  the  presentation  of 
the  object  may  be  existent  from  the  beginning  without  its 
being  aware  thereof.  We  must  not,  however,  confound 
the  empirical  Ego,  the  historic  Ego,  with  the  epistemo- 
logical  subject  which  defies  every  attempt  at  analysis 
or  deduction,  since  such  analysis  and  deduction  neces- 
sarily presuppose  its  existence.  There  is  a  subjective 
side  to  every  thought,  even  though  we  may  not  be  aware 
of  it,  and  it  is  this  common  form  which  brings  within 
the  bounds  of  possibility  the  convergence  and  continuity 
of  individual  thoughts,  which  would  otherwise  remain 
extraneous  to  one  another.  Neither  will  it  avail  to  look 
to  memory  for  an  explanation  of  the  synthesis  of  person- 
ality, since  memory  in  its  turn  presupposes  the  identity 


of  the  Ego  from  the  epistemological  point  of  view.  How 
could  we  recognise  our  thoughts  of  the  past  if  the  Ego 
of  yesterday  had  nothing  in  common  with  the  Ego  of 
to-day  ?  If  the  a  priori  of  reason  be  once  admitted,  does 
not  that  of  the  epistemological  subject  necessarily  follow  ? 
We  cannot  conceive  of  reason  apart  from  the  identity  of 
the  Ego.  Ego  =  Ego  is  the  logical  presupposition  of  every 
/  other  affirmation  of  identity  whatsoever  :  the  coherency 
I  of  human  personality  is  the  concrete  basis  of  the  co- 
I  herency  of  thought.  If,  on  the  other  hand,  as  Wundt 
teaches,  every  thought  bear  the  stamp  of  objectivity, 
reason  in  every  stage  of  its  activity,  whether  conscious 
or  unconscious,  must  always  be  ranked  as  an  objective 
reality.  The  concepts  of  science  and  the  ultimate  ideas 
of  philosophy  must  be  constituent  parts  of  the  real  no 
less  than  are  presentations.  Is  the  distinction  between 
subject  and  object,  then,  illusory  or  not  ?  Is  being 
immanent  in  every  thought  or  not  ?  Only  if  we  look 
upon  reality  as  something  distinct  from  thought  can 
we  fairly  speak  of  purely  formal  activity,  subjective  in 
the  Kantian  sense  of  the  word,  or  of  an  intellectual 
or  rational  elaboration  with  nothing  objective  about 
it ;  but  this,  applied  to  the  theory  enunciated  by 
Wundt,  would  be  meaningless.  In  short,  either  the 
exigencies  of  reason  are  legitimate,  in  which  case  they 
are  so  not  only  with  regard  to  the  construction  of 
individual  concepts,  but  also  with  regard  to  the  ulterior 
processes  of  thought  whose  aim  it  is  to  eliminate  the 
contradictions  latent  in  earlier  stages,  and  to  substitute 
more  coherent  systems  for  the  lower  forms  of  reality ; 
or  else  this  claim  of  reason  to  do  away  with  all  con- 
tradictions in  the  concrete  world  of  experience  is  un- 
founded, in  which  case  we  must  strive  to  undo  this 
work  of  falsification  as  far  as  possible,  in  order  to  return 
to  pure  experience  and  primitive  intuition. 

Once  we  start  in  this  direction  we  must  follow  it 
to  the  end,  i.e.  empiric-criticism  and  Bergson's  doctrine 
of  intuition.  Wundt,  however,  is  reluctant  to  go  so 
far,  and  he  retains  the  concept  of  a  presentation 


which  does  not  bear  the  imprint  of  thought,  and  stops 
short  at  the  generic  image,  which  for  some  reason  or 
other  is  privileged  to  keep  the  characteristic  of  object- 
ivity. We  have  hardly  advanced  a  step  higher,  and 
resolutely  banished  the  concrete  presentation,  when 
the  ensuing  concept  ceases  to  correspond  to  anything 
real  and  becomes  but  a  convenient  symbol  of  a  class 
of  objects.  Now  this  uncertain  position  is  not  tenable  : 
if  the  scientific  concept  does  not  correspond  to  something 
objective,  it  can,  according  to  Mach,  be  nothing  more 
than  a  useful  tool ;  in  that  case  what  becomes  of  the 
a  priori  of  reason  ?  Logical  exigency  too  becomes  but 
a  means  of  saving  mental  energy,  which  would  otherwise 
be  incapable  of  mastering  the  countless  successions  of 
individual  presentations.  It  is  impossible  to  conceive 
of  an  a  priori  reason  which  is  not  also  a  constituent 
part  of  reality.  If,  as  Wundt  affirms,  the  scientific  world 
eliminates  the  latent  contradictions  of  the  world  of  ideas, 
it  cannot  for  that  reason  be  looked  upon  as  less  real 
and  less  objective ;  unless  indeed  we  are  prepared  to 
admjt  the  absurd  paradox  that  the  contradictory  is 
more  real  than  that  which  is  devoid  of  contradictions. 
Thought  and  reality  are  not  exhausted  by  presenta- 
tion ;  it  is  not  true  that  we  can  postulate  nothing  as 
real  which  cannot  be  presented  ;  all  that  can  fairly  be 
asserted  is  that  nothing  exists  which  cannot  be  thought 
or  which,  in  other  words,  is  inconceivable.  Wundt' s 
conclusion  would  be  justifiable  from  the  point  of  view 
of  nominalism,  which  denies  the  existence  of  the  concept 
apart  from  the  individual  image,  but  he  draws  a  dis- 
tinction between  the  concept  and  the  sign  which 
represents  and  defines  it;  that  is  to  say,  he  admits 
its  reality  in  consciousness  ;  and  since,  according  to 
him,  the  being  of  the  object  is  immanent  in  thought, 
the  logical  conclusion  would  be  that  the  concept  of 
the  universe  too  is  of  objective  value.  Does  cognitive 
activity  endeavour  to  ehminate  contradictions  because 
it  aims  at  the  individual,  or  rather  because  amid  the 
various  and  transient  aspects  of  things  it  would  fain 


grasp  the  oneness  of  universal  law  ?  There  is  nothing 
contradictory  about  the  individual,  as  presented  to  us 
by  immediate  intuition ;  the  contradictory  element  is 
introduced  when  we  attempt  to  turn  a  fugitive  experi- 
ence, which  is  real  only  at  that  concrete  moment,  and 
will  never  occur  twice  in  the  same  way,  into  a  persistent 
thing,  existing  independently  of  ourselves,  or,  in  other 
words,  when  we  demand  a  revelation  of  the  universal 
from  immediate  presentation.  The  image  must  then 
of  necessity  seem  inadequate,  and  thought  is  con- 
scious of  the  need  of  transcending  it,  and  constructs 
scientific  and  philosophic  reality  with  the  help  of  its 
concepts.  If  the  aim  of  knowledge  were  to  grasp  the 
concrete  individual  there  would  be  no  contradiction ; 
the  contradiction  arises  the  moment  we  seek  in  sensible 
appearances  the  characteristics  of  universality  which  are 
proper  to  thought.  Wundt's  philosophy,  which  regards 
the  individual  as  the  end  of  knowledge,  whilst  implicitly 
denying  its  starting-point,  the  a  priori  of  the  reason, 
must  perforce,  when  carried  to  its  ultimate  conclusion, 
lead  to  empirio-criticism. 

12.  The  Return  to  the  Voluntarism  of  Schopenhauer. — 
Wundt  shows  himself  even  more  plainly  as  the  opponent 
of  intellectualism  in  psychology  and  metaphysics  than 
in  the  theory  of  knowledge,  regarding,  as  he  does,  will 
as  the  principle,  not  merely  of  psychic  life,  but  also  of 
all  cosmic  development.18  This  return  to  Schopenhauer, 
which  achieved  its  first  startling  success  as  early  as  1869 
in  Hartmann's  philosophy  of  the  Unconscious,  is  closely 
connected  with  the  spread  of  the  theory  of  evolution 
and  of  energetic  conceptions.  The  tendency  of  every 
organism  to  self-preservation — the  motive  power  of  the 
struggle  for  existence — does,  as  a  matter  of  fact,  approxi- 
mate closely  to  Schopenhauer's  will  to  live  ;  hence  the 
derivation  of  intelligence  from  instinctive  life  which 
Darwinism  asserted  itself  able  to  prove  woke  an  answer- 
ing chord  in  his  philosophy.  On  the  other  hand,  the 
active  principle  of  energy,  which  had  already  taken  the 
place  of  the  inert  atom  in  Spencer's  First  Principles,  bore 


a  strong  resemblance  to  the  blind  unconscious  impulse 
which  Schopenhauer  regards  as  the  essence  of  physical 
reality.  Hence  it  was  natural  that  voluntarism  should 
seem  the  metaphysical  view  best  suited  to  explain  the 
processes  of  evolution  and  supply  that  which  was  lack- 
ing in  the  mechanical  theory.  The  spontaneous  and 
productive  activity  of  will  to  which  consciousness 
points  as  the  creator  of  new  concrete  forms  might 
perhaps  have  given  us  the  clue  to  this  historical  develop- 
ment, which  eluded  the  abstract  formulas  of  scientific 
intellectualism.  As  a  matter  of  fact,  von  Hartmann,19 
Wundt,  and  Fouillee  M  all  call  upon  the  will  to  perform 
this  task  in  their  systems,  of  which  a  new  philosophy 
of  evolution  forms  an  essential  part.21 

13.  Von  Hartmann' s  Philosophy  of  the  Unconscious.— 
Metaphysical  voluntarism,  which  was  thus  the  outcome 
of  the  necessity  of  unifying  scientific  intellectualism, 
and  which  was  called  into  being  by  this  very  doctrine 
of  evolution  as  its   complement,   loses   that  absolute 
irrationality  characterising  it  in  Schopenhauer's  philo- 
sophy, when  it  strives  to  absorb  the  results  of  science 
and  to  justify  its  existence  therewith.     It  has  ceased) 
to  be  an  unseeing  impulse  giving  birth  to  the  cosmic) 
process,  and  has  become  a  will,  in  which  reason  andJ 
idea  are  present,  even  though  it  may  be  unconscious^ 
or    but   dimly   conscious   that  this  is    the    case.     As 
we  have  already  seen,  Wundt  regards  will   as  being 
at   the  same  time   rational   thought ;    Fouillee  views 
the  "  idee-force  "  as  the  synthesis  of  the  two  principles. 
Von  Hartmann  looks  upon  the  unconscious  as  being 
both  will  and  idea.22    We  are  still  far  from  the  ex- 
aggerations of  empirio-criticism  and  pragmatism,  against 
which  von  Hartmann  **  and  Fouillee M  protest ;    but 
although  these  philosophers  do  not  go  so  far  as   to 
agree  with  Paulsen's  assertion  that  science  by  reason 
of  its  poor  practical  results  must  be  looked  upon  as 
being  a  thing  of   the  past,  and  that  the  future  lies 
open  to  faith,  they  adopt  a  critical  attitude  towards 
scientific  truth  which  is  very  far  removed  from  the 


j  dogmatic  faith  of  the  old  mechanical  theory.    Hartmann 
|~Tmaintains  that  physical  science  will  never  lead  us  to 

I  certainty,  but  only  to  hypotheses  of  varying  degrees 

f  of  probability.  Every  scientific  concept  presupposes 
an  abstraction  made  from  a  determinate  point  of  view, 
a  selection  of  characteristics  according  to  a  criterion 
which  is  always  hypothetical  and  becomes  less  and  less 
probable  as  the  distance  between  concrete  experience 
and  ourselves  increases,  and  we  approach  the  ultimate 
concepts  of  physical  science  (energy,  potential,  entropy, 
(mass,  matter,  force,  etc.).  The  hypothetical  character 

""^becomes  still  more  obvious  in  induction,  which  goes 
beyond  facts  as  directly  perceived,  and  strives  to 
determine  the  objective  causes  to  which  they  are  due. 
It  is  but  an  hypothesis  that  there  is  such  a  thing  as 
real  nature,  and  that  our  laws  are  valid  in  the  realm 
of  that  real  nature — an  hypothesis,  moreover,  which 
cannot  be  proved,  since  we  can  never  go  beyond  the 
subjective  sphere  of  our  own  consciousness,  and  yet, 
whatever  phenomenalists  may  say,  we  must  leave  it 
behind  if  we  would  construct  a  system  of  physical 
science ;  he  who  never  goes  beyond  the  domain  of 
sensations  and  their  relations  is  a  psychologist,  but  he 
will  never  succeed  in  expressing  the  objective  world 
in  scientific  terms.  I^othing  but  the  realistic  pre- 
sumption that  cause,  time,  and  intelligible  space  of 
three  dimensions  have  a  transcendent  validity  can 
enable  us  to  speak  with  truth  of  natural  laws 
differing  from  those  of  psychology,  or  of  objective 
movements  in  conformity  with  the  ideal  laws  which 
our  thought  conceives ;  but  this  presumption  is  an 
hypothesis  and  must  ever  remain  so.25  The  progress  of 
physical  science  may  enable  us  to  arrive  at  an  accurate, 
quantitative  determination  of  the  coefficients  of  prob- 
ability of  each  individual  law,  but  it  can  never  trans- 
form that  probability  into  certainty.26 

Thus  the  whole  of  von  Hartmann's  system  depends 
upon  an  hypothesis,  since  the  very  unconsciousness 
which  is  supposed  to  be  the  cause  common  to  the  cognitive 


process  and  the  real  world  is  in  its  turn  but  probable 
knowledge  similar  in  nature  to  all  causes  transcending 
the  order  of  phenomena.  The  efforts  of  philosophy  in 
this  direction  are  no  more  successful  than  those  of 
science ;  von  Hartmann  holds,  just  as  does  Wundt,  that 
the  ultimate  principle  to  which  philosophy  leads  us  is, 
in  its  absolute  transcendence,  of  purely  hypothetical 
value.  Human  reason,  whatever  efforts  it  may  make, 
must  always  leave  some  thing  exterior  to  itself  :  that 
element  which  is  beyond  logic,  and  whose  dark  mysterious 
depths  can  never  be  sounded  by  thought.  Philosophy, 
Wundt  tells  us,27  may  prove  the  necessity  of  faith  in.  a 
universal  Will,  but  can  never  transform  that  faith  into 
knowledge  ;  hence  the  assertion  of  the  reality  of  this 
supreme  principle  belongs  to  the  subjective  sphere  of 
feeling,  which  has  its  rights  just  as  much  as  has  that  of 
reason.  Von  Hartmann  bases  philosophy  upon  a  power 
of  divination,  partaking  of  the  nature  of  genius,  which 
identifies  us  with  that  unconscious  spiritual  activity 
lying  at  the  root  of  existence  more  nearly  than  discursive 
intelligence  could  succeed  in  doing.  Every  system  takes 
its  rise  in  mystic  intuition;  hence  it  is  only  capable  of 
proof  to  its  originator  and  to  those  who  by  a  process  of 
mystical  creation  can  rediscover  its  essential  elements 
within  themselves.28  This  intellectual  process,  however, 
which  von  Hartmann  takes  from  Schelling,  must  either 
be  conscious  in  some  way  or  other,  in  which  case  the 
term  absolute  unconsciousness  is  out  of  place,  or  else 
utterly  transcends  our  conscious  life,  in  which  case  it 
is  difficult  to  see  how  its  existence  can  be  stated  as 
a  fact.  Von  Hartmann  in  reality  falls  into  the  very 
error  which  lies  at  the  root  of  Spencer's  agnostic 
evolution ;  he  ascribes  the  character  of  actual  reality 
to  something  which  has  no  essential  connection  with 
consciousness,  which  existed  and  could  have  continued 
to  exist  in  its  absolute  unconsciousness  even  had  the 
idea  never  happened  to  be  born  of  the  will,  and  to 
produce  therein  by  its  sudden  appearance  a  feeling 
of  stupefaction,  a  reaction  which  is  the  beginning  of 


conscious  life.29  Agnosticism  is  the  fatal  result  of  this 
view  of  the  relation  between  being  and  consciousness  ;  it 
is  true  that  von  Hartmann  contrives  to  avoid  this  sceptical 
conclusion,  but  he  does  so  because  his  Unconscious  is 
only  nominally  such ;  in  reality  his  description  of  it 
involves  a  much  higher  form  of  consciousness  than 
our  own,  one  capable  of  grasping  in  a  single  act  of 
intuition  that  which  discursive  intelligence  views  as 
developing  in  the  indefinite  and  inexhaustible  series  of 

14.  Fouillee's  Idee-force. — Fouillee  must  be  credited 
with  having  resolutely  put  aside  the  absurdity  of  the 
epiphenomenal  consciousness  which  is  suddenly  super- 
imposed upon  physical  energy  or  upon  the  idea  emanat- 
I  ing  from  the  will  in  some  unknown  miraculous  way.    Un- 
\  like  those  men  of  science  who  would  fain  reduce  psychic 
life  to  an  automatic  mechanism,  a  complex  of  reflex 
'actions,  Fouillee  passes  from  psychology  to  cosmology, 
and  endeavours  thus  to  prove  that  physical  evolution 
itself  is  inexplicable  if  the  factor  of  consciousness  be 
not  taken  into  account.30    The  starting-point  of  every 
,  process  of  development  is  not  brute  movement,  but 
*    rather  psychical  appetitive  or  reflex  process  which  is 
at  once  an  obscure  presentation,  a  feeling  of  a  more 
or  less  vague  nature  and  an  activity.31 

Mechanical  evolution  is  not  a  primitive  law,  but  the 

/  form  and  outer  sign  of  the  appetitive  process  which  is 

the  true  inner  essence  in  ourselves,  and  in  all  probability 

in  everything  else.      Darwinism  does   not  ask  us  to 

regard   biological  and  psychological  phenomena  as  a 

complication  of  mechanical  laws,  but  would  rather  have 

us  understand  from  the  struggle   for  existence  that 

mechanism  itself  is  a  form  of  this  struggle  for  life, 

which,  rightly  understood,  resolves  itself  in  its  turn 

into  a  struggle  for  the  minimum  of  suffering  and  the 

maximum  of  well-being,  or,  in  other  words,  into  a  struggle 

/•  of  wills.32    The  world  is  not  a  complex  of  inert  atoms, 

)  but  a  vast  social  organism  of  wills  united  by  the  bond 

)  of    mutual    sympathy.      Philosophy    in    its  ultimate 


analysis  looks  upon  the  idea  of  the  universal  association  of 
consciousnesses  as  the  basis  of  that  which  was  formerly 
termed  nature,33  and  thus  replaces  scientific  abstractions 
by  the  full  complete  synthesis  of  living  reality.  Science, 
which  looks  upon  the  relations  of  things  independently 
of  the  subject  which  wills  and  thinks  and  of  existence 
in  its  totality,  affords  us  but  an  abstract  vision,  which 
cannot  take  in  the  fulness  of  reality,  the  unity  of  things 
with  the  mind  which  is  conscious  of  them  and  with  the 
entire  universe.  Philosophy  cannot  therefore  stop  short 
at  the  objective  synthesis  courted  by  positivism,  but  must 
integrate  and  complete  it  by  re-establishing  that  intimate 
relation  with  the  conscious  subject  which  is  ignored 
by  scientific  research.34  As  the  eye  of  the  philosopher 
learns  to  range  over  wider  horizons  he  will  see  less  of 
the  unbending  certainty  which  science  attains  by  limiting 
its  objective  ;  the  outlines  of  ideas  will  become  less 
sharply  defined,  until  they  fade  away  altogether  in  that 
mysterious  distance  which  is  the  domain  of  faith, 
probability,  and  feeling.35  Faith  and  feeling  must  not, 
however,  rise  in  revolt  against  intellectual  knowledge, 
which,  limited  as  it  may  be,  is  yet  our  surest  possession, 
whereas  the  indefinite  character  of  feeling  renders  it 
most  liable  to  fall  into  error.  The  heart  may  have 
reasons  which  carry  weight,  but  it  is  to  reason  that  we 
must  look  for  recognition  of  their  truth.  Love  and  will 
may  in  practice  supply  that  which  is  lacking  in  knowledge, 
but  they  cannot  turn  uncertainty  into  certainty,  except 
by  means  of  an  illusion  which  cannot  be  taken  as  a  rule 
of  life.  The  most  important  of  the  duties  of  man  is 
to  search  for  the  greatest  possible  number  of  assured 
truths ;  and  there  can  be  no  true  certainty  apart  from 
intellectual  certainty.  The  efficacy  of  faith  is  an 
incontrovertible  fact,  but  its  efficacy  is  no  proof  of  its 
truth  ;  the  creed  of  the  Mohammedan  is  false,  although 
it  has  led  him  to  victory.36 

Fouillee  thus  raises  the  standard  of  rebellion  against  S 
the  excesses  of  pragmatism  and  the  doctrine  of  con- ) 
tingency,  and  resolutely  asserts  that  morality  without  / 



reason  cannot  exist,  and  that  if  liberty  could  only  be 
had  at  the  price  of  intelligence,  it  would  be  better  to 
retain  reason  even  at  the  cost  of  liberty  than  to  enjoy 
freedom  without  reason,  and  in  defiance  of  reason  itself.37 
Yet,  although  Fouillee's  psychological  determinism38  is 
the  very  antipodes  of  the  doctrine  of  contingency,  there 
can  be  no  doubt  that  he  too  has  helped  to  initiate  and 
spread  the  reaction  from  intellectualism  by  means  of 
his  evolutionary  theory  of  knowledge,  which,  while 
striving  to  correct  and  modify  the  Spencerian  doctrine 
of  evolution,  is  in  agreement  with  its  fundamental 
principle — the  biological  significance  of  the  intellectual 
function.  He  may  not  fall  into  the  error  of  deriving 
consciousness  from  a  physical  process,  but  he  persistently 
looks  for  the  origin  of  the  supreme  categories  of  the 
intelligence  in  the  need  for  the  preservation  of  the 
species,  in  that  will  to  live  which  is  the  motive  power 
of  the  struggle  for  existence. 

The  proposition  he  endeavours  to  prove  in  the 
Psychologic  des  Idees-Forccs  is  to  all  intents  and  purposes 
identical  with  that  which  becomes  later  the  dominant 
note  of  pragmatism ;  knowledge  is  but  a  means  which 
we  have  artificially  turned  into  an  end  by  severing  it 
from  the  sensitive,  emotional,  and  motor  process,  the 
living  circle  of  which  it  naturally  forms  part.39  Neither 
physical  nor  logical  evolutionism  can  account  for  that 
thought  which  is  deeply  rooted  in  the  will,  understood, 
not  in  the  intellectual  sense  of  an  ultimate  or  exemplary 
cause  acting  in  view  of  an  end  which  it  has  before  it,  of 
an  ideal  good  ideally  conceived,  but  rather  as  a  tendency 
to  preserve  unimpaired  the  immediate  feeling  of  pleasure 
which  affords  satisfaction  to  the  organism.40 

15.  The  Endeavour  to  reconcile  Pragmatism  and 
InteUectualism. — If  these  premises  be  granted,  may  not 
the  conclusions  drawn  from  them  by  empirio-criticism 
and  pragmatism  be  regarded  as  justifiable  ?  If  the 
theoretical  function  be  really  of  no  intrinsic  value  by 
itself ;  if  it  be  but  a  tool  forged  by  the  will  to  live  in  order 
to  ensure  the  preservation  of  the  organism,  then  science 


and  philosophy,  which  are  the  offspring  of  that  function, 
have  no  end  of  their  own,  but  owe  any  importance  they 
may  poselites  to  their  relation  to  practical  activity.  That 
belief  or  theory  which  enables  us  to  gain  the  victory 
in  the  struggle  for  existence  must  be  true ;  that  which 
fails  to  attain  that  end,  false  :  such  is  the  one  and  only 
criterion  of  this  new  instrumental  logic.  Fouillee,*/ 
however,  shrinks  from  going  to  such  extremes,  though 
such  a  conclusion  is  the  logical  outcome  of  his  biological 
theory  of  knowledge,  and  takes  up  a  dubious  position, 
a  half-way  house  between  intellectualism  and  prag- 
matism. By  conceiving  the  idea  as  possessed  of  force,41 
he  deems  it  possible  to  reconcile  the  theory  of  the 
intellectualists,  which  looks  on  truth  as  a  harmony, 
with  that  of  voluntarism,  which  regards  it  as  an  action 
or  active  belief,  since  truth  is  simultaneously  and  in- 
divisibly  a  harmony  of  actions  and  ideas,  derived  from 
an  intelligent  will  or  an  active_intelhgence.  Even 
though  the  main  claim  of  knowledge  to  importance 
may  be  the  work  it  acaornplishes  as  an  instrument  of 
life  in  the  course  of  evolution,  this  does  not  constitute 
its  only  value  ;  ideas  are  undoubtedly  of  value  as  forces, 
but  they  are  also  valuable  as  ideas.42  They  are  not 
merely  a  residuum  of  abstraction,  but  are  a  manifesta- 
tion of  higher  reality,  because  the  process  of  elabora- 
tion to  which  thought  subjects  data  enables  us  to 
penetrate  more  deeply  into  the  heart  of  nature.  Only 
by  a  dogmatic  abuse  of  the  transcendent  unknowable 
does  it  become  possible  to  affirm  that  thought  trans- 
forms reality,  as  if  thought  were  not  the  same  reality 
at  a  more  advanced  stage  of  development,  a  higher  level 
of  consciousness  and  action.  Reality  does  not  shrink, 
but  rather  attains  to  its  full  stature  in  the  full  con- 
sciousness of  thought  and  in  the  moral  will.43 

Now  I  quite  agree  with  Fouillee  in  this  vindication 
of  the  objective  value  of  thought,  and  readily  subscribe 
to  his  criticism  of  the  relativity  of  knowledge,  and  of 
the  subjectivism  of  Kant,  whose  weak  points  he 
exposes  more  clearly  than  Wundt,  recognising,  as  he 


does,  the  character  of  objectivity,  not  in  sensible  know- 
ledge of  phenomena  alone,  but  also  in  every  stage  of 
scientific  and  philosophic  elaboration ; u  but  I  fail  to 
\  see  how  this  declaration  of  the  value  of  the  understanding 
(  can  be  reconciled  with  the  biological  view  which  would 
(  trace  its  origin  to  the  elementary  needs  of  life.     If,  as 
j  Fouillee  himself  says,  it  is  to  the  loftiest  forms  of  the 
mind  that  we  must  look  for  the  deepest  and  fullest 
revelation  of  reality,  if  the  participation  of  this  reality 
in  the  life  of  things  be  in  proportion  to  the  higher 
intellectual,  moral,  and  above  all,  social  determinations 
it  contains  ;    if  we  approximate  more  closely  to  the 
universal  will  when  we  think  than  when  we  feel,45  then 
neither  psychic  reflex,  obscure  appetition,  nor  the  im- 
pulsive will  to  live  which  aims  at  immediate  satisfaction 
can  afford  us  an  explanation  of  that  intelligent  volition 
which  is  capable  of  setting  universal  ends  before  itself  ; 

!we  must  rather  look  to  the  moral  will  infused  with  intel- 
ligence for  the  explanation  we  desire  of  the  rudimentary 
forms  of  volition,  "  How,"  we  would  ask  in  Fouillee's 
own  words,  "  can  the  meanest  existence  be  the  most 
faithful  transcript  of  the  world  ?  " 46  Whilst  Fouillee, 
the  idealistic  philosopher,  proclaims  that  man  mirrors 
the  universe  more  faithfully  than  does  the  animal, 
Fouillee,  the  biologist  and  psychologist,  who  is  still 
under  the  influence  of  the  preconceptions  of  positivism, 
looks  for  the  cause  of  the  birth  of  intelligence  in  the  blind 
instinct  of  the  animal,  and  in  the  vague  feeling  of  the 
protozoa  and  its  tendency  to  preserve  agreeable  stimuli. 
Thus  the  way  is  cut  off  which  leads  to  that  synthesis 
of  volition  and  idea,  whose  living  expression  is  found 
in  personality  conscious  of  its  ends,  not  in  the  rudi- 
mentary forms  of  primitive  impulse.  The  idee- force 
reconciles  in  itself  the  opposing  systems  of  voluntarism 
and  intellectualism,  if  we  understand  by  it  active  thought} 
or  intelligent  will ;  if,  on  the  other  hand,  we  identify  it 
with  obscure  appetition  and  the  instinctive  tendency  to 
preserve  life,  it  degenerates  into  the  absolute  irrationalism 
taught  by  Schopenhauer.  Fouillee  halts  between  the 


two  meanings,  but  leans  more  toward  the  latter,  which, 
alleging  as  it  does  that  thought  is  a  product  of  vital 
adjustment,  certainly  cannot  be  said  to  recognise  its 
intrinsic  value. 

16.  Ultimate  Consequences  of  Voluntarism  as  seen  in 
Paulsen. — Fouillee's  undecided  position  is  not  tenable : 
if  we  are  to  look  to  the  will  to  live  for  the  origin  and 
meaning  of  the  intelligence,  we  must  resolutely  put 
on  one  side  the  thesis  of  the  intellectualists  according 
to  which  the  idea  is  possessed  of  autonomous  value, 
and  we  must  accept,  as  do  Paulsen  and  Nietzsche,  the 
extreme  conclusions  of  the  voluntarism  which  regards 
reason  merely  as  an  organ  of  volition.  Paulsen 
affirms 47  that  the  whole  structure  of  the  mind  is  a 
contingent  product  of  the  evolution  of  species  :  time, 
space,  and  the  categories  have  come  into  being  in 
the  course  of  development,  just  as  the  eye,  the  ear, 
and  the  brain  have  done  ;  hence  they  represent  the 
variable  and  secondary  part  of  consciousness,  whilst 
will,  which  is  present  in  all  manifestations  of  life  alike, 
and  may  by  analogy  be  assumed  to  be  at  the  basis  of 
material  activity,  is  the  true  first  and  constant  principle 
of  both  mind  and  universe.  Will,  not  reason,  defines 
the  end  of  life  :  intelligence  plays  but  a  subordinate 
part — that  of  finding  the  means  best  suited  to  the  accom- 
plishment of  that  end ;  and,  since  the  true  task  of 
philosophic  research  is  to  determine  the  meaning  of 
existence,  which  is  manifested  only  in  the  relations 
existing  between  things  and  our  will,  and  in  that 
obscure  feeling  which  forms  the  basis  of  all  our  valua- 
tions, we  must  not  look  to  intellectual  knowledge  with  its 
indifference  to  every  value  to  bring  us  into  contact  with 
the  underlying  life  of  things,  but  rather  to  moral  and 
religious  belief .«  The  certainty  that  the  world  is  not  an 
utterly  meaningless  game  of  unseeing  forces,  that  the 
supreme  good  to  which  our  will  is  directed  is  also  the 
end  and  aim  of  the  cosmic  process  is  not  bestowed  upon 
us  by  science,  which  is  but  an  apparatus  for  the  registra- 
tion of  the  real  in  the  sphere  of  phenomena,  but  owes 


its  origin  to  our  keen  sense  of  duty,  and  to  the  religious 
faith  which  we  place  without  asking  for  theoretical 
proof  in  a  perfect  Being,  the  creator  of  all  values.49 

17.  Criticism  of  Voluntarism  and  the  Theory  of  Faith. 
— Paulsen  thus  returns  to  the  antiquated  mysticism  of 
tradition ;  he  exaggerates  the  agnostic  subjectivism 
which  is  the  weak  point  of  Kant's  system,  and  finds 
fault  with  Kant  for  precisely  that  which  is  of  the  greatest 
value  in  his  Kritik  der  reinen  Vernunft,  namely  the 
distinction  he  draws  between  the  epistemological  method 
and  psycho-genetic  research,  the  piece  de  resistance  of  the 
English  empiricists.  It  is  indeed  strange  that  Paulsen, 
who  insists  so  strongly  on  the  inadequacy  of  the  scientific 
method  for  the  determination  of  values,  should  yet  call 
upon  the  scientific  theory  of  evolution  to  assist  him  in 
his  denial  of  the  value  of  intelligence  !  As  a  matter  of 
fact,  whatever  he  may  say  to  the  contrary,  he  is  still 
fettered  by  the  science  he  would  fain  reject :  is  not  the 
analogy  which  forms  the  basis  of  his  system,  the  process 
of  induction  from  subjective  volition  to  cosmic  will 
manifested  in  phenomena,  an  intellectual  process  ?  Is  not 
the  identification  of  the  end  of  the  universe  with  good— 
our  loftiest  aspiration — a  thought  rather  than  a  feeling  ? 
Are  we  to  form  no  idea  or  conception  of  the  end  of 
activity  ?  Paulsen,  whilst  deluding  himself  into  the 
belief  that  he  derives  the  cognitive  function  from  will, 
really  assumes  its  existence  the  moment  he  states 
that  it  aims  at  the  preservation  of  the  individual  and 
the  species,  even  though  it  may  do  so  unconsciously  ; 
because  it  is  at  bottom  the  idea  of  this  end  which  enables 
the  philosopher  to  deduce  the  cognitive  organ  as  a 
means  of  its  realisation ;  logically  then,  if  not  psycho- 
logically, this  concept  is  present  in  the  most  elementary 
forms  of  life.  Moreover,  in  order  to  explain  the  biological 
process  of  evolution  we  are  continually  forced  to  refer 
to  the  conditions  present  in  the  environment,  to  take 
for  granted,  that  is  to  say,  an  external  reality  having  a 
specified  structure  to  which  the  organism  must  adapt  itself 
if  it  would  live  ;  and  the  concept  of  this  external  reality 


has  already  called  into  action  the  forms  of  space  and 
time  and  all  the  categories  which  are  supposed  to  be 
born  in  some  miraculous  way  of  the  will  to  five,  whereas 
the  mind  of  the  philosopher  has  already  taken  them 
for  granted  the  very  instant  he  begins  his  so-called 
genetic  explanation  of  the  intelligence. 

Moreover,  the  very  will  to  live,  which  is  the  starting- 
point  of  the  whole  process  of  deduction,  is  (if  by  it  we 
understand  a  universal  activity)  not  a  feeling,  but 
a  concept ;  it  is  not  pure  volition  directly  experienced, 
but  will  reflected  by  thought,  which  has  thus  become  the 
idea  of  a  cosmic  will  embracing  all  things.  The  more 
capable  volition  is  of  becoming  a  principle  of  philosophic 
explanation,  the  more  will  it  become,  so  to  speak, 
infused  with  intellect :  philosophy  cannot  be  built  up 
on  nothing  but  feeling.  Faith,  which  would  fain  take 
the  place  of  knowledge  as  the  basis  of  the  system, 
though  undoubtedly  comprising  an  active  and  feeling 
element,  also  implies  an  intellectual  aspect,  no  matter 
in  what  form  it  may  present  itself.  The  presentation  or 
concept  of  a  thing  is  essential  to  belief  therein. 

Paulsen,  like  all  the  apostles  of  the  will,  turns  to 
psychological  analysis  for  proofs  of  the  primacy  of 
will ;  but  although  the  voluntaristic  tendency  was 
welcomed  so  warmly  by  psychology  (it  will  suffice  to 
quote  the  names  of  Hoffding,  Stout,  Ward,  and  Jodl, 
in  addition  to  the  philosophers  already  mentioned), 
it  does  not  appear  to  me  that  the  results  of  obser- 
vation of  consciousness  afford  sufficient  proof  of 
such  a  theory.  The  strong  point  of  voluntarism  was 
that  it  combated  Herbart's  mechanical  theory  of 
presentations,  by  laying  stress  upon  the  active  and 
spontaneous  element  in  psychic  life  ;  but  it  went  to  the 
other  extreme  when  it  treated  the  will  as  the  principle 
of  all  psychological  explanation.  It  is  true  that  if 
we  examine  into  consciousness  we  shall  find  that 
there  is  no  such  thing  as  an  intellectual  manifestation 
in  which  will  does  not  take  part,  and  that  theoretical 
investigation  is  impossible  without  an  act  of  volition 


^having  a  definite  aim  in  view,  but  we  must  also  recognise 
that  there  is  no  stage  of  practical  activity  of  which 
sensation  (vague  and  confused  as  it  may  be),  presentation, 
and  thought  do  not  form  constituent  parts.  Intellect 
and  will  always  manifest  themselves  to  us  as  two 
aspects  of  a  single  process,  these  two  aspects  being  only 
separable  by  a  process  of  abstraction.  Nor,  on  the 
other  hand,  can  the  evolutionary  genesis  of  con- 
sciousness be  adduced  in  support  of  the  primacy  of 
the  will ;  whatever  Paulsen  may  say  to  the  contrary, 
practical  activity  is  no  less  variable  than  theoretic 
function,  and  true  will  is  due  to  a  process  of 
development  just  as  much  as  intelligence  ;  the  gulf 
between  the  impulsive  tendency  of  the  protozoa  and 
the  moral  will  is  no  less  wide  than  that  between 
elementary  sensibility  and  the  most  abstract  thought. 
It  is  nothing  but  an  abuse  of  terms  to  apply  the  word 
mil  to  such  widely  differing  phenomena,  an  abuse 
which  has  given  birth  to  the  illusion  of  the  constancy 
of  volition  in  contradistinction  to  the  variability  of 
cognitive  function  in  the  course  of  evolution  ;  in  reality 
the  two  aspects  develop  on  parallel  lines,  and  each  is 
implied  by  the  other. 

18.  Nietzsche's  Individualistic  Voluntarism. — The  reac- 
tion from  intellectualism  reaches  its  zenith  in  the  works 
of  Friedrich  Nietzsche,50  in  which  are  foreshadowed  the 
aestheticism  of  Bergson  and  the  pragmatism  of  Schiller 
and  James,  while  voluntarism  is  divested  of  its  universal 
and  determinist  character,  the  last  vestige  of  traditional 
intellectualism,  and  assumes  the  picturesque  attitude  of 
the  rebel  against  all  and  every  necessary  law,  and  of  the 
champion  of  individual  genius — the  creator  of  new  values 
—against  the  universal  norms  which  would  reduce  every- 
thing to  the  same  level.  vNietzsche  regards  knowledge 
merely  as  a  manifestation  by  the  will  towards  power  which 
constructs  the  concept  of  permanent  being  and  causal 
necessity,  creates  space,  homogeneous  time,  and  all  the 
scientific  categories,  classifying  events  with  their  help 
in  such  a  way  as  to  render  it  possible  to  foresee  them, 


and  doing  so  in  order  that  it  may  assert  itself  in  a  given 
sphere  of  reality,  and  establish  its  supremacy  over  the 
perennial  flux  of  phenomena,  and  the  chaotic  alternation 
of  variable  and  fugitive  sensations.  The  significance 
of  truth  does  not  lie  in  correspondence  with  an  objective 
order,  but  rather  in  the  needs  and  vital  tendencies 
which  it  satisfies  by  ensuring  the  triumph  of  the  indi- 
vidual and  the  species — an  assertion  as  ingenious  as 
it  is  paradoxical,  into  which  we  shall  enter  more  fully 
in  the  more  systematic  form  given  to  it  by  empirio- 
criticists,  pragmatists,  and  the  upholders  of  the  doctrine 
of  contingency. 

<j  «/  , 

19.  The  Philosophy  of  Freedom :  Ravaisson,  Secretan. 
—In  addition  to  the  causes  already  enumerated,  there 
are  certain  other  exigencies  of  an  ethical  order  which 
helped  to  bring  about  the  triumph  of  voluntarism, 
regarded  in  its  negative  aspect  as  the  adversary  of 
scientific  knowledge  ;  of  these  the  most  important  is 
the  necessity  of  ensuring  the  freedom  of  the  will  which 
the  universal  determinism  of  science  threatened  to 
destroy.  Kant  in  his  doctrine  of  the  primacy  of 
practical  reason  had  pointed  out  clearly  the  way  of 
escape  from  this  difficult  position,  and  it  was  along 
these  lines,  already  boldly  pursued  by  Fichte,  that  a 
number  of  philosophic  systems  were  developed,  even 
before  the  yoke  of  materialism  had  been  shaken  off, 
which  regarded  free  moral  action  as  the  principle  of  the 
whole  cosmic  process,  and  necessity  merely  as  a  more 
or  less  illusory  presentation  of  the  spontaneity  lying  at 
the  root  of  ah1  being.  According  to  Ravaisson,51  the 
apparent  fatality  of  nature  is  the  result  of  a  habit  formed 
by  the  repetition  of  a  free  action ;  hence  it  is  in  the 
spontaneous  act  that  we  shall  find  the  true  essence 
of  the  world  :  things  are  not  the  outcome  of  brute 
mechanism,  but  of  the  development  of  a  voluntary 
tendency  to  perfection  and  beauty.  In  like  manner 
Secretan 52  maintains  that  necessity  owes  its  origin 
to  free  divine  creation,  that  it  is  not  determined  by 
logical  reasons,  but  is  the  spontaneous  outpouring  of 


love  and  grace.  Knowledge  is  not  the  absolute  end, 
but  rather  a  means  to  the  edification  of  the  world  whose 
supreme  reason  is  to  be  found  in  the  moral  order ;  the 
will  is  at  the  root  of  everything  ;  consciousness  is  a  means 
by  which  the  will  takes  possession  of  itself ;  the  per- 
fecting of  the  will  is  the  end  of  science.53  "  I  believe," 
says  Secretan,  "  in  the  primacy  of  practical  reason  and 
cast  my  vote  freely  for  liberty." 

20.  Lotze  and  the  Primacy  of  Practical  Reason  — 
Hermann  Lotze  is  the  most  illustrious  representative  of 
this  form  of  ethical  or  teleological  idealism M  which 
arose  in  opposition  to  the  invading  forces  of  materialism. 
Lotze,  though  a  deliberate  and  strenuous  advocate  of 
the  advantages  of  the  mechanical  view  in  the  field  of  em- 
pirical science,  was  not  carried  away  by  the  current  of 
his  day,  and  thus  did  not  over-rate  its  importance  in  the 
realm  of  speculation.  He  was  too  sensible  of  ethical  and 
religious  needs  M  to  rest  content  with  a  system  of  philo- 
sophy which  robbed  the  world  of  all  significance,  and 
regarded  the  soul  of  man  as  the  product  of  some  un- 
seeing mechanism  ;  hence,  he  is  unwilling  to  stop  short 
at  that  which  he  and  Kant  alike  view  as  the  inevitable 
conclusion  of  the  theoretic  spirit,  and  turns  to  the  moral 
life  and  the  world  of  values  in  his  search  for  the  basis 
of  metaphysics,56  and  to  the  good,  and  the  ethical  norm 
for  the  true  content  of  the  world,  and  the  substance  of 
all  process.57 

Only  by  looking  at  that  which  ought  to  be  can  we 
understand  that  which  is,  since  nothing  takes  place  in 
nature  independently  of  the  end  and  meaning  of  the  whole 
to  which  each  part  owes  its  existence,  and  its  efficacy.58 
And  in  the  light  of  the  whole  and  the  absolute,  we  see 
that  the  actions  of  beings  which  from  the  finite  point 
of  view  of  science  would  seem  to  be  determined  by 
mechanical  laws,  are  in  reality  spontaneous  acts ;  and 
necessary  laws,  passively  obeyed,  are  transformed 
into  ideal  norms,  voluntarily  recognised.59  Value  is 
then  the  gauge  of  all  reality  ;  each  thing  exists,  and  will 
endure  only  in  proportion  to  its  value ;  that  only  will 


last  for  ever  which  has  a  part  to  play  in  the  harmony 
of  the  whole.60  The  cognitive  function  too  is  sub- 
ordinated to  the  end  of  practical  activity,  and  truth 
is  of  value  merely  as  a  necessary  presupposition  of  the 
actualisation  of  the  good.61  The  doctrine  of  the  primacy 
of  practical  reason,  which,  together  with  the  idea  of 
value,  is  the  pivot  on  which  the  whole  of  Lotze's  system 
turns,  becomes  later  on  the  ruling  principle  of  the 
philosophies  of  Windelband,  Miinsterberg,  Royce,  and 
Eickert,  and  we  shall  therefore  have  occasion  to  discuss 
it  fully  in  its  epistemological  and  metaphysical  develop- 
ments, when  we  analyse  that  form  of  reaction  from 
intellectualism  which  constitutes  the  new  philosophy 
of  values.  We  shall  also  see  a  new  current  of  thought 
spring  from  the  philosophy  of  liberty,  a  current 
which,  flowing  down  from  the  precipitous  peaks 
of  speculation  into  the  field  of  criticism,  and  bringing 
the  spontaneity  of  the  transcendent  sphere  of  the 
absolute  into  the  immanent  order  of  phenomena, 
will  burst  asunder  that  iron  mechanism  which  Lotze, 
like  Kant,  recognised  as  confining  liberty  within  the 
noumenal  principle,  which  is  both  eternal  and  beyond 
time.  The  neo-criticism  of  Renouvier  marks  a  vital 
stage  in  this  transition,  which  is  of  immense  importance 
in  the  beginning  of  the  reaction  from  intellectualism, 
because  it  leads  to  the  denial  of  the  value  of  intelligence 
even  in  the  sphere  of  phenomena,  within  which  it  had 
hitherto  been  considered  unassailable,  since  its  in- 
capacity was  limited  to  the  domain  of  metaphysical 

21.  Psychological  Development  of  the  Theory  of  the 
Primacy  of  Practical  Reason  in  the  Phenomenalism  of 
Renouvier. — Liberty,  confined  to  the  absolute,  is  non- 
existent as  far  as  we  are  concerned ;  that  which  is  of 
moment  to  us  as  an  essential  condition  of  moral  responsi- 
bility is  not  the  liberty  of  God,  but  that  of  man ;  that 
is  to  say,  the  efficacy  of  free  will  in  the  domain  of  pheno- 
menal consciousness.  If  our  empirical  character  be  a  link 
in  the  necessary  chain  of  phenomena,  how  can  the  human 


being  in  his  concreteness  act  freely  without  breaking  the 
bonds  of  this  natural  necessity  ?  We  have  to  choose 
between  the  law  of  necessity  which  lays  an  iron  grasp 
upon  us,  stifling  our  most  living  aspirations,  and  the 
free  spontaneity  of  feeling  which  knows  no  limits  to  the 
sphere  of  action  of  the  mind  ;  and  of  these  alternatives, 
duty  commands  us  to  choose  the  second.62  The  will  must 
-not  be  subordinated  to  the  intellect ;  on  the  contrary, 
the  will  must  conquer  the  intellectual  function.  Accord- 
ing to  Renouvier,63  all  knowledge  is  belief,  and  every 
I  belief  implies  a  voluntary  decision.  Thinking  involves 
affirming  and  judging,  every  judgment  is  a  voluntary 
act :  thus  liberty  lies  at  the  very  root  of  intelligence. 
The  problem  of  certainty  is  not  a  logical,  but  a  psycho- 
logical and  moral  problem,  whose  solution  depends  on 
that  of  the  problem  of  liberty.  Every  assertion  which 
goes  beyond  the  immediately  present  state  of  conscious- 
ness presupposes,  in  addition  to  the  reasons  for  belief, 
an  act  of  will,  a  parti  pris  to  affirm. 

Thought  is  not  something  necessary  and  impersonal 
— we  only  believe  in  proportion  as  we  ardently  long  and 
will  so  to  do  :  reason  is  practical  in  all  its  degrees,  in 
all  its  forms  and  in  all  its  functions.  The  distinction 
between  phenomenon  and  noumenon  must  disappear 
together  with  that  between  pure  and  practical  reason  : 
there  is  but  one  world,  the  world  of  phenomena,  the 
world  which  we  picture  to  ourselves,  the  world  of  space 
and  time,  and  it  is  just  this  world  which  we  must  con- 
template in  the  light  shed  upon  it  by  the  idea  of  moral 
order.  The  postulates  of  practical  reason  do  not  carry 
us  beyond  the  bounds  of  experience,  they  rather  extend 
it  in  accordance  with  our  moral  requirements.  The 
categories  exist  by  the  same  right  as  do  phenomena, 
and  are  given  with  them :  they  are  neither  more  nor 
less  than  universal  phenomena,  which  cannot  be  deduced 
a  priori  from  a  single  principle,  but  which  must  be 
extracted  from  experience.  The  special  characteristic 
of  the  categories  lies  in  the  fact  that,  while  they  are 
manifested  in  a  particular  form  in  phenomenal  data, 

s*c.  i  THE  VOLUNTAEISTS  45 

they  are  still  presented  as  something  superior  to  experi- 
ence, able  to  act  as  its  guide,  and  to  subject  it  to  laws ; 
so  that  we  expect  to  see  them  verified  constantly.  It 
is  thus  that  we  must  understand  the  a  priori,  not  as  a 
subjective  form  applicable  to  the  data  of  the  outer 
world.  Subject  and  object  are  but  two  aspects  of 
the  phenomenon,  that  which  presents  and  that  which  is 
presented.  If  I  apply  the  term  "  mine  "  to  presenta- 
tions, I  do  so  because  they  are  bound  up  with  feel- 
ings, acts  of  volition,  and  certain  material  and  organic 
phenomena  in  such  a  way  as  to  form  a  distinct  whole, 
subject  to  laws  of  its  own;  in  like  manner,  when  I  speak 
of  an  object  or  thing,  I  understand  thereby  merely  the 

The  idea  of  substance  is  inadmissible,  because  it 
leads  to  the  actual  infinite  which  Renouvier  looks 
upon  as  a  contradictory  concept.  By  the  very  law 
of  its  formation  a  number  must  have  a  successor  ; 
we  cannot  conceive  of  an  actual  number  without  any 
successor,  than  which  therefore  no  greater  number 
exists.64  Let  us  take  the  infinite  series  of  numbers  as 
data  ;  let  us  find  the  square  of  each  number  in  the  series, 
we  shall  then  obtain  another  series  which  must  on  the 
one  hand  contain  the  same  number  of  terms  as  the  first 
series,  but  which  must  on  the  other  hand  (since  it  is 
made  up  of  squares  only)  contain  a  smaller  number, 
since  the  first  contains  in  addition  to  these  all  the  other 
numbers  ;  now  it  is  absurd  that  a  number  should  be  at 
the  same  time  greater  and  smaller  than  another.65  The 
law  of  finite  number  delivers  us  from  the  metaphysic 
of  materialism,66  and  enables  us  to  resolve  the  anti- 
nomies by  rejecting  the  antithesis,  which  violates  the 
law  of  contraction,  and  by  forming  the  concept  of  finite 
and  interrupted  series  of  phenomena.  Renouvier  regards 
the  principle  of  discontinuity  or  discreteness  of  phenomena 
as  the  supreme  law  of  the  real,67  a  law  directly  opposed 
to  the  principle  of  continuity  advocated  by  Leibnitz. 
We  are  thus  led  to  look  upon  the  elements  of  bodies  as 
being  separate  from  one  another,  to  regard  contact 


as  an  appearance,  forces  as  acting  between  distant 
points,  and  acting  in  time  as  discontinuous  and  in- 
termittent, of  an  essentially  periodic  and  ejaculatory 
character.  All  movements,  although  they  appear  con- 
tinuous, are  composed  of  a  series  of  initiatory  acts  and 
beginnings,  interconnected  by  laws,  i.e.  mathematical 
functions  which  give  expression  to  their  reciprocal 
relations.  *The  idea  of  cause  is  thus  transformed  and 
purged  from  the  gross  images  of  contact,  impulse,  and 
the  transference  of  force  from  one  object  to  another ; 
the  old  fetish  of  causality,  and  all  its  attendant  images 
are  brought  with  the  help  of  our  reflective  knowledge  into 
harmony  with  phenomena  and  with  our  experience  of 
their  determinate  and  invariable  concatenation  in  certain 
cases  by  means  of  certain  preceding  data.  We  are 
enabled  to  restore  to  phenomena,  under  the  form  of 
laws,  those  elements  of  stability  and  regularity  of  which 
the  ehmination  of  the  idea  of  substance  apparently 
deprived  them.  There  is  as  a  matter  of  fact  no  pheno- 
menon which  does  not  present  itself  in  a  complex  of 
relations  :  everything  is  relative  ;  nor  can  it  be  asserted 
that  every  relation  implies  terms,  that  is  to  say,  some- 
thing which  is  not  relative,  since  terms  are  only  in- 
telligible in  their  relations ;  nor  need  we  say  that  the 
relative  presupposes  the  absolute,  and  is  a  proof  thereof, 
since  the  absolute  itself  is  but  the  correlative  of  the 
relative.68  Even  the  identity  of  consciousness  or 
the  permanency  of  personality  does  not  depend 
upon  a  spiritual  substance,  its  one  condition  is  the 
identity  and  relative  permanency  resulting  from  the 
harmonious  diversity  and  variations  of  a  group  of  pheno- 
mena subject  to  one  law.  Consciousness  is  but  an 
extremely  complex  function  (in  the  mathematical,  not 
the  physiological  sense  of  the  word),  which  implies  a 
large  number  of  laws  and  subordinate  functions  (intelli- 
gence, sensibility,  will).  If  it  be  true  that  everything  is, 
as  far  as  we  are  concerned,  presentation,  relation, 
phenomenon,  that  that  which  presents  and  that 
which  is  presented  are  alike  essential  constituents  of  any 


and  every  object  of  knowledge,  and  that  pure  being  in 
itself  has  no  sense,  then  the  concrete  unity  of  the  abstract 
categories  will  be  found  in  the  phenomenon  of  conscious- 
ness. Without  consciousness  there  can  be  no  intelligible 
presentation  ;  by  which  I  do  not  mean  without  my  con- 
sciousness, but  without  the  other  functions  of  the  kind 
which  I  perceive  in  the  outer  world,  and,  since  the  world 
resolves  itself  into  a  combination  of  presentations, 
reality  in  its  ultimate  analysis  is  but  a  complex  of 

22.  Criticism  of  Renouvier' s  Phenomenalism. —  Re- 
nouvier's  theory  of  phenomena  differs  from  empiricism 
in  as  much  as  it  admits  law  to  be  a  universal  phenomenon 
comprehending  and  dominating  other  phenomena  ;  but,  -•' 
since  it  introduces  discontinuity  into  the  network  of/ 
things,  it  puts  the  existence  of  stable  relations  of  any 
kind  whatsoever  beyond  the  power  of  conception.  If 
every  phenomenon  be  a  fresh  beginning,  how  can  it  be 
dependent  on  preceding  phenomena  ?  If,  on  the  other 
hand,  it  be  dependent  on  and  conditioned  by  these 
preceding  phenomena,  where  is  its  freedom  and 
spontaneity  ?  If  time  be  discontinuous,  if  the  series 
of  phenomenal,  presenting,  or  presented  facts  be  also 
discontinuous,  then  each  moment,  as  a  fresh  beginning 
of  being,  neither  can  nor  should  know  anything  of  the 
moments  which  have  preceded  it,  but  must  be  regarded 
as  isolated,  and  as  forming  a  world  in  itself.  If  there 
be  any  relation  between  the  then  and  the  now,  this 
relation  cannot,  according  to  Renouvier,  be  regarded 
as  other  than  a  phenomenon ;  we  have  then  to  choose 
between  two  possibilities  :  either  the  relation  has  con- 
tinuous duration,  and  thus  affords  an  explanation  of  the 
concrete  transition  from  one  term  to  another,  and  of  their 
reciprocal  interpenetration — which  is  of  course  a  contra-  ' 
diction  of  Renouvier' s  thesis — or  it  is  discontinuous,  in 
which  case  it  must  be  the  outcome  of  successive  elements 
between  which  relations  exist.  Are  these  relations  also 
discontinuous  ?  If  so,  we  stand  committed  to  that 
indefinite  process  which  Renouvier  sought  to  avoid. 


There  is  no  way  of  escape  short  of  admitting  the  con- 
tinuity of  time  together  with  its  necessary  basis,  the 
continuity  of  the  subject :  the  discrete  terms  may  be 
related,  but  only  on  condition  that  there  be  a  subject 
which,  while  passing  from  one  to  the  other,  preserves 
its  persistent  and  continuous  identity.  The  ideas 
of  relativity  and  discontinuity  forming  the  basis  of 
Renouvier's  system  exclude  each  other,  since  they  cannot 
be  united  without  contradiction.  If  indefinite  retro- 
gression in  the  order  of  causes  be  inconceivable,  the 
transition  from  nothingness  to  being  and  the  relation 
between  them  are  still  more  so.  What  would  be  the  value 
or  purpose  of  the  persistence  of  law  and  order  in  such  a 
world  of  fresh  beginnings  ?  Where  and  how  could  a  law 
persist  ?  As  a  general  phenomenon  it  is  non-existent 
in  experience,  which  brings  only  individual  phenomena 
to  our  notice  ;  if  it  be  an  abstraction,  a  product  of 
thought,  it  presupposes  a  subject  which  lives  continuously 
in  such  a  way  as  to  be  capable  of  referring  one  to  the 
other,  and  of  comparing  individual  instances  of  the  past 
and  present.  If  consciousness  also  be  merely  a  general 
phenomenon,  where  must  we  look  for  the  condition 
essential  to  the  construction  of  these  general  relations  ? 
A  reality  made  up  of  nothing  but  phenomena,  and  of 
discontinuous  phenomena  as  well,  is  merely  a  series  of 
individual  facts,  and  in  such  a  world  we  cannot  fairly 
speak  of  either  laws  or  universal  functions,  and  the 
categories  become  but  an  incoherent  collection  of 
phenomena  and  individual  relations. 

Renouvier  turns  for  proof  of  the  discontinuity  of 
the  real  to  the  alleged  contradictions  implied  in  the 
concept  of  the  infinite,  which  are  supposed  to  be  derived 
from  the  impossibility  of  thinking  of  a  series  as  ended 
which  is  denned  as  being  inexhaustible.  The  main 
argument  he  adduces  is  and  ever  has  been  the 
stock  one  of  those  who  would  deny  the  infinite, 
and  may  be  briefly  stated  as  follows :  In  order  to 
conceive  of  an  infinite  series  in  its  actuality,  we  must 
make  the  synthesis  of  an  infinite  number  of  parts  ;  this 


is,  however,  an  impossibility,  since  to  do  so  would  demand 
infinite  time  ;  hence  the  synthesis  will  never  be  com- 
pleted.70 Now  it  is  not  difficult  to  see  that  this  argu- 
ment derives  its  probative  value  from  the  presumption 
that  it  is  impossible  to  think  of  a  series  or  class  of  objects 
without  passing  those  objects  successively  in  review,  • 
and  that  the  concept  results  from  the  synthesis  of  this 
enumeration :  premises  which,  if  true,  would  render 
it  impossible  to  think  even  of  finite  numbers.  Let  us,  • 
for  example,  take  a  number  a  thousand  times  greater 
than  the  number  of  seconds  in  the  average  life  of  man ; 
it  is  self-evident  that,  even  if  we  were  sufficiently  perse- 
vering to  count  all  our  lives,  we  could  never  reach  that 
number  :  are  we,  then,  to  conclude  that  it  is  unthink- 
able ?  Certainly  not :  thought  does  not  proceed  per 
enumerationem  simplicem ;  the  concept  is  not  a  series 
of  moving  pictures  of  individuals  or  individual  objects 
belonging  to  the  same  class,  but  determines  simul- 
taneously the  whole  series  with  the  characteristics 
defining  it.  In  other  words,  the  presentation  of  the 
extension  of  a  concept  is  not  necessary  for  the  forma- 
tion of  that  concept,  that  of  its  comprehension  will 
suffice  :  a  finite  number  of  indications  will  enable  us  to 
determine  an  infinite  class  of  individuals.  Every  concept, 
every  universal  law  is  in  itself  the  positing  of  an  infinite  ; 
the  denial  of  the  infinite  is  equivalent  to  the  denial  of  ^ 
the  universality  of  thought.  The  apparent  contradiction 
arises  from  the  alleged  exhaustion  of  this  infinity  or 
f  universality  by  means  of  an  empirical  succession  of  pre- 
sented terms,  whereas  the  concept  of  the  infinite,  like 
every  thought  of  universal  and  necessary  law,  in  as  much 
as  it  comprehends  all  time,  is  external  to  temporal 
succession.  The  absurdity  comes  in  when  this  same 
thought  is  transferred  in  unvarnished  nominalism  to  the 
empirical  series  of  moments,  since  it  is  then  obvious 
that,  as  it  cannot  issue  therefrom,  it  can  only  realise 
the  concept  thereof  by  passing  through  the  series  in 
its  successive  order.  We  conceive  of  the  infinite  in  the 
very  act  of  formulating  the  law  which  determines  it  in 



its  essential  characteristics ;  thus  it  is  not  something 
at  which  we  arrive  by  enumerating  all  the  terms  which 
succeed  each  other  in  time.  Those  who  deny  the 
infinite  say :  "  Let  the  will  strive  as  it  may,  it  can  never 
reach  an  ultimate  term."  We  do  not,  however,  define 
the  infinite  as  the  last  term  of  a  series  ;  we  do  not 
assign  it  a  place  in  the  sequence  of  finite  numbers  ;  on 
the  contrary,  we  maintain  that  it  is  external  to  that 
empirical  series  which  develops  in  time.  The  neo-criticists 
have  the  best  of  it,  because  they  look  upon  it  from  the 
first-mentioned  point  of  view,  that  is  to  say,  they  regard 
it  as  the  end  of  a  series,  and  assert  that  it  must  be  pos- 
sessed of  the  same  properties  as  are  finite  numbers  and 
that  the  axiom,  "  the  whole  is  greater  than  the  part,' 
must  hold  good  of  it.  This  axiom,  which,  translated  into 
mathematical  language,  would  be  more  clearly  expressed 
as  follows,  "  The  sum  of  two  magnitudes  is  greater  than 
either  of  them,"  holds  good  of  absolute  lineal  magnitude, 
but  there  are  other  kinds  of  magnitude,  such  as  vectors, 
to  which  it  does  not  apply.  In  like  manner,  if  it  be 
true  of  positive  numbers,  it  is  not  so  of  negative  ones, 
nor  is  it  valid  for  complex  numbers,  the  difference 
between  which  cannot  be  defined.71  What  wonder, 
then,  that  it  should  not  be  applicable  to  infinite  cardinal 
numbers  ? 

The  law  of  number  is  at  bottom  but  a  dialectic 
weapon  which  Renouvier  places  at  the  service  of  the 
will  to  believe  ;  nor  does  he  hesitate  to  distort  reality 
to  such  a  degree  as  to  render  it  inconceivable,  in  order 
to  facilitate  the  introduction  of  the  voluntary  act  into 
the  series  of  phenomena. 

We  can  already  trace  in  his  phenomenalism  the  germs 
of  the  doctrine  of  contingency,  since  it  regards  the  caprice 
of  the  will  and  the  ardour  of  passion  as  the  basis  of 
all  judgment  and  belief,  subordinates  the  demands  of 
the  intellect  to  the  exigencies  of  sentiment  and  moral 
aspirations,  and  denies  the  necessity  of  thought  which 
it  derives  from  a  voluntary  affirmation  of  the  mind. 
On  the  other  hand,  the  elimination  of  the  idea  of  sub- 


stance,  the  reduction  of  the  bond  of  causality  and 
law  to  a  purely  functional  relation,  and  the  dissolution 
of  reality,  including  the  world  of  consciousness,  into  a 
conglomeration  of  phenomena  and  phenomenal  relations 
are  the  very  concepts  which  serve  later  on  as  the  basis 
of  empiric-criticism. 


1  Histoirc  du  matirialisme  (Paris,  1877),  vol.  ii.  p.  171. 

2  Op.  cit.  vol.  ii.  p.  579. 

3  Op.  cit.  voL  ii.  p.  596. 

4  Handbuch  der  physiologischen  Optik,  p.  455  (1877). 

6  Die  Tatsachen  in  der  Wahrnehmung  (Berlin,  1879),  p.  42. 

'  Ober  die  Tatsachen,  die  der  Geometrie  zu  Grunde  liegen  (Gottingen, 

7  Zur  Analyse  der  Wirklichkeit  (Strassburg,  1880),  pp.  224  and  251. 

8  Philosophic  der  Naturwissenschaft  (Leipzig,  1881-82),  vol.  ii.  p.  36. 
*  Kant  und  die  Epigonen  (Stuttgart,  1865),  p.  27. 

10  Op.  cit.  voL  ii.  p.  248. 

11  Der  philosophische  Kriticismus  (Leipzig,  1876-87),  vol.  ii.  p.  64. 

12  Zur  Einfiihrung  in  die  Philosophic  der  Gegenwart  (2nd  ed.,  Leipzig, 
1904),  p.  59  ff. 

18  Schuppe,  ErJccnntnisthcoretische  Logik  (Bonn,  1878),  p.  68;  Grun- 
driss  der  Erkenntnistheorie  und  Logik  (Berlin,  1894),  p.  7  ff. 

14  System  der  Philosophic  (Leipzig,  1889),  p.  91  ff. 

15  Op.  cit.  p.  107. 

18  Op.  cit.  p.  116  ff. 

17  Op.  cit.  p.  141. 

18  System  der  Philosophic,  p.  387  ff.,  p.  415  ff.,  p.  442  ff. 

19  Philosophic  de  Vinconscient  (Paris,  1877),  voL  ii.  p.  237  ff.     Le  Dar- 
winisme  (8th  ed.,  Paris,    1905).      The  first  German  edition,   published 
under  the  title  Wahrheit  und  Irrthum  im  Darwinismus,  came  out  in  1875. 

20  IS  Evolution  des  idees-forces  (Paris,  1890). 

81  Nietzsche's  Wille  zur  Macht  is  an  interpretation,  though  a  para- 
doxical and  romantic  one,  of  Darwinism  and  the  principle  of  selection, 
which,  just  as  it  has  raised  man  above  the  level  of  the  ape,  prepares  the 
way  for  the  advent  of  the  super-man,  the  raison  d'etre  of  the  existence 
of  the  earth. 

22  Philosophic  de  Vinconscient  (Paris,  1890). 

28  Die  Weltanschauung  der  modernen  Physik  (Leipzig,  1902),  p.  221  ff. 

24  Le  Mouvement  idealiste  et  la  reaction  contre  la  science  positive 
{Paris,  1896),  2nd  ed.  p.  63  ff. 

"  Hartmann,  op.  cit.  pp.  211-219 ;  Das  Grundproblem  der  Erkenntnis- 
theorie (Leipzig,  1889),  pp.  104-126 ;  Kritische  Grundlegung  der  trascen- 
dentalen  Bealismus  (Leipzig,  1885),  3rd  ed.  pp.  81-90,  107-116  ;  Kategorien- 
lehre  (Leipzig,  1896),  pp.  127-142. 

26  Die  Weltanschauung,  p.  222. 

27  System,  p.  444. 

28  Philosophic  de  Finconscient,  vol.  i.  p.  400  ff. 

29  Ibid.  voL  ii.  p.  43. 

30  L'fivolution  des  idees-forces,  p.  247. 


81  Op.  cit.  pp.  77-78. 

81  Op.  cit.  Introduction,  pp.  53-54. 

83  Le  Mouvement  idealiste,  Introduction,  p.  48.     This  theory  is  more 
fully  developed  in  the  other  book,  Le  Mouvement  positiviste  et  la  con' 
ception  sociologique  du  monde. 

84  Op.  cit.  Introduction,  pp.  37-42. 
88  Op.  cit.  Introduction,  p.  56. 

8*  Op.  cit.  Introduction,  pp.  61-62. 

87  Op.  cit.  p.  227. 

88  La  Liberte  et  le  determinisme  (Paris,  1872). 

89  Psychologie  des  idles-forces  (Paris,  1893),  vol.  i.  p.  274. 

40  Le  Mouvement  idealiste,  pp.  94  and  146. 

41  Op.  cit.  Introduction,  p.  66. 
48  Op.  cit.  p.  237. 

43  Op.  cit.  p.  214  ff. 

44  Op.  cit.  pp.  211-220. 

45  Op.  cit.  Introduction,  p.  67. 
«  Ibid. 

47  Einleitung  in  die  Philosophie  (17th  ed.,  Stuttgart  and  Berlin,  1907), 
p.  432  ff.,  p.  129  ff. 

48  Op.  cit.  p.  8  ff.,  p.  131  ff.,  p.  459  ff. 

49  Op.  cit.  p.  451. 

50  Werke,  vol.  xv.  (Leipzig,  1900),  p.  265  ff. 

61  De  Fhabitude  (Paris,  1838),  reprinted  in  the  Revue  de  metaphysique, 
1894;  La  Philosophie  en  France  au  19*  siecle  (Paris,  1868);  "  Morale  et 
metaphysique"  in  the  Revue  de  metaphysique  et  de  morale  (1893); 
"Testament  philosophique,"  ibid.,  1900. 

52  La  Philosophie  de  la  liberte  (2nd  ed.,  Paris,  1866),  p.  354  ff.r 
p.  438  ff.,  p.  437  ff.  "  Je  suis  ce  que  je  veux,"  is  in  Secretan's  eyes 
the  motto  of  the  absolute  (op.  cit.  p.  365). 

63  Op.  cit.  p.  389  ff. 

54  This  term  is  applied  by  Lotze  himself  to  his  system:  "In  diesen 
teleologischen  Idealismus  hat  unsere  Betrachtung  sich  aufgelost,  ..." 
Metaphysik  (Leipzig,  1841),  p.  329. 

85  "  I  am  old-fashioned  enough,"  he  says,  "  to  be  sensible  of  religious 
needs,"  Metaphysique  (Paris,  1883),  p.  477. 

*•  "  Der  Anfang  der  Metaphysik  ist  nicht  in  ihr  selbst,  sondern  in  der 
Ethik,"  Metaphysik  (Leipzig,  1841),  p.  329. 
57  Op.  cit.  vol.  i.  p.  427. 

88  Mikrokosmus,  2nd  ed.  (Leipzig,  1869),  vol.  i.  p.  442. 

89  Op.  cit.  voL  i.  pp.  323,  326. 
M  Op.  cit.  vol.  i.  p.  439.' 

61  Metaphysik,  p.  328. 

62  Renouvier,  Les  Dilemmes  de  la  metaphysique  pure  (Paris,    1901), 
p.  247  ff . 

M  Essais  de  critique  generale :  Deuxieme  Essai,  Traite  de  psychologic 
rationnelle  (2nd  ed.,  1875),  vol.  ii.  p.  135  ff. 

44  Annie  philosophique,  1868,  p.  37. 

•8  Troisieme  Essai,  Les  Principes  de  la  nature  (2nd  ed.,  1892,)  vol.  i. 
p.  55. 

••  Premier  Essai,  vol.  i.  p.  66  ;  Critique  philosophique,  1876,  voL  ii.  p.  69. 

•7  Troisieme  Essai,  pp.  20-30,  70-80. 

M  Premier  Essai,  vol.  i.  p.  110. 

•9  Premier  Essai,  vol.  iii.  p.  207. 

70  Evellin,  La  Raison  pure  et  les  antinomies  (Paris,  1907),  p.  2. 

71  Couturat,  De  Finfini  mathematique  (Paris,  1896),  p.  452. 



1.  Old  and  New  Positivism. — We  must  distinguish  two 
periods  in  the  history  of  positivism :  of  these  the  first 
is  marked  by  a  dogmatic  belief  in  physical  science,  which 
is  set  up  as  the  model  of  every  form  of  knowledge  ;  the 
second,  dating  from  about  1870,  goes  still  farther,  and 
subjects  science  itself  to  searching  criticism  in  order  to 
eliminate  any  traces  of  metaphysics  which  might  be 
sheltering  themselves  beneath  the  cloak  of  experimental 
theories ;  it  no  longer  looks  upon  science  as  an  unchange- 
able model,  but  studies  the  process  of  formation  through 
which  it  passes,  and  turns  to  the  human  organism  in  its 
search  for  the  psycho-physiological  basis  of  this  evolu- 
tionary genesis.  This  latter  period  approximates  less 
closely  in  its  methods  to  the  older  system  of  positivism 
than  it  does  to  the  empiricism  of  David  Hume  and  Stuart 
Mill,  of  which  it  is  the  logical  conclusion,  and  which  it 
completes  by  the  addition  of  the  biological  concept  of 
consciousness  and  the  latest  researches  of  physiological 
psychology.  While  positivism  in  its  earner  forms' 
endeavoured  to  eliminate  metaphysics  by  proving  all 
reality  to  be  capable  of  scientific  explanation,  taking 
refuge  in  agnosticism  when  this  synthetic  effort  failed 
rather  than  acknowledge  itself  beaten  by  speculation, 
the  new  positive  philosophy  resorted  to  a  purer  and  more 
ingenuous  form  of  experience  than  self-styled  scientific 
experience,  and  set  itself  the  task  of  proving  the  enigmas 
of  the  universe  to  be  non-existent.  Metaphysical 



problems  are  the  result  of  faulty  perspective ;  if  we  will 
but  change  our  point  of  view,  divest  our  minds  of  all 
a  priori  schemes,  and  look  at  things  as  they  are  immedi- 
ately brought  to  our  notice  instead  of  through  the 
tangled  web  of  mechanical  formulas,  the  illusion  will 
vanish  and  problems  cease  to  exist. 

2.  Factors  determining  the  Transition  from  One  Form 
to  the  Other,  and  their  Influence  upon  the  Thought  of 
Mach. — This  change  in  the  concept  of  science  was  to  a 
great  extent  brought  about  by  those  general  factors 
with  which  we  have  already  dealt  in  the  introductory 
chapter.  When,  between  1860  and  1870,  Ernst  Mach 
first  began  to  give  specimens  of  his  scientific  labours, 
three  great  events  had  taken  place  which  could  not  fail 
to  be  of  permanent  influence  on  the  mind  of  the  young 
thinker.  It  was  but  a  short  time  since  the  publication 
of  Darwin's  Origin  of  Species,  a  work  which  Mach 
described  as  "  initiating  new  life  in  every  branch  of 
science  by  means  of  a  revolution  in  method  no  less 
fruitful  than  that  which  owed  its  first  great  impulse  to 
Galileo."  Helmholtz  was  giving  to  the  world  the 
results  of  his  researches  into  the  analysis  of  optical 
and  auditory  perceptions,  which,  with  the  works  of 
Fechner  and  Hering,  threw  open  a  hitherto  unexplored 
world  to  experimental  research.  A  more  comprehensive 
theory,  the  outcome  of  the  new  principles  of  energetics, 
was  being  put  forth  by  Carnot,  Mayer,  Joule,  Clausius, 
and  Kelvin — a  theory  far  loftier  than  the  mechanical 
conception  of  nature,  which  in  its  ultimate  analysis  in- 
evitably ended  in  the  Ignordbimus  of  De  Bois-Reymond ; 
whilst  in  the  work  of  Eankine1  we  have  the  first  pro- 
clamation of  the  reform  in  physical  methods.  If  we 
would  form  a  right  estimate  of  the  importance  of  Mach's 
work,  we  must  bear  these  three  factors  in  mind.  From 
Darwin  he  derived  the  historical  evolutionary  method, 
together  with  the  biological  valuation  of  science  ;  from 
the  analyses  of  Helmholtz  and  Hering  those  sensorial 
elements  which  he  regarded  as  the  ultimate  basis  of 
reality,  and  as  neutral  ground  on  which  the  conflicting 


claims  of  nature  and  mind  might  be  reconciled  ;  whilst 
the  failure  of  the  mechanical  theory  impelled  him  to 
search  for  the  reasons  of  that  failure  and  to  purge  science 
from  the  last  traces  of  metaphysics  still  lurking  in  it. 
Mach's  first  writings  treat  of  the  psycho-physiology  of 
the  senses,  that  is  to  say,  of  that  class  of  research 
work  which  had  been  so  splendidly  inaugurated  by 
Helmholtz,  Fechner,  and  Hering,  and  the  fact  that  he 
had  done  experimental  work  of  this  kind  during  the 
ten  years  from  1860  to  1870  was  certainly  not  with- 
out influence  on  his  philosophic  thought ;  indeed,  his 
enthusiasm  for  the  analysis  of  the  perceptions  and  for 
the  resultant  sensorial  elements  induced  him  to  place 
too  much  reliance  upon  them :  sensation,  to  which 
he  had  devoted  so  many  years  of  patient  research,  is 
ever  present  in  his  consciousness  like  an  idee  fixe,  and 
this  thought  obsessed  him  till  it  gradually  developed 
into  a  sort  of  monomania.  He  sees  sensorial  elements 
everywhere  !  What  is  perception  ?  a  group  of  sensa- 
tions !  the  presentation  ?  another  sensation !  the 
concept  ?  a  combination  of  sensations  !  human  reason  ? 
a  special  sense  !  the  Ego  ?  a  collection  of  sensations  ! 
the  will  ?  a  series  of  sensations  !  Mach  has  fallen  victim 
to  the  very  malady  which  his  keen  eye  had  noted  in 
physicists,  who  are  so  accustomed  to  making  use  in  the 
course  of  their  daily  work  of  the  concepts  of  mass,  atom, 
and  force,  that  they  end  by  overrating  these  means  for 
the  classification  of  phenomena,  and  confound  the  means 
with  the  end  of  research,  positively  raising  them  to 
the  rank  of  reality.  Thus  the  mental  habit  formed  by 
Mach  during  these  first  ten  years  of  experimental  work 
in  the  domain  of  the  sense  organs  led  him  to  over- 
estimate those  sensorial  elements  which  were  but  the 
product  of  artificial  analysis,  but  which  he  regards  as 
facts  immediately  given  in  direct  experience,  and  there- 
fore real  apart  from  that  complex  known  as  the  mind 
of  man. 

3.  Hypostatisation  of  the  Sensorial  Elements. — Accord- 
ing to  Mach,2  reality  is  a  combination  of  sensations  stand- 


ing  in  definite  relation  to  one  another.  It  is  erroneous 
to  consider  them  as  symbols  of  things ;  on  the  contrary, 
, ,  the  thing  is  a  mental  symbol  of  a  complex  of  sensations 
1 1  of  merely  relative  stability.  The  true  elements  of  the 
| 'i  world  are  colours,  sounds,  pressures,  spaces,  and  dura- 
tions, not  things  (objects  or  bodies).  The  exigencies  of 
practical  life  force  us  to  seek  something  persistent, 
some  unchanging  nucleus,  amid  the  unceasing  variations 
of  these  elements,  and  this  gives  rise  to  the  common 
distinction  between  the  thing  and  its  quality,  whence 
is  derived  the  metaphysical  concept  of  substance  in 
which  the  accidents  are  inherent.  As  a  general  rule, 
the  nucleus  of  the  object  is  considered  to  be  the  com- 
bination of  tactile  and  spatial  qualities  which  appear  to 
be  more  stable  than  colours,  sounds,  or  odours.  When 
the  ulterior  development  proves  such  a  distinction 
between  primary  and  secondary  qualities  to  be  arbitrary, 
since  these  qualities  are  at  bottom  all  sensorial  elements 
and  are  all  more  or  less  variable,  the  need  of  finding 
something  persistent  leads  to  the  absurd  thought  of  a 
thing  in  itself  from  which  sensations  emanate.  But 
if  we  divest  the  object  of  all  its  sensible  qualities,  what 
is  left  of  reality  ?  This  absurdity  is  eliminated  when 
we  reflect  that  the  idea  of  permanent  substance  is  an 
illusory  construction  of  thought,  resulting  from  the 
practical  necessity  of  finding  stable  points  of  orienta- 
tion amid  the  continual  renewal  of  the  facts  of 
experience ;  and  that  things  are  artificial  schemes, 
stereotyped  forms  which  we  have  substituted  for  the 
manifold  variety  of  sensations  in  order  that  we  may 
make  use  of  them  more  easily  and  more  readily,  and 
that  they  are  on  that  account  of  purely  economic  value. 
The  idea  of  a  substantial  Ego  originates  in  an  illusion  of 
the  same  kind.  We  regard  the  complex  of  memories, 
tendencies,  and  filings  which  is  apparently  bound  up 
with  that  particular  group  of  sensations  composing  our 
bodies  as  a  persistent  quid,  but  in  reality  it  too  is 
subject  to  transformations  which  are  so  gradual  as  to 
escape  our  notice.  This  complex  does  not  indeed  change 


suddenly  or  as  a  whole,  but  new  elements  are  added 
to  the  relatively  stable  mass  of  memories  by  a  continuous 
process  of  development  which  has  an  illusory  appearance 
of  permanence.  The  Ego,  then,  like  the  objects  of  the 
outer  world,  is  a  structure  serving  a  purely  practical 
purpose  :  this  complex  of  elements  closely  connected 
with  the  body  and  its  conservation  is  of  the  utmost 
importance  to  the  will  with  its  shrinking  from  pain  and 
desire  for  pleasure  ;  but  to  the  intellect  considered 
apart  from  economic  advantages  the  line  drawn  between 
the  Ego  and  the  world  seems  an  arbitrary  one.  There  is 
no  reason  why  only  those  elements  should  enter  into  the 
content  of  the  Ego  which  are  of  more  direct  interest  to 
our  organism — pleasure  and  pain,  for  example — and  the 
sensations  of  seeing  and  hearing  be  excluded.  There 
are  no  sharply  denned  boundaries  beyond  which  the  Ego 
may  not  pass ;  on  the  contrary,  it  may  expand  until  it 
comprehends  and  embraces  the  whole  world.  The 
alleged  contrast  between  the  mind  of  man  and  external 
reality  is  non-existent ;  the  Ego  and  material  bodies  are 
alike  the  result  of  different  combinations  of  the  same 
elements.  If  the  fundamental  identity  of  psychic  and 
physical  facts  be  admitted,  it  will  naturally  follow  that 
there  is  no  real  difference  between  psycho -physio- 
logical and  physical  research  :  it  is  the  aim  of  both 
to  establish  functional  relations  between  the  elements  ; 
only  whereas  physical  science  studies  the  sensations 
considered  apart  from  the  complex  which  we  call  the 
human  organism,  physiological  psychology  determines 
the  ties  of  dependence  uniting  these  same  elements 
to  the  group  of  sensations  composing  our  body  and  to 
the  complex  of  facts  (memories,  feelings,  acts  of  volition) 
forming  the  essence  of  our  personality.  There  is  nothing 
in  either  the  inner  or  the  outer  world  which  is  not  the 
outcome  of  combinations  of  these  elements.  Percep- 
tions, presentations,  concepts,  will,  sentiments,  in  a 
word  the  whole  of  conscious  life,  are  but  different 
combinations  of  a  limited  number  of  elements.  Wherein 
lies  the  difference  between  presentation  and  sensation  ? 


Is  it  not  in  the  fact  that  we  have  placed  them  in  different 
domains,  that  is  to  say,  in  relation  to  different  elements  ? 
The  difference  between  the  illusory  image  and  the  per- 
ception of  the  real  is  one  of  a  practical  order  only  :  the 
most  fantastic  dream  is  just  as  much  a  fact  as  any  other, 
and  if  dream  images  were  more  coherent,  more  normal, 
and  more  stable,  they  would  be  of  even  greater  practical 
importance  to  us.  The  question  whether  the  world  be 
real  or  merely  a  dream  is  one  of  no  scientific  import- 
ance. If  presentation  be  identical  with  sensation,  it 
is  no  difficult  matter  to  reduce  perception  to  a  group 
of  sensorial  elements  with  their  associative  links  ;  Mach 
therefore  eliminated  the  word  "  perception  "  from  his 
vocabulary,  substituting  for  it  the  term  "  sensation." 
Our  concepts  owe  their  origin  to  sensations  and  the 
connections  existing  between  them : 3  the  sensorial 
elements  are  latent  in  the  concepts,  just  as  are  chemical 
elements  in  bodies.  The  apparent  distance  between 
the  sensorial,  concrete,  and  individual  presentation  and 
the  concept  is  illusory,  there  is  a  continuous  process  of 
transition  from  one  to  the  other.  The  whole  value  of 
the  concept  really  lies  in  the  fact  that  it  sums  up  in  a 
simple  and  orderly  manner  a  long  series  of  experiences, 
and  can  suggest  these  experiences  at  the  right  moment ; 
it  is  "  potentially  intuitive  "  (potentiell  Anschauliches). 
The  concept  of  sodium,  for  instance,  results  from  the 
combination  of  its  properties,  which  are  in  their  turn 
nothing  but  as  many  sensorial  experiences,  either  actu- 
ally passed  through  or  merely  presented. 

4.  Science  as  Mental  Economy. — The  definition  of 
the  concept,  or,  when  this  is  obvious,  its  name,  acts  as 
a  stimulus  to  an  activity  which  is  exactly  determined, 
critical,  comparative,  or  constructive.  This  may  be  a 
series  of  physical,  chemical,  anatomical,  or  mathematical 
operations,  either  actually  completed  or  merely  pre- 
sented, and  whose  sensible  result  is  usually  part  of  the 
extension  of  the  concept.  The  concept  is  to  the  scientist 
what  notes  are  to  the  pianist,  a  scheme  suggesting 
corresponding  actions.  If  this  be  the  nature  of  concepts, 


then  the  knowledge  of  the  outer  world  gained  by  their 
help  can  be  only  of  practical  value  :  science,  the  out- 
come of  the  needs  of  life,  like  every  other  manifesta- 
tion of  organic  life,  must  be  subject  to  the  universal 
law  of  evolution  ;  it  is  not  a  fixed  system  of  immutable 
truth,  as  was  maintained  by  the  supporters  of  the 
mechanical  method,  but  changes  in  accordance  with  the 
varying  requirements  of  adjustment.  The  ideas  which 
age-long  experience  had  rendered  habitual  jostle  one 
another  as  if  struggling  for  their  very  existence  every 
time  it  is  a  question  of  grasping  a  new  idea,  and  form  the 
starting-point  of  the  necessary  change.  The  hypothetical 
method  of  accounting  for  new  phenomena  is  entirely 
based  on  this  procedure  ;  for  instance,  when,  in  order 
to  explain  to  ourselves  the  movements  of  the  heavenly 
bodies,  we  represent  them  as  phenomena  of  gravity, 
we  do  but  adapt  the  schemes  of  past  experience  (with 
which  we  are  familiar)  to  a  new  fact.  It  is  by  means  of 
this  process  of  adjustment  of  thought  to  facts,  and  of 
the  reciprocal  adjustment  of  ideas  to  one  another,  that 
scientific  life  develops  ;  the  former  process  constitutes 
observation,  the  latter  originates  theories.4  The  origin 
of  science  clearly  proves  to  us  that  its  work  is  purely 
biological,  that  is  to  say,  its  task  is  to  serve  as  a  guide 
to  man  in  the  intricate  maze  of  natural  facts.  The 
starting-point  of  its  formative  process  will  be  found  in 
the  mechanical  arts.  The  birth  of  science  was  due  to 
the  need  of  making  it  possible  to  communicate  the 
experience  gained  in  the  practice  of  the  arts  and  of 
extending  it  beyond  the  limits  of  place  and  the  necessity 
of  the  moment.5  We  must  distinguish  three  periods 
in  the  evolution  of  science  :  the  first  experimental,  the 
second  deductive,  the  third  formal.  The  first  is  in  direct 
contact  with  reality.  The  second  inaugurates  the  sub- 
stitution of  mental  images  for  facts,  thus  obviating  the 
necessity  of  having  recourse  to  observation  on  each 
occasion :  scientific  work  then  becomes  essentially 
subjective,  a  structure  raised  by  the  mind  for  the  mind 
in  which  imagination  plays  an  important  part.  The 


traditional  mechanical  theory  belongs  to  this  second 
stage  of  science.  When  we  come  to  the  third  period 
all  idea  of  objectivity  seems  to  be  entirely  eliminated  : 
the  attempt  is  made  to  arrange  scientific  results  in  a 
synthetic  framework,  with  no  other  end  in  view  than 
that  of  convenience  and  utility ;  when  science  has 
reached  this  stage,  it  no  longer  imagines  itself  able  to 
sound  the  depths  of  reality,  but  strives  to  avoid  mental 
toil  and  to  economise  the  efforts  of  thought.6  The 
aim  of  all  the  works  of  Mach  is  to  hasten  the  advance  of 
science  from  the  second  to  the  third  period,  from  the 
mechanical  to  the  purely  formal  stage. 

5.  Criticism  of  the  Traditional  Mechanical  Theory.— 
Mach  regards  the  view  that  mechanical  science  is  the 
basis  of  all  other  branches  of  physics  as  a  prejudice 
arising  out  of  the  fact  that  the  fundamental  discoveries 
of  mechanics  were  the  first  to  be  made  in  point  of  time  ; 
but,  although  this  may  afford  a  psychological  explanation 
of  the  genesis  of  the  mechanical  doctrine,  it  is  no  justifica- 
tion thereof.7  We  must  first  of  all  observe  that  there 
is  no  such  thing  as  a  purely  mechanical  phenomenon  : 
such  phenomena  are  the  result  of  a  process  of  abstraction 
which  may  be  either  instinctive  or  intentional  and  serves 
to  facilitate  their  study  ;  but  every  phenomenon  must, 
strictly  speaking,  belong  to  all  the  branches  of  physical 
science.  The  general  laws  of  mechanics  are  on  the  same 
level  as  the  other  general  laws  of  physics  ;  therefore 
they  can  enjoy  no  special  privileges,  and  we  have  no 
right  to  say  that  some  are  more  fundamental  than  others. 
That  which  is  of  longer  historical  standing  does  not 
necessarily  always  serve  to  explain  later  discoveries  ; 
as  facts  become  known  and  classified,  other  and  wider 
intuitions  will  replace  it  in  the  process  of  scientific 
adjustment.  It  may  be  urged  that  by  reducing  the 
concepts  and  laws  of  other  branches  of  physical  science 
to  those  of  mechanics,  we  are  enabled  to  express  all 
physical  knowledge  in  a  simpler,  more  systematic,  and 
more  convenient  form ;  as  a  matter  of  fact,  however, 
the  mechanical  hypothesis  effects  no  saving  of  either 


time  or  trouble.  In  the  majority  of  cases  it  is  ill  adapted 
to  the  phenomena  it  is  supposed  to  explain;  hence  it 
involves  fresh  corrections,  which  in  their  turn  give  rise 
to  additional  complications,  obscurity,  and  labour.8 
In  our  present  state  of  ignorance  as  to  the  true  con- 
stitution of  bodies  and  their  ultimate  elements,  the 
mechanical  method  can  only  afford  us  approximate 
presentments  ;  it  therefore  follows  that  there  will  be  a 
difference  between  the  logical  deductions  of  the  system 
and  the  data  of  experience  ;  thus  in  many  cases  it  is 
impossible  to  give  even  an  approximate  presentation 
of  real  phenomena,  such  as  the  irreversibility  of  the 
transformation  of  heat  in  work,  according  to  the  principle 
laid  down  by  Carnot.  We  are  then  forced  to  introduce 
invisible  movements  which  experience  has  not  revealed 
to  us  and  never  will  reveal,  and  which  complicate  the 
theory  to  such  a  degree  as  to  divest  it  of  simplicity 
and  economy  alike.  Even  if  it  be  conceded  that  the 
mechanical  theory  can  furnish  a  working  hypothesis 
in  one  branch  of  physical  science,  we  do  but  duplicate 
the  relations  of  these  phenomena  by  adding  a  second 
system  of  symbolic  relations,  thus  augmenting  our 
mental  labours.  The  mechanical  theory  undoubtedly 
served  its  purpose  in  the  period  which  gave  it  birth, 
in  as  much  as  it  emancipated  human  thought  from 
theological  prejudices;  in  reality,  however,  it  did  but 
substitute  a  mechanical  system  of  mythology  for  the 
animism  of  the  ancient  religions,  and  this  mechanical 
mythology  is  just  as  much  a  fantastic  exaggeration  of 
partial  knowledge  as  is  the  conception  it  supplants, 
since  neither  the  world  nor  even  a  part  of  it,  but  merely 
one  of  its  aspects,  is  comprehended  in  mechanical 
formulas.9  Space,  time,  and  movement  can  lay  claim 
to  no  greater  confidence  than  colour,  sounds,  and 
smells,  seeing  that  they  too  are  sensations  ;  mechanical 
concepts  are  allowable  in  the  order  of  mechanical  facts, 
which  they  present  to  our  notice  both  simply  and 
economically ;  but  their  application  elsewhere  is 
arbitrary,  and  inevitably  leads  to  the  Ignorabimus. 


Du  Bois-Reymond  failed  to  see  that  his  riddles  arise 
from  confounding  certain  means  of  classifying  a  series 
of  phenomena  with  the  object  itself,  and  from  treating 
those  means  as  if  they  were  absolute  reality,  and  that 
the  problems  which  he  regards  as  insoluble  cease  to  exist 
when  we  substitute  the  concrete  world  of  our  sensations 
£pr  these  abstract  entities.  If  we  would  remain  true 
to  the  method  which  led  the  greatest  scientists  to  their 
greatest  discoveries,  we  must  confine  our  physical  science 
to  the  exact  expression  of  facts  without  trying  to  set  up 
more  or  less  fantastic  and  arbitrary  hypotheses  beyond 
the  limits  of  perception  and  experience.  Newton's 
maxim,  "  Hypotheses  non  fingo,"  should  be  that  of  every 
experimentalist,  whose  aim  it  should  be  to  discover  the 
connections  between  the  movements  of  masses,  the 
variations  of  temperature,  the  variations  in  the  value 
of  the  functions  of  the  electric  potential,  and  of  chemical 
variations,  without  thinking  anything  into  these  elements 
which  is  not  the  direct  result  of  observation.  For 
instance,  in  the  case  of  the  theory  of  electricity  every 
hypothesis  of  a  fluid  or  ethereal  medium  becomes 
worthless  when  we  reflect  that  all  electrical  facts 
are  given  when  we  know  the  value  of  the  potential 
and  the  electrical  constants.10  If  we  thus  eliminate 
arbitrary  hypotheses,  physical  science  is  reduced  to 
its  merely  formal  aspect,  to  a  quantitative  and  conceptual 
expression  of  facts,  and  all  useless  presentations  will 
disappear,  together  with  the  spurious  problems  con- 
nected therewith.  Modern  formal  physical  science  has 
not  lost  that  characteristic  of  unity  which  was  perhaps 
the  one  and  only  advantage  of  the  atomic  theory ;  it 
attains  the  same  ends  without  having  recourse  to  useless 
complications  and  arbitrary  hypotheses,  by  establishing 
permanent  quantitative  relations  between  the  various 
electric,  calorific,  and  mechanical  processes ;  it  takes 
note  of  the  correspondence  between  the  concepts  of  the 
various  branches  of  physical  science  (between  mass  and 
thermic  capacity,  the  amount  of  heat  and  the  potential 
of  an  electric  charge,  the  velocity  of  movements,  tern- 


perature,  and  the  function  of  the  potential)  without 
allowing  an  exaggerated  love  of  simplicity  to  betray 
it  into  underestimating  their  fundamental  difference, 
and  thus  becomes  a  kind  of  comparative  physics.11 
Though  it  may  still  formulate  a  law  of  balance  between 
vis  viva,  amount  of  heat,  the  potential  of  an  electric 
charge,  etc.,  on  the  one  hand,  and  a  determined  amount 
of  work  on  the  other,  it  does  not  understand  thereby 
that  mechanical  work  is  the  basis  of  these  processes, 
but  merely  that  a  constant  quantitative  relation  exists 
between  mechanical,  electric,  calorific,  and  similar 
processes.  Its  aim  is  to  establish  functional  relations 
between  the  elements  of  experience ;  every  other  aim, 
like  that  commonly  attributed  to  it  of  investigating  the 
causes  of  phenomena,  is  a  remnant  of  the  old  animistic 
conception.  When  we  speak  of  cause  and  effect,  we 
isolate  in  an  arbitrary  manner  those  circumstances 
which  have  most  bearing  on  our  practical  end,  but  in 
nature  cause  and  effect  are  non-existent.  Die  Natur 
ist  nur  einmal  da.12  Nature  never  repeats  herself; 
repetitions  of  the  same  occurrences,  in  which  A  and  B 
are  always  connected,  exist  only  in  our  abstract  imitation 
of  phenomena.  The  science  of  the  future  must  eliminate 
the  concepts  of  cause  and  effect,  which  savour  of 
fetishism,  and  are  lacking  in  clearness  of  form,  and  must 
substitute  for  them  the  more  exact  notion  of  mathe- 
matical function.  Even  temporal  succession  may  in  its 
ultimate  analysis  be  reduced  to  a  system  of  relations  of 
dependence,  and  the  word  "  time  "  in  physical  science  is 
used  merely  in  order  to  save  ourselves  the  labour  of  a 
complex  series  of  relations.  Physical  time  is  an  abstract 
idea,  and  should  be  distinguished  from  the  sensation 
of  time  : 13  the  one  is  real,  as  are  all  the  sensorial  elements 
on  the  same  level ;  the  other  formal,  like  all  concepts, 
and  of  purely  economic  value.  When  we  say  that  the 
acceleration  of  a  falling  body  increases  at  the  rate  of 
9-81  m.  per  second,  it  is  equivalent  to  saying  that  the 
velocity  of  the  body  towards  the  centre  of  the  earth  is 
9-81  m.  greater  when  the  earth  has  completed 


of  its  rotation.  But,  it  may  be  objected,  how  are  we 
to  explain  phenomena  if  the  idea  of  cause  be  elimin- 
ated ?  Mach's  answer  is  that  the  so  -  called  causal 
explanation  is,  in  ultimate  analysis,  but  the  descrip- 
tion of  a  fact  or  real  relation ;  there  is  no  essential 
difference  between  the  naturalist's  system  of  classifica- 
tion and  the  physicist's  explanatory  theory ;  the  only 
advantage  of  the  latter  lies  in  its  greater  simplicity  and 
economy,  an  advantage  which  it  owes  to  the  very  nature 
of  physical  phenomena  and  to  their  quantitative  char- 
acter, which  renders  it  possible  to  comprehend  various 
and  complex  categories  of  phenomena  in  a  small  number 
of  differential  formulae.14  There  is  no  difference  in  the 
degree  of  evidence  on  which  the  various  sciences  rest, 
or  in  the  demonstrative  efficiency  of  their  methods  ; 
their  researches  are  one  and  all  directed  towards  the 
same  object,  are  conducted  in  the  same  way,  and 
have  the  same  end  :  the  facts  of  experience  are  the 
only  source  of  their  principles  and  the  true  reality 
which  they  seek  to  reproduce  in  thought ;  their  common 
aim  is  to  effect  the  greatest  possible  economy  in  the 
operations  of  the  intellect,  and  this  aim  is  the  only 
justification  of  their  existence.  They  do  not,  however, 
all  attain  the  same  measure  of  success  ;  hence  the  differ- 
ence in  their  economic  value.  Mathematics  realises 
this  ideal  of  the  maximum  economy  of  thought  more 
nearly  than  any  of  the  others  ;  physics  approaches 
it  by  reason  of  its  simple  functional  formulae :  herein 
lies  their  value,  not  in  the  greater  degree  of  object- 
ivity to  which  they  attain,  as  the  mystics  of  science 
would  fain  assert.  Scientific  knowledge  gains  economic- 
ally, but  loses  objectively  as  its  schemes  become  more 
generic  and  more  abstract.  Here  we  have  the  weak 
point  of  science,  which  is  forced  to  impoverish  concrete 
reality,  to  look  at  it  from  a  one-sided  point  of  view,  and 
to  reduce  it  to  a  mere  frame-work  of  abstract  formulae 
in  order  to  fulfil  practical  requirements.  Our  intelli- 
gence endeavours  in  this  way  to  make  up  for  the 
natural  limitations  of  memory ;  if  memory  were  able 


to  keep  a  faithful  record  of  facts  and  their  individual 
relations  so  as  to  bring  them  forward  at  the  right 
moment,  science  would  be  useless,  since  we  should 
have  something  else  as  a  guide  of  our  actions  ;  but 
memory  being  unfortunately  very  limited,  its  deficiencies 
must  be  supplemented  by  a  scheme  of  concepts,  which 
can  replace  a  complex  series  of  individual  images  of 
facts.  Since  we  cannot,  for  instance,  recall  case  by  case 
the  spaces  of  descent  corresponding  to  each  individual 
time,  we  substitute  the  much  more  convenient  formula 
s  =  %gt2  for  the  long  table  of  figures  ;  in  the  same  way, 
since  we  cannot  bear  in  mind  the  individual  cases  of 
refraction  of  light  for  different  angles  of  incidence 
and  media  of  refraction,  we  express  this  long  series 

of  numbers  in  the  brief  formula  l^r=(*-  Finally,  the 
human  intellect  does  but  imperfectly  supplement  the 
memory  of  facts  ;  scientific  knowledge  derived  there- 
from, though  a  biological  necessity,  is  really  but  a  matter 
of  practical  order,  whose  value  must  be  gauged  by 
economic  standards. 

6.  Unconscious  Metaphysic  and  Contradictions  in 
Mack's  Phenomenalism. — Mach's  work  falls  into  two 
divisions  ;  negative  criticism  and  positive  construction  : 
the  former,  which  is  a  profound  confutation  of  theM 
traditional  mechanical  theory,  is  undoubtedly  of  the  I  ' 
utmost  value,  and  inaugurates  that  salutary  movement 
of  critical  revision  of  science  whose  development  assumed 
such  large  proportions  later,  more  especially  in  France, 
thanks  to  the  work  of  Poincare,  Milhaud,  and  Duhem. 
It  is  in  great  measure  due  to  the  influence  of  Mach  that 
scientific  men  no  longer  take  up  that  dogmatic  attitude 
towards  their  theories  which  characterised  positivism 
in  its  earlier  form.  When,  however,  he  endeavours  to 
build  up  a  new  intuition  of  the  world  on  the  ruins  of  the 
mechanical  theory,  and  substitutes  the  element  of 
sensation_for  the  material  atom,  he  does  but  replace^ 
mechanical  by7  sensonal  mythology.  The  atom  was 
the  hypostasis  of  an  abstraction  ;  what  else  is  the 


^sensorial  °element  ?  It  is  not  presented  immediately 
to  intuition,  but  is  the  result  of  scientific  analysis. 
Reality,  which  we  experience  directly,  is  the  concrete 
world  of  complex  perception,  which  in  its  turn  does 
not  exist  in  isolation  but  is  presented  to  us  in  the 
organic  context  of  our  conscious  personality.  Physio- 
logical psychology  resolves  this  real  organism  into 
abstract  elements  in  order  to  find  something  constant 
in  the  series  of  individual  intuitions,  or,  as  Mach  would 
put  it,  in  order  to  arrange  them  economically  in  a 
system  of  relations  ;  we  must  not,  however,  confound 
the  result  of  reflective  analysis,  arrived  at  by  a  process  of 
scientific  abstraction,  with  reality  perceived  by  intuition. 
The  world,  as  conceived  of  by  Mach,  is  not  the  world 
of  immediate  intuition,  but  the  world  seen  through  the 
analyses  of  Helmholtz  and  Hering,  seen,  that  is  to  say, 
through  a  schematic  and  artificial  theory  of  his  own, 
which  would  fain  reduce  the  whole  complex  world  of 
consciousness  to  a  mosaic  o^  sensations.  I  will  not 
stop  to  discuss  this  theory,  in  which  the  desire  for 
economy  and  simplicity  is  carried  too  far ;  I  would 
merely  observe  that,  even  if  the  possibility  of  such  a 
reduction  be  granted,  elements  and  relations,  when 
called  upon  to  make  up  psychic  life,  would  not  be  facts 
of  immediate  experience,  but  conceptual  schemes, 
products  of  mental  reflection  of  the  same  nature  as 
those  used  in  physical  science.  Hence  the  words, 
"  Physician,  heal  thyself,"  might  well  be  addressed  to 
Mach.  In  like  manner  his  own  criticism  of  the  con- 
stancy of  causal  relations  might  well  be  turned  against 
his  conception  of  the  object  of  science.  If  it  be  true 
that  die  Natur  ist  nur  einmal  da,  if  it  be  true  that 
nature  never  repeats  herself,  then  not  only  are  the 
persistent  ties  between  cause  and  effect  non-existent, 
but  there  can  be  no  stable  connection  between  facts. 
Mach,  on  the  contrary,  affirms  that  functional  relations 
between  elements  are  not  only  persistent,  but  abso- 
lutely real.15  Does  he  himself  not  in  this  statement 
hypostatise  a  concept  ?  To  sum  up,  are  mathe- 


matical  relations,  as  expressed  in  formulas,  intellectual 
schemes  of  an  economic  nature,  or  do  they  exist 
objectively  in  reality  ?  If  nature  never  repeats  her- 
self, how  can  we  speak  of  bleibende  Gesetze,  or  of 
bestdndige  Beziehungen  ?  Bergson,  following  Mach's 
premisses  to  their  logical  conclusion,  might  well  say  that 
the  constancy  of  laws  and  the  persistency  of  relations 
are  just  as  much  artificial  schemes  originating  in  the 
need  for  action  and  of  orientation  in  reality  as  is  the 
persistency  of  things  and  of  the  Ego  ;  but  nothing  in 
nature  is  ever  repeated,  each  fact  is  a  new  revelation. 
The  economic  theory  of  science,  when  carried  to  its 
logical  consequences,  leads  to  the  intuitive  method  of 
the  new  philosophy ;  Mach  has  stopped  half-way,  and 
his  position  is  therefore  both  equivocal  and  contra- 
dictory. On  the  one  hand  he  asserts  that  the  concept 
does  not  correspond  to  anything  real  by  reason  of  its 
schematic  nature  :  on  the  other  he  affirms  the  reality 
of  functional  relations  which  are  nothing  more  or  less 
than  systems  of  concepts  :  the  constancy  of  relations 
is  not  something  known  by  intuition,  but  rather  the 
product  of  mental  reflection.  The  reality  of  concepts 
is  the  conclusion  to  which  Mach's  reasoning  should 
logically  lead  him ;  if  the  concept  too  be  a  union  of 
sensorial  elements,  it  is  just  as  real  as  are  all  relations 
between  elements. 

7.  Petzoldt's  Law  of  Univocal  Determination. — More- 
over, functional  dependence  cannot  escape  those  very 
criticisms  which  are  applied  by  empiric-criticism  to  the 
concept  of  cause.  Petzoldt,  following  out  Mach's  train 
of  thought,  maintains  that  the  concept  of  cause  is  not 
applicable,  since  the  conditions  determining  a  pheno- 
menon are  infinite,  and  a  selection  of  one  of  these 
conditions  as  its  true  cause  is  an  arbitrary  proceeding ; 
further,  it  is  possible  to  insert  an  infinite  number  of 
intermediate  terms,  having  a  determinate  effect,  between 
one  phenomenon  and  the  next ;  hence  an  infinite  number 
of  causes  might  be  adduced.16  He  therefore  proposes 
to  substitute  the  law  of  univocal  determination  (das 


Gesetz  der  EindeutigJceit)  for  the  causal  relation ;  the 
advantage  of  this  law  lies  in  the  fact  that  it  holds  gooc 
in  cases  of  reciprocal  action  as  well ;  it  may  be  briefly 
enunciated  as  follows :  "  For  every  phenomenon, 
elements  may  be  found  upon  which  the  phenomenon 
depends  uni vocally  ;  no  other  result  could  be  unique, 
since  it  would  admit  the  possibility  of  at  least  one 
(_other  with  equal  rights  to  existence."  For  instance, 
a  ball  moving  on  a  horizontal  plane  under  the  influence 
of  an  impulse  which  propels  it  forward  in  a  direction 
parallel  to  the  horizontal  plane  will  pursue  a  straight 
line,  since,  if  it  deviated  in  an  oblique  direction,  there 
would  be  another  oblique  line  on  the  opposite  side  oi 
the  original  line  and  inclined  at  the  same  angle  to  it 
and  might  equally  well  be  pursued  ;  hence  the  course 
of  the  ball  would  not  be  univocally  determined  as  it 
would  be  in  pursuing  the  original  direction,  which  is 
unique  in  space.17  This  principle  is  not  deduced  from 
individual  experiences,  but  is  the  necessary  presump- 
tion of  our  every  action  and  our  every  thought.  If 
nature  were  indeterminate  we  should  be  in  the  position 
of  a  soldier  exposed  to  the  fire  of  the  enemy  without  any 
means  of  defence.  Indetermination  in  nature  would  be 
chaos ;  in  thought,  madness.18  The  law  of  univocal 
determination  is  independent  of  individual  experiences, 
and  therefore  resembles  an  a  priori  ;  but  Petzoldt,  in  his 
fear  of  going  beyond  the  bounds  of  experience,  hastens 
to  warn  us  that  this  is  but  a  comparison,  since  this  law  in 
ultimate  analysis  is  but  a  general  fact  which  we  must 
be  content  to  recognise  without  attempting  to  explain.1' 
But  whatever  Petzoldt  may  say,  this  principle  will,  if 
it  be  enunciated  as  a  universal  law,  transcend  the  fact 
of  experience,  which  never  justifies  us  in  affirming  any- 
thing beyond  the  limits  of  past  observation  :  the  philo- 
sophy of  pure  experience  must,  if  it  would  remain 
coherent,  stop  short  at  the  fact  immediately  experienced 
in  the  passing  moment,  since  everything  else  is  an 
addition  made  by  thought,  an  interpretation  of  data 
in  accordance  with  its  requirements.  When  you  state 


that  relations  of  mathematical  dependence  exist  between 
elements,  that  nature  is  a  cosmos  determined  in  all  its 
parts,  you  unknowingly  invest  experience  with  the 
organisation  proper  to  your  own  thought ;  you  assume 
that  nature  ever  remains  coherent  in  itself,  and  that  its 
elements  are  linked  together  just  as  are  your  mental 
concepts,  that  is  to  say,  you  implicitly  assert  that  reality 
is  not  a  complex  of  pure  data,  but  an  organic  thought 
governed  by  our  own  human  logic. 

Now  if  we  once  grant  the  necessity  of  going  beyond 
data  and  of  assimilating  them  to  the  intelligence,  if  we 
would  not  be  condemned  to  experience  them  only  in 
their  non-communicable  immediacy,  is  it  not  an  arbi- 
trary proceeding  to  restrict  the  application  of  thought  to 
certain  special  relationships,  and  to  use  the  convenient 
pretext  of  anthropomorphism  as  a  reason  for  placing 
under  a  ban  other  categories  no  less  necessary  to  the 
intelligible  explanation  of  data  ?  The  relations  of 
functional  dependence  do  not  suffice  to  formulate  all  the 
aspects  of  things.  The  functional  formula  cannot  compre- 
hend any  kind  of  activity  or  any  successive  development 
of  events  in  a  determinate  direction.  The  terms  of  mathe- 
matical functions  can  as  a  matter  of  fact  be  inverted  ; 
if  the  variations  of  x  be  dependent  on  the  variations  of 

y,  it  may  equally  correctly  be  said  that  y  varies  whenj; 

ever  that  x  does  so  ;  whereas  the  essential  characteristi<TT 
of  physical  processes  and  of  real  phenomena  in  general 
is  irreversibility,  which  finds  adequate  expression  in  the 
order  of  non-invertible  succession  of  cause  and  effect._j 
Further,  if  functional  relations  can  in  some  way  record 
the  relations  between  abstract  phenomena  which  are 
subject  to  quantitative  relations,  they  are  not  applicable 
to  the  concrete  causality  of  individual  facts.  The  tie 
uniting  an  individual  fact  (which  must  not  be  con- 
founded with  the  abstract  physical  phenomenon)  to  the 
complex  of  its  antecedents  cannot  be  translated  into  a 
functional  formula  :  is  this  fact  then  indeterminate  ? 
I  do  not  think  that  Petzoldt  would  be  prepared  to  make 
such  an  admission,  thus  denying  the  law  of  univocal 


determination.  On  the  other  hand  the  apphcation  of 
this  law  in  no  way  eliminates  those  difficulties  which 
Petzoldt  attributes  to  the  use  of  the  concept  of  cause 
(which  are  not,  however,  as  serious  as  he  supposes)  when 
he  raises  afresh  the  objections  urged  by  Aenesidemus.  It 
is  undoubtedly  possible  to  insert  intermediate  terms 
between  the  antecedent  phenomenon  A  and  the  subse- 
quent phenomenon  B,  but,  even  when  this  has  been 
accomplished  by  the  scientist,  does  it  not  remain  equally 
true  that  A  is  a  necessary  condition  of  the  existence  of 
B  ?  Its  action  may  not  be  a  direct  one,  but  this  in  no 
way  detracts  from  its  efficacy.  We  are  not  justified  in 
declaring  the  concept  of  cause  to  be  obscure  and  in- 
applicable simply  because  a  large  number  of  active  factors 
co-operate  more  or  less  directly  in  the  production  of  a 
phenomenon.  Undoubtedly  every  effect  results  from 
the  action  of  countless  circumstances,  and  if  we  would 
really  determine  it  in  its  totality,  we  should  need  to 
take  them  all  into  consideration;  but  it  should  be 
observed  that  these  factors  are  not  all  on  the  same 
level,  or  of  the  same  importance,  so  that  we  are  justified 
from  the  scientific  as  well  as  from  the  practical  point 
of  view  in  selecting  those  which  act  most  directly  and 
most  effectively,  and  in  neglecting  those  whose  action 
is  unimportant  or  remote.  Thus,  in  Petzoldt's  example 
of  a  building  being  ruined  by  a  snow-storm,  the  main 
and  direct  cause  is  the  excessive  weight  of  snow  on  the 
roof,  and  it  is  superfluous  to  go  back  to  the  circumstances 
to  which  the  formation  of  the  snow  and  its  fall  in  that 
special  place  are  due,  such  as  the  lowering  of  the  tempera- 
ture, the  variations  of  atmospheric  pressure,  the  property 
possessed  by  water  of  freezing  at  zero,  etc.  This 
complexity  of  circumstances  which  makes  it  difficult 
to  determine  individual  events  is  much  simplified  by 
scientific  research,  which  only  takes  into  account  certain 
elements  of  the  fact,  which  it  isolates  from  the  others. 
This  enables  us  to  determine  phenomena  with  precision, 
by  leaving  out  of  consideration  all  those  aspects  which 
are  not  of  interest  to  us  from  the  point  of  view  from 


which  we  are  looking  at  them,  and  which  may  be  traced 
to  the  action  of  other  factors.  If  we  thus  isolate  certain 
aspects  of  the  complex  fact  by  means  of  a  process  of 
abstraction,  we  are  enabled  to  resolve  the  combination 
of  antecedents  into  elementary  factors  each  one  of 
which  determines  one  of  the  consequent  factors  whose 
synthesis  gives  birth  to  the  fact.  Here  we  have  the 
secret  of  the  experiment  leading  to  the  exact  determina- 
tion of  phenomena,  nor  need  we  alter  our  conception 
of  the  causal  relation  in  order  to  attain  thereto ;  more 
especially  since  the  tie  of  functional  dependence  would 
in  no  way  do  away  with  the  difficulties  which  we  en- 
counter in  the  determination  of  the  fact  in  its  c'on- 
creteness.  Petzoldt,  in  order  to  score  an  easy  victory 
in  his  criticism  of  the  causal  relation,  has  recourse  to 
sophistry,  and  confounds  the  abstract  phenomenon  as 
studied  by  physical  science  with  the  fact  in  its  historic 
reality,  failing  to  see  that  the  same  difficulties  arise  in 
the  case  of  functional  dependence,  which  involves  the 
choice  of  one  or  more  of  the  countless  elements  on  which 
the  phenomenon  depends,  just  as  much  as  does  the 
causal  relation.  In  no  case,  moreover,  is  it  possible 
to  determine  the  fact  without  transcending  the  limits 
of  experience,  thus  introducing  into  the  datum 
certain  functions  proper  to  thought,  and  attributing  to 
facts  that  logical  and  mathematical  structure  proper 
to  human  intelligence.  Does  not  Mach  declare 
functional  relations  to  be  real  and  objective  ?  Every 
attempt  to  divest  reality  of  the  forms  of  classification 
introduced  into  it  by  thought  is  of  necessity  doomed  to 
failure  ;  human  intelligence  cannot  get  outside  itself, 
it  works  unconsciously  in  the  consciousness  of  the 
philosopher,  even  when  it  imagines  that  it  has  suc- 
ceeded in  eliminating  itself.  Of  this  we  have  clear  proof 
in  the  case  of  Richard  Avenarius,  who  came  under  the 
same  influence  as  Mach,  and  arrived  at  much  the  same 
conception  of  the  value  of  science,  although  working 
independently  of  him.20 

8.  The  Principle  of  Minimum  Effort,  as  set  forth 


by  Avenarius. — The  work  of  Richard  Avenarius,  the 
founder  of  the  philosophy  of  pure  experience,  aims 
at  re-establishing  pure  experience  by  eliminating  every 
arbitrary  addition  made  by  thought,  and  at  afford- 
ing a  psychological  and  physiological  explanation 
of  the  origin  of  the  metaphysical  illusion.  Avenarius 
holds  that  the  whole  development  of  philosophy  and 
knowledge  in  general  may  be  reduced  to  the  principle 
of  the  minimum  expenditure  of  force.21  Whatever 
our  conception  of  the  mind  in  relation  to  the  organism 
may  be,  we  must  allow  that  its  part  in  the  preservation 
of  life  is  of  the  utmost  importance,  and  it  is  just  this 
biological  utility  which  gives  rise  to  the  principle  of  the 
minimum  expenditure  of  force,  in  order  that  sufficient 
may  remain  for  other  no  less  necessary  functions.22 
If  the  mind  were  endowed  with  inexhaustible  force, 
it  would  not  matter  whether  a  greater  or  smaller  amount 
of  that  energy  were  expended  ;  but,  since  this  force  is 
limited,  it  is  obvious  that  the  mind  must  strive  to 
economise  it.  The  eminently  biological  interpretation 
which  Avenarius  attaches  to  his  principle  is  proof 
positive  of  the  influence  exercised  on  his  thought  by 
the  theories  of  Darwin  :  in  reality,  he,  like  Mach,  does 
but  apply  the  general  law  of  adaptation  to  the  develop- 
ment of  knowledge.  We  see  the  working  of  this  principle 
of  the  minimum  expenditure  of  force  in  the  realm  of 
theoretic  function,  which  Avenarius  includes  as  a 
whole  under  the  Herbartian  term  "  apperception." 
To  what,  if  not  to  the  necessity  of  economising  force, 
is  due  the  logical  demand  for  the  elimination  of  con- 
tradictions ?  When  the  contradictory  element  ceases 
to  exist,  we  have  the  advantage  of  being  able  to  reduce 
two  representative  masses  to  one  only ;  whilst  in  the 
contrary  case,  since  apperception  is  constantly  com- 
pelled to  put  on  one  side  the  representative  group 
which  acted  as  appercipient,  in  order  that  it  may  be 
free  to  produce  another,  there  is  a  useless  expenditure 
of  force,  which  appears  to  consciousness  as  a  sense 
of  discomfort.  Every  method  of  classification  is  in 


itself  a  great  saving  of  labour,  in  as  much  as  it  organ- 
ises the  representative  masses  in  such  a  way  as  to 
facilitate   orientation   and  the  finding  of  a   common 
solution  of  problems  which  would  otherwise  have  to 
be  resolved  one  by  one.     The  results  of  habit,  which 
are   of  the   greatest   importance  in  the   development 
of  knowledge,  are  also  a  special  instance  of  the  same 
principle.      Habitual  reactions    are    the  easiest,  hence 
the  tendency  to  judge  the  new  by  the  old.     The  con- 
cept  merely   represents   a  saving  of   energy,  since  it 
enables  us  to  comprehend  a  large  number  of  objects^ 
with  a  minimum  effort  of  consciousness.     This  principle  / 
is  put  into  practice  in  all  the  sciences,  and  more  especially 
in  the  explanatory  sciences,  and  enables  us  to  condense 
individual  laws   and   concepts  into  general  laws  and   j 
concepts,  thus  effecting  an  economy  of  force.23    PhilcP" 
sophy,  which  aims  at  giving  us  a  universal  concept  of 
the  world,  is  the  goal  to  which  we  are  led  by  the  need 
of  economising  the  force  which  the  consciousness  has  at 
its  disposal. 

We  advance  gradually,  rejecting  as  we  go  all  use- 
less items  added  to  experience  by  the  subject,  and 
endeavour  thus  to  purge  it  of  all  superfluous  elements. 
These  additions  are  of  three  kinds  :  the  mythological, 
which  invest  real  data  with  the  form  of  our  whole 
being ;  the  anthropopathic,  which  attribute  our  feel- 
ings to  objects ;  the  intellectual  or  formal,  which  add  to 
experience  certain  forms  proper  to  the  human  intellect 
(cause,  substance,  etc.).24  In  our  own  day  scientific 
evolution  has  freed  the  concept  almost  entirely  from 
mythological  and  anthropopathic  additions,  but  the 
a  priori  element  of  rational  concepts  has  not  yet  been 
eliminated  and  still  persists  in  the  realm  of  experimental 
science.  The  aim  of  the  criticism  of  pure  experience 
is  to  purge  experience  from  this  last  residuum,  which,  as 
opposed  to  the  principle  of  the  minimum  expenditure 
of  force,  places  more  in  data  than  is  required,  with  the 
result  that  its  thought  involves  waste  of  energy ;  this 
aim  is  the  antithesis  of  Kant's  criticism  of  pure  reason, 


which  asserts  that  phenomena  cannot  be  explained 
without  these  categories.25  Natural  sciences  indeed 
regard  material  atoms  which  are  set  in  motion  by  forces 
and  act  upon  the  other  atoms  of  the  system  with  an 
intrinsic  necessity,  as  the  result  of  experience  ;  but  as  a 
matter  of  fact  these  material  atoms  cannot  be  considered 
as  data  of  pure  experience.  No  observation  of  things 
in  motion,  however  complete,  will  enable  us  to  perceive 
force,  and  in  the  only  case  in  which  such  perception  is 
possible,  i.e.  in  the  sensation  of  our  own  muscular  effort, 
force  is  not  presented  to  us  as  moving ;  the  transition 
from  the  effort  which  we  feel  to  the  muscular  movement 
eludes  us  ;  they  are  two  heterogeneous  facts,  between 
which  no  bond  of  action  has  been  revealed  to  us  by 
experience.  Not  only  force,  but  necessity  also  must 
be  excluded,  since  necessity  can  be  but  the  constraint 
or  violent  action  of  force  ;  experimental  data  tell  us 
nothing  about  such  violence  :  we  are  aware  that  one 
fact  precedes  another,  but  not  that  one  exercises  con- 
straint upon  the  other.  Cause,  conceived  of  as  force 
acting  of  necessity,  must  be  excluded  from  pure  experi- 
ence as  an  anthropopathic  conception  ;  both  it  and  the 
concept  of  force  can  only  be  retained  if  they  are  reduced  to 
mere  empirical  relations  of  sequences,  having  a  definite 
degree  of  probability  of  verification  in  the  future  as  well.26 
The  same  may  be  said  of  the  concept  of  substance  : 
experience  only  gives  us  groups  of  sensations,  some  of 
which  are  variable,  some  relatively  stable  ;  but,  since  the 
qualities  may  change  without  the  thing  being  destroyed, 
we  come  to  regard  the  thing  as  being  to  a  certain  extent 
independent  of  its  properties,  hence  the  illusory  belief 
that  a  certain  substratum  will  be  left,  even  if  the  thing 
be  stripped  of  its  qualities.  We  can  only  retain  the  idea 
of  substance  if  we  look  upon  it  as  an  auxiliary  of  thought, 
which  is  incapable  of  grasping  the  idea  of  change  except 
in  relation  to  something  stable  ;  but  we  must  beware 
of  passing  from  this  subjective  function  of  the  idea  of 
substance  to  its  objective  reality.27 

9.  Biological  Explanation  of  Scientific  and  Philosophic 


Knowledge. — The  whole  complex  process  of  development 
of  psychic  life,  and  more  especially  of  knowledge  in  its 
various  stages  (common,  scientific,  philosophical),  may 
be  reduced  to  a  sequence  of  three  parts,  a  sequence 
having  a  physical  parallel  in  constant  vital  rhythm : 
disturbance  of  the  normal  organic  equilibrium ;  inter- 
mediate processes  for  the  re-establishment  thereof ; 
re-establishment  of  this  equilibrium,  and  of  the  conditions 
favourable  to  its  preservation  :  these  are  the  three 
essential  stages  of  every  vital  series.28  There  is  no 
process  of  knowledge  which  will  not  fit  into  this  scheme  : 
it  is  the  psychological  and  physiological  basis  of  the 
whole  history  of  both  science  and  philosophy,  and 
affords  full  proof  of  the  biological  value  of  knowledge. 
Avenarius,  like  Mach,  recognises  the  influence  exercised 
in  this  direction  by  the  prevalent  Darwinism,  and  by 
psycho-physiological  research,  and,  having  once  admitted 
the  principle,  carries  it  out  to  its  extreme  consequences, 
instead  of  stopping  short,  as  does  Wundt,  at  the  loftier 
functions  of  mind.  There  is  nothing  either  in  the 
realm  of  theoretical  activity  or  in  that  of  practical  and 
artistic  activity  to  which  the  dynamics  of  the  nervous 
system  do  not  correspond  physiologically,  and  of 
which  they  fail  to  afford  an  explanation.  Psycho- 
physical  parallelism  holds  good  of  all  psychic  processes 
without  exception.  These  processes  develop  in  accord- 
ance with  the  common  type  of  the  vital  series,  which 
consists,  as  we  have  already  observed,  of  three  successive 
phases.  In  the  initial  stage  we  find  psychic  values 
which,  in  contradistinction  to  that  which  up  to  now 
has  been  designated  real,  true,  secure,  certain,  known, 
habitual  and  self-evident,  are  rather  unexpected,  unusual, 
extraordinary,  new,  marvellous,  problematic,  and  even 
untenable,  but  which  are  not,  however,  mere  nothing, 
since  they  could  not  in  that  case  be  of  any  interest 
to  us.  This  unpleasant  stage  of  dissatisfaction  stimu- 
lates our  quest  for  everything  which  it  lacks  :  exist- 
ence, security,  certainty,  knowledge,  truth,  evidence, 
order,  law,  clearness  and  determination.  In  the  second 


stage  we  pass  from  dissatisfaction  and  desire  to  the  quest 
itself,  and  there  is  a  tendency  to  close  the  series  with 
the  final  term  which  is  presented  afresh  as  the  same,  the 
true,  the  existing,  the  rule,  the  secure,  the  certain,  the 
known  and  the  self-evident.29 

This  scheme  applies  to  psychic  activity  in  every 
form,  the  most  rudimentary  and  the  most  complex 
alike  :  to  the  processes  of  consciousness  of  the  child 
and  the  savage,  and  equally  to  those  of  the  greatest 
genius  in  the  world  of  thought,  art,  or  action.  The 
functions  of  civilised  man,  endowed  with  all  the  theoretic 
aids  of  art  and  science,  are  but  a  quantitative  intensifica- 
tion of  the  methods  and  experience  of  primitive  man. 
Expressed  in  terms  of  physiology,  this  involves  the 
existence  of  a  fundamental  nervous  process  capable  of 
extraordinary  intensification  and  development,  which 
consequently  forms  the  basis  of  the  most  complicated 
processes  of  the  nervous  system.  Let  us  take  a  very 
simple  example  :  If  you  pinch  a  frog's  leg,  the  animal 
will  draw  it  back.  The  whole  process  falls  into  three 
divisions  :  the  disturbance  of  the  normal  physiological 
conditions  essential  to  organic  life ;  a  series  of  move- 
ments having  the  purpose  of  effecting  an  escape  from 
the  injurious  stimulus ;  the  restoration  of  normal 
conditions.30  The  mechanism  of  the  higher  and  more 
complex  functions  of  the  nervous  system  is  in  no  way 
different :  we  merely  have  a  number  of  reciprocally 
connected  series  instead  of  a  single  vital  series,  as  in 
the  case  of  the  simple  reflex  actions  ;  the  difference  is 
one  of  degree,  not  of  kind.  The  process  of  loss  and 
regain  of  equilibrium  forms  in  its  entirety  a  complete 
oscillation  whose  special  character  determines  the 
psychic  process  depending  thereon.  The  facts  of  know- 
ledge, even  in  its  higher  logical  forms,  rest  upon  the 
same  foundation  :  that  which  we  term  constant,  secure, 
or  known  corresponds  in  ultimate  analysis  to  habitual 
oscillations  of  frequent  recurrence.  The  non-existent, 
uncertain,  and  unknown  are  those  things  which  do  not 
correspond  to  such  oscillations.  We  regard  as  true* 


that  to  which  our  thought  is  adapted  :  the  new,  in  so 
far  as  it  is  in  direct  contrast  to  pre-existing  mental 
systems,  gives  us  at  first  the  impression  of  being  false  and 
impossible,  but  we  gradually  grow  used  to  it,  adapting 
ourselves  to  it  until  we  end  by  looking  upon  it  as  true  ; 
the  theory  of  evolution,  for  instance,  had  to  battle 
against  existing  mental  habits  before  it  in  its  turn 
became  habitual.  Every  epoch  has  a  relatively  stable 
system  of  cognition,  its  logischer  Bestand,  to  quote 
Petzoldt's  expression,31  a  system  corresponding  to  the 
equilibrium  of  the  vital  oscillations  at  that  stage  of 
development ;  the  whole  course  of  human  evolution  tends 
towards  the  attainment  of  an  absolutely  constant  system 
together  with  perfect  adaptation  of  the  organism  to  its 
environment.32  Progress  is  not  indefinite  :  the  various 
series  are  subjected  to  a  process  of  steady  reduction 
to  those  component  parts  which  are  essential  to  a  rapid, 
simple,  and  unalterable  conclusion,  whilst  the  final  term 
approximates  ever  more  closely  to  an  absolute  constant.33 
Concepts  which  were  originally  extremely  unstable  and 
indeterminate  become  more  and  more  determinate  and 
limited  ;  the  new  and  unknown  will  be  more  and  more 
rapidly  reduced  to  the  known,  until  a  concept  is  attained 
which  can  be  applied  to  every  possible  form  of  experience 
by  eliminating  and  leaving  out  of  account  all  variable 
elements.  This  ideal  can  only  be  attained  when 
experience  has  been  purged  from  every  arbitrary 
adjunct  of  thought,  and  a  return  has  been  made  to  the 
natural  concept  of  the  world.  Before  the  birth  of 
philosophical  speculation,  the  world  might  have  been 
described  by  me  (or  any  other  human  being)  as  follows  : 
"  I,  with  all  my  feelings,  am  placed  in  an  environment 
made  up  of  many  constant  parts,  related  to  each  other 
in  various  ways.  In  this  environment  other  human 
beings  with  their  manifold  expressions  have  their  place 
as  well,  and  that  which  they  say  is  usually  to  a  certain 
extent  related  to  and  dependent  on  the  environment. 
Other  men  speak  and  act  as  I  do  myself  ;  they  answer 
my  questions,  as  I  do  theirs  ;  they  modify  certain  parts  of 


the  environment  or  endeavour  to  keep  them  unchanged, 
indicating  their  actions  by  means  of  certain  words  justi 
as  I  do  myself ;  I  am  thus  led  to  suppose  that  other 
men  are  beings  like  myself,  and  that  I  am  a  being  like 

10.  Introjection. — This  is  the  natural  concept  of  the 
world  which  lasts  until  its  transformation  is  broughtj 
about  by  the  theories  of  philosophical  psychology.34  Is 
a  change  thereof  really  necessary  ?  Even  a  superficial 
analysis  will  suffice  to  show  that  this  concept  is  made 
up  of  two  parts,  whose  values  differ  from  a  logical  point} 
of  view :  experience  and  hypothesis.  The  hypothesis 
lies  in  the  meaning  attached  by  me  to  the  actions  of 
other  men,  and  more  especially  to  linguistic  expression,] 
taking  for  granted,  as  I  do,  that  this  expression  has 
reference  to  facts  of  consciousness,  acts  of  volition, 
sentiments  and  thoughts,  as  in  my  own  case.  It  might  i 
be  possible  to  eliminate  this  hypothetical  part,  and  to 
regard  human  beings  as  highly  complicated  pieces  of 
mechanism,  but  we  must  bear  in  mind  that  if  we  deny 
the  consciousness  of  other  human  beings  we  leave  the 
realm  of  experience,  since  in  the  only  case  in  which  we 
know  the  movements  of  a  human  being  in  all  their 
relations  (i.e.  in  the  case  of  our  own  actions)  we  have 
experienced  these  sentiments,  thoughts,  and  volitions, 
whereas  experience  has  never  shown  us  that  these 
actions  are  derived  from  a  purely  mechanical  source. 
Hence  the  hypothesis  that  other  men  are  beings  like 
myself,  which  Avenarius  terms  the  fundamental  empirio- 
critical  hypothesis  of  the  psychological  equivalence  of 
man,  is  admissible.35  If  we  let  R  stand  for  the  whole  of  our 
own  direct  experience  of  the  environment,  and  E  for  the 
expression  of  the  experiences  of  other  human  beings,  we 
may  then  say  that  the  values  R  and  E  do  not  differ  as  to 
their  nature,  but  are  homogeneous  contents  of  experience, 
and  are  mutually  comparable.  The  values  of  experience 
are  commonly  divided  into  thoughts  and  facts  ;  but  there 
is  no  absolute  difference  even  in  the  nature  of  these  two 
categories,  since  thoughts  and  facts  may  be  compared 


with  one  another  :  thus  a  portrait  may  be  compared 
with  the  image  of  the  absent  person.  The  absolute 
division  between  the  inner  and  outer  world  is  due  to 
faulty  perspective,  an  illusory  effect  which  Avenarius 
terms  "  introjection." 36  A  person  tells  me  that  he 
sees  the  same  tree  as  I  do  ;  hence  I  am  led  to  think  an 
image  of  the  tree  into  the  consciousness  of  that  person, 
and  to  draw  a  distinction  between  the  tree  as  a  fact 
of  my  experience  and  his  perception  thereof.  Since 
it  is  possible  for  me  to  put  myself  in  his  place,  I  end  by 
introducing  into  myself  also  an  image  which  I  distinguish 
from  the  tree.  Here  the  error  is  due  to  changing  the 
point  of  view :  the  thing  is  a  presentation  not  for  me 
but  for  the  other  person,  to  whom  by  means  of  intro- 
jection I  attribute  the  perception  of  the  thing  in  question ; 
for  me  it  is  a  presentation  of  fact,  something  which  I 
find  there  (Vorgefundenes). 

The  error  becomes  more  serious  when  the  sensation,  as 
distinct  from  the  thing,  is  localised  in  the  brain,  whence  it 
is  supposed  to  be  projected  outwards  in  the  act  of  percep- 
tion. The  brain  is  not  the  habitation,  seat,  instrument, 
producer,  or  organ  of  thought :  experience  merely  tells 
me  that  I  possess  a  thought  and  a  brain  in  the  sense  that 
both  belong  to  the  group  of  facts  which  we  call  the  Ego ; 
it  merely  authorises  me  to  establish  a  tie  of  logical 
dependence  between  them,  but  not  to  locate  one  within 
the  other.37  On  the  other  hand,  I  find  the  complex  of 
elements  (thoughts,  sentiments,  volitions)  which  make 
up  the  so-called  Ego  in  precisely  the  same  way  as 
I  find  the  complex  of  elements  which  I  call  tree ;  they 
are  both  homogeneous  contents,  and  both  are  found 
already  in  existence  (vorgefunden).  If,  however,  we 
like  to  make  use  of  the  word  "  datum,"  the  Ego  may  be 
considered  as  coming  under  that  designation  in  the  same 
sense  as  the  tree  ;  as  data,  or,  to  put  it  better,  as  things 
found  already  existing  (vorgefunden),  the  various  com- 
plexes are  all  on  the  same  level.38  As  long  as  I 
confine  myself  to  describing  the  content  of  experience, 
as  found,  the  Ego  and  the  environment  differ  only  in  the 


PT.  I 

relations  of  the  elements,  not  in  their  general  form  or 
in  the  fact  that  one  is  immediate  and  the  other  mediate, 
one  subject  and  the  other  object.  As  I  am  in  my 
experience,  so  is  the  tree  in  my  experience  :  if  I  say,  I 
experience  the  tree,  I  understand  thereby  merely  that 
an  experience  results  from  the  more  ample  complex  of  ele- 
ments called  Ego,  and  from  the  other  less  ample  complex 
called  tree.  The  Ego  is  distinguished  from  the  environ- 
ment merely  by  the  greater  wealth  and  complexity  of  its 
elements.  This  co-ordination  proper  to  every  experience, 
in  which  the  complex  Ego  forms  the  relatively  constant 
member,  and  part  of  the  environment,  whether  it  be  a 
tree  or  another  human  being,  the  other  and  relatively 
variable  member,  is  termed  by  Avenarius  "  principal 
empiric-critical  co-ordination."  39  The  human  individual, 
as  the  relatively  constant  member  of  this  co-ordination, 
may  be  designated  as  the  central  member  (Central- 
glied),  and  the  part  of  the  environment  as  the  opposing 
member  (Gegenglied).  In  accordance  with  the  principle 
of  psychological  equality  other  individuals  may  act  as 
central  members  of  empiric-critical  co-ordination,  since 
by  their  Ego  we  do  not  understand  a  subject  of  experience, 
but  something  found  (vorgefunden),  a  datum  amongst 
others  of  the  same  kind.  Fundamental  empiric-critical 
co-ordination,  which  is  taking  the  place  of  illusory 
introjection,  does  not  change  the  natural  concept  of 
the  world,  but  gives  prominence  to  a  general  relation 
included  therein.40  The  variations  of  the  natural 
concept  of  the  world  are  useless,  and  must  be  eliminated 
as  superfluous  in  accordance  with  the  principle  of 
economy.  The  philosophical  concept  of  the  world  must 
approximate  ever  more  closely  to  a  purely  empirical 
content,  which  substitutes  for  the  riddles  of  the  universe 
an  idea  of  the  world  containing  nothing  which  is  not  of 
the  nature  of  something  found,  of  an  experimental  datum. 
In  conclusion,  if  we  would  attain  to  pure  experience, 
we  must  not  only  eliminate  all  concrete  forms  and  the 
products  of  introjection,  that  is  to  say,  every  kind  of 
metaphysic  and  anthropomorphism,  but  also  intro- 


jection  itself  as  an  unconscious  function  of  the  subject. 
There  will  then  remain  that  concept  of  the  world  whose 
content  is  the  totality  of  all  that  is  found,  whether 
belonging  to  the  group  which  acts  as  central  member 
or  to  the  complex  of  an  opposing  member.  We  thus 
return  to  the  natural  concept  of  the  world.41 

11.  Criticism  of  the  Philosophy  of  Pure  Experience. — 
But,  we  would  ask,  is  a  form  of  philosophic  knowledge 
possible  in  which  thought  does  not  add  anything  to 
data  ?  If  we  divest  reality  of  all  the  forms  of  classifica- 
tion which  are  introduced  into  it  more  or  less  consciously 
by  the  subject,  what  is  left  of  it  ?  A  chaos  of  data 
devoid  of  any  relation  of  stable  dependencies.  Philo- 
sophical knowledge,  or,  in  other  words,  intelligence,  which 
must  not  be  confounded  with  the  fact  as  experienced, 
begins  the  moment  a  wider  meaning  is  assigned  thereto, 
as  we  ascend  to  the  law,  the  order  of  which  it  forms  part, 
and  the  concept  which  comprehends  it.  To  stop  short  at 
the  given  is  to  deprive  science  of  the  conditions  essential 
to  its  life.  A  concept  of  the  world,  no  matter  how 
embryonic,  no  matter  how  natural  it  may  be,  always 
goes  beyond  the  fact  of  experience  ;  the  philosophy  of 
pure  experience  itself,  in  so  far  as  it  strives  to  construct 
a  universal  concept  of  the  world,  cannot  avoid  adding 
to  data  something  which  they  do  not  contain.  Do 
we  not  go  beyond  the  limits  of  the  given  when  we 
assume  the  expressive  signs  made  by  other  human 
beings  to  be  the  revelation  of  psychic  life  like  our  own  ? 
Do  we  not  go  beyond  it  when  we,  like  Avenarius, 
endeavour  to  describe  the  manifold  life  of  experience, 
and  to  comprise  it  in  general  schemes  ?  The  centres 
oi  co-ordination,  the  elements,  the  complexes  are  generic 
formulas  answering,  though  but  imperfectly,  to  the  need 
of  finding  in  things  a  certain  unity,  certain  constant 
characteristics  ;  but  unity  is  constructed  by  thought 
and  is  not  a  datum.  When  we  say  that  the 
various  contents  of  experience  are  homogeneous,  no1 
heterogeneous,  we  unconsciously  go  beyond  the  data. 
Facts  are  neither  immediately  heterogeneous  noi 



immediately  homogeneous,  they  are  as  they  are  found,  each 
one  of  them  has  its  own  individual  character.     If,  then, 
we  admit  that  it  is  impossible  to  avoid  adding  something 
to  experience  which  is  not  derived  therefrom,  there  arises 
the  critical  necessity  of  selecting  that  one  of  the  various 
adjuncts  which  will  render  the  data  easiest  of  com- 
prehension.    To  eliminate  them  all  would  amount  to 
dooming  ourselves  to  understand  nothing.    We  should 
dismiss  not  merely  metaphysical  problems,  but  also  prob- 
lems of  every  kind  whatsoever.    The  coherent  conclusion 
of  such  a  system  of  philosophy  would  be  to  condemn 
every  concept  and  every  form  of  intelligence,  and  would 
involve  the  identification  of  knowledge  with  the  imme- 
diate intuition  of  reality.     Avenarius,  however,  whatever 
he  may  say  on  the  subject,  is  not  prepared  to  give  up 
tracing  relations  of  logical  dependence  between  different 
data,  or  arranging  them  in  categories,  or  completing 
experience  with  the  help  of  intellectual  forms  which  go 
beyond  it.    For  the  most  part  his  essays  in  this  direction 
are  not  specially  successful.     His  schemes  of  classification 
savour  too  strongly  of  the  artificial,  and  betray  an  attempt 
to  reduce  by  force  the  countless  processes  of  psychic 
life  to  a  single  type,  so  as  to  make  it  possible  to  connect 
them  with  the  simple  mechanism  which  he  regards  as 
the  basis  of  cerebral  life.      The  same  disturbance  of 
equilibrium    is    called    upon    to    act   as   the   physio- 
logical term  corresponding  to  unlike  psychic  facts,  and 
the  reason  why  in  any  given  case  it  should  produce 
one  process  rather  than  another  is  not  apparent.    At 
best  Avenarius  affords  us  an  explanation  of  the  action 
of  habit  and  practice  on  the  various  functions  of  con- 
sciousness ;  but  he  does  not  give  us  in  the  case  of  each 
psychic  value  a  fact  capable  of  determining  that  value  in 
the  central  nervous  system.    The  habitual,  the  custom- 
ary, the  repetition  of  the  same  oscillations  are  at  one 
time  psychologically  described  as  pleasing,  at  another  as 
beautiful,  at  another  as  true,  at  yet  another  as  good ; 
why  is  this  ?     Let  us  grant  that  all  positive  values  of 
the  mind  correspond  to  habitual  repetitions,  and  negative 


values  to  deviations  from  habit ;  what  is  the  psycho- 
logical basis  of  their  diversity  ?  A  different  form  of 
oscillation  !  This  leaves  us  where  we  were  before,  with 
the  additional  drawback  of  having  two  facts  to  explain 
instead  of  one.  We  have  not  succeeded  by  this  method 
in  determining  the  psychic  fact,  but  have  left  it  as 
undetermined  as  before.  So  much  then  for  rejecting 
the  help  of  physiology  !  The  attitude  of  Avenarius  as 
regards  the  problem  of  reality  in  relation  to  the  subject  is 
extremely  vague  and  undecided ;  he  is  under  the  impres- 
sion that  he  has  definitely  disposed  of  the  idealistic  phase 
by  assigning  equal  importance  to  the  Ego  and  the  world 
as  contents  of  experience,  but  by  regarding,  as  he  does, 
the  Ego  as  the  central  member  of  the  co-ordination,  he  as 
a  matter  of  fact  still  makes  the  reality  of  the  opposing 
member,  i.e.  the  outer  world,  depend  upon  its  existence. 
Avenarius  was  reluctant  to  take  the  final  step  of  the 
hypostatisation  of  sensations,  by  severing  them,  as  did 
Mach  and  his  own  disciple  Petzoldt,  from  the  complex  of 
the  Ego,  and  investing  them  with  entirely  independent 
reality.  If  the  outer  world  can  be  reduced  to  a  complex 
of  sensorial  data,  if  these  data  exist  only  in  connection 
with  the  central  member  termed  the  Ego,  it  follows  that 
the  objective  world  is  not  possessed  of  reality  except  in 
so  far  as  it  is  connected  with  the  Ego.  Thus  we  come 
back  to  idealism,  and  we,  moreover,  implicitly  admit 
that  the  functions  of  the  Ego  and  the  environment  in 
empiric-critical  co-ordination  are  not  identical.  Is  the 
relation  between  the  Ego  and  the  outer  world  the  same,f, 
as  the  extrinsic  relation  between  two  parts  of  the!', 
environment,  or  is  it  a  relation  sui  generis  ?  Avenarius! 
tries  to  get  round  the  difficulty  by  having  recourse  to 
the  metaphors  of  the  centre  of  co-ordination,  and  the 
opposing  member ;  but  these  metaphors,  which  are 
supposed  to  describe  this  special  relation,  misrepresent 
its  nature,  by  leading  us  to  think  of  the  relation  which 
may  exist  between  any  two  complexes  of  the  outer 
world,  as,  for  instance,  between  the  sun  and  one  of  its 
planets,  and  has  nothing  to  do  with  the  cognitive 


relation.     A  complex  may  act  as  the  centre  of  co- 
ordination of  other  complexes  without  being  in  the 
least  aware  of  their  existence.     The  Ego  is  not  a  content 
/.of  experience  which  simply  stands  in  relation  to  other 
//contents  :  its  special  characteristic  is  that  it  knows  that 
//which  stands  in  relation  to  itself,  and  is  conscious  of 
/  its  own  relations,  whereas  the  opposing  member  knows 
[  nothing  of  the  Ego. 

The  cognitive  relation  will  not  result  merely  from 
placing  two  contents  of  experience  in  a  relation  of 
propinquity ;  the  difference  between  the  Ego  and  the 
environment  is  not  just  one  of  complexity  and  fulness ; 
it  is  the  difference  between  a  subject  capable  of  self- 
knowledge  without  reference  to  others  and  an  object 
which  is  a  content  of  experience  merely  in  relation  to 
the  Ego.  One  is  a  value  of  existence  in  itself,  the  other 
becomes  so  only  in  relation  to  the  cognitive  subject. 
The  unity  and  continuity  of  consciousness  cannot  be 
derived  from  a  simple  extrinsic  connection  of  facts  which 
would  remain  extraneous  to  one  another  were  it  not 
for  the  existence  of  a  subject  capable  of  synthesising 
the  various  items  of  the  series  in  a  single  act.  The 
succession  and  co- existence  of  empirical  elements  is 
one  thing,  and  consciousness  of  the  relations  of 
succession  and  co  -  existence  another.  Mach  and 
Avenarius,  whilst  imagining  that  they  take  facts  and 
their  ties  of  dependence  as  the  starting-point  from  which 
to  deduce  the  concrete  unity  of  the  subject,  fail  to  see 
that  they  postulate  it  the  moment  they  admit  the 
consciousness  of  relations.  The  mechanism  of  the 
nervous  system,  to  which  Avenarius  turns  for  an  explana- 
tion of  the  recognition  of  diversity  or  identity,  thus 
reducing  it  to  the  transition  from  a  familiar  cerebral 
oscillation  to  one  which  is  less  habitual  or  vice  versa, 
presupposes  the  existence  of  these  logical  relations  : 
how,  if  this  were  not  so,  could  we  speak  of  the  functional 
dependence  of  psychic  processes  upon  the  vital  series 
of  higher  order  in  the  nervous  system  ?  How  could 
we  state  either  that  the  same  oscillations  have  recurred 


or  that  new  ones  have  been  originated  ?     The  mechanism 
of  the  brain  and  its  relations  to  psychic  life  and  to  the 
environment  do  not  form  a  complex  of  things  found 
(Vorgefundenes),  but  rather  systems  of  relations  already 
bearing  the  imprint   of  thought.    Thought   does   not// 
then  result  from  experience   except  in   so  far  as  wey 
ourselves  have   placed  it  in  experience.     That  which' 
Avenarius  shows  us  is  not  pure  experience  in  the  strict 
sense   of  the  word, 'but  experience  already  formulated 
into  certain  mental  systems.    The  purely  found  which 
is  external  to  every  form  of  thought  and  every  relation 
to  the  cognitive  subject  is  an  abstract  fiction  which 
may  be  found  helpful  in  symbolising  the  starting-point* 
of  psychic  formations,  but  corresponds  to  nothing  real.! 
Moreover,  pure  data,  being  the  product  of  analysis  and  j 
abstraction,   presuppose  the  work  of  reflex  thought, 
which    discriminates    between    the    world    of    naive, 
primitive  experience  and  those  elements  unconsciously 
added  thereto  by  the  activity  of  the  subject.    Hence 
empiric-criticism  is  doomed  to  move  in  a  vicious  circle, 
from  which  it  can  only  hope  to  escape  by  recognising 
the  a  priori  function  of  the  subject.     The  truly  real  is 
the  conscious  personality  in  the   concreteness   of  itsj 
content,  not  scattered  facts,  isolated  from  the  unity  of 
the  subject. 

12.  Hodgson's  Metaphysic  of  Experience.  —  In 
Hodgson's  Metaphysic  of  Experience*2  which  has  many 
points  of  contact  with  German  empirio  -  criticism, 
we  have  the  same  attempt  to  argue  the  antithesis  of 
subject  and  object  from  a  primitive,  undifferentiated 
experience.  Hodgson,  like  Avenarius,  would  fain 
purge  experience  by  analysis  from  the  hypotheses,  the 
"  assumptions,"  which  have  been  added  to  it  in  the 
course  of  psychic  evolution,  such,  for  instance,  as  the 
ideas  of  cause,  action,  mental  substance,  etc.  These 
mental  superstructures,  which  transcend  immediate 
perceptive  experience,  do  not  correspond  to  any  objective 
reality,  but  merely  represent  forms  of  combination  of  real 
facts,  points  of  orientation  amid  the  chaos  of  immediate 


data  of  sensibility.  Eliminate  these  adjuncts,  and  we 
have  the  continuous  flux  of  the  concrete  current  of  con- 
sciousness, the  process  of  immediate  experience  of  which 
every  psychic  fact  is  an  item  separable  from  the  rest 
only  by  means  of  a  process  of  abstraction.  Each  of 
these  items  contains  within  itself  by  virtue  of  the  con- 
tinuity of  conscious  life  all  preceding  phases  ;  hence 
each  perception  mirrors  the  past.  This  retrospective 
reflection  (from  which  Hodgson  derives  the  term 
"  philosophy  of  reflection "  which  he  applies  to  his 
system)  gives  rise  to  the  distinction  between  subject 
and  object,  since  the  psychic  contents  of  the  past  form 
the  object  of  the  present  perception  which  acts  as 
subject.  If  these  premisses  be  granted,  what  should 
be  the  logical  conclusion  of  the  system  ?  If  the  mental 
categories  be  hypotheses  of  purely  practical  value, 
reflecting  nothing  real,  if  the  concept  be  but  an  economy 
of  thought,  then  true,  genuine  reality  is  the  immediate 
life  of  the  transient  moment  of  consciousness.  Hodgson 
ought  then  to  end  in  something  resembling  Bergson's 
intuition,  but  he  too,  like  Avenarius,  finishes  by  con- 
tradicting himself,  and,  while  denying  the  objective 
value  of  the  categories,  yet  makes  use  of  them  in  order 
to  form  a  conception  of  the  material  organism,  the 
nervous  system,  as  a  real  active  substance,  a  condition 
necessary  to  the  existence  of  psychic  life.  According 
to  Hodgson,  consciousness,  though  in  its  nature  a  primi- 
tive and  irreducible  fact,  is  yet  dependent  for  its  existence 
/  on  material  conditions.  This  position  is  equivocal  and 
untenable,  since,  if  consciousness  be  qualitatively  an 
ultimate  fact,  it  is  obvious  that  the  existence  of  this 
irreducible  quality  cannot  be  derived  from  matter. 
Objects  are,  when  all  is  said  and  done,  constructions  of 
the  subjective  perceptions,  fragments  of  consciousness, 
objectified  mental  functions;  hence  Hodgson  ought  really 
only  to  speak  of  psychic  facts  conditioning  other  facts  of 
consciousness,  and  from  his  point  of  view  nothing  justifies 
him  in  positing  anything  differing  from  phenomena  !of 
consciousness,  still  less  in  making  the  existence  of  psychic 


life  dependent  thereupon.  That  which  I  experience 
immediately  is  the  flux  of  consciousness  in  its  continuity, 
and  this  real  continuity  is  the  primal  and  indubitable 
fact  which,  amidst  changeable  perceptions,  constitutes 
the  reality  of  my  concrete  Ego.  If  my  psychic  life  be 
not  the  outcome  of  a  mere  aggregate  of  elements  ranged 
side  by  side  in  an  extrinsic  relation,  as  Mach  and 
Avenarius  would  have  us  believe,  if  it  be  rather  the 
compenetration  of  these  elements  in  a  living  unity,  as 
Hodgson  rightly  maintains,  is  it  not  this  living  unity, 
a  concrete  and  active  substance,  of  which  we  have 
immediate  experience,  while  the  material  substance 
with  all  the  mechanism  of  atoms  is  but  a  hypothetical 
structure  ? 

13.  Kleinpeter's  Subjectivism. — Kleinpeter  saw  this 
plainly,  and  his  teaching  on  this  point  is  a  notable 
advance  on  that  of  Mach  and  Avenarius.43  The  Ego  is 
not  a  sum  of  psychic  facts,  and  even  though  it  is  possible 
to  distinguish  different  distinct  parts  in  consciousness, 
these  parts  have  nothing  to  do  with  the  parts  of  a 
physical  body.  Sensations  are  never  presented  as  such 
apart  from  everything  else,  but  always  as  my  sensations, 
and  the  bond  between  these  elements  in  consciousness 
differs  from  the  connection  which  may  exist  between 
them  outside  the  Ego.  The  primitive  datum  is  not 
the  element  taken  by  itself,  but  the  totality  of  con- 
sciousness, which  we  must  regard  as  an  ultimate  and 
irreducible  fact.  We  may  speak  of  other  beings  in  as 
much  as  we  refer  them  to  our  own  Ego,  the  living  model 
of  all  reality ;  where  could  we  find  anything  we  know 
better  ?  The  elements  of  knowledge  in  all  its  forms 
cannot  but  be  of  psychic  origin,  hence  they  can  never 
leave  the  sphere  of  individual  life.  All  knowledge  is 
originally  only  of  value  to  the  individual  who  has  built 
it  up,  and  the  thought-product  of  one  individual  is  of 
importance  to  another  only  when  certain  presuppositions 
can  be  verified.  It  is  mere  matter  of  chance  that  this 
can  usually  be  done.  Strictly  speaking,  I  cannot  even 
state  with  certainty  that  other  individuals  exist ;  I 


ought  therefore  to  confine  myself  to  that  which  I  am 
experiencing  at  this  moment ;  hence  knowledge  would 
only  be  of  value  during  the  passing  moment  which  gives 
it  birth.44  The  equivalence  of  all  thinking  subjects  is 
but  an  hypothesis  :  that  which  is  valid  in  the  eyes  of  one 
person  may  not  be  so  in  the  eyes  of  another  who  does 
not  start  from  the  same  premisses;  nothing  can  be  proved 
to  him  who  will  make  no  concessions.  "  Subjective 
opinion,  not  objective  certainty,  is  the  one  and  only 
end  to  which  science  can  attain."  45  A  scientific  work 
is  only  of  value  when  the  reader  concedes  certain 
postulates  to  the  author.  The  function  of  science  is 
the  saving  of  mental  labour ;  she  says  to  the  reader  : 
"  You  must  recognise  the  truth  of  certain  principles, 
from  which,  once  they  are  granted,  we  derive  a  long 
series  of  other  theorems  ;  in  the  case  of  the  former 
your  immediate  experience  is  required,  for  the 
latter  you  can  save  yourself  this  mental  labour." 
Our  knowledge  is  relative  and  provisional,  since  its 
existence  depends  upon  the  verification  of  two  funda- 
mental presuppositions,  i.e.  the  psychological  equival- 
ence of  men  and  the  uniformity  of  nature.  Who  can 
guarantee  that  they  will  always  be  verified  ?  **  Human 
thought  is  not  endowed  with  the  spirit  of  prophecy  ; 
it  must  confine  itself  to  the  description  of  that  which 
is  and  that  which  may  be  expected,  but  it  cannot  lay 
down  laws  for  the  future.47  The  natural  series  of  facts 
eludes  the  activity  of  our  mind,  which,  when  confronted 
with  it,  can  but  act  as  looker  on,  and  strive  to  reproduce 
it  as  skilfully  as  possible  in  thought  by  means  of  systems 
whose  validity  is  entirely  dependent  upon  the  probable 
success  of  their  forecasts.  If  the  work  of  science  be 
successful,  it  is  a  lucky  chance  ;  from  our  point  of  view 
this  is  the  utmost  which  can  be  said.48  This  candid 
confession,  with  which  Kleinpeter  concludes  his  critical 
analyses  of  the  value  and  basis  of  the  sciences,  affords  a 
proof  of  the  dire  results  of  the  empirical  method  when  it 
is  carried  to  its  logical  consequences.  A  caprice  of  the 
will  in  the  beginning  of  human  thought ;  a  series  of 


happy  acci^ntsjv\^b^have_rend(eredjt  possible  to  apply 
it  to  the~world  of  experience  ;  behold  m  very  trutlr 
a  system  of  philosophy  before  which  all  riddles  will 
flee  away  !  Empirio-criticism  alleges  that  it  has  ex- 
plained everything  by  reducing  the  intellectual  function 
to  a  combination  of  expedients  destined  to  economise 
mental  labour,  but  it  is  unable  to  know  or  say  how  or 
why  these  expedients  succeed.  It  is  indeed  strange 
that  facts  do  not  revolt  against  our  economic  demands, 
that  they  submit  to  being  classified  in  concepts  and 
logical  systems  and  to  being  foreseen,  that  they  behave, 
in  fact,  for  all  the  world  as  if  they  too  had  a  leaning 
to  economy  and  a  turn  for  mathematics  !  Empirio- 
criticism  must  of  necessity,  if  followed  to  its  ultimate 
consequences  and  freed  from  its  implicit  contradictions, 
lead  to  the  doctrines  of  contingency,  intuitionism,  and 
pragmatism,  since  it  reduces  the  theoretic  function  to  the 
practical  attitude  of  consciousness,  and  looks  to  the  fact  of 
immediate  experience  for  the  truest  revelation  of  reality. 
If  the  fact  in  its  original  immediacy  be  the  true  real, 
how  can  we  grasp  it  without  divesting  ourselves  of  every  "^ 
intellectual  form  ?  The  concept  of  pure  experience,  the 
functional  relation,  the  stable  dependence  of  elements 
are  remnants  of  the  old  intellectualism  :  we  must  go 
farther,  and  deny  all  and  every  permanent  relation, 
law,  and  form  of  conceptual  reflection,  if  we  would  attain 
to  that  deeper  experience  which  abstract  formulae  have 
falsified  and  impoverished.  Mathematical  functions 
too  are  of  merely  practical  value  ;  the  law  of  univocal 
determination  is  but  an  economic  expedient  for  the 
mastery  of  the  inexhaustible  wealth  of  experience. 
Nature  never  repeats  herself  :  her  every  moment  is  a 
new  creation  which  no  intellectual  effort  can  ever  grasp, 
and  which  can  only  be  experienced  by  means  of  intuition. 
Creation,  unfettered  action — these  alone,  Bergson  will 
tell  us,  can  sound  the  depths  of  fugitive  being. 



I  "  Outlines  of  the  Science  of  Energetics,"  Proceedings  of  the  Philo- 
sophical Society  of  Glasgow,  1848-55,  voL  iii.  p.  382. 

*  Die  Analyse  der  Empfindungen  (5th  ed.,  Jena,  1906),  chap.  i. 

8  "Aus  den  Empfindungen  und  durch  deren  Zusammenhang  entspringen 
unsere  Begriffe,"  Erkenntnis  und  Irrtum,  1st  ed.  p.  142. 

4  Erkenntnis  und  Irrtum  (1st  ed.,  Leipzig,  1905),  p.  162. 

5  Die  Mechanik  in  ihrer  Entwicklung  (4th  ed.,  Leipzig,  1901),  p.  78,  etc. 

6  Op.  cit.  p.  80  ff. 

7  Die  Prinzipien  der  Warmelehre  (2nd  ed.,  Leipzig,  1900),  p.  437  ff. 
The  same  thesis  is  maintained  by  Andrade,  lievue  de  mil.  et  de  morale, 
March  1899,  p.  178. 

8  Die  Mechanik,  etc.,  p.  529  ff. 

•  Op.  cit.  p.  543. 

10  Op.  cit.  p.  531  ff. 

II  Op.  cit.  p.  531  ff. 

11  Op.  cit.  p.  513. 

18  Mach  only  looks  upon  the  shortest  times  as  sensorial  data  ;  periods 
of  longer  duration  are  constructed  by  a  process  of  reflection. 

14  Die  Okonomische  Natur  der  physikalischen  Forschung  (Vienna,  1882), 
reprinted  in  the  Popular  wissenschaftliche  Vorlesungen. 

16  "  Diese  Gleichungen  oder  Beziehungen  sind  also  das  eigentlich 
Bestandige "  (Die  Prinzipien  der  Warmelehre,  2nd  ed.  p.  424).  "  Jede 
physikahsche  Bestandigkeit  kommt  schliesslich  immer  darauf  hinaus, 
dass  eine  oder  mehrere  Gleichungen  erfullt  sind,  also  auf  ein  bleibendes 
Gesetz  im  Wechsel  der  Vorgange  "  (ibid.  p.  342). 

16  Einfuhrung  in  die  Philosophic  der  reinen  Erfahrung  (Leipzig,  1900), 
pp.  27  ff.,  and  55.      Lalande  too  makes  an  analogous  criticism  of  the 
principle  of  causality,  which  he  regards  as  a  vague  and  incomplete  idea, 
a  rough  approximation,  for  which  the  principle  of  continuity  and  mathe- 
matical identity  should  be  substituted  ("Remarques  sur  le  principe  de 
causalite,"  Revue  philosophique,  1890,  vol.  ii.  p.  225). 

17  Op.  cit.  p.  37. 

18  Op.  cit.  p.  40  ff. 

19  Op.  cit.  p.  44. 

20  Avenarius  learnt  the  strict  method  of  physiological  research  in 
Lud wig's  school  at  Leipzig,  and  was  initiated  by  Drobisch  into  Herbartian 
philosophy,  whence  he  derived  the  notion  of  the  inertia  of  apperceptive 
masses  being  due  to  the  need  of  conservation  of  the  mind,  which,  when  inter- 
preted physiologically,  harmonised  with  the  new  conceptions  of  Darwinism. 

n  Philosophic  als  Denken  der  Welt  gemdss  dem  Prinzip  des  kleinsten 
Kraftmasses  (2nd  ed.,  Berlin,  1903),  p.  3  ff. 
«  Op.  cit.  p.  12  ff. 
18  Op.  cit.  p.  24. 
M  Op.  cit.  p.  38. 
24  Op.  cit.  p.  46  ff. 

26  Op.  cit.  pp.  52-54. 

27  Op.  cit.  pp.  56-62. 

28  Kritik  der  reinen  Erfahrung  (Leipzig,  1888-91),  vol.  ii.  p.  238  ff. 
M  Op.  cit.  voL  ii.  pp.  218-222. 

80  Op.  cit.  vol.  ii.  p.  204  ff. 

81  Einfuhrung  in  die  Philosophic  der  reinen  Erfahrung  (Leipzig,  1900), 
voL  i.  p.  198.     Petzoldt  has  modified  the  theory  of  Avenarius  on  the 


subject  of  logical,  ethic,  and  aesthetic  values.  Avenarius  looked  upon  these 
values  as  derived  from  the  function  of  language,  by  which  the  psychic  facts  of 
one  individual  assume  a  different  character  of  a  secondary  or  epi-character- 
istic  order  when  communicated  to  another  person:  thus,  for  instance, 
immediately  experienced  pleasure  and  pain  become  aesthetic  pleasure  and 
pain  when  communicated  to  us  by  others ;  knowledge,  communicated 
through  the  medium  of  language,  becomes  science,  true,  if  the  com- 
munication be  made  by  a  reliable  person,  false  in  the  contrary  circumstances. 
Petzoldt,  on  the  other  hand,  regards  these  values  also  as  primary  and 

82  Petzoldt  lays  special  stress  on  this  tendency  to  stability  as  a  motor 
force  of  evolution  (1904,  voL  ii.  p.  72  ff.).  The  principle  of  the  minimum 
effort  of  economy  is  in  its  essence  a  tendency  to  stability  (ibid.  p.  94). 

33  Avenarius,  op.  cit.  vol.  ii.  p.  302. 

34  Der  menschliche  Weltbegriff  (2nd  ed.,  Leipzig,  1905),  p.  6. 

35  Op.  cit.  p.  8. 

34  Op.  cit.  p.  26  ff. 

37  Op.  cit.  p.  76  ff. 

38  Op.  cit.  p.  82. 

39  Op.  cit.  p.  84. 

40  Op.  cit.  p.  93  ff. 

41  Op.  cit.  p.  110  ff. 

42  The  Metaphysic  of  Experience  (London,  1898). 

43  Die  Erkenntnis  der  Naturforschung  der  Gegenwart  (Leipzig,   1905), 
pp.  24-30. 

44  Op.  cit.  p.  43  ff. 
48  Op.  cit.  p.  9. 

46  Op.  cit.  p.  141. 

47  Op.  cit.  p.  124. 

48  Op.  cit.  p.  141. 



1.  Two  Attempts  at  Escape  from  the  Agnostic  Position. — 
Thinkers  have  tried  to  escape  from  the  agnostic  position 
in  two  different  ways :  one,  whose  course  we  have  followed 
through  neo  -  criticism  and  empiric  -  criticism,  aims  at 
the  critical  elimination  of  the  problem  by  the  reduction 
of  all  reality  to  phenomena  only,  and  the  dismissal  of 
that  Absolute  which  appeared  to  baffle  knowledge,  a 
proceeding  reminding  us  of  a  child  who  imagines  that  by 
shutting  his  eyes  to  something  of  which  he  is  afraid  he 
can  destroy  it ;  the  other  is  the  return  to  that  speculative 
method  which  positivism  had  vainly  endeavoured  to 
replace  by  science.  Some  of  these  speculative  attempts, 
which  were  inspired  by  post-Kantian  idealism,  have 
been  already  treated  in  their  relation  to  neo-criticism ; 
this  applies  more  especially  to  those  which  are  closely 
connected  with  the  teaching  of  Fichte,  Schelling,  and 
Schopenhauer,  and  which  are  more  or  less  deeply  tinged 
with  romanticism  and  irrationahsm ;  we  must  now 
sketch  the  outlines  of  that  movement  of  thought  which 
arose  in  England  in  opposition  to  traditional  empiricism 
and  its  ultimate  tendency,  agnostic  positivism,  claiming 
to  be  able  to  supply  that  which  was  lacking  in  scientific 
intellectualism,  and  reaching  in  the  works  of  Hegel  a 
higher  form  of  rationalism. 

2.  The  Eternity  of  Thought,  as  Affirmed  by  Green  in 
Opposition  to  Empiricism. — The  philosophy  of  Thomas 
Hill  Green  l  appears  to  be  a  reaction  from  the  empiricist 



and  psycho-genetic  method  which  had  for  centuries  been 
the  predominant  feature  of  English  philosophy,2 
righteous  vindication  of  the  eternity  of  consciousness 
and  thought  against  those  who  would  fain  regard  it  as 
a  contingent  phenomenon,  having  its  origin  in  time, 
and  doomed  to  vanish  in  time.  It  must  be  said  in 
his  favour  that  he  is  not  carried  away  by  the  facile 
enthusiasm  for  the  new  theory  of  evolution^  and  that 
he  clearly  saw  the  petitio  principi\  concealed  in  every 
alleged  biological  explanation  of  consciousness.3 

The  world  of  nature  and  experience,  in  so  far  as  it  is  a 

series  of  inter-connected  facts,  presupposes  the  conscious 

and  intelligent  principle  which  is  supposed  to  be  derived 

therefrom ; 4   an  experience   without  a   subject  is   an 

epistemological  absurdity,  just  as  would  be  an  eternal 

system  of  relations  (such  as  the  physicist's  conception 

of  the  world)  without  an  Eternal  Thought  to  impart 

reality  to  that  system.     The  consciousness  of  change 

cannot  be  in  its  turn  a  process  of  change,  since  it  must 

.be  present  at  all  stages  of  that  process  ;  experience 

I  of  a  series  developing  in  time_presupposes  a  conscious^-- 

"principle  external  to  time j^anJtience  not  of  naffiaToHginT 

We  cannot  conceive  of  any  reality  external  to  this/?, 
Eternal  Thought  which  comprehends  within  itself  the° 
whole  system  of  objective  relations  :    the  dualism  of 
Kant,  according  to  which  the  form  of  phenomena,  i.e. 
their  relations,  is  derived  from  the  intellect,  while  matter, 
i.e.  sensations,  takes  its  rise  in  some  mysterious  source^ 
beyond  all  thought,  is  therefore  inadmissible.5     Kant's" 
error  lies  in  assuming  as  a  possibility  the  existence  of 
a  formless  sensation,  not  qualified  by  thought ;  whereas 
every  form  of  experience  implies  at  least  the  distinction 
between  the  actual  fact  and  the  preceding  moment, 
and  hence  an  intellectual  reference.     If  everything  be^ 
eliminated  which  can  be  expressed  in  terms  of  relation^, 
no  reality  will  remain.     If  we  divest  our  knowledge  of  a 
thing  of  every  relation,  that  is  to  say  of  every  thought, 
not  even  simple  consciousness  is  left,  since  consciousness 
cannot  exist  where  change  and  difference  cannot  be 


noted,  and  where  there  is  no  relation  of  sequence  and 
intensity  between  the  sensation  experienced  at  the 
moment  and  those  preceding  it.6  In  the  most  elementary 
act  of  perception  we  establish  a  relation  between  terms 
which  can  only  be  given  in  and  by  virtue  of  relations,  and 
that  which  enters  into  this  conscious  relation  is  not 
sensation  as  such,  but  the  fact  that  the  sensation  is  feU? 
If,  for  instance,  I  recognise  the  action  and  presence  of 
the  fire  in  my  vicinity,  that  which  forms  an  integrant 
part  of  my  knowledge  is  not  the  impression  of  heat,  but 
merely  the  idea  that  I  feel  warm.  This  is  proved 
by  the  fact  that  if  I  go  farther  away  in  order  to  make 
sure  that  the  heat  is  produced  by  the  fire,  the  impression 
of  heat  diminishes  in  intensity,  whereas  the  perception  of 
the  scorching  fire  does  not  become  more  precise  or  undergo 
any  change.  Further,  a  too  intense  sensation  does  not 
act  as  an  aid  to  knowledge,  but  rather  as  an  impediment 
in  its  path,  and,  whilst  the  impression  is  perpetually  sub- 
jected to  a  process  of  transformation,  the  fact  conceived 
of  its  existence  remains  always  the  same.  For  instance, 
the  sensation  of  red  conveyed  by  a  lady's  sunshade  may 
vary  in  intensity,  but  there  is  no  change  in  my  knowledge 
of  the  fact  that  the  sunshade  is  red  in  this  determinate 
way.  Knowledge  in  its  ultimate  analysis  consists  of 
relations,  and  experience,  when  all  is  said  and  done,  is 
but  a  manifold  of  thought  relations.  If  it  be  impossible 
to  derive  thought  from  sensation,  as  the  empiricists  do, 
the  inverse  procedure  is  equally  unjustifiable,  because, 
just  as  there  is  no  such  tiling  as  pure  sensation,  there 
is  no  such  thing  as  pure  tEought :  these~twb  phrases 
merely  stand  for  abstractions  to  which  there  exists  no 
corresponding  reality  either  in  the  facts  of  the  world  or 
in  the  consciousness  to  which  these  facts  stand  in 
relation.8  Sensation  and  thought  do  not  exist  inde- 
pendently of  each  other,  but  are  two  inseparable  aspects 
of  the  same  living  experience.9  By  this  we  do  not 
mean  that  all  sentient  animals  must  also  be  capable  of 
thought :  the  relations  from  which  the  reality  of  their 
sensorial  life  is  derived  do  not  exist  for  their  con- 


sciousness,  but  for  the  Absolute  Thought,  in  which 
the  component  relations  of  phenomena  exist  to  all 
eternity,  even  when  empirical  consciousness  is  not 
aware  of  their  presence.  So  long  as  we  feel  without 
thinking,  the  world  of  phenomena  is  non-existent  for 
its,  yet  we  possess  a  certain  form  of  existence,  since, 
even  if  the  relative  sensations  be  not  real  facts  for  our 
consciousness,  they  yet  exist  in  the  consciousness  of  the 
Absolute.10  The  action  of  the  mind  does  not  consist 
in  abstracting  certain  attributes  from  things  as  presented 
to  us  by  experience,  thus  mutilating  experience  and 
rendering  it  barren;  it  is  rather  thought  itself  which 
constitutes  the  attributes  and  makes  them  into  objects 
by  colligating  them  with  one  another.  Knowledge  does 
not  pass  from  the  concrete  to  the  abstract,  from  rich 
and  full  perception  to  poor  and  empty  conception ;  on  the 
contrary,  it  passes  from  the  universal  to  the  individual 
The  categories  do  not  stand  at  the  end,  but  at  the 
beginning ;  they  are  not  ultimate  truth,  but  rather  that 
which  we  apprehend  in  even  the  simplest  perception ; 
they  are  the  most  universal  and  primitive  of  relations,  by 
means  of  which  we  create  objects  in  order  of  progression, 
determining  them  by  means  of  relations  which  grow 
more  and  more  numerous  and  exact,  until  we  attain 
individual  concrete  ideas  possessed  of  a  greater  wealth 
of  synthetical  relations.  Knowledge  goes  through  two 
phases,  the  one  spontaneous,  the  other  reflective :  in  the 
former  we  pass  from  the  universal  to  the  individual,  and 
interpret  things  according  to  the  laws  governing  our 
mental  activity  without  being  aware  that  we  are  doing 
so ;  in  the  reflex  phase  we  retrace  our  steps  from  the 
concrete  to  the  abstract,  defining  clearly  the  relations 
existing  between  individual  objects ;  these  relations 
are,  of  course,  not  derived  from  experience  as  such,  but 
rather  from  that  which  we  ourselves  have  unwittingly 
introduced  ioto  it  in  the  first  stage  of  knowledge. 
Empiricists  leave  this  second  phase  out  of  their  reckoning, 
and  ignore  the  activity  of  the  mental  principle  in  the 
spontaneous  construction  of  the  world. 


PT.  I 

The  difference  between  conception  and  perception, 
the  imaginary  and  the  real,  the  general  abstract  idea 
and  the  individual  concrete  presentation,  amounts  to 
this :  that  in  the  case  of  perception  we  have,  in 
addition  to  the  conceived  relations  which  constitute  the 
idea  of  the  object,  the  thought  that  this  idea  is  or 
has  been  felt ;  whereas  in  pure  conception  relations  are 
considered  independently  of  the  impressions  which 
they  determine,  i.e.  of  the  fact  that  these  impression 
are  or  are  not  present.  In  the  case  of  the  single  concrete 
idea,  there  is  but  one  actual  or  possible  impression, 
determined  by  a  network  of  relations  which  are  extremely 
numerous,  and  which  have  been  noted  more  or  less 
vaguely  from  the  first ;  whilst  simpler  and  more  genera] 
relations  may  be  equally  well  verified  by  a  large  number 
of  relations  without  determining  any  one  of  them.  A 
perfectly  adequate  conception  of  the  conditions  of  a 
phenomenon  would  therefore  in  no  way  differ  from  its 
reality,  since  it  would  of  necessity  include  amongst  those 
conditions  the  relation  that  the  phenomenon  can  be 
and  is  felt. 

If  objects  exist  only  by  virtue  of  their  relations, 
relations  in  their  turn  are  possessed  of  no  consistency 
apart  from  the  harmonious  system  of  all  relations, 
towards  which  of  its  very  nature  thought  must  tend. 
The  consciousness  of  a  unique  system  of  relations  at 
once  universal  and  coherent  is  the  criterion  of  truth 
and  reality  to  which  we  unconsciously  look  even  in  our 
most  elementary  acts  of  judgment :  a  relation  is  real 
and  true  when  it  is  in  logical  agreement  with  the  whole 
manifold  of  known  and  knowable  relations,  and  is  false 
when  it  contradicts  them.u  Macbeth,  when  he  imagines 
that  he  sees  a  dagger  before  him,  is  deceived  because  he 
has  established  false  relations  between  his  own  actual 
sensations  and  other  sensations,  relations,  that  is  to 
say,  which  are  out  of  harmony  with  the  whole  system 
of  relations  constituting  the  universe.  All  our  researches 
into  the  objective  nature  of  appearances  have  one  and 
the  same  aim — the  discovery  of  an  unchangeable  order 


of  relations,  a  complete  system  having  nothing  external 
to  itself.  The  unity  of  the  system,  i.e.  the  unity  of 
nature,  is  presupposed  in  all  knowledge,  and  is  the  basis 
and  gauge  of  its  certainty.  In  mathematics  this 
certainty  is  undoubtedly  more  stable,  and  rests  upon 
a  surer  foundation,  but  we  are  not  therefore  justified  in 
placing  the  exact,  a  priori,  necessary  science  in  opposi- 
tion to  the  a  posteriori  and  contingent  natural  sciences. 
In  reality,  mathematics,  like  other  sciences,  is  the 
result  of  experience,  in  the  sense  that  it  consists  in 
the  analysis  of  the  unconscious  products  of  primordial 
mental  creation,  and  that  it  rediscovers  in  things 
the  relations  unconsciously  infused  into  them  by 
thought.  Its  one  and  only  claim  to  superiority  lies 
in  the  fact  that  it  is  based  on  the  simple  and 
general  conditions  governing  the  existence  of  natural 
objects,  that  is  to  say,  on  quantitative  and  spatial 
conditions,  of  which  it  is  possible  to  conceive  apart  from 
all  others.  The  natural  sciences,  on  the  other  hand,  are 
not  contingent,  as  is  thought  by  those  who  place  them 
in  opposition  to  mathematics,  since  induction  is  not 
based  on  experience,  analogy,  or  custom  derived  from 
many  repetitions,  which  could  never  be  sufficient 
authority  for  laying  down  a  universal  law.  We  do  not 
pass  from  the  known  to  the  unknown,  since  such  a 
transition  would  be  unintelligible,  nor  from  like  to  like, 
since  we  should  have  no  authority  for  such  a  transition, 
but  from  identical  to  identical.  In  order  to  assert  that 
that  which  has  been  recognised  as  true  in  one  case  holds 
good  of  a  whole  class,  we  must  know  that  all  the  cases 
in  question,  whether  they  have  come  under  observation 
or  not,  are  identical  as  regards  a  certain  aspect,  that  is 
to  say,  as  regards  that  relation  at  all  events  to  which 
the  present  induction  refers. 

The  conditions  of  a  natural  phenomenon  are  extremely 
numerous  and  are  never  repeated,  hence  it  follows  that 
at  times  some  of  them  may  escape  us ;  a  geometrical 
problem,  on  the  other  hand,  depends  only  upon  condi- 
tions with  which  we  are  thoroughly  acquainted,  therefore 



in  the  one  case  we  attain  unconditioned,  in  the  other  con- 
ditioned, truths.  Our  knowledge  of  nature  is  constantly 
being  extended  by  connecting  facts  which  are  increasingly 
coherent  in  their  nature,  and  co-ordinating  relations 
which  tend  to  become  more  and  more  complex,  and 
the  proof  and  criterion  of  the  truth  of  the  simpler 
relations  are  to  be  found  in  the  system  which  harmonises 
them  in  itself.  The  falsity  of  a  theory  can  only  be 
demonstrated  by  proving  it  to  be  inexplicable  ;  that  is  to 
say,  by  showing  that  it  cannot  be  connected  with  other 
groups  of  relations.  The  uniformity  and  unity  of 
nature  become  more  and  more  evident  the  more 
closely  we  enquire  into  it,  but,  on  the  other  hand, 
we  cannot  investigate  it  without  believing  it  to  be 
already  uniform  and  one,  and  without  implicitly 
admitting  that  nature  constitutes  in  itself  a  unique 
system  of  relations  which  condition  each  other  ad 
infinitum,  presuppose  and  imply  one  another  ab  aetemo, 
of  which  individual  objects  are  but  the  ultimate  con- 
sequences and  combinations,  that  is  to  say,  without 
presupposing  that  nature  has  a  significance  present 
in  its  totality  to  Absolute  Thought.12  Our  conscious- 
ness, being  subject  to  the  limitations  of  time,  cannot 
fully  grasp  this  significance  or  identify  itself  entirely 
with  the  Divine  Mind,  but  all  human  knowledge  pre- 
supposes this  significance,  of  which  our  knowledge  is 
the  gradual  revelation  in  time.  In  the  interpretation 
of  the  great  book  of  nature,  in  which  the  Thought  of 
God  is  revealed  to  the  soul  of  man,  the  same  thing 
occurs  which  each  one  of  us  may  observe  when  reading 
a  sentence  or  phrase  ;  single  words  succeed  one  another 
by  means  of  a  process  developing  in  time,  but  the  thought 
that  the  whole  sentence  or  phrase  must  have  a  meaning  ia 
present  with  us  from  the  moment  we  begin  to  read,  and< 
when  we  have  reached  the  end,  this  meaning  is  present 
to  our  consciousness  as  a  simultaneous  whole,  not  as  a 
series  of  successive  elements.13  Thus,  although  the 
psycho-physiological  organism  may  develop  empirically 
in  time,  our  thought  in  the  act  of  grasping  universa 


relations  places  itself  outside  time,  and  shares  in  the 
Absolute  Thought.  That  which  we  term  our  mental 
history  is  not  the  development  of  this  eternal  aspect 
of  consciousness  by  which  we  are  made  one  with 
God,  and  which  is  not  subject  to  development  in  time, 
but  is  rather  a  history  of  the  process  by  which  the 
animal  organism  becomes  the  vehicle  of  this  develop- 
ment. The  empirical  consciousness  in  its  incessant 
evolution  and  its  interruptions  and  disturbances  should 
not  make  us  forget  its  eternal  element,  that  Absolute 
Thought,  which  is  consciousness  of  time,  but  which  is 
not  itself  in  time ;  which  is  consciousness  of  becoming, 
but  escapes  all  change.14 

3.  Criticism  of  Green's  Pan-logism. — Green's  philo- 
sophy with  regard  to  scientific  research  differs  widely 
from  the  empty  dialectic  of  Hegel,  which  alleged 
that  all  the  determinations  of  nature  could  be  con-, 
structed  out  of  nothing  by  means  of  artificial  negations. 
English  Neo-Hegelianism  lays  no  claim  to  the  place  of 
science ;  its  aim  is  rather  to  integrate  the  fragmentary 
results  attained  by  science,  and  to  find  amid  the  isolated 
laws  and  supreme  categories  of  the  real  the  ultimate 
tie  of  necessity  binding  them  together  in  thought.  In 
this  direction  Green's  epistemology  makes  a  notable  step 
in  advance  on  the  logic  of  Hegel,  but  he  does  not  succeed 
in  shaking  off  the  prejudice  of  pan-logism,  and  persists  in 
the  assertion  that  living  concrete  reality  can  be  recon- 
structed by  means  of  a  system  of  abstract  relations. 
There  is  something  in  the  psychic  jacjb  jts  immediately^ 
experienced  which  no  effort  of  (dialectic'  can  ever  identify]' 
with  a  system  of  conceptual  relations ;  sensations,  *f 
feelings,  passions,  impulses,  volitions  as  they  are  given 
in  the  concreteness  of  the  human  personality,  are 
possessed  of  an  individual  aspect  which  cannot  be  fore- 
seen, and  which,  as  we  shall  see,  plays  into  the  hands 
of  the  opponents  of  intellectualism.  Green  asserts  that 
there  is  no  difference  between  conceiving  and  feeling, 
that  it  will  suffice  to  add  to  the  idea  of  horse,  for  instance, 
the  relation  of  being  felt,  for  the  concept  of  horse  to  be 


transformed  into  the  perception  thereof ;  it  is,  however, 
one  thing  to  think  of  feeling  and  another  actually  to 

Green,  however,  passes  with  the  greatest  ease  from 
the  concept  of  the  sensation  to  the  sensation  itself, 
without  perceiving  that  between  the  two  there  is  an 
impassable  gulf  fixed.  We  may  think  that  all  the  con- 
ditions necessary  to  the  verification  of  a  sensation  have 
been  fulfilled,  but  this  will  not  make  us  feel.  If  it 
were  so,  the  blind  could  restore  their  own  sight  by 
studying  a  treatise  on  optics  !  Nor  can  the  sophistical 
argument  be  adduced  that  one  of  the  essential  con- 
ditions is  lacking,  namely,  the  normal  structure  of  the 
eye,  since,  according  to  Green,  the  complete  concept 
of  this  structure  should  suffice  to  transform  the  idea 
into  a  real  fact.  The  intuitionists  cannot  succeed  in 
accounting  for  the  constant  and  universal  in  reality ; 
Green  goes  to  the  opposite  extreme,  and  places  himself 
in  a  position  which  prevents  his  understanding  that 
which  is  individual,  concrete,  and  changeable  in  the 
history  of  the  world.  From  his  point  of  view,  indeed, 
••there  is  no  such  thing  as  time,  there  exists  merely  the 
concept  of  time,  which  is  something  external  to  time ; 
there  is  no  such  thing  as  change,  but  only  the  idea  of 
change,  which  is  external  to  it ;  there  is  no  such  thing  as 
an  individual,  but  only  the  concept  of  one  which  by  its 
very  nature  must  of  necessity  be  universal.  If  reality 
then  be  a  network  of  eternal  relations,  present  in  their 
totality  to  the  Absolute  Consciousness  ;  if  even  a  human 
person  be  but  a  fragmentary  group  of  those  relations, 
does  it  not  become  impossible  to  explain  the  evolutionary 
motion  of  things,  their  incessant  transformation,  and 
everything  which  is  most  spontaneous,  living,  and  fruitful 
in  the  concrete  development  of  our  inner  hfe  ?  In  the 
eternal  immobility  of  the  idea,  time  with  its  efficacious 
rhythm,  and  the  world  as  a  whole,  become,  to  quotej 
Bradley,  merely  an  illusory  appearance.  But  is  not 
the  birth  of  this  illusion  too  an  inexplicable  mystery, 
if  human  consciousness  be  a  web  of  unchangeable 


relations  ?  How  did  it  issue  from  the  eternity  of  thought 
in  order  to  project  itself  into  time  ?  Moreover,  if  the 
Absolute  live  in  it,  must  not  its  every  idea  perforce 
be  true  ?  In  Green's  philosophy  there  is  no  room  for 
error  and  illusion,  which  can  only  be  understood  if  we 
admit  a  certain  degree  of  independence  and  spontaneity 
in  the  individual  subject  as  against  Absolute  Conscious- 
ness. We  can  form  no  conception  of  objective  reality  as 
a  system  of  relations,  complete,  fixed,  and  unchangeable 
from  all  eternity,  since  every  new  form  which  makes 
its  appearance,  every  individual  in  his  concrete  physiog- 
nomy, becomes  the  centre  in  cosmic  evolution  of  a  fresh 
network  of  countless  relations  which  tend  to  become 
more  widely  extended,  more  interwoven,  and  more  com- 
plicated in  successive  moments.  The  reduction  of  the 
Absolute  to  the  eternal  contemplation  of  ideas  eternally 
present  to  its  consciousness  amounts  to  the  same 
thing  as  turning  it  into  a  caput  mortuum,  like  the 
impassive  deities  of  Epicurus  in  their  blissful  ease.  We 
^cannot  conceive  of  a  consciousness  which  is  not  lifeT 
..development,  perennial  creation,  and  fruitful  activity, 
jDLor  of  a  thought  which  cannot  be  enriched  by  new 
relations,  whilst  preserving  the  coherency  and  identity 
of  its  fundamental  laws  ;  nor  of  any  form  of  spirituality 
without  qualitative  development,  or  which  is  not 
manifested  in  original  actions  which  cannot  be  foreseen.] 
Pan-logism  aims  at  the  absorption  of  everything  into 
ji  system  of  eternal  relations,  and  must  therefore 
inevitably  end  in  denying  the  reality  of  that  which 
is  most  vital  and  most  concrete  in  the  world  of  con-} 
sciousness.  If  its  premisses  be  granted,  Bradley's  philo- 
Isbphy  is-the  necessary  conclusion. 

4.  The  Iteductio  ad  Absurdum  of  Pan-Logism  in 
Bradley's  Philosophy.  —  Bradley15  maintains  that  the 
world,  as  given  to  us  by  experience  and  as  con- 
structed by  science  in  its  concepts,  is  but  an  illusory 
appearance  of  a  deeper  reality  of  which  philosophy 
should  strive  to  sound  the  depths  by  speculative  methods, 
after  having  exposed  the  contradictions  latent  in  the 


world  of  appearances.  The  concepts  of  which  physical 
science  makes  use  lend  themselves  perfectly  to  the 
determination  of  limited  phenomena,  but  lead  to  con- 
tradictions when  we  attempt  to  use  them  to  express 
the  true  essence  of  reality  ;  they  are  relative  concepts, 
characterising  things  in  relation  to  and  in  comparison 
with  other  things,  but  they  can  tell  us  nothing  of  the 
terms  of  those  relations ;  they  are  working  ideas,  which 
are  of  no  theoretical  importance,  but  have  only  the 
value  of  useful  fictions,  practical  compromises.16  Bradley 
starts  from  the  principle  of  contradiction,17  which  he 
regards  as  the  supreme  criterion  of  every  reality,  and, 
acting  on  the  strength  of  this,  the  one  and  only  article  of 
his  logical  code,  considers  himself  entitled  to  administer 
summary  justice  to  all  scientific  concepts  and  intellectual 
categories  —  substance,  quality,  relation,  space,  time, 
movement,  change,  causality,  force,  activity  —  which 
from  his  point  of  view  imply  contradictions  and  hence 
cannot  correspond  to  anything  real.  Let  us,  for  example, 
consider  the  relation  between  the  thing  and  its  prop- 
erties :  its  substance  is  not  identical  with  any  one  of 
them ;  what  is  it  then  ?  Merely  a  link  connecting  its 
qualities ;  but  what  do  we  mean  by  the  assertion  that 
one  quality  is  related  to  another  ?  Neither  of  them 
is  identical  with  the  other  or  with  the  relation  to  the 
other  ;  thus  the  number  of  contradictions  is  augmented 
rather  than  diminished.  Quality  does  not  exist  apart 
from  relations,  but  relation  in  its  turn  is  not  conceiv- 
able except  as  existing  between  qualitative  terms : 
on  the  one  hand,  it  would  appear  that  quality  is  the 
result  of  relations,  since  qualitative  difference  cannot 
exist  apart  from  a  process  of  distinction  ;  on  the  other, 
it  would  appear  that  relations  in  their  ultimate  analysis 
are  forms  of  quality.  Nor  is  it  of  any  avail  to  draw 
a  distinction  between  two  elements  in  a  quality,  one 
pre- existent  to  the  relation,  and  rendering  that 
relation  possible ;  the  other  resulting  from  the  relation 
itself ;  since  we  should  have  to  explain  the  '  mutual 
relation  of  these  two  elements,  both  belonging  to  one 


and  the  same  thing ;  we  are,  that  is  to  say,  confronted 
with  the  problem  of  a  new  relation  no  less  inexplicable 
than  the  first,  and  so  on  ad  infinitum.  The  relation 
cannot  be  identified  with  the  things  related,  and,  taken 
by  itself,  is  nothing.18  .  No  less  contradictory  are 
space,19  time,20  movement,21  activity,22  causality,23  etc., 
because  when  these  concepts  are  resolved  into  various 
combinations  of  qualities  and  relations,  the  difficulties 
set  forth  above  will  arise  afresh.  The  fundamental  con- 
cepts of  the  special  sciences  are  then  mere  appearances 
due  to  faulty  perspective,  which  must  be  eliminated 
by  rising  to  a  higher  experience  embracing  all  possible 
appearances  transfigured  to  a  greater  or  less  degree 
in  an  integral  harmonious  system;  these  illusions, 
however,  are  possessed  of  a  certain  degree  of  reality  ; 
there  is  no  such  thing  as  a  truth  which  is  entirely  true, 
just  as  there  is  no  such  thing  as  an  error  which  is  entirely 
false  ;  we  can  only  speak  of  a  greater  or  lesser  degree 
of  truth  ;  error  is  partial  truth,  it  is  false  only  because  it 
is  one-sided  and  incomplete.  All  appearances  are  real  in 
some  way  or  other,  and  to  some  extent,  and  the  right 
modifications  and  transformations  (supplementation  and 
arrangement,  addition,  qualification)  may  bring  them  too 
into  the  system  of  the  Absolute.24  In  like  manner 
every  finite  truth,  like  every  fact,  must  be  to  a  certain 
extent  unreal  and  false,  and  the  unlimited  nature  of 
the  unknown  renders  it  impossible  to  determine  with 
certainty  in  the  last  analysis  the  proportion  of  error 
contained  therein.  If  our  knowledge  were  a  system, 
we  could  determine  the  position  of  each  thing  in  the 
whole,  and  gauge  accurately  the  proportion  of  truth  and 
error  contained  therein,  but  the  nature  of  our  knowledge 
renders  such  a  system  out  of  the  question.25  Thought 
originates  in  the  separation  of  the  what,  the  ideal 
meaning,  the  predicate,  from  the  that,  immediately 
felt  existence,  the  subject ;  error,  falseness,  lies  in 
uniting  a  what  and  a  that  which  do  not  corre- 
spond to  each  other.  In  the  harmony  of  the  whole, 
each  what  will  find  its  proper  that,  and  every  illusion 


will  consequently  vanish ;  the  ideal  will  coincide 
with  the  existent,  the  intelligible  with  the  thing  given. 
This  is  impossible  to  our  finite  consciousness,  which 
develops  in  time  and  has  its  being  in  the  world  of 
appearances  derived  from  the  separation  of  idea 
from  fact;  notwithstanding  this,  we  can  approximate 
in  some  fashion,  and  with  varying  degrees  of  success, 
to  the  total  harmonic  system  by  striving  to  eliminate 
the  contradictory  element  in  phenomena,  and  to  render 
our  thought  more  coherent  and  more  complete.26  The 
ideal  at  which  knowledge  aims  is  the  re-union  of  idea 
and  fact — an  ideal  which  it  can  never  fully  realise  ;  thus 
its  efforts  in  this  direction  imply  a  latent  contradiction, 
since,  on  the  one  hand,  knowledge  is  only  possible  in 
virtue  of  the  distinction  between  the  what  and  the 
that,  the  predicate  and  its  subject,  which  are  elements 
indispensable  to  the  judicial  function  ;  whilst  on  the 
other,  its  development  and  perfecting  should  lead  to  the 
elimination  of  this  distinction.  There  can  be  no  clear 
and  full  understanding  of  truth  with  this  distinction 
between  data  and  their  ideal  significance  ;  the  moment 
this  difference  vanishes,  truth  ceases  to  exist  and 
knowledge  gives  place  to  the  true  and  real  life  of  the 
Absolute.27  Truth  and  knowledge  are  then  but  illusory 
appearances,  like  everything  else  which  implies  the 
separation  of  idea  from  fact,  and  they  tend  to  transcend 
the  bounds  of  intellect,  and  to  become  fused  in  a  form 
of  intuition  and  universal  life  of  which  we  can  hardly  form 
an  abstract  idea,  an  immediate  concrete  experience,  in 
which  all  the  elements — sensation,  emotion,  thought, 
and  will — are  fused  into  one  comprehensive  feeling.28 
Finite  beings  cannot  enter  into  the  fulness  of  the  life 
of  the  Absolute,  or  have  specific  experience  of  its  con- 
stitution, but  human  consciousness  can  form  a  certain 
idea  of  it  by  retracing  its  steps  to  that  primitive 
and  diffused  feeling  to  which  the  distinction  between 
subject  and  object,  and  the  differentiation  of  elements 
was  as  yet  unknown.  This  intuition,  which  must 
embrace  and  harmonise  the  various  phenomenal  aspects 


of  consciousness,  will,  intellect,  imagination,  which, 
considered  separately  and  postulated  as  absolutes,  give 
rise  to  contradictions,  although  it  possesses  the  immediacy 
of  feeling,  is  nevertheless  not  subject  to  the  limitations 
of  every  kind  of  distinction  and  relation  as  feeling  is, 
but  transcends  all  distinctions  and  relations,  and  there- 
fore contains  them  in  a  higher  unity  within  itself.29 
It  is  a  form  of  psychic  or  spiritual  experience  (sentient 
experience)  ^  because  there  can  be  no  reality  external 
to  the  mind,  and  the  truth  of  a  thing  is  in  proportion 
to  its  spirituality ; 31  but  the  modes  of  conscious  experi- 
ence are  too  one-sided  for  any  one  of  them  to  give  us 
the  immediate  intuition  thereof,  hence  we  must  rest 
content  with  forming  an  abstract  conception  of  it  by, 
so  to  speak,  "  passing  to  the  limit "  of  the  various 

5.  Criticism  of  Bradley' s  Dialectic.  —  Pan  -  logism 
thus  ends  in  an  act  of  apostasy,  and  its  dialectic  leads 
to  its  own  annihilation  in  a  form  of  mystical  intuitionism, 
whose  static  and  contemplative  character  distinguishes 
it  from  that  of  Bergson.32  It  is  the  conception  of  the  one 
unchangeable  and  eternal  being  of  the  ancient  Eleatic 
philosophers,  as  opposed  to  the  perennial  flux  of  Hera- 
clitus,  and  the  inevitable  end  of  those  who  give  them- 
selves over  to  the  hollow  dialectic  of  reason  divorced  from 
its  vital  content  and  articulated  in  rigorously  identical 
formulas.  What  then  is  left  of  reality  ?  A  principle 
devoid  of  life  and  motion,  something  which  has  not  even 
the  logical  coherence  of  our  thought,  since  this  thought 
is  only  valuable  and  important  in  so  far  as  it  opposes 
itself  to  the  fluctuations  of  experience  and  assures  the 
stability  of  concepts  amid  the  manifold  changes  of  images. 
Removed  from  this  environment,  its  function  ceases  to 
be  possible,  and  thought  itself  is  arrested  and  vanishes 
into  nothingness.  The  law  of  identity,  if  it  is  to  be  of 
any  efficacy  and  value,  must  be  applicable  to  a  multi- 
plicity in  which  the  movement  of  thought  is  developed  ; 
if  it  be  divested  of  such  a  content,  it  ceases  to  be 
conceivable.  The  Absolute,  as  a  mere  identity  of 


permanence,  is  something  the  reality  of  whose  existence 
is  beyond  our  power  of  thought.  Moreover,  even  if 
we  admit  that  it  is  possible  to  think  of  it  as  a  limited 
concept,  it  will  still  be  incomprehensible  how  such 
perfect  identity  can  give  birth  to  the  illusion  of 
multiplicity,  or  an  inviolable  law  of  permanence  to  the 
phantasmagoria  of  a  world  in  process  of  evolution. 

It  is  useless  to  say  that  change  is  illusory,  since 
we  still  have  to  explain  how  the  illusion  arises,  because, 
even  if  it  be  nothing  else,  it  is  a  psychical  fact  which  we 
experience  directly,  and  whose  existence  is  consequently 
undeniable.  Our  thought  refuses  to  admit  that  if  the 
law  of  things  is  a  perfect  identity  the  manifold  content 
of  consciousness  with  its  unceasing  transformations 
can  be  derived  therefrom  without  the  imperturbable 
inflexibility  of  being  undergoing  any  change.  Either  it 
is  unrelated  to  phenomenal  occurrences  and  abstract, 
lifeless  unity  remains  immovable  to  all  eternity  in  its 
ataraxy,  in  which  case  it  is  a  caput  mortuum  with  which 
the  world  of  phenomena  can  readily  dispense  ;  or  it 
must  be  the  adequate  reason  of  the  constant  renewal 
of  consciousness  and  experience,  in  which  case  it  cannot 
preserve  its  fixity  of  quietism.  But,  Bradley  would 
urge,  even  the  change  of  finite  consciousness  in 
time  is  illusory  in  so  far  as  it  assumes  the  separation 
of  fact  from  idea,  the  that  from  the  what.  What 
authority  have  we,  then,  for  forming  such  an  opinion 
of  it  ?  The  principle  of  contradiction  is  only  of  value 
as  the  law  governing  the  judgment,  and  implies  the 
distinction  between  two  concepts  standing  in  a  definite 
relation  to  each  other,  that  is  to  say,  they  must  be 
such  that  one  excludes  the  other  ;  now,  according  to 
Bradley,  judgment  and  the  distinction  between  con- 
ceptual terms  are  appearances  relative  to  our  finite 
point  of  view  ;  Jience^  eyen^  the_prmciple  of^gntradiction 
cjinjbejmt^ji  law  ofjippearances,  an  illusory  law  ;  JIQW 
.can  it7then,1t)e  set  ujTasa^ criterion  of  absolute  reality  ? 
Who  can  guarantee  that  this  law  is  applicable  to  absolute 
reality,  and  is  not  rather  an  error  of  perspective  like 


the  rest  ?  May  not  Hegel  be  right  in  assigning  to 
contradiction  a  place  in  the  very  heart  of  the  idea,  and 
in  looking  upon  it  as  the  germ  from  which  its  develop- 
ment springs  ?  When  we  assert  with  Bradley  that"? 
finite  thought  is  an  appearance,  we  can  no  longer  con-  J 
sistently  regard  the  principle  of  contradiction  as  an/ 
absolute  criterion  any  more  than  any  other  logical  axiom.] 
If  logical  principles  be  set  up  as  judges  of  reality, 
we  grant  by  implication  the  value  of  finite  thought, 
judgment,  and  human  reason.  On  the  other  hand,  if 
the  unconditioned  value  of  the  axioms  be  granted,  it 
is  not  a  necessary  inference,  as  Bradley,  following  in  the 
footsteps  of  Herbart  and  the  ancient  Eleatics,  would 
have  us  believe,  that  movement  and  change  are  illusory, 
because  they  contradict  the  laws  governing  our  thoughts. 
Multiplicity  and  transformation,  as  we  receive  them 
directly  from  intuition,  are  not  contradictory  in  them- 
selves, the  contradiction  exists  only  between  our  one- 
sided concepts.  We  may  resolve  movement  as  pre- 
sented to  us  by  intuition  into  abstract  elements,  but 
in  that  case  we  must  bear  in  mind  that  each  one  of  these 
elements  is  but  a  partial  view,  a  limit  which  we  our- 
selves have  laid  down  in  order  to  facilitate  analysis 
and  research,  and  which  does  not  correspond  to  any 
real  division.  Thus,  on  the  one  hand,  if  we  isolate 
certain  persistent  and  uniform  elements  from  the  process 
of  change  which  we  apprehend  by  means  of  immediate 
intuition,  we  may  state  that  body  remains  unchanged  ; 
if,"  on  the  other  hand,  we  look  at  it  from  another 
point  of  view,  and  introduce  only  varying  elements 
into  the  idea,  regarded  in  abstraction  from  the  complex 
of  intuitive  data,  we  should  be  led  to  a  diametrically 
opposite  conclusion.  Who,  however,  can  fail  to  see 
that  the  opposition  in  such  a  case  is  the  artificial  creation 
of  our  partial  view  ?  Change  is  in  no  way  contradictory 
to  the  principles  of  human  intellect ;  it  is  true  that  the 
birth  of  the  new  amid  the  unceasing  flux  of  experience 
eludes  the  grasp  of  our  abstract  concepts,  which  are 
constrained  to  sacrifice  the  wealth  of  mind  and  nature 


on  the  altar  of  their  universality  and  identity,  but  even 
if  concrete  becoming  cannot  be  adequately  transcribed 
into  terms  of  abstract  thought,  it  does  not  follow 
that  it  is  illogical.  The  contradiction  vanishes  when 
we  substitute  intuited  reality  in  its  fulness  for  incomplete 
abstract  terms.  In  like  manner  will  vanish  the  other 
alleged  contradictions  seen  by  Bradley  in  the  exercise 
of  thought ;  if  thought  appear  to  be  overwhelmed  by  a 
flood  of  absurdities,  it  is  because  its  supreme  categories 
have  been  divested  of  all  intuitive  content,  and  are 
then  supposed  to  fulfil  their  functions  in  the  resulting 
void.  The  activity  of  judgment  may  be  explained 
by  establishing  relations  between  terms  which  are  not 
wholly  the  creation  of  thought,  as  is  asserted  by  Green, 
but  always  have  their  source  in  intuitive  data  ;  there 
must  necessarily  be  a  limit  to  the  resolution  of  terms 
into  relations,  since  there  is  always  something  left  which 
cannot  be  translated  into  relations.  Thus,  to  use 
Bradley's  illustration,33  there  is  nothing  contradictory 
in  the  relation  between  the  two  properties  of  whiteness 
and  sweetness  in  sugar,  since  the  two  terms  do  not  exist 
merely  by  virtue  of  the  relation  which  we  set  up  between 
them,  but  exist  also  in  as  much  as  they  are  immediately 
felt.  Their  relation  is  rendered  sufficiently  consistent 
by  the  unity  of  the  subject,  even  though  it  be  impossible 
to  identify  it  with  either  of  the  two  terms.  The  absurdity 
arises  only  when  the  relation  is  separated  from  the 
subject,  and  considered  as  an  entity  in  itself,  a  thing. 
In  like  manner  the  necessary  basis  of  the  relations  of 
succession  implied  in  the  concepts  of  cause,  action, 
force,  energy,  etc.,  will  be  found  in  the  continuity  of  the 
epistemological  subject,  hence  it  is  not  surprising  that 
they  should  give  rise  to  contradictions  if  we  isolate  them 
from  that  subject.  Nothing  but  the  continuous  presence 
of  the  subject  can  bridge  over  the  gulf  between  one  term 
and  another,  and  enable  the  intellect  to  grasp  the  relation 
between  an  antecedent  which  has  ceased  to  exist  and 
a  certain  consequence  which  has  not  yet  come  into 
existence.  Duration,  extension,  action,  and  change 


only  become  contradictory  when  looked  upon  apart 
from  the  living  continuity  of  consciousness,  and,  even 
though  we  cannot  succeed  in  re -constructing  them 
analytically  in  their  concreteness  by  means  of  pure 
acts  of  thought  without  being  confronted  by  in- 
surmountable difficulties,  it  does  not  follow  that  either 
they  or  thought  are  empty  appearances,  but  only  that 
logical  relations  do  not  exhaust  the  whole  of  reality  in 
every  concrete  moment  of  consciousness,  and  that  there 
exists  an  individual  physiognomy  of  the  world  which 
cannot  be  reduced  to  mere  systems  of  relations. 

6.  Mystical  Degeneration  of  English  Neo-Hegelianism : 
McTaggart. — English  Neo-Hegelianism,  after  striving 
in  vain  in  the  teaching  of  Green  to  dispose  of  the  agnostic 
position  of  intellectualism  by  absorbing  into  an  eternal 
system  of  relations  those  irreducible  elements  which  are 
ignored  by  scientific  knowledge,  degenerates  with  Bradley 
into  a  form  of  scepticism  and  intuitionism.  The  mystical 
degeneration  of  Hegelianism  is  still  more  marked  in 
McTaggart,  who  no  longer  regards  dialectic  as  the  very 
life  of  the  Absolute,  as  did  Hegel,  but  considers  it  to  be 
merely  a  subjective  means  for  the  re-construction  of 
the  eternally  perfect  system  of  individual  minds,  whose 
harmonious  synthesis  gives  birth  to  the  Absolute,  by 
disposing  of  the  abstract  appearances  of  the  reality 
which  develops  in  time. 

This  ultimate  synthesis  of  reality  cannot  be  attained 
by  discursive  thought,  which  is  unable  to  reconcile 
perfect  and  imperfect,  temporal  and  eternal,  the  Ego  and 
the  non-Ego,  experienced  immediacy  and  mediate  or 
rational  knowledge,  but  can  be  reached  only  in  the 
state  of  love  in  which  other  beings  lose  their  exteriority 
and  appear  to  us  in  the  very  form  of  our  Ego.™ 
English  Neo-Hegelianism  thus  ranks  sentiment  above 
reason,  and  aims  at  the  pole  of  convergence  of 
contemporary  philosophy,  the  denial  of  the  cognitive 
value  of  intelligence,  and  the  search  for  some  more 
direct  means  of  penetration  into  reality.  Thus  the 
many  and  various  currents  of  thought  which  spring 


from  the  irresistible  longing  to  burst  the  bonds  of 
agnosticism  which  stifle  the  most  living  aspirations 
of  the  soul,  mingle  their  waters  in  the  wild,  rushing 
torrent  of  the  reaction  from  intellectualism. 


I  Green  published  nothing  in  his  life-time  but  articles  in  reviews  and 
an  Introduction  to  the  works  of  Hume  (1874-75).     After  his  death  his 
Prolegomena  to  Ethics  was  edited  by  A.  C.  Bradley  and  published  in  1883, 
and  his  complete  works  were  collected  and  published  in  three  volumes  by 
Nettleship  (Longmans,  Green  &  Co.,  London,  1885). 

*  Hume,  A  Treatise  on  Human  Nature,  edited  by  T.  H.  Green  and 
T.  H.  Grose  (new  edition,  London,  1878).     The  "  Introduction  "  prefixed 
by  Green  to  voL  i.  is  a  criticism  of  the  philosophy  of  Locke  (pp.  5-132), 
Berkeley  (pp.  133-151),  and  Hume  (p.  161  to  end). 

*  "  Mr.  Herbert  Spencer  and  Mr.  G.  H.  Lewes :   Their  Application  of 
the  Doctrine  of  Evolution  to  Thought,"  Contemporary  Review,  1877-78, 
voL  xxx.  pp.  25-53,  745-69 ;  voL  xxxii.  pp.  751-772. 

'  "  .  .  .  Experience  in  the  sense  of  a  consciousness  of  events  as  a 
related  series  .  .  .  cannot  be  explained  by  any  natural  history,  properly 
so  called.  It  is  not  the  product  of  a  series  of  events  "  (Prolegomena  to 
Ethics,  Oxford,  1899,  4th  ed.,  p.  25.  See  also  his  introduction  to  Hume, 
p.  164  ff.). 

8  Prolegomena  to  Ethics,  p.  45. 

*  Op.  cit.  p.  54  ff. 

7  Op.  cit.  p.  75  ff. 

8  "  We  admit  that  mere  thought  can  no  more  produce  the  facts  of 
feeling  than  mere  feeling  can  generate  thought  "  (op.  cit.  p.  60). 

*  Op.  cit.  p.  58. 

10  Op.  cit.  p.  57. 
"  Op.  cit.  p.  18  ff. 

11  Prolegomena  to  Ethics,  p.  34,  p.  62  ff. 
"  Op.  cit.  p.  85  ff. 

"  Op.  cit.  p.  80  ff. 

16  Principles  of  Logic  (London,  1883) ;  Appearance  and  Reality  (London, 

w  Appearance  and  Reality,  p.  284. 

17  "  Ultimate  reality  is  such  that  it  does  not  contradict  itself  :   here  is 
absolute  criterion  "  (op.  cit.  p.  136  ff.). 

18  Op.  cit.  p.  20  ff. 

19  Op.  cit.  p.  35  ff. 
10  Op.  cit.  p.  39  ff. 

II  Op.  cit.  p.  44  ff. 
"  Op.  cit.  p.  62  ff. 
M  Op.  cit.  p.  54  ff. 

14  "  Error  is  truth,  it  is  partial  truth  that  is  false  only  because  partial 
and  left  incomplete  "(op.  cit.  p.  192).  "  Error  is  truth  when  it  is  supple- 
mented "  (op.  cit.  p.  195). 

"  Op.  cit.  p.  54. 

*  Op.  cit.  p.  364  ff.    According  to  Bradley,  the  appearance  which 


most  nearly  approximates  to  reality  and  is  possessed  of  the  greatest 
proportion  of  truth  is  the  one  which   demands  the  least  addition  and 
rearrangement  for  its  conversion  into  the  Absolute. 
17  Op.  cit.  pp.  163  ff.,  361,  545  ff. 

28  Op.  cit.  p.  227.     "  For  our  Absolute  was  not  a  mere  intellectual 
system.     It  was  an  experience  overriding  every  species  of  one-sidedness, 
and  it  was  a  living  intuition,  an  immediate  individuality. 

29  Op.  cit.  p.  242. 
8»  Op.  cit.  p.  144. 

31  Op.  cit.  p.  551. 

32  F.  C.  S.  Schiller  in  an  article  entitled :    "  Mysticism  versus  Intel- 
lectualism,"  published  in  Mind  (January  1913,  p.  87),  protests  against  my 
interpretation  of  Bradley' s  philosophy.     He  is  under  the  impression  that 
I  intended  to  say  that  Bradley  wilfully  and  deliberately  reduced  English 
Neo-Hegelianism  ad  dbsurdum ;  it  is,  however,  obvious  that  I  merely 
assert    that    Bradley's  dialectic    unconsciously   reduces    pan-logism    ad 
absurdum,  and  on  this  point  Schiller  and  I  are  really  agreed. 

33  Appearance  and  Reality,  p.  20. 

34  Studies  in  Hegelian   Cosmology  (Cambridge,   1901),   pp.    270-292; 
Studies  in  Hegelian  Dialectic  (Cambridge,  1896),  pp.  214-276. 





1.  The  Aesthetic  and  Moral  Conception  of  the  Universe  : 
Secretan,  Ravaisson. — Modern  French  philosophy  results  ^ 
from  the  confluence  of  two  great  currents  of  thought :  ; 
the  philosophy  of  liberty,  of  which  Kant's  doctrine 
of  the  primacy  of  pure  reason  is  the  source,  which 
vindicates  the  rights  of  will  and  feeling  against  the 
claims  of  the  intellect ;  and  the  work  of  critical  revision 
of  science,  of  which  Mach  was  the  pioneer.  ItTderives 
its  moral  and  aesthetic  conception  of  the  universe  from 
the  philosophy  of  liberty  as  developed  by  Secretan  and 
Ravaisson,  and  its  arguments  against  the  necessity  of 
law  from  the  new  criticism  of  science,  thus  striving  to 
eliminate  the  antitheses  existing  between  the  intelligence 
and  free  will.  It  holds,  as  does  Secretan,  that  the 
essence  of  the  world  is  an  act  of  unfettered  expansion, 
an  act  of  love  and  infinite  benevolence  ;  hence^  the_real 
tool  of  philosophy  is,  as  Ravaisson  clearly  saw,  artistic  x 
inspiration  and  feeling  for  religion,  not  definition  and 
scientific  analyses ; 1  it  is  intuition  which  enables  us  to 
grasp  the  active  substance  of  the  Ego,  and  affords 
the  irresistible  evidence  of  feeling,  evidence  above  all 
argument  and  all  calculation.  This  sense  of  indefinite 
effusion,  to  which  French  philosophers  of  the  new  school 
look  for  the  revelation  of  the  Absolute,  is  neither  Kant's 
Good  Will  nor  yet  the  free  affirmation  of  the  Ego, 
governed  by  the  imperious  law  of  duty  inherent  in 
its  very  nature,  as  conceived  of  by  Fichte,  but  rather 



that  feeling  of  untrammelled  expansion  and  abandon- 
ment proper  to  creation  and  aesthetic  contemplation.! 
"  Beauty,"  as  Ravaisson  had  already  said,2  "  and  morej 
especially  beauty  in  its  most  divine  and  perfect  form, 
contains  the  secret  of  the  world."     The  cosmic  process 
is  not  a  mechanism  of  necessary  and  eternal  movements, 
circumscribed  within  the  inflexible  limits  of  a  system  oi 
mathematical  formulae,  as  intellect,  guided  by  science^ 
had  imagined  it  to  be  ;  it  is  rather  the  perennial  creatiori 
of  a  marvellous  work  of  art,  which  from  the  rude  out-l 
lines  of  the  inorganic  world  has  gradually  evolved  intc 
the  higher  forms  of  spiritual  life.     T^_sj^ni|Lc.ajQce.  oj 
cosmic  evolution  lies  not  in  that  to  which  natural  beings 
have  already  attained,  but  in  their  higher  aspiration* 
and  in  the  ideal  towards  which  they  more  or  less  con 
sciously  tend.     True   reality  is   not  the   necessity   o 
phenomena,  as  Kant  imagined  in  his  Kritik  der  reinet 
Vernunfi,  but  the  world  as  seen  in  the  light  shed  upoi 
*    it  by  the  idea  of  beauty  and  liberty,  as  he  beheld  it  ii 
his  Kritik  der  Urteilskraft. 

2.  fimile  Boutroux  and  the  Contingency  of  Natypei 
Laws. — This  concept  of  the  moral  and  aesthetic  finalit; 
of  the  universe  is  the  dominant  feature  of  the  systen 
of  philosophy  set  forth  by  Boutroux,  in  which  the  tw< 
currents  of  which  we  have  already  spoken  meet  fo 
the  first  time.  According  to  Boutroux,  the  suprem 
principles  of  things  are  moral  and  aesthetic  laws  regulat 
ing  the  spontaneous  activity  of  beings  in  their  ascen 
to  God.  Natural  laws  are  in  themselves  in  no  wa; 
absolute  or  eternal,  they  are  merely  the  expression  of  : 
transitory  phase  which  may  be  superseded  or  left  behind 
they  are  but  habits  formed  by  the  creature  whict 
instead  of  going  forward,  rests  content  with  form 
already  realised  and  tends  to  persist  in  those  forms, 
in  which  it  recognises  the  imprint  of  the  ideal.3  Wlie 
the  Good  and  the  Beautiful  are  completely  triumphant 
these  artificially  acquired  fixed  images  of  an  essentiall 
living  and  flexible  model  will  vanish,  and  necessary  la' 
will  give  place  to  the  spontaneous  effort  of  the  will  t. 


attain  perfection  and  the  free  hierarchy  of  minds.  The 
inner  heart  of  things  is  manifested  in  the  concrete  work 
of  imagination  and  in  the  spontaneity  of  will,  not  in 
the  empty,  stereotyped  forms  of  the  intellect.  When 
we  try  to  confine  them  within  the  bonds  of  abstract 
formulae  of  permanency,  that  which  is  most  real  in 
them  —  qualitative  multiplicity  in  the  inexhaustible 
wealth  of  its  creations — eludes  our  grasp.  Science  then 
increases  rather  than  diminishes  the  distance  between 
ourselves  and  the  inmost  nature  of  reality.  How  and 
why,  then,  have  the  constructions  of  science  ^ma  j™tn 
beingJ.  Boutroux  maintains  that  all  the  labour  of  science 
is  but  an  attempt  to  adjust  things  to  the  law  of  identity 
of  thought,  and  to  make  them  carry  out  our  will  more 
readily.4  "*  We  see  the  beginning  of  this  work  of  adjust- 
ment in  the  realm  of  logic  itself  ;  concept,  judgment, 
syllogism  all  contain  something  more  than  mere  logical 
principles,  i.e.  the  multiple  as  contained  in  the  one,  the 
relation  between  the  explicit  and  the  implicit,  so  that, 
while  they  are  not  exactly  a  priori,  neither  are  they 
a  posteriori  :  the  mind  of  man  contains  within  itself 
the  laws  of  pure  logic  ;  but,  since  the  matter  presented 
to  its  notice  does  not  appear  to  it  to  be  strictly  in  con- 
formity with  these  principles,  it  endeavours  to  adapt 
logic  to  things,  and  devises  a  complex  of  proceedings 
and  symbols  designed  to  make  reality  easier  of  appre- 
hension.5 The  laws  of  pure  logic  are  necessary,  and 
there  can  be  no  doubt  as  to  their  objective  validity ; 
but  their  weakness  lies  in  the  very  thing  which  con- 
stitutes their  strength,  since  they  fail  to  determine  the' 
nature  of  the  things  to  which  they  apply.  The  art  of 
syllogism  in  its  turn,  being  a  product  of  the  mind,  affords 
in  itself  no  guarantee  of  objective  validity,  but  the  fact 
that  our  reasoning  attains  its  end  is  a  proof  that 
there  must  be  some  relation  between  human  intelligence 
and  the  nature  of  things  in  general.  There  must  be 
something  at  the  heart  of  things  which,  though  it  may 
not  be  intelligence  such  as  that  with  which  man  is 
endowed,  is  yet  possessed  of  some  analogous  property 


or  quality,  a  tendency  towards  intelligibility ;  hence 
reasoning  represents  a  method  of  interrogation  and 
interpretation  which  we  may  rightly  apply  to  nature. 
Things  tend  to  order,  classification,  and  the  relation  of 
genus,  species,  and  law  ;  but,  just  as  we  ourselves  are 
possessed  not  only  of  intelligence,  but  also  of  a  complex 
of  active  faculties,  so  we  may  attribute  a  principle  of 
activity  and  spontaneity  to  nature.6  The  intelligence 
is  the  rule  of  this  activity,  but  it  is  impossible  to  say 
to  what  extent  it  is  realised  therein  ;  knowledge  of  the* 
special  laws  in  question  can  alone  afford  us  any  idea 
of  the  degree  to  which  logical  necessity  is  active  in 

As  we  advance  by  slow  degrees  from  the  abstract 
sciences  to  the  more  concrete,  from  the  indeterminate  to 
the  complete  determination  of  facts,  we  leave  necessity 
and  logical  evidence  farther  and  farther  behind.  Mathe- 
matical laws,  which  most  nearly  approach  this  evidence, 
cannot,  however,  be  deduced  from  pure  logical  relations, 
as  was  thought  by  Leibnitz.  Logic  presupposes  a  given 
whole,  a  concept  which  we  propose  to  analyse,  and  admits 
into  it  elements  placed  in  juxtaposition  without  deter- 
mining the  connecting  link  between  them ;  the  work  of 
mathematics  is  on  the  contrary  essentially  synthetic  : 
it  posits  those  relations  which  logic  presupposes,  creates 
a  connecting  link  between  the  parts,  generates  the 
composite  whole  instead  of  assuming  it  as  a  datum. 
It  thus  introduces  new  elements  beyond  the  grasp  of 
thought,  inasmuch  as  it  constructs  these  relations  of 
composition,  differentiates  the  identical  by  means  of 
intuition,  and  uses  in  its  generalisations  the  argument 
from  recurrence,  that  is  to  say,  from  complete  induction, 
Even  though  mathematical  laws  be  not  immediately 
derived  from  the  nature  of  the  mind,  and  are  not  there- 
fore a  priori,  we  are  not  justified  in  affirming  that  they 
are  a  posteriori  forms  of  knowledge,  since  they  refer  to 
limits  which  are  not  the  result  of  experience,,  but 
represent  purely  ideal  terms  towards  which  tends  a. 
.quantity  which  is  supposed  to  increase  or  decrease 


indefinitely.  Matneioatics  must  be  regarded  as_jm 
intelligent,  voluntaryadjustmejQt  oi.  thought  to  things, 
a^orrn  which  enables  us to  eEmma/Be  qualitative 
diversTlyTirmould  into  which^  reality  must  be  poured 
in  order  that  it  may  become  intelligible,  but  we  must 
beware  of  making  it  objective,  if  we  would  not  risk 
falling  into  the  absurdity  of  infinite  actual  number  : 
the  rock  on  which  every  system  of  mathematical  realism 
has  foundered.  Idealism  in  its  turn  imagines  that  it 
can  save  the  reality  of  mathematical  laws  by  regarding 
them  as  the  indispensable  basis  of  the  world  of  presenta- 
tions which  the  mind  projects  out  of  itself;  whereas 
these  laws  fail  on  the  one  hand  to  attain  perfect  in- 
telligibility, and  on  the  other,  are  not  the  only  ones 
possible.  We  give  them  the  preference  merely  because 
they  afford  a  simpler  and  more  convenient  explanation 
of  external  phenomena  than  any  others.7  It  is  a  fact 
that  our  mathematical  system  is  applicable  to  reality,  but 
we  cannot  say  a  priori  to  what  extent  it  is  so.  Man  is 
not  an  anomaly  of  nature,  hence  that  which  satisfies 
his  intelligence  cannot  fail  to  be  related  to  other  things ; 
we  may  therefore  conjecture  a  correspondence  between 
the  laws  of  mathematics  and  those  of  nature,  but 
experience  alone  can  show  us  how  far  this  analogy 
extends.  The  laws  of  reality  which  most  closely  re- 
semble mathematical  relations  are  the  laws  of  mechanics, 
but  these  laws  introduce  a  new  element — force — which 
cannot  be  reduced  to  purely  mathematical  relations,  since 
it  contains  the  concept  of  physical  causality.  Many 
agree  with  Kant  in  his  assertion  that  the  notion  of  causal 
law  is  derived  from  our  mental  constitution,  and  is 
therefore  a  priori  and  necessary  in  order  to  bring 
phenomena  within  the  scope  of  thought,  and  to  unify 
them  in  consciousness.  Now  there  can  be  no  doubt 
of  the  need  of  unity,  but  it  cannot  be  maintained  that 
this  need  is  greater  than  any  other  and  is  tEe  motive 
power  of  our  whole  intellectual  life  ;  .nor,  on  the  other 
hand,  can  the  categories  be  regarded  as  means  suited 
to  that  end,  since  they  leave  things  external  and 


extraneous  to  one  another,  joining  them  together  in 
a  purely  artificial  way  like  the  stones  in  a  building, 
whereas,  if  we  would  conceive  of  things,  we  must 
necessarily  apprehend  their  relations  and  natural 
affinities,  and  see  into  what  groups  they  fall,  and  how 
they  are  unified.8 

Mechanical  laws  are  not,  however,  the  result  of  experi- 

"  ence  :  we  cannot  observe  the  uniform  and  rectilinear 
movements  of  a  body  which  is  subjected  to  no  extraneous 
influence,  or  the  persistency  in  repose  of  a  body  to  which 
no  impulse  has  been  given.  We  do  not  find  continuity^ 
precision,  isolated  relation,  and  the  constancy  of  law  in 
experience,  they  are  one  and  all  constructions  of  thought* 
Mechanical  laws  are,  howgy£r,  no  arbitrary  fiction,  but 
represent  the  character  we  must  ascribe  to  things  if 
things  are  to  be  expressed  by  help  of  IJe  symbols  at  our 
command,  the  matter  which  physical  science  must  place 
at  the  service  of  mathematics  in  order  to  effect  its  union 
therewith.  Moreover,  facts  prove  that  certain  natural 
phenomena  lend  themselves  to  this  need,  so  that  the 
notion  of  mechanical  law  makes  itself  feltln  all  scientific 
research,  at  all  events  in  the  form  of  a  guiding  principle.9 
But  we  cannot  think  of  mechanical  laws  as  such  being 
realised  in  the  nature  of  things  :  the  concepts  from  which 
they  result  cease  to  be  intelligible  when  they  are  turned 

'  into  objective  entities.  On  the  other  hand,  we  cannot 
accept  the  idealistic  conception  of  them  as  projections 
of  the  mind,  since  they  bear  witness  to  the  existence  of 
something  differing  from  the  mi^d,  even  though  it 
cannot  be  absolutely  severed  from  it.  Things  are 
possessed  of  certain  characteristics  wnich  suggest  the 
invention  of  mechanical  laws  and  show  a  certain 
analogy  with  that  which  takes  pjace  in  conscious  life, 
more  particularly  in  our  habitual  actions,  which, 
although  originally  produced  by  the  activity  of  thought, 
become  detached  therefrom  and  go  on  independently. 
Words  follow  one  another  without  being  determined 
by  thought ;  our  states  of  consciousness  persist  and  act 
on  one  another  with  a  certain  inertia  and  mechanical 


force  analogous  to  that  of  things.  We  isolate  the  world 
of  atoms  and  mechanical  forces  by  means  of  a  process 
of  artificial  abstraction,  and  look  upon  it  as  sufficient 
to  itself ;  in  reality,  not  only  is  it  impossible  to  conceive 
of  atoms  and  mechanical  causality  apart  from  a  mind 
which  thinks  them,  but  also  to  isolate  mechanical  move- 
ment from  the  physical  and  organic  phenomena  existing 
in  nature.  Can  we  tell  whether  mechanical  laws  are  the 
cause  or  the  effect  of  other  laws  ? 10  The  mathematical 
element  in  mechanical  laws  cannot  be  applied  strictly 
to  reality,  and  the  nature  and  cause  of  the  experimental 
element  they  contain  remain  unknown.  Physical 
phenomena  cannot  all  be  reduced  to  abstract  mechanics 
in  which  all  movement  is  reversible,  whilst  in  concrete 
mechanics  friction  stands  in  the  way  of  reversibility,  as 
for  instance  in  the  case  of  the  oscillations  of  a  pendulum 
which  should  theoretically  go  on  for  ever,  but  which 
in  experimental  reality  is  retarded  and  finally  actually 
arrested  by  the  resistance  of  the  air.  Thus  the 
principle  of  degradation  of  energy  is  in  direct  contra- 
diction to  the  laws  of  reversible  movement.  AU 
physicallawsjaid  downjby  us  are  but  the  jesult  ofji 
process  of  abstraction,  hence  they  cannot  be  alreSection 
of  facts  in  their  concrete  complexity  ;  we  isolate  certain 
elements  in  order  to  facilitate  study,  but  can  there  be 
such  a  thing  as  a  phase  of  nature  which  is  sufficient 
to  itself  and  is  not  susceptible  to  the  influence  of  ] 
the  other  phases  ?  Do  all  the  qualities  and  forms  of 
existence  which  we  have  eliminated  in  order  to  include 
phenomena  in  the  system  of  our  equations  remain 
inactive,  beyond  measurable  forms  of  magnitude,  like 
the  impassive  gods  of  Epicurus  above  this  world  of  ours  ? 
What  guarantee  have  we  that  physical  laws  are  not 
the  result  of  evolution,  just  like  the  species  of  the 
animal  world,  and  that  their  stability  may  not  therefore 
be  contingent  and  transitory  ? u  The  complication 
and  degree  of  contingency  are  still  greater  in  the  case 
of  chemistry,  since  that  science  admits  elementary 
bodies  differing  as  to  quality.  The  services  rendered 


to  chemistry  by  the  atomic  theory  are  of  undoubted 
value  since  that  theory  affords  a  ready  means  of 
notation,  but  it  can  lay  no  claim  to  being  a  metaphysical 
revelation  of  the  nature  of  things.  The  atom  is  certainly 

/  useful  as  a  unit  of  classification,  but  we  must  beware 
of    confounding    metaphor    and    entity.12      The    only 
reason  impelling  us  to  believe  in  universal  mechanism 
is,  as  Descartes  rightly  points  out,  the  confidence  we 
place  in  the  truth  of  clear  ideas  and  in  their  relation 
to  reality.13    The  attempt  to  express  everything  proper 
to  living  organisms,  to  the  processes  of  consciousness  and 
the  forms  of  social  life,  in  terms  of  mathematics  and 
mechanics  is  of  necessity  doomed  to  failure,  since  the 
qualitative  element  which  mechanics  treat  as  negligible 
is  the  dominant  element  in  these  phenomena,  where 
spontaneity  triumphs  over  automatism^     Thus  realit; 
in  its   entirety   cannot   be   reduced   to   mathematics 
elements,  still  less  to  the  necessity  of  logical  principles 
as  we  descend  from  the  lofty  heights  of  pure  reaso 
to   living,    concrete    reality,    it   will   steadily    becom 
more  and  more  impossible  to  comprehend  existence  i 
its  multifarious  aspects  within  the  limits  of  our  intel 
lectual  schemes.     The  necessity  of  law  is  rigorous! 
valid  only  for  logical  principles;  beyond  these  boun 

7  liberty  and  contingency  reign  supreme  over  the  pro 
cesses  of  nature,  and  our  efforts  to  assimilate  thing 
to  our  thought  and  to  introduce  logical  necessity  in 
them  can  never  meet  with  a  full  meed  of  success 
Science,  the  outcome  of  these  endeavours,  is  therefor 
never  of  objective  value,  and,  while  failing  on  the  on< 
hand  to  satisfy  our  demand  for  evidence  and  logica 
universality,  stands  condemned  on  the  other  to  leav 

•  external  to  itself  that  which  is  most  real  in  things 
their  qualitative  aspect,  their  incessant  transformatio 
the  act  of  perennial  creation  which  is  their  very  essenc 
just  as  it  is  the  basis  of  the  mind  of  man. 

3.  Criticism  of  the  Theory  of  Contingency.  —  Th 
philosophy  of  Boutroux  is  a  legitimate  reaction  from  th< 
excesses  of  the  mathematical  spirit,  which  endeavourec 


to  reduce  reality  to  a  bare  skeleton  of  empty  formulas  and 
looked  upon  everything  as  illusory  which  could  not  be 
thus  classified.  The  world  of  sound,  colour,  and  form 
in  its  varying  moods  is  just  as  much  an  aspect  of  reality 
as  are  the  constant  and  universal  relations  revealed  to  us 
by  thought.  Every  moment  of  the  life  of  the  universe 
is  a  fresh  revelation,  hence  the  absurdity  of  the  theory  of 
Laplace  that  the  whole  future  history  of  the  world  could 
be  foreseen  did  we  but  know  all  the  mechanical  condi- 
tions at  a  given  moment.  Science  does  not  and  cannot 
foresee  facts  in  their  historic  reality,  but  merely  certain 
general  characteristics  of  phenomena.  If  nothing  new 
were  ever  to  happen  in  nature,  no  evolutionary  move- 
ment would  be  possible,  since  such  a  movement  pre- 
supposes the  birth  of  new  forms,  which,  because  new, 
cannot  be  foreseen.  But  although  the  f  aotjn^its_concrete 
individuality  cannot  be  forced  to  submiFto  the  rule  of 
which"fesu!ts"  f  rum  the  abstfacHon  of  tEe 

variable  element  and  the  individual  aspect  of  things,  it 
does  jaoiLJolLQw  that  it  cannot  be  comprehendedjlLtlie 
formula  of  lawjLS_Jar_as  certain  of  its  characteristics 


concerned  which  are  subject  to  constant  repetition.  Itis_ 
true  that  every  fact  contains  a  new  element,  but  it  always 
contains  as  well  something  which  recurs,  properties  which 
persist  in  spite  of  ^variations  in  specific  conditions,  and 
can  therefore  be  foreseen.  Boutroux  himself  is  forced 
to  acknowledge  that  science  assumes,  is  indeed  con- 
strained to  assume,  the  existence  in  things  of  a  certain 
tendency  to  intelligibility,  although  he  tries  to  prove 
this  tendency  to  be  but  an  inveterate  habit  impelling 
Nature  to  repeat  herself.  The  moment,  however,  habit 
presupposes  repetition  it  ceases  to  be  able  to  afford  an 
explanation  thereof  :  an  action  cannot  become  habitual 
and  mechanical  unless  it  has  been  repeated  several  times. 
It  is  nonsense  to  speak  of  habits  in  a  world  of  ever  new 
and  original  creations.  The  identity  of  the  ideal  after 
which  every  being  strives  affords  no  explanation  of  the 
repetition  of  the  same  actions  unless  a  certain  structural 
homogeneity  and  persistency  in  these  actions  be  taken 


for  granted.  If  there  were  nothing  constant  in  these 
beings,  if  their  life  differed  completely  from  moment  to 
moment,  whilst  yet  aiming  at  the  same  ideal  and  striving 
to  reproduce  their  previous  work  out  of  mere  caprice, 
as  Boutroux's  bold  imagination  led  him  to  suppose, 
the  same  actions  could  never  be  repeated,  since  neither 
their  interior  tendencies  nor  the  means  of  actualising 
them  would  be  the  same  as  before.  Habit  demands 
the  repetition  of  the  same  acts,  and  this  repetition 
involves  in  its  turn  a  certain  persistency  of  previous 
conditions.  Nor  is  this  all ;  ^it  further  presupposes 
tVmjrrinp.iplft  nf  p.n/naaljty,  sipp.ft^ahnnlfl  tTip.sp-  condltlOBS. 

remain_unchange4_aiid  yet-oiot^give  rise  to  the__same 
acfTonsT^abits  coukLjiot  be  formed.  Boutroux,  in 
order  td^noTsomT  explanation  of  the  success  achieved 
by  science,  should  in  the  last  analysis  admit  the 
existence  in  reality  of  persistent  and  universal  char- 
acteristics corresponding  to  the  laws  laid  down  by 
thought.  Far  from  so  doing,  he  arbitrarily  reduces 
evidence  and  necessity  to  mere  logical  principles  in  their 
empty,  abstract  forms,  and  considers  himself  entitled 
to  deny  the  characteristic  of  universal  necessity  to  the 
formations  of  thought,  since  they  contain  elements 
which  cannot  be  deduced  from  these  pure  principles. 

4.  Milhaud  and  the  Limits  of  Logical  Certainty. — 
Milhaud,  following  out  Boutroux's  line  of  thought,14 
asserts  that  the  mind  must  renounce  all  certainty  in 
the  domain  of  reality,  because  the  recognition  of  this 
certainty  would  involve  the  reality  of  an  ideal  condition 
which  may  be  approximated :  but  can  never  be  attained, 
namely,  the  exclusion  of  all  "matter  imposed  upon  the 
mind  in  the  construction  of  the  elements  concerning 
which  it  reasons.  The  more  nearly  this  ideal  condition 
is  fulfilled,  thus  justifying  the  use  of  the  principle  of 
contradiction,  the  more  subjective,  that  is  to  say 
relative  to  ourselves  and  not  to  things,  will  be  the 
knowledge  resulting  therefrom.  In  the  sphere  of 
mathematics,  for  instance,  the  more  we  gain  in  cer- 
tainty by  forming  concepts  of  ideal  elements,  divested 


of  every  sensible  quality,  purely  mental  structures, 
the  more  we  lose  in  objectivity.  TTip.  snhjp.p±i.vf>  nlmr 
acter  of  logir.fl.1  .certainty  is  nhvirma  in  thfi^  formation 
of  concepts  which  synthetise  cejrt^yn_jpraperties — of 
things  but  can  never  exhaust  the  entire  content  of 
reality;  hence  there  will  ever  remain  something  which 
is  not  comprised  in  our  concepts,  and  which  may  be 
revealed  to  us  by  future  experience.  If  then  our  con- 
cepts be  always  of  necessity  incomplete,  the  principle 
of  contradiction  which  holds  good  of  them  can  never 
be  a  criterion  of  reality,  since  it  is  not  impossible  that 
the  incompatibility  of  the  thing  with  a  given  character- 
istic may  be  due  to  the  incompleteness  of  our  concept, 
as  for  instance  in  the  case  of  black  and  white  swans.15 
The  principle  of  contradiction  cannot  be  a  criterion  of 
objective  reality  even  in  the  case  of  2  +  2  =  4,  since  it  is 
not  absolutely  impossible  to  conceive  of  a  world  in  which 
the  union  of  2  and  2  may  result  in  the  creation  of  another 
unit.  Milhaud  goes  even  farther  than  Mill,  and  asserts 
that  this  criterion  does  not  apply  even  in  the  case  of 
A  and  not- A,  because,  since  the  attribute  A  and  the 
attribute  not- A  are  sensations  or  syntheses  of  sensations 
which  present  themselves  to  us  in  the  record  of  known 
phenomena,  we  cannot  decide  a  priori  that  their  union 
is  an  impossibility  ;  experience  may  yet  have  surprises 
in  store  for  us.  Here  it  is  obvious  that  Milhaud  fails 
to  distinguish  between  contradictory  and  contrary ; 
the  negation  of  A  is  not  a  positive  quality  to  be  found  in 
experience,  it  merely  expresses  the  thought  that  a  certain 
characteristic  is  not  compatible  with  a  certain  concept ; 
but  Milhaud  insists  that  if  we  define  not-A  by  means 
of  its  property  of  being  absent  when  A  is  present,  the 
principle  of  contradiction  resolves  itself  into  a  mere 
tautology.  This  is  not  the  case  :  we  do  not  define 
not-A  as  the  property  excluding  A,  but  as  the  absence 
of  A  from  a  concept,  and  the  principle  of  contradiction 
teaches  us  that  if  A  be  conceived  of  as  incompatible 
with  a  given  concept,  it  cannot  be  thought  of  at  the 
same  time  as  being  amongst  the  characteristics  thereof. 


Milhaud  is  wrong  when  he  agrees  with  Boutroux's 
assertion  that  thought  cannot  go  beyond  the  affirmation 
of  barren  identities,  devoid  of  any  content  whatsoever, 
without  losing  its  universality  and  certainty.  ^Thought, 
in  its  real  activity_is_sy^.thetic,^  and  gives  birth-icLjiew 
concepts  Imd  relationsT^wEichT^while  they  are  suggested 
to  it  by  experience,  yet  acquire  a  universal  and  necessary 
character  in  the  course  of  the  process  of  elabora- 
tion to  which  it  subjects  them.  The  principle  of 
identity  severed  from  all  concrete  activity  of  thought, 
from  every  concept,  and  from  every  judgment,  as 
presented  to  us  by  Boutroux,  is  a  mere  flatus  wcis, 
which  is,  and  must  be,  devoid  of  all  significance. 
Between  what  terms  can  identity  be  established  if  not 
between  concepts  ?  What  is  the  affirmation  of  identity 
if  it  be  not  an  act  of  judgment  ?  It  is  true  that  multi- 
plicity cannot  be  deduced  from  identity ;  but  can 
identity  exist  apart  from  multiplicity  ?  Every  moment 
of  thought  without  exception  is  a  search  for  the  one 
in  the  manifold,  for  the  identical  in  the  diverse. 
The  advance  and  development  of  thought  are  possible 
just  because  thought,  whilst  amplifying  its  content  in 
the  constructive  work  of  the  individual  sciences,  is  con- 
tinually affirmiftg  its  identity,  coherence,  and  universality. 
Fftigin  lies,  the  significance^of^Kaat^  a_priori  synthesis 
which  enables  thoughtjto_£scape  from  the  grave  dilemma 
in~^w^cir'Hum£~£a-d  placed  it,  the  choice  between 
barren  certainty  ancf  uncertain,,,  fruitfulness,  which 
appears  in  another  form  in  the  philosophy  of  Milhaud 
and  Boutroux.  The  limitation  of  the  certainty  of 
thought  to  A  =  A  amounts  to  the  same  thing  as  denying 
that  certainty  altogether ;  even  the  simplest  argument 
contains  a  diversity  of  terms,  though  Boutroux  would 
regard  this  as  removing  it  from  logical  necessity.  Would 
it  not  be  more  accurate  from  your  point  of  view  to  say  that 
logical  certainty  is  a  pure  fiction  which  is  non-existent 
just  because  no  such  thing  as  perfect  identity  exists  ? 
This  is  the  logical  conclusion  to  which  your  philosophy 
should  lead  you,  rather  than  to  the  limitation  of  certainty 


to  A  =  A,  which,  apart  from  the  multiplicity  of  the  con- 
cept and  the  judgment,  is  an  absurdity,  or  rather  a 
combination  of  meaningless  signs.  Boutroux  appears 
to  prove  his  case  because  he  compares  scientific  laws 
with  a  non-existent  model  of  certainty,  i.e.  that  type 
of  absolute  identity  which  amounts  to  the  denial  of 
thought.  He  does  not  venture  to  deny  the  value  of 
logical  necessity,  but  he  strives  to  isolate  it  as  far  as 
possible  from  the  world  of  experience,  lest  even  a 
suspicion  of  it  should  find  its  way  into  that  world  in 
defiance  of  the  doctrine  of  contingency.  But  how  is 
it  possible  for  a  world  of^  unceasing  creation  "suddenly: 
to  give  birth  foa  th^ghtwhich  proclaims  itself  identical 
and  demands  the"  identicaTJ  Is  this  tendency  to 
intelligence  whicTT  Boutroux^  sees  in  things  original,  or 
is  it  rather  a  product  of  habit  ?  Can  the  logical  tendency 
and  effort  made  by  thought  to  assimilate  the  manifold 
content  of  experience  to  the  principle  of  identity  be 
regarded  as  legitimate,  or  is  it  too  rather  a  habit  formed 
by  the  mind,  a  kind  of  inertia,  a  cessation  of  creative 
activity  which  doubles  on  its  own  track  instead  of  going 
forward  ?  Boutroux  does  not  venture  to  go  as  far  as  this 
absolute  denial  of  the  value  of  logical  thought,  and  is 
forced  to  make  a  certain  concession  to  intellectualism 
in  the  shape  of  this  tendency  to  intelligibility,  which 
has  its  mysterious  source  in  the  indeterminate  flux  of 
the  real. 

5.  Bergson9  s  Doctrine  of  Intuition.— The  reaction 
from  intellectualism  reaches  its  zenith  in  the  teaching 
of  Bergson.  This  reaction  would  undoubtedly  be 
salutary  did  it  confine  itself  to  affirming  the  value  of 
the  individual  and  of  concrete  reality,  and  if  it  tended 
to  accentuate  once  more  the  fulness  of  the  conscious 
individual  and  of  the  world  of  which  he  is  the  reflection, 
as  opposed  to  those  philosophical  systems  which  im- 
poverish the  content  of  mind  by  reducing  it  to  a 
handful  of  abstract  formulae  devoid  of  life  and  move- 
ment. Bergson,  on  the  contrary,  opposes  exaggeration 
to  exaggeration,  impoverishment  to  impoverishment. 

FT.  I 


Intellectualism  reduced  nature  and  the  mind  to  an  inert 
skeleton,  doomed  by  the  working  of  an  inflexible  law 
to  reproduce  itself  in  the  vacant-solitude  of  time  ; 
Bergson's  fantastic  mysticism  reduces  the  universe  to  a 
I  perennial  streajn  oliorms  flowing  in  no  definite  direction, 
'  a  shoreless,  river  whose  source  and  mouth  are  alike 
unknown,  deriving  the  strength  for  its  perpetual  renewal 
from  some  mysterious,  blind,  and  unintelligent  im- 
pulse of  nature,  akin  to  the  obscure  will  of  Schopen- 
hauer. The  new  method  of  knowledge  advocated  by 
Bejrgson  consists  in  drifting  with  this_stream,  divesting 
ourselves  as  far  as  possible  of  all  intellectiiaL  thought, 
retracting. our  false  conception  of  distinct  things  clearly 
determined  in  space  and  ordered  in  necessary  series 
in  time,  retiring  from  the  world  which  is  but  the 
deceptive  work  of  our  own  needs  into  the  intimacy 
of  our  minds  in  order  to  identify  ourselves  with 
creative  activity.  The  Deity  of  Plotinus  was  a 
lifeless,  abstract  unity,  and  mind  by  identifying 
itself  therewith  lost  all  mobility ;  Bergson's  Deity  is 
continually  in  process  of  formation  and  is  perpetually 
being  renewed  in  the  productiveness  of  unexhausted 
creation,16  and  our  mind,  by  being  reabsorbed  into  the 
swift  current  of  Divine  life,  becomes  once  more  possessed 
of  this  evolutionary  power  of  movement,  from  which 
the  fixed,  stereotyped  forms  of  pure  intellect  generally 
divert  it  by  turning  it  towards  the  material  things  which 
owe  their  existence  to  the  necessity  of  action.  .JELow, 
and  why  do  they  divert  it  ?  Why  does  consciousness 
turn  suddenly  to  the  past  and  solidify  its  fluidity  into 
distinct  objects  instead  of  pursuing  its  course  towards, 
the  new  and  the  future  ?  Here  we  have  an  enigma  which 
the  metaphysic  of  Bergson  would  fain  conceal  beneath 
the  decent  veil  of  poetry,  but  which  the  expert,  penetrat- 
ing eye  of  the  philosopher  sees  in  all  its  nakedness. 
Can  it  be  for  the  sake  of  action  ?  But  need  and  practical 
necessity  are  only  significant,  and  can  only  arise  in  a 
world  of  things  and  persons  distinct  from  the  active) 
subject ;  or,  in  other  words,  in  the  empirical  world  of 


atter  as  already  constituted  with  its  various  divisions. 
iitside  the  material  order,  there  is  no  meaning  in  the 
jed  of  action,  or,  at  all  events,  the  meaning  is  a  different 
ie,  and  the  backward  return  of  mind  and  the  formation 
the  practical  world  unnecessary.  Is  not  the  perennial 
eation  of  consciousness  the  loftiest  affirmation  of  its 
eedom  of  action  ?  Why  should  it  not  rest  content, 
hy  should  it  seek  an  outlet  in  the  current  of  its  time 
stead  of  remaining  within  the  magic  circle  of  its  con- 
nual  self -renewal  ?  The  presupposition  in  the  Absolute 
:  a  practical  need,  the  source  of  intelligence  and  matter 
ike,  amounts  to  moving  in  a  vicious  circle,  since 
:actical  need  in  its  turn  cannot  exist  apart  from 
tellect  and  matter. 

Bergson   maintains   that    the   intellectual   function 

not   original,  but   owes   its  being  to   the  practical 

incjion,  since  it  is  in  reality  neither  more   nor   less 

tan  a  more  a^urajteadaptgition  of  cons.ciousness_bo 

ie   conctitions  of   life.^    For   this  reason  intelligence, 

hich~~caine  into  being  merely  in  order  to  ensure  that 

IT  body   should  fit  perfectly  into  its   environment, 

oves  at  its  ease  amid,  solid  and  inert  objects,  the 

Icrum  of  our  action  and"  the  tools  of  our  industry, 

it  is  unable  to  grasp  the  true  nature  of  life  or  the  true 

^nificance  of  the  evolutionary  movement.17    No  one 

the  categories  of  thought,  such  as  unity,  multiplicity, 

echanical    causality,   intelligent    finality,   is    exactly 

jplicable  to  the  phenomena  of  life-;    our  intellectual 

rmulas  cease  to  be  adequate  when  we  pass  from  inert 

>jects  to  Hvjn^jorganiams.     Shall  we  then  proclaim 

e  essence  of  life  to  be  unknowable  ?     Shall  we  not 

ther  acknowledge  that  our  difficulties  and  contradic- 

ms  arise  from  the  desire  to  apply  to  it  the  habitual 

rms  of  our  thought  which  are  only  suited  to  matter  ? 

ie  intelligence  can  grasp  something  of  theTbsolute 

long  as  it  confines  itself  to  the  physical  objects  upon 

lich  it  is  modelled  ;  it  becomes  powerless  the  moment 

attempts  to  cross  these  limits,  and  to  invade  the  realm 

life.    We  must  not,  however,  be  led  to  conclude  that 



life  transcends  the  limits  of  our  cognitive  faculties,  sine* 
conceptual    logical  thought  is  not'Tine   only  form  o: 
knowledge  ;    around  it  is  a  misty  cloud  of  the  same 
substance  as  the  luminous  nucleus  we  call  intelligence-] 
intuition,  which  gives  us  a  direct  grasp  of  the  real  ii 
that    process   of  perennial   creation    which  is  its   ver 
life.    Intelligence  sees  nothing  in   things   beyond  thj 
aspect  of  repetition ;    the  irreducible  and  irreversib] 
element  in  the  successive  movements  of  cosmic  evolutio 
eludes  it.     Mechanical  explanations  hold  good  of  th 
systems  which  our  thought  has  artificially  severed  fro 
the  continuous  flux  of  the  universe  ;   but  it  cannot 
admitted  a  priori  that  the  universe  in  its  totality  togetb 
with  the  systems  which  naturally  are  "formed  in  i 
image  are  capable  of  a  mechanical  explanation,  sin* 
in  that  case  time*  would  be  useless  and  devoid  of 
reality.     The  "essence  of  the  mechanical  explanation 
to  look  upon  the"  past  and  the  future  as  calculable 
terms  of  the  present,  and  to  argue  from  this  that  eve: 
thing   is  given ;   according   to  this  hypothesis,    p 
present,  and  future  would  all  be  visible  at  a  glance 
a    superhuman    intelligence    capable    of    making 
necessary~caTculation,  and  the  apparent  duration 
things,  together  with  its  creative  process,  would  be  me: 
the  expression  of  the  weakness  of  a  mind  which 
not  know  everything  at  once. »  Thus  a  confusion  a 
between  time — ever  fresh  multiplicity — and  mathematj 
space,  constructed  so  as  to  be  able  to  act  upon  thi 
the  living  world  of  quality  gives  place  to  the  abst 
schematism  of  pure  quantity.    If  we  would  grasp  re 
in  its  creative  essence,  we  must  divest  conscious 
of  the  whole  of  the  artificial  superstructure  whic 
have  raised  in  order  to  adapt  it  to  the  exigenci 
practical  life,  place  ourselves  once  more  in  pure  dura 
and  live  in  the  depths  of  the  Ego.     Time  as  understjj 
by  physical  science  is  not  true,  real  duration,  the  pr 
of  incessant  creation,  but  rather  a  homogeneous  scb 
conceived  by  analogy  to  mathematical  space,  w 
by  solidifying  the  flowing  life  of  the  mind  into  ho: 

ssc.  n          CONTINGENCY  AND  INTUITIONISM  131 

geneous  moments  external  to  one  another,  turns  it  into 
a  necessary  mechanism  of  recurring  states.  Beneath 
homogeneous  duration,  the  extensive  symbol  of  true 
duration,  psychological  analysis  reveals  to  us  a  duration 
whose  heterogeneous  moments  are  perpetually  penetrat- 
ing one  another ;  beneath  the  numerical  multiplicity 
of  conscious  states  it  shows  us  a  qualitative  multiplicity  ; 
and  beneath  the  superficial  and  symbolic  Ego,  an  Ego  in 
which  succession  implies  fusion  and  organisation.18  Since 
the  symbolic  Ego  is  better  suited  to  the  requirements  of 
social  life,  we  generally  lose  sight  of  the  deeper  Ego,  and 
tend  to  solidify  our  impressions  so  as  to  express  them  in 
language.  Mere  rude  speech,  with  its  clear-cut  outlines, 
giving,  as  it  does,  definite  form  to  the  stable,  common, 
and  therefore  impersonal  element  in  the  impressions 
of  mankind,  is  incapable  of  recording  the  delicate 
fugitive  impressions  of  our  individual  consciousness. 
If,  however,  we  remove  these  schemes  and  eliminate 
from  the  Ego  everything  which  we  have  introduced  into 
it  in  order  to  render  it  easier  of  communication  and 
better  suited  to  practical  requirements,  every  moment 
of  its  life  will  be  revealed  in  its  concrete  physiognomy, 
which  cannot  be  foreseen ;  the  bonds  of  necessity  will 
be  burst  asunder,  and  the  mind  stand  forth  as  a  free 
creation  of  qualities  which  are  ever  new.  Science,  the 
outcome  of  the  necessity  of  action,  is  fated  to  leave 
exterior  to  itself  true  reality  with  its  unceasing  changes 
and  creative  spontaneity ;  it  can  only  act  on  time  and 
movement  if  it  first  eliminates  the  qualitative  element, 
which  is  its  very  essence.  Reality  in  its  fulness  eludes 
the  methods  of  science  ;  if  we  would  grasp  it,  we  must 
leave  intelligence  behind  and  retrace  our  steps  to  the 
springs  which  the  need  of  action  drove  the  mind  to 
forsake.  This  undertaking,  which  Bergson  regards  as 
the  task  of  the  theory  of  knowledge^^gresents  many 
difficulties,  and  is  b^eyondr^th'e  powerofjDure  intellect. 
^Alnere  careful  analysis  o^the  categories  of  tHought  will^ 
not  suffice,  they  must  be^geherateoT  As  regafds~space, 
we  must  make  an  effort  swJTgemris'iQ  trace  the  retro- 


gression  and  degradation  of  the  mind  into  spatiality.1* 
If  we  place  ourselves  at  the  apex  of  our  consciousness, 
and  gradually  descend  thence,  we  feel  that  our  Ego 
extends  into  inert  recollections  external  to  one  another, 
instead  of  tending  towards  an  indivisible  and  acting 
will.  We  thus  grasp  the  principle  of  this  movement  of 
descent  towards  spatiality,  which  is  contJnued~mthe 
matter  ol  perception  ancT  is  completed  by  the  physicist, 
who  shows  a  thorough  understanding  of  his  task  when 
he  impels  matter  towards  the  ideal  space  of  geometry. 
The  philosopher,  on  the  other  hand,  misconceives  the  goal 
which  he  should  strive  to  attain,  when  he  follows  in 
the  footsteps  of  the  physicist  in  the  vain  hope  of  being 
able  to  advance  still  farther  in  the  same  direction,  since 
he  ought  rather  to  climb  the  hill  which  the  physicis 
is  descending  in  order  to  bring  matter  back  to  its  sourc 
and  form  a  cosmology  which  is,  if  I  may  so  express  it, 
inverted  psychology.  From  this  new  standpoint  every 
thing  which  the  physicist  and  geometrician  regard  as 
positive  becomes  an  interruption  or  inversion  of  true 
positivity,  which  must  be  defined  in  terms  of  psychology.28 
The  reluctance  shown  by  philosophers  to  consider  things 
from  such  a  point  of  view  is  to  be  attributed  to  the  fac 
that  the  logical  work  of  the  intelligence  is  in  their  ey 
a  positive  effort  of  the  mind,  but,  if  by  spirituality 
are  to  understand  an  advance  towards  ever  new  creations 
towards  conclusions  which  cannot  be  deduced  from  th 
premisses  and  which  are  not  determined  thereby,  i 
must  be  acknowledged  that  a  representation  which 
hedged  in  by  relations  of  necessary  determination 
through  premisses  whose  conclusion  has  been  inheres 
in  them  from  the  beginning,  is  moving  in  the  opposi 
direction  to  spirituality.  The  special  laws  of  the  physic 
world  are  derived  from  this  tendency,  which  is  really 
negative  one.  No  one  of  them,  looked  at  separatel 
is  possessed  of  objective  reality  ;  it  is  but  the  wor 
of  a  man  of  science  who  has  looked  at  things  fro 
one  particular  point  of  view,  isolating  certain  variabl 
elements,  and  measuring  them  by  certain  conventional 


units.  There  is,  however,  a  certain  approximately 
mathematical  order"  immanent  in  matter,  an  objective" 
order  to  which  our  science  approximates  as  it  advances, 
because,  if  matter  be  the  relaxation  of  the  inextensive 
into  the  extensive,  and  hence  of  liberty  into  necessity, 
it  must  tread  in  the  footsteps  of  geometry,  since,  though 
it  does  not  originally  coincide  with  pure  homogeneous 
space,  it  is  derived  from  the  same  movement ;  and  if  it 
never  fully  attain  that  goal,  if  mathematical  laws  be  not 
wholly  applicable  to  it,  it  is  merely  because  it  cannot 
entirely  shake  off  duration,  and  thus  transform  itself  into 
pure  space.21  It  is  impossible  to  lay  too  much  stress 
upon  the  artificial  character  of  the  mathematical  form 
of  a  physical  law,  and  hence  also  of  our  scientific  know- 
ledge of  things.  Our  units  of  measurement  are  conven- 
tional and,  so  to  speak,  extraneous  to  the  intentions  of 
nature :  how  can  it  be  supposed  that  nature  has  gauged 
the  related  modalities  of  heat  by  the  dilations  of  a  mass 
of  mercury,  or  by  the  varying  pressure  of  a  mass  of  air 
maintained  at  the  same  volume  ?  The  act  of  measuring 
is  a  purely  human  one,  implying  the  real  or  ideal 
superposition  of  two  objects  a  certain  number  of  times. 
Nature  has  made  no  provision  for  such  a  process,  she 
neither  measures  nor  counts ;  yet  physical  science  adopts 
this  plan  successfully,  how  are  we  to  account  for  this  ? 
Its  success  would  be  inexplicable  were  the  movement 
which  constitutes  materiality  not  identical  with  the 
movement  which,  when  extended  by  us  to  its  limit,  i.e. 
to  homogeneous  space,  teaches  us  to  count,  measure, 
and  follow  the  variations  of  certain  terms,  some  of  which 
are  functions  of  the  rest.  The  intelligence  effects  this 
extension  simply  by  means  of  a  process  of  self -extension, 
because,  since  intellectuality  and  materiality  are  of  the 
same  nature  and  are  originated  in  the  same  way,  it 
naturally  tends  towards  space  and  mathematics.  If 
mathematical  order  were  something  positive,  if  laws 
like  those  of  our  codes  were  immanent  in  matter,  the 
success  achieved  by  science  would  partake  of  the 
miraculous.  What  chance  would  there  be  of  our  finding 


nature's  unit  of  measurement,  and  isolating  just  those 
variables  chosen  by  her  in  order  to  determine  their 
reciprocal  variations  ?  On  the  other  hand,  the  success 
attained  by  mathematical  science  would  be  no  less  in- 
comprehensible if  matter  were  not  possessed  of  every- 
thing  requisite  for  its  inclusion  in  our  schemes.  There 
remains,  then,  but  one  plausible  hypothesis — that  there 
is  nothing  positive  in  mathematical  order,  but  that  it 
is  the  form  to  which  the  interruption  of  the  evolutionary 
movement  automatically  tends,  and  that  materiality  is 
an  interruption  of  the  same  kind.  It  then  becomes 
comprehensible  that,  while  science  is  contingent,  relative 
to  the  variables  it  has  chosen  and  to  the  order  in  which 
its  problems  have  been  set,  it  can  yet  achieve  success. 
It  might  have  been  totally  different  as  a  whole  and  yet 
have  been  successful,  simply  because  no  definite  system 
of  mathematical  laws  is  based  upon  nature,  and  mathe- 
matics in  general  merely  represents  the  direction  towards 
which  matter  tends.22 

6.  The  Fundamental  Error  of  Bergson's  System. — 
In  Bergson's  view  that  the  intellectual  function  is 
derivative  lies  the  fundamental  error  of  his  system ; 
this  view  gives  rise  to  the  attempt — as  vain  as  it  is 
ingenious — to  deduce  intelligence^Jrpm  the  practical 
attitude  of  consciousness,  which  is  in  its  turn  confounded 
wTffrth~e  imaginative~or  creative  function.  Bergson's 
intuition  is  as  a  matter  of  fact  neither  more  nor  less  than 
the  aesthetic  attitude  of  the  human  mind,  in  which  we 
find  that  experience  of  unfettered  creative  spontaneity 
and  unbounded  expansion  which  his  poetic  imagination 
regards  as  the  very  essence  of  universal  reality,  so  that 
he  might  join  with  Schelling  in  acclaiming  art  as  the 
fullest  revelation  of  the  Absolute,  and  with  Froschammer2* 
in  looking  upon  imagination  as  the  heart  of  the  cosmic 
process.24  But  if  the  essence  of  the  life  of  things  is  to 
be  sought  in  creation  and  in  artistic  contemplation, 
it  is  difficult  to  understand  how  intellect  and  the  practical 
world  of  matter  can  have  sprung  from  such  a  source,! 
or  why  the  duality  of  subject  and  object  and  the  other 


factors   determining   the   real   came  into   being.     The 
contemplative  mind  should  indeed  remain  for  ever  in 
the  magic  realm  of  dreams  and  flow  on  to  all  eternity 
in  a  poetic  phantasmagoria,  growing  ever  richer  in  new 
creations  as  it  takes  its  course.    What  freak  of  fancy 
induces  it  to  turn  back  instead  of  pursuing  the  even 
tenor  of  its  way  ?    Why  does  it  try  to  dam  the  stream 
of  its  day,  double  on  its  own  track,  and  endeavour  to 
return  to  the  past,  thus  letting  matter  limit  its  freedom 
instead  of  rejoicing  in  its  liberty  ?   Bergson  deceives  him-  \ 
self  into  thinking  that  in  practical  need,  the  mysterious 
offspring  of  universal  consciousness,  we  have  the  ex- 
planation  of  all  difficulties.     Is  the  practical  function  of 
mind  primitive  or  derivative  ?     If  it  be  primitive,  it 
assumes  a  distinction  of  terms  as  co-existent,   since 
action,  as  Bergson  himself  maintains,  can  find  no  hold 
in  the  unceasing  flux  of  time ;   matter,  that  is  to  say, 
in  Bergson's  sense  of  the  word,  would  in  such  a  case 
have  no  beginning,  but  would  be  primitive,  like  the 
practical  function.     If  practical  activity,  on  the  other 
hand,  be  of  later  origin,  Bergson  should  make  clear  to 
us  how  and  why  the  intuitive  life  of  the  real  and  its 
creative  power  suddenly  give  place  to  the  empirical  world 
of   action   and  intelligence.    With   all  his   metaphors 
Bergson  fails  to  convince  us  that  continuous,  creative 
activity    can   give    birth   to    practical,    discontinuous 
activity,  and  this  activity  in  its  turn  to  the  objective 
world  with  all  its  determinations.     The  pure  act  of  will 
is  psychological  in  its  nature,  and  is  of  itself  powerless  to 
leave  the  sphere 'of  intimate  consciousness;  even  if  it  be 
granted  that  it  demands  a  discontinuity  of  terms,  these 
terms  will  never  appear  external  to  the  consciousness, 
but  will  always  keep  the  character  of  inner  experience. 
The  mere  fact  that  discontinuity  makes  its  way  into  the 
psychic  world  cannot  give  rise  to  the  apprehension  of 
something  which  is,  or  at  all  events  appears  to  be, 
exterior  thereto.     Consciousness  might  be  able  to  dis- 
tinguish a  series  of  states  in  its  continuous  flow,  and 
to  find  in  them  a  foothold  for  its  actions  without,  for 


that  reason,  coming  out  of  itself.  Do  we  not  experience 
this  when  we  voluntarily  modify  our  train  of  thought  ? 
It  is  true  that  freedom  of  action  implies  the  distinction 
between  subject  and  object,  between  the  agent  and  his 
act,  but  the  two  terms  can  both  exist  as  part  of  con- 
sciousness. The  mind  is  not  compelled,  if  it  would 
affirm  its  liberty,  to  come  out  of  itself  and  create  the 
illusion  of  a  world  completely  extraneous  to  itself,  and 
jvhich  it  must  endure  as  an  extraneous  necessity. 
According  to  Bergson,  the  arrest  of  the  vital  flux,  the 
turning  back  of  creative  activity,  will  suffice  to  produce 
the  intellectual  process ;  it  is  the  inversion  of  the 
evolutionary  movement  which  has  given  birth  both 
to  the  intellectuality  of  mind  and  the  materiality  of 
things  ;  the  intellect  is  negative  in  value  in  comparison 
to  intuition,  it  is  the  mind  abjuring  itself,  turning  in  a 
moment  of  weariness  to  gaze  at  what  it  has  already 
accomplished  instead  of  creating  new  forms,  ceasing 
its  march  forwards  and  relaxing  into  the  materiality 
of  space.  It  would  be  out  of  place  here  to  enter  into 
the  question  whether  the  work  of  the  intellect  does 
not  demand  as  great  (or  even  greater)  intensity 
of  effort  as  artistic  creation  :  Bergson  himself,  if  he 
could  but  divest  himself  of  systematic  preconceptions 
and  put  the  question  to  his  own  consciousness,  would  be 
forced  to  admit  that  it  is  an  error  to  look  upon  intel- 
lectual work  as  a  relaxation.  Another,  looking  at  the 
matter  from  another  point  of  view,  might  rather  assert 
that  the  logical  process  involves  an  excessive  mental 
strain,  and  that  aesthetic  contemplation  is  productive  of 
a  sense  of  calm  and  repose,  almost  as  if  the  mind  were 
drifting  at  the  mercy  of  its  own  current.  These  are 
but  subjective  impressions  on  which  I  will  not  insist 
lest  I  should  seem  to  attach  too  much  importance  to 
Bergson's  metaphors.  His  view  of  intelligence  is 
too  limited  and  fragmentary,  and  he  altogether  fails 
to  see  its  poetical  side.  The  creative  activity  of  the 
mind  is  revealed  in  concepts  no  less  clearly  than  in 
intuition  ;  the  abstract  logical  schemes  and  the  deduc- 



tions  of  an  already  systematised  science  are  one  thing, 
logical  scientific  work  in  its  concrete  process  of  discovery 
quite  another.  The  demonstration  of  a  new  relation 
between  phenomena  which  before  appeared  to  be 
heterogeneous,  the  harmonisation  of  laws  already  known 
to  us  in  a  new  theory  with  the  help  of  a  new  principle, 
the  formulation  of  the  equation  of  a  new  curve,  this  is 
a  function  of  intellect,  and  a  creative  function  as 
well ;  and  if  progress  towards  the  new  and  the  genesis 
of  new  products  be,  as  Bergson  states,  the  sign  of  a 
positive  movement  of  the  mind,  then  intelligence,  no 
less  than  intuition,  stands  revealed  as  a  positive  process, 
and  the  world  as  conceived  by  it  is  no  less  real  than  that 
continuous  flux  of  images  which  Bergson  regards  as  the 
essence  of  the  universe. 

7.  The  Two  New  Rules  of  Invention  propounded  by 
Wilbois. — The  intuitionists  do  not  really  deny  the 
creative  activity  in  the  realm  of  science,  but  endeavour 
to  reduce  it  to  the  aesthetic  function.  Wilbois,25  in 
opposition  to  the  methods  of  Stuart  Mill,  which  postulate 
determinism,  propounds  two  rules  of  invention  :  the 
aesthetic  sense  and  the  sense  of  progress.  The  rules  of 
scientific  invention  should  constitute  as  a  whole  a  kind 
of  aesthetic  of  the  laboratory :  no  strictly  scientific  rule 
can  enable  us  to  discover  truth,  which  lies  concealed 
amid  the  complexity  of  our  qualitative  perceptions, 
and  aesthetic  instruments  alone  can  reveal  it  to  us  ; 
the  search  for  beauty  is  then  a  condition  of  science. 
Aesthetic  is  a  chapter  of  logic.26  The  history  of  a 
scientific  work  bears  a  strong  resemblance  to  the  history 
of  a  work  of  art ;  discovery  is  a  creation,  a  poem.27 
The  truth,  however,  which  is  based  on  beauty  can  be  of 
a  provisional  order  only ;  the  aesthetic  sense  must 
therefore  be  united  to  the  sense  of  progress,  which  will 
spur  us  on  to  the  criticism  and  continual  renovation 
of  facts  and  theories.  It  is,  of  course,  true  that  there  is 
nothing  less  bound  by  rule  than  the  creation  of  a  principle, 
since  genius  is  always  something  which  cannot  be  fore- 
seen ;  there  is,  however,  a  certain  effort  which  is 


characteristic  of  all  great  inventors ;  they  have  only 
reached  the  goal  of  discovery  by  means  of  a  process  of 
self -renewal,  preceded  by  a  long  dark  night.  Facts 
will  only  reveal  themselves  to  him  who  seeks  them 
with  the  temperament  of  the  artist,  and  whose  whole 
mind  strives  after  the  future  of  science.28 

8.  The  Arbitrary  Character  of  Spiritual  Activity  in 
Scientific  Construction,  as  viewed  by  Le  Roy. — This  pre- 
valently aesthetic  character  of  intuitionism  leads  it  to 
exaggerate  and  exalt  the  element  of  personal  activity  in 
scientific  construction :  not  only  theory,  not  only  law, 
but  fact  itself  is  a  free  creation  of  the  man  of  science. 
Positivism  in  its  older  form  went  into  ecstasies  over  the 
fact,  which  it  failed  to  distinguish  from  pure  data  ; 
the  new  positivism,  as  the  new  French  philosophy  has 
been  termed  by  one  of  its  most  ardent  disciples,  Le  Roy,2* 
sees  in  the  fact  of  common  sense  an  unconscious  pro- 
duct of  spiritual  activity  directed  towards  practical 
action.  The  very  name  of  fact,  says  Le  Roy,30  should  put 
us  on  our  guard  against  the  common  belief :  that  which 
has  been  made  cannot  be  an  immediate  datum.  There 
are  no  such  things  as  isolated  facts,  but  all  is  diffused 
in  all ;  nothing  of  any  kind  can  be  defined  except  by 
means  of  the  ties  binding  it  to  the  universe  as  a  whole. 
All  isolation,  all  fragmentation,  is  relative  to  the  selected 
point  of  view.  The  relativity  of  facts  is  still  more 
obvious  in  science,  in  as  much  as  it  is  not  satisfied  with 
any  facts  whatsoever,  but  seeks  for  facts  of  significance 
for  the  law  or  theory  which  is  to  be  proved.  Of  course, 
everything  is  not  created  by  men  of  science;  facts  contain 
a  mysterious  residuum  of  objectivity,  but  science, 
employed  as  it  is  in  that  fragmentation  necessary  from 
its  point  of  view,  does  not  take  into  account  this  primitive 
material  which  philosophic  criticism  alone  can  reveal  to 
^  us  in  intuition.  /  It  is  not  what  is  objective  but  what 
is  artificial  in  facts  which  is  of  interest  to  science.31 
The  character  of  personal  creation  and  of  artificial 
schematism  becomes  more  marked  in  the  scientific  law 
and  theory.  The  law,  whose  office  it  is  to  fix  that  which 


is  constant  in  the  variations  of  phenomena,  is  but  a 
general  formula,  a  schematic  model,  a  type  of  classifica- 
tion summing  up  under  a  single  heading  an  inexhaustible 
multitude  of  individual  events.  The  only  characters  of 
facts  persisting  in  the  law  are  those  which  are  of  greatest 
interest  to  us,  and  whose  relative  permanency  gives  us  a 
handle  for  our  action.  Thus  the  laws  of  Galileo  are  a 
brief  condensation  of  all  that  is  worth  recording  amongst 
the  infinite  details  of  all  the  real  or  possible  falls  of 
bodies.  Laws  are  then  but  aids  to  memory,  principles  of 
arrangement,  which,  by  simplifying  and  impoverishing 
concrete  reality,  cause  us  to  lose  immediate  contact  with 
nature.  They  appear  to  us  less  like  elements  of  things 
than  constructions  of  our  minds,  products  and  symbols 
of  our  disposition  to  vary  perpetually  the  angles  from 
which  we  contemplate  the  constancy  of  the  world,  and 
much  more  like  true  and  proper  definitions  established  by 
an  arbitrary  decree.  The  law  of  fall  defines  the  closed 
system,  the  law  of  definite  proportions  does  the  same  in 
the  case  of  the  chemical  combination  as  distinct  from 
the  mechanical  mixture.32  From  such  a  point  of  view 
laws  cannot  be  verified,  because  they  are  the  instruments 
with  which  we  effect  in  the  continuity  of  primitive  data 
that  splitting  up  into  fractions  which  is  indispensable  to 
the  action  of  our  thought,  and  because  they  themselves 
constitute  the  method  and  criterion  of  which  we  must 
make  use  in  order  to  test  them  accurately.  For  instance, 
in  order  to  verify  the  law  of  the  reflection  of  light  we 
should  require  a  plane  mirror,  and  in  order  to  make  such 
a  mirror  we  must  make  use  of  this  same  law.  Further, 
the  very  project  of  seeking  for  laws  in  the  world  involves 
the  postulate  of  universal  determinism,  which  is  neither 
an  evident  a  priori  principle  nor  yet  capable  of.  a  posteriori 
proof,  but  is  a  mere  decree  of  our  mind  which  never  fails, 
because  each  time  it  is  endangered  science  rushes  to 
the  rescue  by  inventing  a  new  concept  and  setting  up 
a  new  convention.  Law  is  then  purely  arbitrary,  in  as 
much  as  it  demands  the  definition  of  a  unit  of  measure. 
The  smallest  appliance  of  the  laboratory,  the  minimum 


of  experimental  technique,  presupposes — as  Duhem  and 
Milhaud  in  particular  have  pointed  out — in  its  apparent 
simplicity  a  large  number  of  definitions,  postulates, 
conventions,  and  decrees  of  the  mind.  The  contingency 
of  laws  is  further  dependent  upon  the  method  by  which 
they  are  obtained :  physical  science  seeks  for  constant 
quantities  and  finds  them,  because  it  desires  to  do  so, 
by  doing  ingenious  violence  to  nature ;  but  these 
constant  quantities  do  not  reflect  anything  objective, 
and  express  in  reality  but  the  weakness  of  our  senses, 
,  the  approximations  we  have  accepted,  the  requirements 
/  of  our  practical  needs  and  of  our  discursive  reason. 
j£ut,  it  may  be  asked  at  this  stage,  how  does  itjcome 
about_jLhalL^a  phenojoenoa— j&— always  produeecLJn 
de!}ejrm'nate--circumstances  ?  Is  not  this  a  proof  of 
the  reality  of  constants  ?  It  is  hardly  surprising, 
\~replies  Le  Roy,  that  the  law  should  be  verified  the 
'  moment  we  decide  to  exempt  from  its  rule  all  those 
cases  in  which  it  is  not  verified  ;  when  experience  fails 
we  calmly  declare  that  the  requisite  conditions  have 
not  all  been  fulfilled,  or  that  some  as  yet  unknown 
cause  (which  is  thus  defined)  is  at  work,  and  has  deter- 
mined a  modification  of  the  phenomenon.33  As  regards 
theory,  all  agree  in  recognising  its  conventional  and 
hypothetical  character,  which  in  no  way  distinguishes 
it  from  law,  as  is  erroneously  believed,  when  the 
variability  of  theory  is  placed  in  opposition  to  the 
stability  of  law.  The  chief  office  of  theory  is  not 
to  forestall  the  known,  but  to  furnish  us  with  a 
general  scheme  of  representation,  capable  of  adaptation 
to  a  category  of  laws.34  Theory  absolutely  eludes 
control ;  it  cannot  be  proved  a  priori,  since  it  is  based 
upon  contingent  definitions,  nor  a  posteriori,  since  in 
its  case  an  experimentum  crucis  is  out  of  the  question  : 
experimental  contradiction  proves  the  existence  of  an 
error  in  the  system  of  laws  applying  to  the  case  in 
point,  but  does  not  tell  us  exactly  where  this  error  is 
to  be  found,  and  it  is  possible  for  us  to  modify  some  law 
in  such  a  way  as  to  leave  the  theory  intact.35  Theory 


is  not  the  outcome  of  experience,  but  is  a  system  of 
symbols  wholly  created  by  the  mind,  a  conventional 
language  which  can  be  changed  as  often  as  we  choose 
to  do  so  ;  hence  the  possibility  of  different  theories  o£ 
the  same  order  of  facts.  The  man  of  science  is  at  liberty 
to  choose  the  one  for  which  he  has  a  personal  preference, 
or  which  is  best  suited  to  the  end  he  has  in  view,  con- 
ceiving of  phenomena  by  means  of  differential  equations 
and  integrating  symbols,  having  recourse  to  geometrical 
and  mechanical  schemes,  or  making  use  of  the  images  of 
the  flow  and  circulation  of  energy.  Each  of  these  modes 
of  expressions  is  legitimate  from  its  own  point  of  view  ; 
and  our  choice  of  one  in  preference  to  another  is  due  to 
the  fact  that  the  one  selected  is  better  suited  to  the 
type  of  our  mentality,  corresponds  more  nearly  to  our 
habits,  and  proves  more  convenient  to  us.  There  is  no 
such  thing  as  a  universal  limiting  theory,  which  should 
serve  as  a  unit  of  measurement  by  which  to  judge  the 
degree  of  truth  of  the  others ;  there  merely  exists  theories 
to  which  we  give  the  preference.  Even  in  the  realm  of 
geometry,  as  has  been  proved  by  Poincare,36  there  do 
not  exist  evident  principles  possessed  of  universal  and 
objective  value  in  preference  to  all  others,  there  are 
merely  conventions  established  by  the  mind  which 
have  become  more  or  less  habitual,  and  whose  con- 
venience is  the  only  point  capable  of  discussion. 
Rational  science,  the  ultimate  aim  of  all  scientific  work, 
f  Js-ajjeyjce  oQhe  mind  for  the  conQfuesiijQJLthe-werid, 
constructing  with  the  aid  jp^^ur_jc^sj^rc^s_^lorie_a. 
scEeme  of  the  urnverstTjwhich  enables  discursive 
thought  to^reproduce~at  wjll_thejwhole  development 
of  n^Lturej^thout^^having  recourse_to_ex]p^rience.  The 
ideaFof  science  is  the  attainment  of  knowledge  which 
is  wholly  ours,  which  is  entirely  our  creation,  subject 
to  us  and  contained  within  us.  Its  mission  is  not 
to  attain  to  some  external  necessity  or  other  concealed 
ready-made  in  the  real,  but  rather  to  manufacture 
the  truth  for  which  it  seeks,  the  perfect  instrument 
of  action,  the  system  of  perfectly  tractable  discursive 


symbols.37  Scientific  truth  is  like  moral  good ;  it  is 
not  received  from  without,  it  makes  and  creates  itself  ; 
i*  is  a  system  of  fictions,  of  merely  social  value,  which 
[^succeed  in  the  practical  world.  How  is  it  that  they 
are  successful  ?  Here  we  have  a  difficult  problem 
which  Boutroux  and  Bergson  vainly  strove  to  solve, 
and  with  which  Le  Roy  too  finds  himself  face  to  face. 
It  will  not  suffice  to  show  that  this  success  is  obtained 
by  eliminating  everything  which  cannot  be  made  to  fit 
into  our  schemes  ;  or  that  science  is  not  relative  to  true 
knowledge,  and  that  its  successes  belong  to  the  order 
of  discourse  and  industry  :  all  these  observations,  says 
Le  Roy,38  are  legitimate,  but  leave  something  still 
unexplained.  In  order  to  establish  any  determinism 
whatsoever,  the  data  must  lend  themselves  thereto  : 
nature  must  contain  certain  elements,  must  be  possessed 
of  certain  characteristics  which  bring  our  science  within 
the  bounds  of  possibility.  Were  incoherency  the  basis 
of  things,  the  decrees  of  our  legislative  action  would 
be  continually  overturned  by  the  unexpected  ;  whereas 
we  see  that  our  elaboration  works  well.  Is  not  this  a 
sign  that  it  is  true,  that  it  has  at  all  events  a  partial 
grasp  of  reality,  that  something  in  the  universe  corre- 
sponds thereto  ?  Knowledge  is  power  and  foresight, 
but  inversely,  power  and  foresight  are  knowledge. 
Hence  Le  Roy  is  forced  to  admit  that  laws  are  in  some 
way  possessed  of  objective  value,  because  they  enable 
us  to  grasp  a  real  and  constant  order  of  phenomena, 
at  least  with  the  approximation  of  common  life.*  Matter 
contains  something  which  thrusts  itself  upon  us,  opposes 
our  undertakings,  and  limits  our  liberty  :  how  are  we 
to  conceive  of  it  ?  If  everything  be  eliminated  from 
matter  which  is  due  to  the  work  of  the  mind,  nought 
but  potentiality  will  be  left :  nature  is  only  actualised, 
developed,  and  made  explicit  by  the  work  of  minds 
which  by  means  of  discrimination  introduced  number  and 
space  into  primitive  continuity ;  which  contract  by 
means  of  memory  a  plurality  of  moments'  into  differ- 
entiated syntheses  which  become  sensible  qualities,  and 


chisel  out  and  solidify  by  means  of  action  the  objects 
and  facts  of  common  sense.  As  criticism  undoes  their 
work,  matter  becomes  less  clear  and  more  involved, 
bodies  dissolve,  qualities  are  confused,  images  vanish 
away,  till  nothing  is  left  but  a  kind  of  latent  tension 
towards  development  and  actuality.39  We  thus  reach 
pure  matter,  which  can  only  be  conceived  of  as  the 
virtuality  of  an  order  common  to  all  minds,  as  the 
capability  of  laws.  Matter  at  times  rather  resists  the 
decrees  of  the  reason  and  the  will  ;  hence  it  seems  to 
us  to  be  endowed  with  true  activity,  a  tendency,  a 
desire,  a  straining  after  determinism.  It  is  no  ready- 
made  web,  no  tissue  into  whose  unyielding  meshes  our 
action  cannot  hope  to  penetrate  ;  it  merely  shows  that 
it  is  impossible  for  the  mind  to  vary  the  rhythm  of  its 
duration  beyond  a  certain  limit,  it  is  a  combination  of 
stationary  waves  in  our  psychic  life,  or  rather  of  waves 
which  advance  less  rapidly.  Thej^aL  .activity  mam\ 
fested  in  matter  induces  me  to  believe  instinctively  in 
its  ob]ec^ve_existence7~ln  order  "to 

in  those  regions  where  common  sense  jsees  butjbrute 
matter  :„  consciousness  more  or  less  clear,  at  a  lower 
or~Egher  degree  of  tension,  endowed  with  a  greater 
or  lesser  degree  of  reality  and  liberty.  Matter  is 
illusory  in  the  sense  that  it  is  our  work,  it  is  like  a 
decree  by  virtue  of  which  every  free  action  develops 
reactions  ;  but,  on  the  other  hand,  it  is  real  in  the  sense 
that  we  are  pre-  determined  to  construct  it.  We  feel 
its  weight  in  two  ways  :  as  an  institution  which  is  the 
outcome  of  human  art  (actual  matter),  and  as  a  decree 
which  aims  at  pre-forming  our  action  (pure  matter).40 
If  it  be  not  the  work  of  the  individual  mind,  it  is  that 
of  mind  in  general  ;  the  fact  that  each  of  us  finds 
at  the  dawn  of  life  matter  which  has  already  been 
elaborated  must  not  lead  us  to  conclude  that  this  holds 
good  of  the  totality  of  monads.  A  group  of  hereditary 
habits,  re-inforced  by  education,  a  relatively  stationary 
wave  in  the  flux  of  my  becoming,  a  knot  in  my  duration 


which  I  have  neither  strength  nor  time  to  unloose  : 
this  is  a  material  reality.  The  world  is  born  and  advances 
by  means  of  the  inventions  of  liberty ;  it  is  preserved 
and  assured  by  the  inertia  of  habits.41  Pure  matter 
has  a  certain  existence,  it  is  not  a  meaningless  word ;  but 
it  only  becomes  a  thing  through  consciousness  :  in  itself 
it  is  merely  an  obscure  desire  of  images  and  attitudes, 
an  instinct,  an  appetency,  a  will  to  live,  a  kind  of  tension 
towards  a  final  cause  which  develops  it  and  puts  it  in 
motion  ;  it  exists  de  iure  rather  than  de  facto. 

9.  The  Physical  World  as  an  Instrument  of  Moral 
Life. — If  we  thus  conceive  of  the  world  as  an  appeal  to 
the  mind,  a  limit  placed  on  its  action,  we  still  have  to 
explain  the  origin  of  this  obscure  tendency  and  its 
office  like  that  of  a  decree  ;  hence  we  must  refer  to 
a  Being  transcending  necessity  which  subjects  mind  to 
matter.  Thus  we  have  once  more  in  modern  philosophy 
the  old  cosmological  proof  of  the  existence  of  God.4* 
Why  does  matter  exist  ?  To  what  end  have  we  this 
invention,  which  must  be  regarded  as  an  unfortunate 
one  from  a  certain  point  of  view,  limiting  the  liberty 
of  the  mind  ?  According  to  Le  Roy,  the  answer  is 
simple  enough :  the  ballast  of  matter  is  necessary  in 
order  to  enable  the  mind  to  descend  from  the  plane  of 
dreams  to  the  plane  of  effective  action.  Matter  is  a 
fatal  result,  and  at  the  same  time  an  unavoidable  means, 
of  discursive  life  without  which  the  formation  of  society 
would  not  take  place,  the  individual  would  not  enter 
into  possession  of  himself,  and  the  world  would  not 
exist :  such  is  its  nature  and  its  mission.  The  new 
philosophy  admits  a  hierarchy  in  which  moral  and 
religious  action  occupies  the  highest  place,  and  brings— 
as  means — both  practical  and  discursive  action  into 
subjection  unto  itself.  Matter,  the  creation  of  mind, 
is,  according  to  Wilbois,43  the  stadium  in  which 
morality  is  prepared.  In  the  act  of  discovery  the 
intuition  of  the  beautiful,  the  dominion  of  time,  the 
duties  of  abstinence,  humility,  and  abnegation  to  which 
we  have  striven  to  submit  and  which  leave  their  seal 


and  imprint  in  the  most  profound  of  facts,  the  appeal 
to  the  future  to  which  we  feel  ourselves  to  be  more 
subject  than  we  are  to  the  past,  the  creative  power 
which  we  feel  stirring  within  us,  which  raises  us  above 
matter,  and  introduces  us  into  a  new  world,  all  these 
afford  us  unique  moments  of  experience  which  we  shall 
only  find  again  in  the  fullest  hours  of  our  moral  and  religi- 
ous action.  Scientific  life  is  then  the  first  step  towards 
loftier  spontaneity ;  invention  is  fulfilled  in  virtue. 
Matter  has  a  final  cause  which  only  permits  it  to  become 
solidified  into  determinism  in  a  certain  direction,  and  this 
final  cause  must  be  sought  in  the  activity  of  the  scientist : 
the  formula  of  inertia  is  the  final  cause  of  the  fact  of  the 
fall  of  heavy  bodies,  the  Newtonian  formula  of  the  fact 
of  universal  attraction :  matter  tends  towards  law. 
Axioms  and  categories,  forms  of  intellect  and  sensibility, 
all  become,  all  are  evolved.44  The  mind  of  man  is  plastic, 
and  can  change  its  most  intimate  desires,  provided  it 
takes  the  requisite  time  to  do  so.  Intelligence  and 
the  categories  are  then  no  mere  inflexible,  fixed  forms, 
as  Kant  would  have  us  believe  ;  one  a  priori,  however, 
remains  :  the  primordial  needs  and  natural  tendencies  of 
action,  because  primordial  action  to  which  we  turn  for  an 
explanation  of  the  genesis  of  matter  and  reason,  must  not 
be  incoherent ;  it  must  be  regulated  in  order  that  it  may 
carry  out  lasting  and  coherent  work.  •  The  true  a  priori 
is  of  a  religious  and  moral  order.  We  organise  matter 
and  create  practical  life  and  social  relations,  because 
the  moral  law  rules  and  directs  us  :  everything  is  in 
the  last  analysis  based  upon  the  mystery  of  duty. 
The  task  of  philosophy  is  to  illuminate  it  and  subject 
it  to  a  scrutiny  which  will  cause  it  to  reveal  its  specific 
originality  and  inspire  our  intuition  of  it  with  fresh  life.45 
Science,  by  reason  of  the  very  attitude  it  assumes,  and 
the  artifices  of  which  it  makes  use,  increases  the  distance 
between  itself  and  living  concrete  reality,  which  thus 
becomes  for  it  a  noumenon  which  it  cannot  penetrate. 
Philosophic  intuition  alone  can  bring  us  once  more  into 
immediate  contact  with  reality.  The  work  of  the  new 


philosophy  is  to  throw  off  the  bonds  of  number  and  space ; 
to  break  through  the  lifeless  forms  of  a  crude  language;  to 
rise  above  discursive  thought  in  order  to  define  it  and 
pass  judgment  upon  it ;  to  rediscover  the  living  springs 
of  logical  mechanism  in  the  mobile  depths  of  spiritual  life.46 
This  direct  appeal  to  the  inner  soul  of  things,  the  method 
peculiar  to  philosophic  intuition,  will  be  found  also  in 
art,  which  enables  us  to  penetrate  the  symbolic  meaning 
and  dim  soul  of  appearances,  and  shows  us  the  dynamic 
penetration  of  the  living  being  beneath  the  rigidity  of 
the  outline ;  but  it  will  be  found  to  a  greater  degree 
in  the  subtle  and  illogical  art,  so  full  of  dreams  and 
mystery,  of  the  modern  symbolists  than  in  musical  and 
•penetrating  art.47  Art  is,  as  it  were,  the  preface  to 
philosophy ;  but  its  fictions,  though  they  may  reveal 
the  mysterious  basis  of  being,  do  not  penetrate  it,  as 
philosophy  does,  just  because  they  are  fictions.  The 
real  in  its  intimate  and  autonomous  value  is  in  no  case 
discursive  ;  it  can  only  be  experienced,  loved,  or  accom- 
plished according  as  it  is  termed  truth,  beauty,  or  good. 
10.  Ethical  Action  as  a  Means  of  penetrating  Reality : 
Blondel. — Blondel,48  another  opponent  of  intellectualism, 
states  that  according  to  that  which  we  have  experienced, 
loved,  and  done,  we  shall  know  and  possess  in  another 
way,  we  shall  touch,  penetrate,  and  enjoy  things 
differently.  In  love  and  sacrifice  will  be  found  the 
fullest  revelation  of  being :  without  love  there  can  be 
no  understanding.  Charity  is  the  organ  of  perfect 
knowledge,  because  it  puts  into  us -that  which  is  in  others,! 
whereas  selfishness  isolates  us  and  makes  us  impene-j 
trable.  The  willing  acceptance  of  suffering,  voluntary! 
submission  to  the  natural  necessity  which  we  find' 
within  us,  and  which  imposes  limits  upon  us  from! 
without  through  the  extrinsic  action  of  things,  these 
alone  will  enable  us  to  attain  to  the  full  possession  ot 
ourselves  and  of  the  universe.  In  this  supreme  act  of 
abnegation,  which  is  an  act  of  faith,  in  this  ultimate 
option  of  the  will  in  favour  of  true  Being,  which  is  not 
to  be  found  in  the  ephemeral  enjoyment  of  the  passing 


moment,  but  in  the  life  of  the  Eternal,  the  true  and 
intimate  experience  of  Absolute  Reality  will  be 

11.  Criticism  of  Intuitionism.  —  The  intuitionists 
endeavour  with  all  their  might  to  prove  that  there  is 
nothing  objective  in  facts,  laws,  and  scientific  theories  ; 
that  the  whole  of  science  is  an  arbitrary  and  artificial 
construction,  which  is  entirely  created  by  the  mind  for 
the  needs  of  action,  and  that  its  success  is  due  to  the 
fact  that  the  matter  to  which  it  applies  is  also  an  un- 
conscious creation  of  the  mind  of  the  race  under  the 
pressure  of  these  same  needs.  But  this  merely  shifts 
the  problem ;  Le  Roy  perceived  this  and  accordingly 
modified  Bergson's  theory  to  a  certain  extent,  a  theory 
which,  as  we  have  already  pointed  out,  failed  to  explain 
how  free  creative  activity  could  suddenly  give  birth 
to  a  practical  need.  He  recognises — and  in  this  he  is 
at  one  with  Boutroux — that  we  must  admit  the  existence, 
at  all  events  in  pure  matter, — matter,  that  is  to  say, 
which  has  not  been  elaborated  by  the  mind, — of  a 
tendency  towards  intelligence  owing  its  existence  to  a 
moral  imperative.  Moreover,  Le  Roy  considers  intuition 
to  be  not  only  feeling  and  volition,  but  more  especially 
reason ; 49  it  is  the  mind  experienced  in  the  wealth  of 
all  its  aspects.  I  consider  that  this  view  virtually 
transcends  Bergson's  fantastic  intuitionism :  the  mind 
is  no  longer  an  indefinite  creative  power,  but  an  activity 
regulated  by  an  end,  which  is  not  the  product  of  our 
action  nor  yet  of  the  action  of  the  race,  but  a  command 
emanating  from  a  transcendent  Being.  How  is  it 
possible  to  conceive  of  a  universal  end  without  pre- 
supposing the  mind  which  tends  thereto  to  be  possessed 
of  a  certain  vision  of  that  end,  that  is  to  say,  of  a  certain 
intelligence  ?  If  this  end  exists  in  us,  does  it  not  deter- 
mine our  actions,  and  guide  them  in  certain  directions  ? 
What  becomes  of  intuitionism  if  action  be  governed 
by  motive  ?  Further,  if  there  be  a  certain  coherence 
in  the  actions  which  result  in  the  construction  of  matter, 
the  mind  which  performs  those  actions  must  also  partake 


of  the  character  of  coherency  proper  to  logical  thought. 
How  can  we  then  say  that  thought  falsifies  reality  ? 
The  moral  law,  as  a  universal  command,  calls  for  a  mind 
capable  of  thinking  the  universal.  If,  amid  the  manifold 
and  transient  appearances  of  things,  we  seek  the  nature 
common  to  them  all,  if,  even  adopting  Le  Roy's  point 
of  view,  we  affirm  monads  to  be  spiritual  essences  having 
common  tendencies  and  aspirations,  we  go  beyond  the 
moment  of  intuition,  to  grasp  in  our  own  and  in  countless 
other  consciousnesses  the  universal  characteristics  of 
spirituality,  which  cannot  be  intuited,  but  only  conceived. 
There  can  be  no  philosophy  without  concepts  :  even 
your  metaphysic  is  not  the  immediate  life  and  intuitive 
communication  of  ever  new  impressions,  but  conceals 
beneath  its  metaphors  a  system  of  concepts  every  whit  as 
abstract  as  those  of  intellectualism ;  the  organon  of  your 
philosophy  is  not  intuition,  which,  however  far-reaching 
it  may  be,  cannot  give  more  than  the  passing  moment , 
but  the  concept  of  intuition,  the  thought  that  that  immedi- 
ately experienced  activity  is  not  peculiar  to  your  mind 
alone,  but  is  common  to  all  consciousnesses ;  the  thought 
that  your  inmost  actions,  like  the  actions  of  all  mankind, 
tend  towards  a  universal  end.  The  concept  is  not  just  an 
expedient  for  rendering  social  life  possible,  but  is  the  one 
and  only  way  in  which  the  universal  can  be  manifested 
to  consciousness  ;  even  that  which  the  new  philosophy 
terms  intuition  is  at  bottom  but  a  vague,  dim,  indis- 
tinct concept,  which  is  unconscious  of  itself.  Further, 
scientific  activity  as  a  whole,  in  as  much  as  its  aim  is  to 
emphasise  that  which  is  universal  amid  the  various 
and  changing  aspects  of  phenomena,  is  not  directed 
towards  action  only,  but  tends  to  show  us  a  charac 
of  reality.  In  short,  either  you  believe  that  the  vario 
spiritual  actions  have  something  in  common  which 
ever  being  repeated,  in  which  case  you  must  recogni 
the  value  of  intelligence,  which  alone  is  capable  o 
grasping  this  universal  element ;  or  you  hold  that  eac 
action  is  entirely  new,  in  which  case  you  are  not  justifi 
in  affirming  that  all  the  appearances  of  nature  a 


spiritual  actions,  that  all  tend  equally  to  the  same  end, 
have  their  source  in  the  same  supreme  principle,  in  one 
and  the  same  moral  command.  There  undoubtedly  exist 
in  man  forces  other  than  intelligence,  and  of  these 
philosophy  must  take  account,  but  it  can  only  do 
so  by  means  of  concepts.  Feeling  and  instinct,  as 
Poiricare  rightly  observes,50  may  act  as  its  guide,  but 
cannot  render  it  of  no  avail ;  they  can  direct  the  glance, 
but  not  take  the  place  of  the  eye.  Intelligence  is  a 
tool  with  which  we  cannot  dispense,  if  we  would  philo- 
sophise and  not  compose  music  or  poetry ;  even  if  we 
conclude  with  the  primacy  of  action,  it  is  intellect 
which  arrives  at  this  conclusion.  Philosophy  which 
does  not  make  use  of  the  intelligence  is  a  contradiction 
in  terms  :  in  order  to  set  up  a  system  of  philosophy,  any 
system  of  philosophy  whatsoever,  even  the  new  philo- 
sophy itself,  we  must  leave  behind  us  concrete  duration, 
and  the  intuitively  experienced  moment,  and  look  at 
the  world  sub  specie  aeternitatis.  We  must  not  confound 
the  cognitive  function  with  the  aesthetic  function. 
Both  contain  creation  and  activity ;  but  the  product 
of  intelligence  is  always  something  of  universal  value, 
whereas  the  product  of  imagination  gains  in  value  in 
proportion  as  it  is  original,  and  gives  utterance  to  the 
individual  personality  even  in  its  transient  impressions. 
Art  may  break  the  bonds  of  natural  necessity  and  create 
for  itself  a  world  which  is  ever  new ;  but  this  freedom 
of  creation  is  denied  to  science  and  philosophy  alike. 
The  concept,  too,  is  a  production  of  mind,  but  it  is  not 
of  value  as  a  creation  or  as  a  flash  of  fruitful  genius, 
as  is  asserted  by  Wilbois,  who  strangely  confounds  the 
beautiful  and  the  true,  but  only  in  as  far  as  it  corre- 
sponds to  something  objective  which  is  independent  of 
the  creative  consciousness.  Moreover,  we  cannot  set  up 
this  correspondence  by  artificial  means  :  there  are  always 
elements  beyond  the  control  of  our  will,  which  are  thrust 
upon  us,  not  only  in  actual  matter,  which  Le  Koy  regards 
as  a  construction  of  the  race  which  has  in  the  course 
of  time  become  an  instinctive  mechanism,  but  also  in 


pure  matter,  divested  of  everything  introduced  into  it 
by  the  act  of  perception. 

12.  Theoretical  Value  of  Science. — The  scientific  man 
I  does  not  createscjejitificJa£t_at-»dll,  But  aHowsTumself 
to-  be  guiHeoT^ythe  suggestions  of  brute  fact.  The 
examples  adduced  by  Le  Roy  are  no  proof  to  the  con- 
trary. When  the  astronomer  states  that  the  eclipse 
took  place  at  nine  o'clock,  he  does  not  create  the 
hour,  but  deduces  it  from  a  brute  fact,  from  what  his 
watch  tells  him  :  undoubtedly  he  might  say  that  it  was 
eleven,  but,  by  doing  so,  he  would  set  up  another  con- 
vention. The  only  truth  contained  in  Le  Roy's  _thesis 
is  that  the  scientific  jp_ajj_j>ja.ya  an  active  p^rt  jp  thp. 
selectionof Jl^  lasts  which  are-^yorthv  of  notice  :  an 
isolatecTTact  is  of  no  interest  to  him ;  he"  selects  one,  if 
it  can  aid  him  to  predict  others  ;  but  facts  are  facts, 
and  their  conformity  to  previsions  is  not  dependent 
upon  our  free  activity.51  In  like  manner  the  choice  of 
the  unit  of  measurement  is  certainly  arbitrary,  but  this 
[  is  no  proof  of  the  arbitrariness  of  natural  law.  Abbe 
L~Mariotte  estimated  the  volume  of  gases  in  cubic  inches, 
and  the  column  of  mercury  by  which  their  pressure  is 
measured  in  feet ;  has  the  law,  which  was  true  according 
to  the  old  units  of  measurement,  ceased  to  be  so  since  the 
adoption  of  the  new  units  ?  The  only  thing  which  is 
dependent  on  the  choice  of  the  unit  is  the  number  which 
measures  a  given  magnitude,  not  the  magnitude  itself  : 
the  principle  of  homogeneity  allows  the  physicist  to 
pass  from  one  system  of  fundamental  units  to  another 
by  means  of  a  simple  calculation,  without  being  obliged 
to  take  fresh  measurements.  The  formulas  of  physical 
laws  do  not  change  when  the  unit  is  altered,  because 
the  relations  between  magnitude  which  they  express 
are  independent  of  the  units  selected.52  To  this  Le 
Roy  rejoins  that  Mariotte's  law  undoubtedly  still  holds 
good  when  the  metre  instead  of  the  yard  is  taken  as 
the  unit  of  length  ;  but  that  this  is  due  to  the  fact  that 
the  two  units  stand  in  a  constant  relation,  so  that  the 
transition  from  the  one  to  the  other  is  really  but  a  change 


of  script ;  this,  however,  would  no  longer  hold  good  if 
the  distance  from  the  sun  to  the  earth  were  adopted  as 
the  unit ;  in  that  case  time  would  intervene,  and  the 
formula  of  the  law  would  be  modified,  yet  it  would 
not  cease  to  be  of  use  in  the  ordering  of  phenomena. 
Moreover,  may  not  the  constancy  of  the  unit  of  measure- 
ment be  a  fiction  ?  The  choice  of  a  unit  is  equivalent  to 
the  choice  of  a  point  of  view  from  which  to  contemplate 
the  world ;  and  this  point  of  view  depends  upon  the 
conditions  of  our  physical  activity,  our  habits  of  speech, 
and  the  feebleness  of  our  senses.  In  conclusion,  the 
devices  used  to  define  these  units,  and  the  fact  that  every 
measurement  is  made  by  means  of  a  more  or  less  compli- 
cated experiment,  force  us  to  state  that  the  most  insigni- 
ficant quantitative  law  is  dependent  upon  an  immense 
number  of  conventions  and  decrees  which  make  it  solidary 
with  science  as  a  whole.53  But,  we  may  ask,  is  then  the 
postulate  that  the  unit  of  measurement,  and  hence  the 
magnitude,  is  possessed  of  constant  value  absolutely 
arbitrary  ?  It  is  true  that  experience  never  affords  us 
absolute  constancy,  but  we  see  that  the  more  nearly  the 
causes  of  error  are  eliminated,  the  more  nearly,  that  is  to 
say,  we  succeed  in  isolating  the  phenomenon,  thus  realis- 
ing the  ideal  conditions  of  our  thought,  the  more  closely 
does  it  approximate  thereto.  We  see  then  that  experi- 
ence yields  to  our  exigencies,  and  that  it  may  be  resolved 
into  abstract  elements  and  translated  into  our  formulas  ; 
may  we  not  fairly  argue  from  this  that  there  must  be 
some  constants  in  nature,  even  if  they  are  not  the 
same  as  ours  ?  We  cannot  of  course  assert  that  our 
concepts,  our  divisions,  our  points  of  view,  the  structure, 
that  is  to  say,  of  our  science  in  its  minutest  details 
corresponds  to  the  structure  of  things ;  our  knowledge 
is  always  a  reconstruction  which  may  be  accomplished 
in  various  ways,  by  means  of  various  systems  of  concepts 
and  various  relations,  and  hence  with  the  help  of  different 
formulas ;  but  this  variety  is  no  proof  that  science  is 
arbitrary  and  unable  to  afford  us  anything  real ;  it  is 
rather  a  proof  of  the  contrary,  since  it  shows  us  that  the 


possibility  of  translating  that  group  of  phenomena  into 
mathematical  language  is  not  a  contingent  fact,  relative 
to  a  point  of  view,  but  is  in  the  very  nature  of  things, 
and  is  independent  of  our  special  way  of  looking  at  them. 
Le  Roy  himself  M  ends  by  recognising  that,  if  the  choice 
of  the  unit  of  measurement  be  arbitrary,  there  is  some- 
thing which  is  independent  of  our  will,  i.e.  the  fact  that 
nature  is  measurable.  We  can  decompose  phenomena 
into  abstract  elements  in  various  ways,  and  take  certain 
functional  relations  into  consideration  rather  than 
others,  but  it  does  not  depend  upon  us  whether  the  law 
be  verified  or  not:  once  we  have  chosen  a  point  of 
view,  we  are  no  longer  free  to  make  facts  say  what  we 
please  :  nature  sets  us  a  limit,  pits  her  decrees  against 
ours,  and  puts  us  in  danger  of  failure  if  we  do  not  respect 
them.  Le  Roy  says  that  our  laws  are  but  definitions 
in  disguise,  and  succeed  merely  because  we  choose,  and 
because  we  eliminate  the  cases  which  do  not  accord 
with  them.  When  I  state  that  phosphorus  melts  at  a 
temperature  of  44°  C.,  I  am  under  the  impression  that  I 
am  enunciating  a  law  ;  in  reality,  however,  I  am  merely 
defining  phosphorus  ;  were  another  body  to  be  discovered 
which,  while  possessed  of  all  the  properties  of  phosphorus, 
did  not  melt  at  44°,  another  name  would  be  given  to 
it,  and  the  law  would  still  be  true.  Thus,  again,  when 
I  say  that  heavy  bodies,  falling  freely,  traverse  spaces 
proportional  to  the  squares  of  the  times,  I  do  but  define 
free  descent ;  whenever  the  condition  is  not  fulfilled  I 
shall  say  that  the  descent  is  not  free,  so  that  the  law  can 
never  be  contradicted.  Now  it  is  obvious  that,  were  it 
possible  to  reduce  the  law  to  this,  it  would  be  of  no  use 
either  as  a  means  of  knowledge  or  as  a  principle  of 
action.  When  I  say  that  phosphorus  melts  at  44°,  I 
mean  thereby  that  every  body  possessed  of  all  the 
properties  of  phosphorus  except  the  point  of  fusion 
will  melt  at  44°  ;  taken  in  this  sense,  the  proposition 
is  a  law  which  may  be  of  service  to  me,  since,  if  I  find 
a  body  possessed  of  these  properties,  I  can  predict 
that  it  will  melt  at  44°.  It  is  possible  that  another 


body  like  phosphorus  may  be  discovered  which  will  not 
melt  at  44°,  but  in  that  case  the  other  properties  will 
not  be  absolutely  identical,  and,  should  they  seem  to 
be  so,  it  will  be  due  to  our  imperfect  means  of  observa- 
tion.55 Thus  it  would  avail  me  nothing  to  have  given 
the  name  of  free  descents  to  those  descents  which  take 
place  in  conformity  with  the  laws  of  Galileo,  if  I  did  not 
know  under  what  conditions  the  descent  can  be  termed 
free  or  approximately  so ;  the  law  establishes  precisely 
that  if  these  conditions  be  fulfilled,  the  descent  will  take 
place  in  accordance  with  the  formula  of  Galileo.  The  free 
descent  is  not  defined  by  the  law,  but  is  determined  by 
other  criteria,  absence  of  any  obstacle,  perfect  void, 
etc.  If  this  were  not  the  case,  the  law  would  be  reduced 
to  a  meaningless  tautology.  Poincare  has  endeavoured 
to  correct  and  moderate  the  paradoxical  conclusions 
reached  by  Le  Roy  by  exaggerating  the  importance 
of  the  conventional  element  in  scientific  construction. 
When  a  law  has  been  sufficiently  confirmed  by  experience^! 
we  are  at  liberty  to  adopt  two  attitudes  towards  it : 
we  may  either  leave  it  amongst  the  other  laws  which  are 
subject  to  constant  revision,  or  we  may  set  it  up  as  a 
principle,  by  adopting  a  convention  of  such  a  nature 
that  the  law  must  of  necessity  always  remain  true.  In 
order  to  do  so,  we  intercalate  between  the  two  brute 
facts  A  and  B — the  former  terms  of  the  primitive  law 
— an  abstract  concept  of  a  more  or  less  fictitious  order, 
resolving  that  law  into  a  principle  which  is  a  definition, 
and  thus  removed  from  all  experimental  control,  and 
a  part  which  can  still  be  verified.  Thus  the  law, 
"  the  stars  follow  the  law  of  Newton,"  may  be  resolved 
into  these  two  others  :  gravitation  follows  the  law  of 
Newton ;  gravitation  is  the  only  force  which  can  act 
upon  the  stars  ;  of  these  the  former  is  a  definition  which 
is  beyond  the  control  of  experience,  the  latter,  on  the 
contrary,  must  be  verified.  The  latter  only  can  be  termed 
true  or  false ;  whereas  the  principle,  which  has  now  been 
crystallised,  is  neither  true  nor  false,  but  merely  con- 
venient.56 If  it  be  possessed  of  a  degree  of  truth  and 


certainty  which  is  lacking  in  the  experimental  truths  from 
which  it  has  been  extracted,  this  is  due  to  the  fact  that 
it  may  be  reduced  in  the  last  analysis  to  a  mere  con- 
vention, which  we  are  entitled  to  set  up,  since  we  are 
assured  that  no  experience  will  contradict  it.  That 
which  is  gained  in  certainty  is  lost  in  objectivity. 
Principles  are  disguised  conventions  and  definitions ; 
but  their  adoption  is  not  a  purely  arbitrary  proceeding, 
it  is  not  a  whim  of  ours,  because  certain  experiences 
have  shown  us  that  these  conventions  are  useful.57  On 
the  other  hand,  the  term  conventional  cannot  be  applied 
to  the  whole  of  science  :  there  is  always  a  portion  of 
the  law  which  cannot  be  transformed  into  principle. 
Although,  then,  the  conditions  may  vary,  something 
constant  will  always  be  left,  the  relation  between  the 
two  brute  facts.  The  part  of  facts  which  is  the  creation 
of  the  man  of  science  is  only  the  convenient  language  in 
[  which  he  enunciates  them.58 

13.  Criticism  of  the  Arguments  of  Duhem  against  the 
Objective  Value  of  Science. — Duhem  M  has  adduced  new 
arguments  in  favour  of  the  thesis  of  Le  Roy,  and  against 
the  criticisms  of  Poincare.  Physical  observation  is  not 
merely  the  observation  of  a  phenomenon,  but  is  also 
the  theoretical  interpretation  of  this  phenomenon, 
which  replaces  the  concrete  data  of  observation  by  an 
abstract  and  symbolic  presentment.  Thus,  for  instance, 
Regnault  has  not  left  us  the  description  of  the  concrete 
facts  of  his  experiments  on  the  compressibility  of  gases, 
but  only  a  transcription  of  them  into  abstract  terms, 
temperature,  pressure,  volume,  etc.  ;  and  each  of  these 
notions  presupposes  a  theory  which  must  be  known 
in  order  that  the  explanation  of  the  experiment  may  be 
intelligible.  Between  phenomena,  as  actually  observed 
in  the  course  of  an  experiment,  and  the  result  of 
this  experiment  as  formulated  by  the  physicist,  an 
extremely  complicated  intellectual  elaboration  is  inter- 
polated, which  substitutes  an  abstract  and  symbolic 
judgment  for  a  description  of  concrete  facts.  The 
use  of  the  instruments  found  in  the  laboratory  woul" 


be  impossible,  unless  the  concrete  objects  composing 
these  instruments  were  replaced  by  an  abstract  and 
symbolic  representation,  giving  a  hold  to  mathematical 
reasoning,  and  if  this  combination  of  abstractions  were 
not  subjected  to  deductions  and  calculations,  in  which 
adhesion  to  the  theory  is  already  implied.  Before 
accepting  the  result  of  the  experiment  made  by  the 
physicist,  we  must  then  see  the  theory  on  which  it  is 
based.  The  contradiction  which  so  frequently  exists 
between  experimental  data  does  not  he  in  the  facts  but 
in  the  theories  upon  which  the  interpretation  of  them  has 
been  based.60  The  result  of  an  experiment  in  physics  is 
not  as  certain  as  a  fact  observed  in  a  non-scientific  way, 
by  the  mere  sight  or  touch  of  a  man  of  healthy  mind 
and  body,  because  it  is  always  subordinated  to  the 
confidence  inspired  by  a  whole  mass  of  theories.  A 
law  of  common  sense,  being  a  general  judgment,  may 
be  true  or  false  ;  not  so  the  laws  which  physical  science, 
at  its  highest  stage  of  development,  enunciates  in  the 
form  of  mathematical  propositions.  These  laws  are 
indeed  always  symbolic,  and  a  symbol  is,  strictly 
speaking,  neither  true  nor  false  ;  it  can  only  be  said 
that  it  has  been  more  or  less  well  chosen  to  represent 
a  certain  reality,  that  it  expresses  this  reality  in  a  more 
or  less  accurate,  and  more  or  less  detailed  form.  Let 
us  consider  a  series  of  analogous  facts  :  to  the  physicist 
the  discovery  of  the  law  governing  these  facts  means  the 
discovery  of  a  formula  containing  the  symbolic  repre- 
sentation of  each  of  them ;  and,  since  the  symbols  are 
indeterminate,  the  formula  uniting  them  will  be  so  also. 
An  infinite  number  of  different  formulas  can  be  made 
to  correspond  to  one  and  the  same  group  of  facts,  seeing 
that  there  is  an  infinite  number  of  values  which  may 
be  chosen  as  the  approximate  results  of  experimental 
measurements.  These  formulas  are  algebraically  incom- 
patible, but  they  are  all  equally  acceptable  to  physics, 
since  they  determine  the  phenomenon  more  nearly 
than  observation  can  do.  The  choice  of  one  rather 
than  another  of  these  formulas  is  made  not  because 


the  one  selected  is  truer  than  the  others,  but  because 
it  is  simpler.61  A  physical  law  is  provisional,  because 
it  represents  the  facts  to  which  it  applies  by  means  of 
an  approximation  which  physicists  at  present  consider 
to  be  adequate,  but  which  will  one  day  cease  to  satisfy 
them  ;  it  is  relative  in  the  sense  that  this  approximation 
may  suffice  for  the  use  which  one  physicist  desires  to 
make  of  it,  but  not  for  another.  The  same  physicist 
at  two  different  periods  of  his  life  may  accept  or  reject 
a  law ;  this  would  not  be  possible  could  the  law  be 
either  true  or  false,  since  in  that  case  a  contradiction 
would  be  involved.62  A  physical  law  is  provisional  also 
because  it  is  symbolic,  and  cases  will  always  be  found  in 
which  the  symbols  which  enter  into  it  no  longer  represent 
reality  in  a  satisfactory  manner.  The  struggle  between 
reality  and  laws  will  continue  indefinitely :  sooner  or 
later  reality  will  confront  every  law  formulated  by 
the  physicist  with  some  rude  contradictory  fact ;  but 
physical  science  will  never  weary  of  correcting,  modifying, 
and  complicating  the  law,  that  it  may  give  place  to 
one  which  is  more  comprehensive,  containing  the  rule 
applying  to  the  exception  revealed  by  experience. 

Duhem  is  right  in  asserting,  in  contradiction  to 

Poincare,    that    the    transition    from    brute    fact    to 

scientific  fact,  and  hence  to  law,  is  not  a  mere  change 

of    language,    but    is    fact    pervaded    by    theoretical 

elements ;   except  that  from  these  premisses  it  is  not 

allowable  to  conclude  that  law  is  purely  conventional, 

approximate,    and   symbolic,    and   cannot   be   termed 

either  true  or  false.    We  must  clearly  understand  what 

meaning  we  attach  to  the  idea  of  scientific  truth.    We 

'have  already  seen,  when  discussing  empiric-criticism, 

I  that  to  reduce  the  true  to  the  useful,  convenient,  and 

I  economical  is   simply  to  beg  the  question,  because  a 

"law  or  theory  would  be  of  no  service  in  foreseeing,  did 

it  contain  nothing  objective,  or  did  it  fail  to  reflect 

some  real  relation.     The  true  criterion  of  which  science 

makes  use  is  the  harmony  and  logical  coherency  of  the 

system  on  the  one  hand,  and  agreement  with  the  facts 


and  relations  of  experience  on  the  other.  The  experience 
of  things,  however  largely  spiritual  activity  may 
contribute  to  it,  is  not  entirely  the  creation  of  the 
subject,  but  contains  elements  derived  from  extraneous 
factors,  which  to  a  certain  extent  guide  and  regulate 
the  development  of  the  scientific  construction :  the 
fact  that  sensations  succeed  one  another  and  co-exist 
in  this  or  that  way  does  not  depend  upon  our  will^J 
and  is  not  a  convention  of  our  making.  Even  £Ee 
most  rabid  contingentists  have  been  forced  to  stop  short 
at  this  insuperable  barrier.  The  two  criteria  of  which 
we  have  spoken  are  not  of  course  a  measure  of  absolute 
and  eternal  truth,  which  will  ever  remain  a  pure  limit- 
ing concept,  a  regulating  idea  of  the  cognitive  function  ; 
they  will,  however,  enable  us  to  estimate  our  knowledge, 
and  to  determine  the  degree  of  truth  contained  therein, 
according  to  the  greater  or  less  degree  to  which  it 
realises  that  ideal.  The  system  which  is  absolutely 
coherent  from  the  logical  point  of  view,  and  which 
affords  perfect  satisfaction  to  the  intelligence,  will  never 
be  fully  realised,  hence  the  ceaseless  efforts  made  by 
philosophy  and  science  ;  this  does  not,  however,  amount 
to  saying  that  all  systems  are  of  equal  value,  or  that 
they  are  all  on  the  same  level :  though  no  one  of  them 
be  absolute  and  eternal  truth,  a  hierarchy  may  be  estab- 
lished among  them,  in  which  those  which  are  most 
harmonious  and  comprehensive  will  rank  highest.  Thus 
we  shall  never  arrive  at  the  construction  of  a  theory 
able  to  resist  all  the  attacks  of  future  experience,  we 
shall  never  succeed  in  exhausting  the  realm  of  the 
unknown,  but  comparison  with  the  mass  of  known 
facts  will  teach  us  to  decide  which  is  the  most  adequate 
formula,  and  which  most  nearly  approaches  the  truth. 
Duhem  says  that  law  is  not  true,  but  approximate ; 
what  meaning,  however,  are  we  to  attach  to  the  word 
approximation,  and  how  are  we  to  decide  its  degree  if 
we  do  not  admit  the  existence  of  a  law  which  is  true  in 
the  absolute  sense,  a  law  which  we  are  ever  striving  to 
approach  more  nearly  by  correcting  and  completing  our 


formulas  ?  The  results  of  our  measurements  are  not  pos- 
sessed of  absolute  constancy,  hence  various  values  may  be 
obtained  which  are  mutually  exclusive  from  the  mathe- 
matical point  of  view,  but  which  are  equivalent  from  the 
physical  point  of  view,  because  our  appliances  are  not 
sensible  of  those  differences ;  are  we  then,  asks  Duhem, 
to  say  that  they  are  all  true  ? 63  Is  not  this  a  logica 
absurdity  ?  Assuredly,  if  we  take  the  word  true  in  the 
absolute  sense,  because  in  that  case  the  real  value  of  that 
magnitude  can  be  but  one  ;  but  in  the  relative  sense  the 
other  values  may  be  more  or  less  true,  in  proportion  as 
they  approach  more  or  less  closely  to  this  real  value;  and, 
though  we  do  not  at  present  succeed  in  drawing  such  a 
distinction,  the  future  of  science  will  enable  us  to  do  so 
by  perfecting  our  appliances.  We  shall  then  be  forced 
to  correct  our  formulas  ;  this  does  not,  however,  imply 
that  these  formulas  were  absolutely  indifferent  to  truth 
and  falsehood.  The  physicist  does  not  accept  two 
ifferent  formulas  as  equivalent  because  he  is  indifferent 
(  to  the  search  after  truth ;  he  is  well  aware  that  one  ol 
them  must  be  more  nearly  true  than  the  other,  but 
science  does  not  for  the  time  being  afford  him  the  means 
of  selection.  If  truth  be  thus  understood  in  the  relative 
sense,  Duhem's  criticism  confirms  rather  than  weakens 
the  truth- value  of  scientific  law  :  the  law  is  true  just 
in  so  far  as  it  is  approximate ;  the  more  approximate 
it  is,  the  truer  will  it  be.  If  we  put  aside  this  unit  of 
measurement,  if  we  deny  that  law  is  of  any  value  as  a 
revealer  of  one  aspect  of  the  real,  will  not  the  affirma- 
tion that,  as  science  advances,  formulas  will  become 
more  precise  and  laws  more  approximate  become  utterly 
meaningless  ?  Our  thought  is  not  Absolute  Thought ; 
but  neither  is  it  a  system  of  fictions  devoid  of  all  objective 
value.  Our  knowledge,  fragmentary  as  it  is,  yet  reveals 
one  aspect  of  reality  to  us  ;  it  can  lay  no  claim  to  embrace 
all  the  relations  of  things,  but  it  strives  to  comprehend 
as  many  as  possible  by  varying  its  points  of  view  ;  it 
contains  something  false,  but  it  strives  ever  more 
earnestly  to  eliminate  it,  by  extending  the  range  of  its 


observations.  It  is  certainly  an  arbitrary  act,  a  pure 
convention  to  isolate  a  phenomenon,  and  to  take  into 
consideration  merely  one  of  its  aspects  apart  from  the 
rest ;  but  the  scientific  man,  when  he  does  this,  is  well 
aware  that  the  aim  of  this  separation  is  only  to  facilitate 
study,  and,  when  he  wishes  to  think  of  the  phenomenon 
in  its  true  reality,  he  takes  into  account  the  other 
elements  which  he  has  neglected.  Something  will 
always  escape  him,  his  system  is  of  necessity  incomplete, 
but  the  laws  which  he  formulates,  though  they  may  not 
be  exactly  the  relations  of  things,  and  all  the  relations, 
approximate  ever  more  nearly  thereto,  as  they  become 
increasingly  true.  Thus,  then,  if  there  is  no  absolutely 
certain  experimental  law,  there  are  principles  which 
have  stood  the  test  of  facts  better  than  others,  and  have 
shown  us  how  to  render  the  world  of  experience  intel- 
ligible, so  that  we  may  regard  them  as  being  relatively 
more  certain  than  others  ;  therefore,  should  an  experi- 
ment not  verify  a  prevision  of  ours,  we  are  justified  in 
suspecting  this  failure  to  be  due  to  the  less  solid  portion 
of  our  construction.  If,  when  we  have  modified  one 
of  these  less  certain  laws,  we  see  that  the  experiment 
is  successful,  we  may  be  relatively  sure  that  the  defect 
originated  there.  Finally,  if  Duhem's  arguments  prove 
that  the  value  of  absolute  reality  cannot  be  ascribed 
to  physical  law,  they  fail  entirely  to  show  it  to  be  in- 1 
capable  of  a  greater  or  lesser  degree  of  truth. 


1  Revue  de  metaphysique  et  de  morale  (1893),  vol.  i.  pp.  20-22. 

2  La  Philosophie  en  France  dans  le  19e  siecle,  p.  322. 

3  De  la  contingence  des  lois  de  la  nature  (Paris,  1899),  2nd  ed.  p.  170. 
The  reduction  of  physical  laws  to  habits  had  already  been  accomplished 
by  Ravaisson  (De  F  habitude,  p.  39). 

4  De  Fidee  de  loi  naturelle  dans  la  science  et  la  philosophie   contem- 
poraines  (Paris,  1901),  2nd  ed.  p.  143. 

8  Op.  cit.  pp.  15-16. 
'  Op.  cit.  p.  20. 

7  Op.  cit.  p.  26. 

8  Op.  cit.  p.  35. 


•  Op.  cit.  p.  38. 
"  Op.  cit.  p.  49. 
u  Op.  cit.  p.  60. 
12  Op.  cit.  p.  68. 
»  Op.  cit.  p.  81. 

14  Essai  sur  les  conditions  et  les  limites  de  la  certitude  logique  (Paris, 
1894),  p.  233. 

"  Op.  cit.  p.  19. 

16  U  Evolution  creatrice  (Paris,  1907),  p.  270. 

17  Op.  cit.  p.  216  ff. 

18  Bergson,  Essai  sur  les  donnees  immediates  de  la  conscience  (Paris 
1889),  p.  96  ff. 

19  Plotinus  also  regards  extension,  if  not  as  an  inversion  of  the  origina 
Being,  as  a  weakening  of  its  essence,  one  of  the  last  stages  of  degradation 
(Enneads,  iv.  iii.  9-10  ;  and  m.  vi  17-18). 

10  Op.  cit.  p.  227  ff. 
n  Op.  cit.  p.  237. 
"  Op.  cit.  p.  239. 

23  Die  Phantasie  als  Orundprinzip  der  Weltprozess  (Munich,  1898). 

24  Baldwin,  too,  in  his  Thought  and  Things,  voL  i.  preface,  p.  x.  sq. 
looks  to  aesthetic  experience,  which  alone  is  capable  of  transcending  th 
dualism  of  subject  and  object,  individual  and  universal,  etc.,  created  b 
logical  and  practical  activity,  for  the  fullest  and  most  direct  revelatio 
of  reality :    "  It  is,  on  the  contrary,  in  a  form  of  contemplation,  aestheti 
in  character,  that  the  immediacy  of  experience  constantly  seeks  to  re 
establish  itself.     In  the  highest  form  which  comes  to  itself  as  genuine  an 
profound  aesthetic  experience,  we  find  a  synthesis  of  motives,  a  mode  i 
which  the  strands  of  the  earlier  and  diverging  dualisms  are  merged  an 
fused.     In   this   experience  .  .  .  consciousness   has   its   completest   an 
most  direct  and  final  apprehension  of  what  reality  is  and  means." 

25  "  L' Esprit  positif,"  Revue  de  metaphysique  et  de  morale  (Septembe 
1901),  p.  597  ff. 

24  Op.  cit.  p.  598. 
17  Op.  cit.  p.  608. 

28  Op.  cit.  p.  643. 

29  "  Un  Positivisme  nouveau,"   Revue  de  metaphysique  et  de  mora 
(March  1901),  p.  140  ff. 

80  "  Science  et   philosophic,"   Revue    de    metaphysique   et  de   mora 
(September  1899),  p.  515  ff. 

81  Le  Boy,  "  Science  et   Philosophic,"  Revue  de  metaphysique   et 
morale  (September,  1899),  p.  518. 

82  Un  Positivisme  nouveau,  p.  144. 
88  Op.  cit.  p.  524. 

84  Op.  cit.  p.  527  ff. 

88  Cp.  on  this  point  the  analyses  of  Duhem,  La  Theorie  physique  (Paris, 
1906),  p.  308,  and  of  Milhaud,  Le  Rationnel,  p.  66. 

84  We  will  enter  on  a  more  detailed  discussion  of  these  new  theories 
in  the  realm  of  mathematics  and  physics  in  the  second  part  of  this  work 

87  Le  Roy,  op.  cit.  p.  559  ff . 

88  "  Sur  quelques  objections   adressees   a   la   nouvelle   philosophic, 
Revue  de  metaphysique  et  de  morale  (July  1901),  p.  409  ff. 

•»  Op.  cit.  p.  413. 

40  Op.  cit.  p.  415. 

41  Op.  cit.  p.  417. 
«  Op.  cit.  p.  425. 


«3  U  Esprit  positif,  p.  638. 

44  Le  Roy,  op.  cit.  p.  428. 

45  "  Science   et  philosophic,"   Revue  de    metaphysique    et'   de  morale 
(January  1900),  p.  66. 

48  "  Science    et    philosophic,"   Revue    de  metaphysique  et  de  morale 
(November  1899),  p.  719. 

47  Op.  cit.  p.  731. 

48  "  L'lllusion  idealiste,  "  Revue  de  metaphysique  et  de  morale  (November 
1898),  p.  742  ;  V Action  (Paris,  1893),  pp.  443  ft.,  468,  479. 

49  Op.  cit.  pp.  314-317. 

60  La  Valeur  de  la  science  (Paris,  1906),  p.  217. 

51  Poincare,  op.  cit.  p.  233. 

52  Couturat,  "  Contre  le  nominalisme  de  M.  Le  Roy,"  Revue,  de  meta- 
physique et  de  morale  (January  1900),  p.  88.     Cp.  also  Brunschwigg,  "  La 
Philosophic  nouvelle  et  1'intellectualisme,"  ibid.  (July  1901),  p.  468. 

58  "  Reponse  a  M.  Couturat,"  Revue  de  metaphysique  et  de  morale 
(March  1900),  p.  225  ff. 
54  Op.  cit.  p.  226. 

65  Poincare,  La  Valeur  de  la  science,  p.  236. 
M  Poincare,  op.  cit.  p.  238  ff. 
67  Science,  et  Hypothese  (Paris,  1905),  p.  163. 
58  La  Valeur  de  la  science,  p.  231. 
69  La  Theorie  physique,  p.  235  ff. 

80  Op.  cit.  p.  261. 

81  Op.  cit.  p.  279. 
8i  Op.  cit.  p.  283. 

63  Duhem,  op.  cit.  p.  246. 




1.  Pragmatism  as  Evolutionary  Transformation 
English  Empiricism.  —  Anglo  -  American  pragmatism 
though  at  first  sight  it  may  appear  to  be  a  revolutionar] 
philosophy,  is  in  reality  but  an  evolutionary  transf orma 
tion  of  the  old  English  empiricism.  James  himsel 
shows  this  clearly  in  the  dedication  of  his  last  volume 
Pragmatism,  to  the  memory  of  Stuart  Mill,  and  also  in  the 
sub-title  of  that  work,  A  New  Name  for  Some  Old  Way 
of  Thinking.1  Into  what  facts  can  an  idea  be  resolved  ? 
What  is  its  value  in  terms  of  special  experiences  ?  This 
is  the  problem  which  James  considers  that  the  English 
school  has  always  more  or  less  consciously  striven  to 
solve.  Locke,  in  fact,  treats  the  question  of  persona 
identity  in  this  way,  reducing  its  meaning  to  the  series 
of  our  detailed  recollections,  the  only  part  thereof  which 
can  be  verified  in  a  concrete  manner,  and  eliminating 
the  idea  of  spiritual  substance  as  useless  and  unimportant, 
By  means  of  the  same  procedure  Berkeley  finds  in 
sensations,  connected  and  ordered  in  different  ways, 
the  practical  value  of  the  idea  of  matter,  and  David 
Hume  recognises  in  the  concept  of  cause  merely  the| 
habitual  tendency  to  expect  like  phenomena  in  like 

2.  The  Pragmatism  of  Peirce. — Charles  Sanders 
Peirce,8  who  was  the  first  to  make  use  of  the  word 
pragmatism,  really  did  nothing  but  set  forth  explicitly 
that  principle  which  had  been  the  instinctive  guide  oi 



these  philosophers.  According  to  Peirce,  the  activity 
of  thought  tends  to  attain  rest  in  a  belief,  because  it  is 
only  then  that  we  can  have  a  stable  and  sure  guide  to 
our  actions  upon  objects.  Beliefs  are  rules  of  action, 
and  the  function  of  thought  has  no  other  end  than  the 
production  of  active  habits.  All  ideas  which  fail  to 
determine  any  difference  in  the  practical  results  of 
thought  form  no  true  and  proper  part  of  its  meaning. 
In  order  to  develop  such  a  content,  we  need  therefore 
merely  specify  exactly  what  line  of  conduct  it  is  suited 
to  produce  :  there  is  no  possible  distinction  in  the 
meaning  of  our  ideas  which  does  not  give  rise  to  a 
difference  of  a  practical  order.  Hence,  if  we  would 
attain  to  complete  lucidity  of  thought  relative  to  an 
object,  we  must  merely  consider  what  sensations,  either 
immediate  or  remote,  are  to  be  expected  from  it,  and 
what  reactions  we  should  prepare  in  case  the  object 
should  prove  to  be  true.  The  positive  significance  of 
ideas  lies  in  these  practical  consequences,  all  other  more 
or  less  subtle  distinctions  are  valueless. 

3.  Utilitarianism  and  Pragmatism.  Anglo-American 
pragmatism  did  not,  however,  stop  short  at  Peirce's 
position,4  but  went  still  farther.  It  does  not  merely 
say :  "  The  value  of  ideas  lies  in  the  practical  con- 
sequences," but  speaks  of  good  results,  and  ends  by 
simply  identifying  the  true  with  the  useful  and  opportune. 
The  utilitarianism  of  Bentham  and  Mill,  which  was  at 
first  confined  to  the  sphere  of  moral  life,  boldly  entered 
upon  a  desperate  undertaking,  rather  than  confess 
itself  vanquished  in  the  age-long  struggle  against  the 
loftiest  human  ideals.  The  cognitive  and  aesthetic 
functions  alike,  with  their  disinterested  ends,  contrasted 
too  forcibly  with  the  thesis  of  utilitarianism,  proving, 
as  they  did,  the  mind  to  be  capable  of  recognising  values 
external  to  and  above  social  and  individual  pleasure  : 
were  not  the  search  for  truth  and  the  creation  of  beauty 
the  strongest  contradiction  of  utilitarianism  ?  It  was 
natural  that  empiricism  should  muster  its  forces  for 
the  assault  on  this  impregnable  citadel  of  human 

PT.  I 

disinterestedness.  Bacon  had  already  insisted  on  the 
practical  end  of  science,  stating  that,  ipissimae  res 
sunt  veritas  et  utilitas,  but  he  had  also  added :  Atque 
opera  ipsa  pluris  jacienda  sunt  quatenus  sunt  veritalis 
pignora,  quam  propter  vitae  commoda : 5  and  had  placed 
the  contemplatio  rerum  above  the  inventio  fructus. 
We  rejoice  in  the  light  because  with  its  help  we  can 
work,  read,  and  see  one  another,  but  the  very  sight  of 
the  light  is  of  greater  value  than  all  its  manifold  advan- 
tages. Locke,  in  his  De  arte  medica,  had  stated  still 
more  forcibly  :  "  Those  who  apply  themselves  seriously 
to  finding  and  combining  abstractions  take  great  pains 
for  a  thing  of  little  account,  and  would  do  well,  although 
they  be  men,  to  play  with  the  puppets  of  their  child- 
hood .  .  .  there  is  no  knowledge  worthy  of  the  name 
but  that  which  leads  to  some  new  and  useful  invention, 
which  teaches  us  to  do  something  better,  more  quickly, 
and  more  easily  than  formerly.  Every  other  specula- 
tion, however  singular  and  ingenious  it  may  be,  what- 
ever its  appearance  of  depth,  is  but  vain  and  idle 
philosophy,  an  occupation  for  those  who  have  nothing 
to  do."  "  Our  business  in  this  world  is  not  to  know 
everything,  but  to  know  that  which  concerns  the  conduct 
of  our  life."  David  Hume  says  :  "  Indulge  your  passion 
for  science,  says  she  (nature),  but  let  your  science  be 
human  and  such  as  may  have  a  direct  reference  to  action 
and  society.  ...  Be  a  philosopher,  but,  amidst  all 
your  philosophy,  be  still  a  man."  6  Empiricism,  how- 
ever, although  containing  germs  which,  when  developed 
and  carried  to  their  ultimate  consequences,  might 
easily  degenerate  into  pragmatism,  was  far  from  deny- 
ing the  value  of  disinterested  research.  "  Were  the 
generality  of  mankind  contented,"  says  Hume,  "to 
prefer  the  easy  philosophy  to  the  abstract  and  profound, 
without  throwing  any  blame  or  contempt  on  the  latter, 
it  might  not  be  improper,  perhaps,  to  comply  with  this 
general  opinion  and  allow  every  man  to  enjoy,  without 
opposition,  his  proper  taste  and  sentiment.  But  as 
matter  is  often  carried  farther,  even  to  the  absolute 


rejecting  of  all  profound  reasonings,  or  what  is  commonly 
called  metaphysics,  we  shall  now  proceed  to  consider 
what  can  reasonably  be  pleaded  on  their  behalf."  7 
Treating  of  the  problem  of  human  liberty,  he  makes 
an  observation  which  might  well  have  been  written 
by  William  James  :  "  There  is  no  method  of  reason- 
ing more  common  and  yet  more  blamable  than,  in 
philosophical  debate,  to  endeavour  the  refutation  of 
any  hypothesis  by  a  pretence  of  its  dangerous  con- 
sequences to  religion  and  morality.  When  an  opinion 
leads  into  absurdities  it  is  certainly  false,  but  it  is  not 
certain  that  an  opinion  is  false  because  it  is  of  dangerous 
consequences."  8 

Notwithstanding  these  reserves,  it  was,  however, 
but  a  step  from  utilitarian  empiricism  to  pragmatism. 
One  of  the  factors  which  contributed  most  effectually 
to  this  transformation  was  undoubtedly  the  evolutionary 
theory  applied  to  the  development  of  human  conscious- 
ness. Had  not  Spencer  said  that  thought  with  its 
logical  structure  is  but  a  means  of  adaptation,  an 
organ  originating,  like  all  other  organs,  in  vital  necessi- 
ties ?  Is  not  the  advantage  of  the  species  the  biological 
meaning  of  psychic  life  ?  Empirio-criticism,  transfer- 
ring the  old  English  empiricism  to  Germany,  had  already 
applied  this  principle  to  the  evolution  of  science  and 
philosophy : 9  what  wonder,  then,  that  in  the  native  lands 
of  Spencer,  Darwin,  and  Romanes10  a  logical  and  epistemo- 
logical  theory  was  built  up  on  this  postulate,  which  had 
never  been  called  in  question  ?  Why  should  pragmatism 
indeed  waste  time  in  discussing  the  theoretic  value  of 
that  principle  when  it  was  so  convenient  to  accept  it  ? 
What  matter  if  the  intellect  were  not  convinced  by  it  ? 
It  is  opportune,  and  that  is  enough  :  "  Human  arbitrari- 
ness," pronounces  James,  "has  done  away  with  the 
divine  necessity  of  scientific  logic."  u 

4.  Reasons  for  the  Prevalence  of  Pragmatism: 
James's  Will  to  Believe. — Pragmatism  would  not,  how- 
ever, have  taken  hold  and  spread  so  rapidly  had  it  not 
found  favourable  soil  in  minds  weary  of  the  abstract 


PT.  I 

formulas  of  scientific  naturalism  and  dissatisfied  with 
the  dreary  prospects  which  it  held  out  to  souls  yearning 
for  faith  and  hope.  The  will  to  believe  came  at  just 
the  right  moment  to  fill  the  void  left  in  the  mind  by 
Spencer's  Unknowable,  that  fatal  outcome  of  the 
scientific  method  which  had  been  exalted  to  the  rank 
of  a  philosophic  method.  The  door  was  open  to  the 
inspirations  of  feeling;  since  intellect,  backed  up  by 
mathematical  science,  had  done  such  poor  service,  and 
had  been  constrained  to  own  itself  beaten,  why  not  try 
to  find  a  substitute  for  it  ?  Is  not  the  human  mind 
endowed  with  other  and  greater  energies  capable  of 
surmounting  these  obstacles  and  breaking  down  those 
barriers  with  which  agnosticism  strove  to  hamper  its 
free  activity  ?  The  raisons  de  cceur  of  the  mystic 
Pascal,  the  moral  and  religious  arguments  which  David 
Hume  would  fain  banish  from  philosophic  disputes, 
take  their  part  in  the  fray.  We  have  once  again  in  the 
contemporary  social  consciousness  that  tragic  situation 
which  led  to  Kant's  Primacy  of  the  Practical  Reason, 
which  is  called  upon  to  decide  the  struggle  between 
intellectual  exigencies  and  the  imperious  needs  of  duty. 
James's  essay  on  the  Will  to  Believe 12  is  at  bottom  but 
a  revised  and  corrected  edition  ad  usum  Delphini  of  the 
doctrine  of  the  primacy  of  the  practical  reason,  which 
had  already  been  taken  up  again  and  elucidated  with 
greater  acumen  and  philosophical  depth  by  Lotze  and 
Renouvier,  yet  James  is  not  ashamed  to  say :  '  The 
mind  of  Kant  is  the  strangest  and  most  intricate  possible 
of  museums  of  antiquities  !  "  1S 

In  this  first  essay  James  does  not  as  yet  declare 
himself  plainly  to  be  an  opponent  of  intellectualism, 
but  suggests  his  method  to  us  as  a  means  of  deciding  \u 
those  questions  only  which  intellectualism  leaves  open.  1 1 
Our  passional  nature  not  only  may  but  should  decide  M 
in  all  cases  of  true  option  between  two  opposite  alterna- 
tives in  which  a  choice  based  on  intellectual  grounds  is   i 
impossible,    since  to   say  under   such   circumstances :  I  j 
"  I  will  not  make  any  decision,  but  will  leave  the  matter 


open,"  is  in  itself  a  passional  decision  just  as  much  as 
a  decision  in  the  negative  or  affirmative  would  be,  and 
is  equally  exposed  to  the  risk  of  missing  the  truth.14 
Even  James  himself  puts  us  on  our  guard  against  carrying 
anti-intellectualism  too  far :  in  the  concrete  the  liberty  to 
believe  should  only  be  applied  to  those  practical  options 
which  the  intellect  is  unable  to  decide ;  and  these 
passional  decisions  must  be  avoided  as  much  as  possible, 
whenever  facts  allow  of  our  doing  so.  Whenever  the 
choice  between  missing  and  gaining  a  truth  is  not 
absolutely  indispensable  to  life,  we  may  relinquish 
the  probability  of  gaining  a  truth,  or  in  any  case  avoid 
the  risk  of  believing  in  something  which  is  not  true,  by 
not  deciding  until  we  are  in  possession  of  objective 
evidence.  In  science  more  especially  we  must  never 
be  in  too  great  a  hurry  to  choose  hypotheses ;  doubt 
is  preferable  to  falling  into  error.15 

So  far,  James  has  not  left  the  "museum  of  antiquities" 
of  the  primacy  of  the  practical  reason  :  will  and  feel- 
ing are  called  upon  merely  to  supply  that  which  is 
lacking  in  the  intellect  which  may  and  should  await 
conviction  when  it  is  a  question  of  beliefs  which  are  not 
vital.  James,  although  he  takes  up  the  standpoint  of 
"  radical  empiricism," 16  still  recognises  the  autonomous 
existence  of  truth  and  the  ability  of  the  human  mind 
to  attain  to  it  by  means  of  successive  approximations, 
but,  while  absolutists  not  only  believe  themselves  to 
be  capable  of  truth,  but  affirm  that  they  are  already 
in  possession  thereof,  and  can  see  no  salvation  apart 
from  their  dogmatic  philosophy,  the  empiricist  is  never 
sure  that  he  has  attained  it.17 

5.  Differences  between  "  la  Philosophic  nouvelle " 
Pragmatism. — Anglo-American  pragmatism  soon 
t  beyond  this  stage  of  prudent  relativism,  and, 
intoxicated  by  its  easy  success,  did  not  hesitate  to  declare 
war  on  intellectualism  in  the  realm  of  science  as  well. 
This  result  was  brought  about  to  no  small  degree  by  the 
criticisms  of  Mach,  Ostwald,  Pearson,  Milhaud,  Poincare, 
and  Duhem,  and  more  especially  by  those  of  Bergson 


and  Le  Roy,  who  had  laid  special  stress  on  the  economic 
value  of  scientific  theories  and  on  the  active,  personal, 
and  arbitrary  element  in  the  determination  of  facts 
and  laws.  The  Philosophic  Nouvette,  to  which  indeter- 
ministic  idealism  in  France  gave  birth,  yet  bears  to 
a  certain  extent  the  stamp  of  its  metaphysical  origin ; 
whereas  pragmatism,  which  is  derived  by  natural 
evolution  from  empiricism,  strives  as  far  as  possible 
to  remain  true  to  the  programme  drawn  up  by  Peirce. 
This  imparts  a  physiognomy  of  its  own  to  Anglo-American 
pragmatism,  which  distinguishes  it  clearly  from  the  new 
French  philosophy.  The  action  spoken  of  by  Bergson, 
Le  Roy,  and  Blondel  is  not  practical  external  action, 
empirical  fertility  in  the  realm  of  facts,  but  profound, 
interior,  experienced  action,  the  concentration  of  the 
mind  on  itself  in  order  that  it  may  intuitively  grasp  its 
creative  activity.18  The  truth  of  the  idea,  according 
to  pragmatists,  lies  in  its  consequences,  in  its  empiric 
content ;  according  to  intuitionists,  on  the  other  hand, 
its  true  reality  fies  in  that  spiritual  action  which 
precedes  it.  The  former  descend  from  ideas  to  facts, 
and  hence  tend  to  realism;  the  latter  rise  from  dis- 
cursive thought  to  the  creating  mind,  and  therefore 
reach  idealism. 

6.  The  Humanism  of  Schiller. — The  logical  and 
epistemological  development  of  pragmatism  is  mainly 
due  to  Schiller  and  Dewey :  James  has  merely  spread 
their  doctrines  and  applied  that  method  more  especially 
to  religious  problems.19  He  is,  however,  after  Peirce,  the 
first  inspirer  of  the  new  current  of  thought,  and  must 
be  therefore  regarded  as  the  spiritual  leader  of  the  school,20 
which  gathers  together  in  the  unity  of  the  method 
tendencies  and  applications  of  different  kinds.21  It  is 
indeed  to  him,  as  the  most  human  of  philosophers,  that 
Schiller  dedicates  his  chief  work,  which  proclaims  itself, 
with  a  touch  of  the  solemnity  of  a  Novum  Organum,  to  be 
a  reform  of  customary  logic.22  This  has  been  up  to  now 
a  pseudo-science  of  that  non-existent  and  impossible 
process  commonly  called  pure  thought,  in  whose  name 


we  have  undertaken  to  banish  from  our  mind  the  most 
minute  trace  of  interest,  desire,  and  emotion,  as  we  should 
the  most  pernicious  source  of  error.  The  new  logic,  on 
the  contrary,  considers  that  it  is  an  emotional  postulate, 
which  takes  the  first  place  in  the  acquisition  of  our 
knowledge  because  there  is  no  such  thing  as  an  argument 
which  is  not  derived  from  an  internal  passion  of  the  mind, 
and  which  is  not  based  upon  a  more  or  less  sentimental 
belief,  and  upon  a  subjective  need.23  The  old  saying 
of  Protagoras,  "  Man  is  the  measure  of  all  things," 
is,  when  interpreted  aright,  the  greatest  discovery  of 
philosophy  :  it  does  not  lead  to  scepticism,  but  impels 
science  to  enquire  how  man  can  measure,  and  what 
expedients  will  enable  him  to  bring  his  measures  into 
agreement  with  those  of  his  fellows.  Humanism  regards 
human  consciousness  as  the  centre  of  the  universe,  and 
makes  use  of  its  guidance  alone  in  the  world  of  experience, 
rejecting  every  a  priori  principle  in  whose  name  the 
possibility  is  claimed  of  reducing  that  which  is  the 
concrete  type  of  every  reality  to  an  illusory  appear- 
ance of  some  fantastic  Absolute.24  Knowledge  is  not 
impassive  contemplation  of  the  Absolute,  but  a  form  of 
practical  activity  which  belongs  to  the  sphere  of  moral 
responsibility.  Pure  reason  is  a  mere  fiction :  an 
intellect  which  is  of  no  value  to  the  ends  of  life  is  a 
monstrosity,  a  pathological  aberration,  a  failure  in 
adaptation  which  must  sooner  or  later  be  eliminated 
by  natural  selection.25  The  idea  of  value  is  more 
primitive  than  that  of  fact;  without  valuation  there 
is  no  knowledge.  The  ultimate  problem  of  philosophy 
may  be  summed  up  in  these  questions  :  What  is  reality  ? 
To  what  end,  for  what  useful  purpose  is  it  real  ?  The 
reply  will  naturally  vary  according  to  the  end.  The 
direction  of  our  effort,  which  is  determined  by  the  desire 
and  the  will  to  know,  enters  as  a  necessary  factor  into 
the  revelation  of  reality.  Reality,  considered  as  un- 
knowable, is  nothing  ;  as  something  unknown  it  is  only 
potentially  real.  The  nature  of  things  is  not  deter- 
minate but  determinable.  like  that  of  our  fellows ;  the 


nature  of    the   answers   given  is  determined  by  our 
questions.       The    notion    of    a    fact   in   itself    is   an 
anachronism,  just  as  is  the   idea  of  a  thing  in  itself 
It  is  quite  untrue  that  we  count  for  nothing  in  the 
construction  of  the  world  ;    on  the  contrary,  our  action 
is  essential  and  indispensable,  since  without  us   fac 
would  not  be  what  is  made.    Within  what  limits  anc 
in  what  direction  the  world   is   plastic   and  can  b 
moulded  by  our  action  we  do  not  yet  know  for  certain 
but  we  know  enough  to  transfigure  the  aspect  of  existence 
in  relation  to  ourselves.     The  disparity  between  out 
power  and  exterior  forces,  great  as  it  may  be,  is  ye 
not  incommensurable,  and  nature  has  never  yet  refuse< 
to  reply  when  she  has  been  questioned  in  the  pragmatica 
method.26     We  make  choice  of  the  conditions  unde: 
which  reality  is  to  be  manifested  to  us,  and  may,  if  wi 
have  chosen  badly,  provoke  by  our  action  a  hostili 
reply,  and  therewith  our  destruction,  hence  the  choice 
is  at  our  own  risk.     Pragmatism  thus  imparts  fresl 
vigour  to  the  sense   of  responsibility  by  leaving   in 
the  world  much  that  is  indeterminate. 

Every  cognition,  however  theoretic  it  may  be,  is  o 
practical  value,  and  is  therefore  potentially  a  mora 
act.  Even  the  so-called  eternal  principles  of  mathe- 
matics are  human  constructions,  postulates,  that  is  to 
say,  demands  which  we  make  of  our  experience  becaus( 
it  is  necessary  to  us  that  it  shall  become  a  cosmos 
adapted  to  life ;  they  appear  to  be  obvious  and  axio 
matic  because'  they  are  so  firmly  rooted  in  our  menta 
habits  that  it  occurs  to  no  one  to  call  them  into  dispute. 
At  bottom,  theoretic  principles,  like  practical  ones 
derive  the  whole  of  their  meaning  and  value  from  theii 
utility  to  us.  That  alone  is  necessarily  true  which  ii 
necessary  to  our  needs.  The  true  is  the  useful,  th( 
useless  is  t&e  false.  The  definition  of  the  true  as  agree- 
ment with" the  object  is  not  tenable,  because  we  shoulc 
need  to  have  independent  knowledge  of  the  thought 
on  the  one  hand  and  the  reality  on  the  other,  which  if 
absurd.  The  other  method  of  conceiving  of  truth  as 


systematic  coherency  is  no  better,  first  of  all  because 
not  every  system  is  true,  and  we  should  therefore  need 
another  criterion  to  distinguish  the  true  from  the  false 
systems,  and  secondly,  because  the  bodies  of  truth  which 
we  acquire  in  our  science  are  all  partial  and  incomplete 
systems  which  are  not  in  harmony  with  the  rest,  hence 
it  follows  that  no  actual  system  is  true.  It  may  be  urged  v 
that  actual  systems  are  approximations  to  an  ideal 
system,  which  is  absolute  coherency,  but  what  right 
:  have  we  to  suppose  that  there  is  one  system  only  and 
not  several  different  ones  ?  Reality  may  be  constructed 
in  different  ways  by  varying  our  efforts,  and  the  exigency 
i  of  the  system  is  but  the  need  of  some  harmony  producing 
i  emotional  satisfaction,  and  not  of  a  purely  logical  and 
formal  coherency.28  Pure  thought  is,  as  we  have  already 
stated,  non-existent :  logic  cannot  be  divorced  from 
psychology.  A  truth  which  is  actually  present  is  in 
the  first  place  a  process  of  consciousness,  and,  as  such, 
i  subject  to  a  large  number  of  psychological  influences, 
i  such  as  desire,  interest,  attention,  will,  etc.  The  same 
thing  may  be  said  of  coherency,  which  is  primarily  a 
i  psychic  fact  and  cannot  therefore  be  attained  by  means 
!  of  argument,  but  is  immediately  felt.  The  movement 
of  thought  is  initiated,  sustained,  and  guided  by  interest : 
knowledge  is  a  form  of  valuation  which  does  not  differ 
essentially  from  the  rest.  There  is  nothing  to  guarantee 
the  agreement  of  the  valuations  of  one  man  with  those 
of  his  fellow -men,  or  with  his  own  made  at  another 
time;  but  the  necessities  of  social  life  demand  the 
systematic  coherence  of  all  truths.  Single  interests 
are  subordinated  to  the  principal  ends  of  life,  therefore 
certain  of  them  disappear  according  to  the  law  of  natural 
selection :  of  the  subjective  valuations  of  truth  those 
only  survive  which  are  of  social  utility,  and  which 
answer  best  to  the  common  aspirations  of  man.29  Our 
preference  for  certain  conceptions  is  due  to  a  mere 
criterion  of  convenience  :  the  Copernican  hypothesis 
gained  the  preference  over  the  Ptolemaic  only  because 
it  required  a  smaller  number  of  auxiliary  hypotheses, 

PT.  : 

and  because  the  calculations  it  involved  were  simpler. 
Thus,  too,  the  geometry  of  Euclid  still  practically  reigns 
supreme  over  other  systems,  because  its  application 
to  the  world  of  our  experience  is  easier  and  more  con- 
venient ;  metageometricians  have  had  to  confine 
themselves  to  imagining  other  worlds  subject  to  laws 
other  than  those  of  Euclid's  geometry.  Certainty  in 
the  sense  of  intrinsic  coherency,  of  harmony  with 
the  definitions  and  postulates  from  which  we  start,  has 
nothing  to  do  with  the  question  of  the  objective  validity 
of  principles,  which  depends  upon  the  possibility  of 
systematising  our  experience  by  means  thereof.  Applied 
geometry  is  not  certain,  but  useful.30  Geometrical 
judgments  are  universally  valid,  solely  because  it  is 
greatly  to  our  interest  to  keep  them  so.31  In  like 
manner,  if  in  the  realm  of  physical  sciences  we  admit 
the  existence  of  universal  and  eternal  laws,  and  also 
that  the  individuality  of  things  in  their  special  spatial 
and  temporal  determinations  is  negligible,  we  do  not 
so  act  because  we  are  convinced  of  the  theoretic 
validity  of  that  supposition,  but  rather  because  we  are 
constrained  thereto  by  its  practical  convenience;  we 
must,  that  is  to  say,  make  previsions  concerning  the 
future  existence  of  things  in  order  to  regulate  our 
conduct.  The  postulate  of  the  persistency  of  laws  does 
not  reveal  to  us  any  necessity  of  nature,  but  is  merely 
a  methodological  expedient,  answering  to  the  need  of 
finding  formulas  which  will  enable  us  to  calculate  events 
without  awaiting  their  verification.32  The  things  of 
common  sense,  the  atoms  of  the  physicist,  the  Absolute 
of  the  philosopher  are  but  schemes  for  ordering 
the  manifold  qualities  of  phenomena  corresponding  to 
certain  practical  requirements,  but  these  abstractions, 
in  as  much  as  they  are  instruments  which  can  produce 
effects  upon  experience,  become  possessed  in  our  thought 
of  the  value  of  reality.33  Immediate  experience  does 
not  satisfy  our  needs,  and  for  this  reason  we  construct 
realities  answering  our  practical  requirements  better; 
this  must  not,  however,  lead  us  into  the  error  of  regarding 


as  illusory  that  sensible  world  which  must  always  remain 
a  necessary  point  from  which  we  start  and  to  which 
we  refer.  We  can  make  different  constructions  accord- 
ing to  the  ends  we  have  in  view,  and  these  constructions 
are  frequently  of  a  contradictory  nature :  even  in  the 
one  realm  of  physical  phenomena  we  have  the  theories 
of  atoms,  electrons,  and  vortex-rings ;  and  explanatory 
schemes  become  more  numerous  when  we  pass  from 
one  science  to  another  ;  so  much  so  that  we  might  well 
ask :  Is  the  real  world  that  postulated  by  physical 
science,  or  that  of  geometry,  psychology,  or  ethics  ? 
The  philosopher  feels  the  need  of  eliminating  the  discords 
between  these  worlds/ of  attaining  to  an  ultimate  reality 
of  a  more  satisfying  nature,  capable  of  embracing  within 
itself  and  harmonising  the  schemes  of  the  different 
sciences,  and  thus  putting  an  end  to  our  uncertainties  ; 
but  this  ultimate  reality  must  preserve  its  connecting 
links  with  the  world  of  appearances  which  it  was  called 
upon  to  explain.  Immediate  experience  is  to  a  certain 
extent  more  real,  that  is  to  say  more  directly  real,  than 
those  schematic  constructions  which  have  been  erected 
upon  its  foundations  :  if  we  destroy  this  foundation, 
the  whole  edifice  will  collapse.34  Phenomenal  appear- 
ances must  be  preserved  :  the  world  is  really  coloured, 
sonorous,  hard,  painful,  spatial,  and  temporal.  The  units 
of  measurement  of  the  reality  introduced  will  in  ultimate 
analysis  be  found  in  these  appearances,  and  the  assump- 
tion thereof  will  be  vain  if  they  in  no  way  serve  to  fill 
the  gaps  therein  and  to  transform  them  actively.  That 
which  must  decide  whether  an  introduced  reality  be 
merely  a  fiction  of  the  imagination  or  exist  effectively  is 
its  efficacy,  the  power  imparted  to  us  by  its  aid.  The 
scientific  theory  of  the  transmission  of  light  through 
the  air  is  preferable  to  the  poetical  idea  of  the  fluttering 
of  the  wings  of  hypothetical  cherubim,  since  we  may 
discover  how  to  act  upon  the  air  but  could  never  have 
any  means  of  control  over  the  movements  of  these 
invisible  cherubs.35  The  more  capable  reality  shows 
itself  of  rendering  life  harmonious,  the  truer  it  is  ;  that 


FT.  I 

knowledge  which  fails  to  satisfy  and  which  imparts  no 
power  to  us  is  false.  The  ultimate  goal  of  cognitive 
activity  is  not  an  infinite  and  complete  system  of 
relations,  within  the  limits  of  which  there  is  room  for 
endless  discussion,  but  the  vision  or  immediate  per- 
ception of  a  reality  which  has  absorbed  into  itself  all 
truths  without  destroying  or  denying  them,  the  luminous 
and  transparent  contemplation  of  that  perfect  harmony 
which  embraces  all  things  and  reveals  the  whole  meaning 
of  the  cosmic  process  in  the  full  expression  of  its 
supreme  goodness  and  its  divine  beauty.36  The  ideal 
of  life  is  not  the  arrest  of  motion,  but  the  perfection 
of  motion  in  the  equilibrium  of  an  activity  which  is 
self-sustaining :  the  'Evepyeia  aKivija-iaf  of  Aristotle.37 
True  being  is  not  immutable  substance,  but  perennial 
activity ;  it  is  not  something  transcending  experience, 
but  that  which  brings  it  to  perfection.  There  is  no 
reason  to  confine  this  perfection  to  divinity,  as  does 
Aristotle.  We  can  easily  conceive  of  a  cosmos  of  beings 
whose  activity  has  overcome  change  and  attained  to 
perfect  equilibrium.  The  realisation  of  themselves,  and 
of  the  potentiality  possessed  by  each  one  in  its  own 
nature,  should  take  the  form,  not  of  a  revolting,  cruel, 
and  pathological  restlessness,  not  of  an  unending  effort, 
but  rather  of  an  activity  which,  overcoming  change 
and  time,  is  preserved  in  a  harmonious  equilibrium.38 
The  harmony  of  the  cosmos  is  not  capable  of  logical 
proof,  but  we  must  assume  it  as  a  postulate  which 
satisfies  a  profound  longing  of  ours ;  in  the  last  analysis 
there  is  no  stronger  evidence  of  the  intelligibility  of 
the  world  which  is  taken  for  granted  by  physical  science 
than  there  is  of  ethical  and  religious  beliefs,  such  as  the 
belief  in  a  moral  order  and  in  the  immortality  of  the  soul.  I ' 
There  is  only  one  method  of  valuation,  i.e.  the  measure 
of  efficacy  in  life  ;  there  is  only  one  foundation,  which  is 
always  a  postulate  of  an  emotional  nature.39 

7.  Dewey's  Instrumental  Logic. — John  Dewey  lays 
special  stress  upon  this  analogy  between  scientific  and 
moral  jurlgTnp.nt^  whip.h  may  be  said  to  constitute  the 


essence  of  pragmatism.40  It  is  usual  to  draw  a  distinction 
between  moral  judgments,  whose  aim  is  the  solution 
of  special  cases,  and  which  are  dependent  upon  the 
personality  of  the  judge,  and  scientific  judgments,  which 
give  expression  to  universal  and  objective  relations,  inde- 
i  pendent  of  individual  tendencies.  Now,  according  to 
Dewey,  this  is  erroneous :  it  is  true  that  the  man  of  science 
seeks  for  general  laws,  but  he,  too,  in  reality  sets  himself 
i  the  task  of  solving  special  cases ;  the  laws  are  but  the 
:  means,  not  the  end,  so  much  so  that,  if  the  law  proves 
!  inadequate  to  solve  the  special  problem  in  question, 
i  it  is  changed,  whereas  the  specific  case  always  remains 
i  unaltered:  science  and  morals  alike  aim  at  the  individual. 
'  On  the  other  hand,  even  in  scientific  judgments,  the 
personality  of  the  judge  affects  the  preliminary  classifica- 
tion of  possibilities  or  predicates,  the  choice  of  the 
individual  cases  to  be  studied,  and  the  method  of  verifying 
the  hypotheses,  whether  by  means  of  experiment  or  of 
demonstration.  The  character  modifies,  guides,  and 
suggests  the  judgment.  If  the  use  of  the  resources  of 
science,  of  experimental  technique,  of  systems  of 
classification,  etc.,  which  guides  the  act  of  judging  and 
therefore  determines  the  content  of  the  judgment,  be 
dependent  upon  the  interest  and  inclination  of  the 
judge,  we  are  forced  to  recognise  that  the  two  forms 
of  judgment  are  perfectly  analogous.41  There  is,  how- 
ever, a  certain  difference  :  whilst  the  intrusion  of  the 
personal  element  is  of  no  consequence  in  scientific 
judgments,  in  moral  judgments,  on  the  contrary,  this 
factor  qualitatively  colours  the  meaning  of  the  situa- 
tion ;  hence,  seeing  that  this  element  practically  amounts 
to  nothing  in  scientific  judgments,  it  is  logically  useless 
to  take  it  into  account,  whereas  it  is  impossible  to  ignore 
it  in  moral  judgments,  which  are  of  themselves  true 
and  proper  acts  whose  efficacy  is  felt  in  the  practical 
conduct  of  life.  In  short,  whereas  in  scientific  judgments 
the  character,  that  is  to  say  the  complex,  of  natural 
tendencies,  technique,  habits  of  thought,  etc.,  is  a 
uniform  and  impartial  condition,  in  the  moral  sphere 


its  action  is  explicit,  causing  us  to  prefer  one  specia 
judgment  to  another,  and  it  becomes  hence  the  pre- 
dominant factor.42  This  does  not,  however,  entitle 
us  to  regard  scientific  judgments  as  differing  in  nature 
from  others,  or  to  abstract  thought  arbitrarily  from 
the  individual  psychological  content.  Dewey  expresses 
surprise  that,  in  spite  of  the  progress  made  by  the 
evolutionary  method  in  natural  science,  certain  systems 
of  logic  (it  would  have  been  more  accurate  had  he  sak 
all  sensible  ones)  persist  in  drawing  a  sharp  distinction 
between  the  problem  of  origins  and  that  of  nature, 
between  genesis  and  analysis,  between  the  history  anc 
the  validity  of  thought.43  The  whole  meaning  of  the 
evolutionary  method,  which  has  brought  forth  so  much 
fruit  when  applied  to  biology  and  sociology,  is  that  each 
distinct  organ,  each  structure,  each  formation  group 
of  cells  and  elements  must  be  regarded  as  a  means  o 
adjustment  to  special  situations  of  the  environment : 
its  meaning,  character,  and  value  are  known  only  when 
it  is  considered  as  an  instrument  demanded  by  a  specific 
situation.  Psychology,  as  the  natural  history  of  the 
various  attitudes  and  various  structures  through  which 
thought  passes  in  the  course  of  its  development,  anc 
as  the  knowledge  of  the  conditions  from  which  it  issues 
and  the  ways  in  which  it  acts  by  the  stimulation  01 
inhibition  of  other  states  of  consciousness,  is  indis- 
pensable to  logical  valuation.  Thought  is  but  a  form 
of  adaptation  to  its  generative  conditions,  and  its 
validity  must  therefore  be  judged  in  relation  to  its 
efficacy  in  the  solution  of  these  problems.  Instruments 
logic,  according  to  Dewey,  knows  nothing  of  the  object 
in  itself  of  a  thought  in  itself,  but  recognises  a  series 
of  values  varying  with  the  variation  of  the  functions, 
and  which  can  therefore  be  determined  only  by  reference 
to  them.44  Thought  is  not  something  pure  and  absolute, 
existing  for  itself,  whose  office  is  to  reflect  and  represent 
a  world  of  independent  realities,  but  a  function  which 
has  been  formed,  like  the  rest,  in  the  course  of  experience, 
and  which  originated  in  determinate  needs.  Its  every 


I  stage  is  of  value  in  so  far  as  it  corresponds  to  the  exigency 
of  certain  conditions ;  the  later  stage  in  which  other 

I  values  arise  does  not  entitle  us  to  pronounce  the  pre- 

;  ceding  moment  to  be  false.  The  stimulus  to  the  function 
of  thought  must  be  sought  in  a  situation  in  which  the 
elements  conflict,  in  a  state  of  reciprocal  tension,  which 
would  lead  to  the  dissociation  of  experience  were  the 
re-organising  work  of  reflective  thought  not  to  inter- 

,  vene  and  re-establish  the  equilibrium  of  the  system, 

1  causing  distinctions  to  arise  in  the  heart  of  the  primitive 
non-differentiated  totality.45  In  this  work  of  restoration 
and  re-integration  (re-definition,  re-relation),46  lies  the 
whole  meaning  of  the  logical  function,  whose  antecedent 

'is  therefore  always  to  be  found  in  a  conflict  between 
the  various  parts  of  the  world  of  physical,  social,  or 
intellectual  experience.  This  situation,  which  con- 
stitutes the  starting-point,  with  its  tensional  elements 

i  remains  something  objective,  but  is,  in  as  much  as  it 
sets  thought  a  problem,  suggestive  of  the  subjective 
phases  of  another  system,  that  is,  which  at  present 
appears  to  us  to  be  the  more  or  less  uncertain  solution 
of  the  conflict.  In  short,  the  situation,  from  being  a 
single  principle,  inevitably  tends  to  become  polarised 
and  to  dichotomise  itself  :  there  is  something  which 
is  not  affected  by  the  contest  of  incompatibles, 
there  is  something  which  remains  assured  and  beyond 
question  ;  on  the  other  hand,  there  are  elements  which 
become  doubtful  and  precarious.  This  gives  rise  to  the 
general  division  of  the  sphere  into  facts  (the  given,  the 
presented)  and  ideas  (the  conceived,  the  thought).  That 
which  remains  indubitable  is  the  fact  of  the  conflict 
or  tension  with  that  specific  colouring,  that  individual 
physiognomy  which  cannot  be  replaced,  but  which  is 
immediately  felt ;  the  new  relations  and  new  positions 
assumed  by  the  elements  in  the  re-integrated  system 
are,  on  the  other  hand,  of  a  problematic  nature.  The 
memory  of  the  past  gives  us  other  experiences,  other 
contents  which  teach  us  to  interpret  present  facts  ;  these 
contents  are  distinct  from  the  facts  themselves,  as  pure 



possibilities,  ideas,  thoughts,  ways  of  conceiving ;  bu 
this  division  is  merely  relative  :  in  other  words,  th 
given  and  the  thought  are  but  divisions  of  labour 
co-operative  instruments  of  an  economic  commerc 
whose  object  is  the  preservation  of  the  integrity  o 
experience.47  The  concept  is  not  a  formal  stamp  o 
seal  of  the  ready-made  order,  applying  to  a  content 
but  is  a  continuous  transformation  of  data  in  a  certain 
direction.  The  proof  of  the  validity  of  an  idea  is  it 
functional  or  instrumental  efficacy  in  effecting  th 
transition  from  an  experience  which  is  relatively 
conflict  to  another  which  is  relatively  integrated.  Th 
difference  between  ideas  and  facts  does  not  he  in  theii 
content,  but  in  their  function  :  the  idea  is  simply  tha 
part  of  total  experience  which  is  regarded  as  tentativ 
and  corresponds  to  the  predicate  of  the  judgment 
whilst  the  situation  which  has  called  it  forth  form* 
its  subject.48  The  idea  is  not  universal  in  itself,  bu 
is  a  particular  content  which  acquires  universality 
through  its  re-organising  function ;  it  is  not  of  vahu 
in  as  much  as  it  is  a  copy  or  sign  of  other  contents,  bu 
in  so  far  as  it  is  an  instrument  of  action,  an  econonr 
in  the  process  of  thought.49  In  other  words,  the  idea 
being  chosen  because  it  fulfils  a  certain  office  in  th< 
evolution  of  unified  experience,  can  only  be  proved  b 
verifying  whether  it  succeeds  in  the  task  which  it  hai 
set  itself.  The  conception  of  thought  as  a  purely  forma 
activity,  which  is  exercised  upon  an  independent  matter 
is  meaningless  ;  moreover,  the  success  of  such  an  actioi 
would  be  a  miracle  of  a  most  remarkable  order.  Wen 
the  instrument  and  the  material  originally  extraneou 
to  one  another  and  to  the  result,  their  reciprocal  adapts 
tion  to  the  attainment  of  a  valid  result  would  be  simplj 
miraculous  ;  it  is  however  easy  to  explain  when  w] 
reflect  that  both  of  them  have  been  chosen  and  elaborated 
with  special  view  to  that  end,  that  is  to  say,  to  th 
preservation  of  harmonious  experience.  The  adaptatio 
of  thought  is  not  pre-arranged  all  at  once  from  the  firs 
but  is  accomplished  little  by  little,  case  by  case,  accorc 



ing  to  the  exigency  of  the  particular  situations.     The 

problem  of  the  validity  of  thought  in  general,  as  distinct 

from  the  value  of  this  or  that  special  process,  is  only 

raised  when  thought  is  arbitrarily  considered  apart  from 

its  historical  position  and  its  material  context.     The 

logical  function,  on  the  contrary,  is  an  active  and  fruitful 

part  of  the  evolution  of  experience  :  each  cognitive  act 

makes  a  difference  to  and  in  things,  and  the  more  it 

reveals  to  us  the  perennial  becoming  of  the  word,  and 

teaches  us  to  see  the  universe  not  sub  specie  aeterni- 

tatis,  but  sub  specie  generationis,  the  more  adequate 

it  is  to  its  object.    This  does  not,  of  course,  imply  that . 

thought  creates  reality,  as  is  alleged  by  idealism,  since 

'its  function  is  merely  to  reorganise  and  reconstruct  an 

empirical   situation  which  already  exists.50     But  this 

sxistence,  on  the  other  hand,  must  not  be  conceived  of 

is  something  transcending  that  conscious   experience, 

vyhich  is  non-differentiated  matter,  and  gives  birth  by 

i  simultaneous  process  to  subject  and  object.51    When 

ictivity  develops  without  being  interrupted  or  arrested, 

ind  no  conflict   arises  between  the   motor  responses 

idapted  to  the  various  parts  or  aspects  of  the  situation 

as,  for  instance,  in  aesthetic  activity),  the  distinction 

3etween  subjective  and  objective  is  not  apparent  to  the 

consciousness  of  the  agent ;  but  this  opposition  is  formed 

>nly  when  an  impulse  to  reaction  in  a  certain  direction 

:  neets  with  an  obstacle  to  its  complete  manifestation.52 

8.  Pragmatical  Elimination  of  the  Duality  of  Subject 
ind  Object. — With  regard  to  the  problem  of  the  reality 
)f  the  external  world,  it  will  be  seen  that  pragmatism 
•  s  in  agreement  with  empirio-criticism,  in  as  much  as 
t  does  not  admit  the  primitive  duality  of  subject  and 
>bject,  but  claims  to  be  able  to  rise  to  an  undifferentiated 
•xperience  which  is  their  common  source.  James 
naintains 53  that  sensible  reality  and  our  sensation 
hereof  are  absolutely  identical  with  each  other  :  our 
ensations  are  not  miniature  internal  duplicates  of 
hings,  but  things  themselves  in  so  far  as  they  present 
o  us.  The  content  of  the  physical  world  does  not 


differ  from  that  of  the  psychic  world ;  even  when  w 
dream  of  a  mountain  of  gold,  which  undoubtedly  doe 
not  exist  apart  from  our  dream,  it  appears  to  us  in  our 
dream  like  an  object  possessed  of  physical  existence 
In  the  same  way  the  content  of  our  memories  is  not  an 
internal  subjective  fact,  projected  outwards  by  our 
selves,  but  is  the  distant  object  itself.  The  act 
thinking  this  content  is  not  a  duplication  thereof,  bu 
is  the  association  into  one  group  of  other  mental  facts 
such  as  the  emotions  which  it  has  excited,  with  th 
effort  of  attention  and  the  ideas  which  have  recalle 
it.  The  phenomenon,  placed  in  these  relations,  appear 
to  us  to  be  thought ;  if,  on  the  other  hand,  we  conside 
it  in  relation  to  the  other  facts  of  a  physical  order,  it  wil 
appear  objective.  Consciousness  is  not  an  entity,  ai 
activity  which  is  added  to  its  content,  but  is  reducibl 
to  the  complex  of  these  "  pure  experiences,"  which  ca: 
be  mutually  related  in  various  ways  and  belong  ix 
various  groups  at  one  and  the  same  time,  so  that  tha 
which  in  a  certain  context  of  contiguous  facts  is  classing 
as  a  physical  phenomenon  may  figure  in  another  grouj 
as  a  fact  of  consciousness,  just  as  a  particle  of  ink  ma 
belong  simultaneously  to  two  straight  lines,  one  vertica 
the  other  horizontal,  provided  it  be  situated  at  thei 
point  of  intersection.54  Subject  and  object,  though 
and  thing,  are  but  practical  distinctions,  of  great  im 
portance  certainly,  but  of  functional  order  only,  no 
ontological,  as  classical  dualism  represents  them  to  b< 
since  they  are  in  the  last  analysis  made  of  the  sam 
stuff,  which  cannot  be  denned  but  must  be  experience] 
immediately,  namely,  the  stuff  of  experience  in  general 
9.  Plasticity  of  Experience  according  to  James. — Th' 
starting-point  of  reality  is  the  flux  of  our  sensation 
which  are  thrust  upon  us,  coming  to  us  without  od 
knowing  whence  :  their  nature,  their  order,  and  the} 
quantity  elude  our  action.  They  are  neither  true  ncj 
false,  they  merely  are ;  the  distinction  between  tnj 
and  false  only  applies  to  what  we  say  of  them,  to  th 
name  we  give  them,  to  our  theories  touching  their  natui 


and  their  relations.55  The  second  element  of  reality 
consists  in  the  relations  between  our  sensations  or 
between  their  images  in  our  consciousness.  Some  of 
these  relations  are  variable  and  accidental,  as,  for 
example,  those  of  time  and  place  ;  others  are  fixed  and 
essential,  because  they  are  based  upon  the  internal 
!  nature  of  their  terms.  Both  these  kinds  of  relations 
'are  immediately  perceived,  and  are  "  facts,"  but  the 
latter  kind  is  of  greater  importance  to  the  theory 
;of  knowledge,  because  it  embraces  the  "eternal" 
relations,  which  are  apprehended  each  time  their 
sensible  terms  enter  into  relation,  and  which  must  be 
i  eternally  recognised  by  logical  and  mathematical 
thought.  The  third  element  of  reality  is  formed  by 
preceding  truths,  which  are  taken  into  account  in  all  new 
research  :  this  second  factor,  which  is  of  less  resistent ! 
^quality  than  the  others,  always  ends  by  giving  way  to 
•us,  but  even  the  two  first  are  not  entirely  impervious 
to  our  action.  It  is  true  that  the  sensations  "  are  "  : 
their  flux  is  independent  of  us,  but  we  make  our  choice 
among  them,  according  to  what  best  serves  our  interests, 
'recording  some  of  them,  omitting  others,  and  arranging 
them  in  the  order  most  convenient  to  us.  What  we 
say  of  reality  depends  upon  the  point  of  view  from 
which  we  regard  it :  the  Englishman  looks  upon  the 
battle  of  Waterloo  as  a  victory,  the  Frenchman  as  a 
defeat ;  to  the  optimist  the  universe  is  a  good  thing,  to 
the  pessimist  it  is  the  worst  possible  evil.  That  which 
>is  proper  to  things  is  their  indeterminate  being  — 
the  that,  —  but  their  determinate  nature,  the  what, 
depends  upon  the  which,  that  is  to  say,  upon  our  way 
of  regarding  it.  We  are  given  the  block  of  marble, 
but  we  have  to  carve  the  statue  out  of  it.56  The  same 
thing  may  be  said  of  the  "  eternal "  parts  of  reality  : 
we  disturb  and  arrange  at  will  our  perceptions  of  intrinsic 
relations,  we  classify  them  in  one  series  rather  than  in 
another,  consider  one  more  fundamental  than  another, 
until  our  beliefs  with  regard  to  them  constitute  those 
systems  of  truths  which  we  term  logical  and  geometrical, 


whose  form  and  order  are  obviously  the  work  of 
man.  The  two  first  elements  of  reality,  sensations  and 
relations,  are  mute  elements,  and  tell  us  absolutely 
nothing  about  themselves  :  we  must  speak  for  them. 
It  is  impossible  to  conceive  of  reality  independently  of 
human  thought,  unless  it  be  regarded  as  something 
in  course  of  arising  in  the  realm  of  experience,  an 
evanescent  and  indeterminate  flux,  plastic  matter,  to 
which  we  must  give  the  finishing  touches.  The  world 
is  not,  as  rationalists  would  have  us  believe,  the 
infinite  folio  edition,  the  edition  de  luxe  complete  to 
all  eternity,  which  individual  consciousnesses  fail  to 
decipher  in  its  entirety,  and  which  they  reproduce 
in  so  many  small,  finite  editions,  full  of  misprints, 
and  more  or  less  mutilated  and  distorted  ;  it  is  rather 
an  edition  which  is  not  yet  perfect,  and  is  in  process 
of  gradual  completion,  more  especially  through  the 
activity  of  thinking  beings.57  These  beings  tend  to 
mould  reality  in  various  ways,  according  to  the  special 
ends  they  have  in  view,  and  the  flux  of  sensations 
passively  assumes  those  forms.  The  number  27,  for 
instance,  can  be  regarded  as  the  cube  of  3,  the  product 
of  3  x  9,  as  26  + 1,  as  100-73,  and  in  infinite  other  ways, 
all  of  them  equally  correct ;  thus  a  chessboard  may  be 
regarded  as  made  up  of  black  squares  on  a  white  ground, 
or  of  white  squares  on  a  black  ground.  Reality  can  be 
printed  in  our  human  editions,  which  are  all  equally 
true,  provided  they  answer  the  purpose  for  which  they 
were  elaborated.  The  historian  and  the  moralist  regard 
the  individual  as  a  person  ;  the  anatomist  as  an  aggre- 
gate of  tissues ;  the  histologist  as  a  complex  of  cells ; 
the  chemist  as  an  aggregate  of  molecules.  It  is  for  us 
to  condense  into  things  at  will  the  liquid  flux  of  sensible 
reality,  thus  creating  not  only  the  subjects,  but  also  thei 
predicates  of  our  judgments,  which  merely  express  thei 
relations  in  which  things  stand  to  human  interests  and! 
feelings.58  In  the  cognitive  function,  as  in  practical 
life,  we  are  the  creators  of  truth  and  law. 

10.  Ideas  as  Instruments  of  Action. — Ideas  are  not 


true  in  themselves,  but  rather  in  as  much  as  they  put 
us  into  a  satisfactory  relation  with  other  portions  of  our 
experience,  they  are  abbreviating  schemes,  which  save  us 
the  trouble  of  following  the  interminable  series  of  special 
phenomena.59  Each  scientific  theory  solves  a  problem 
of  maxima  and  minima  :  it  is  instrumentally  true  if 
it  demands  the  minimum  of  intellectual  effort,  and  if  it 
adapts  previous  systems  to  new  facts  with  the  minimum 
amount  of :  alteration.  The  view  expressed  by  Ramsay, 
which  seeks  the  origin  of  radiations  in  the  internal 
potential  energy  of  the  atom,  is  generally  accepted  as 
true,  because  it  extends  the  old  concept  of  energy  with 
the  least  possible  alteration  in  the  nature  thereof.  We 
declare  those  ideas  to  be  true  which  serve  to  connect  the 
stable  mass  of  previous  knowledge  with  the  new  contents 
of  experience,  thus  fulfilling  a  mediatory  function 
(marriage-function,  go-between).60  There  is  no  absolute 
criterion  of  truth :  each  theory  is  merely  possessed  of 
an  instrumental  value  of  adaptation  to  certain  special 
conditions.61  The  idea  does  not  exist,  but  is  made, 
and  becomes  true  with  the  facts  :  its  truth  is  the  process 
of  its  verification  (veri-ficatiori) ;  its  validity  is  the 
process  of  its  convalidation  (valid-ation).  If  we  follow 
up  the  mental  image  of  a  thing,  we  are  led  actually 
to  see  the  thing  :  we  thus  have  the  complete  verifi- 
cation of  it.  These  guides  of  thought,  simply  and 
completely  verified,  are  undoubtedly  the  originals  and 
prototypes  of  the  process  of  truth ;  the  other  mediate 
and  abstract  forms  of  knowledge  are  conceivable  as 
primary  verifications,  inhibited,  multiplied,  or  sub- 
stituted for  one  another.62  The  larger  number  of  the 
notions  of  our  life  are  not  directly  verified,  the  possibility 
of  verifying  them  is  in  practice  enough  for  us,  so  long 
as  we  find  nothing  contradictory  of  them,  and  we 
generally  give  credence  to  our  ideas  if  they  harmonise 
with  past  experience,  even  if  it  be  that  of  other  persons. 
The  reality  of  the  past  is  guaranteed  by  its  possible 
agreement  with  the  present,  with  actual  facts,  which  are 
the  final  term  of  reference,  because  every  true  process 


must  in  the  last  analysis  lead  to  sensorial  experiences 
which  can  be  directly  verified.  In  practice  the  work 
of  verification  is  much  facilitated  by  the  fact  that  in 
nature  things  do  not  exist  singly,  but  are  arranged  into 
species  ;  hence,  when  we  have  verified  part  of  the  class, 
we  feel  ourselves  entitled  to  extend  our  judgment  to 
the  rest.  In  addition  to  these  truths  which  are  only 
indirectly  or  potentially  verified,  there  exist  ideal 
relations  (for  instance,  2  +  2  =  4;  the  effect  begins  when 
the  cause  begins  to  act)  which  we  recognise  as  being 
eternal  and  immediately  true,  and  which  therefore 
seem  to  be  exempt  from  the  common  law  of  verification  ; 
but  even  in  this  sphere  of  pure  mental  relations  truth 
is  in  reality  gauged  by  the  convenient  direction  it  is 
able  to  give  to  our  activity  in  the  world  of  experience. 
We  refer  one  abstract  idea  to  another,  and  arrange 
them  in  the  great  system  of  logical  and  mathematical 
truths,  into  which  sensible  facts  will  eventually  fit ; 
and  it  is  just  this  possibility  of  application,  this  char- 
acteristic with  which  the  logical  structure  is  endowed 
of  being  prepared  for  every  kind  of  imaginable  object 
of  experience,  which  gives  our  eternal  truths  their 
guarantee  of  reality.63  Truth  is  but  a  collective  name 
serving  to  indicate  certain  processes  of  verification,  just 
as  health  and  strength  are  names  for  certain  vital 
processes.  The  true  is  merely  the  convenient  in  the 
sphere  of  our  thought,  just  as  the  right  is  merely  the 
opportune  in  the  sphere  of  our  action;  and,  just  as 
there  is  no  such  thing  as  absolute  convenience,  so 
there  is  no  such  thing  as  absolute  truth  :  Ptolemaic 
astronomy,  Euclidean  space,  the  logic  of  Aristotle, 
are  examples  of  systems  which  were  convenient  for 
some  centuries,  and  from  certain  points  of  view  only, 
and  have  since  been  changed  by  science.64  Finally, 
truth  is  a  form  of  good,  not,  as  is  usually  supposed,  a 
category  distinct  from  the  good  and  co-ordinate  with 

11.  Criticism  of  Pragmatism. — All  the  efforts  made 
by  Anglo-American  pragmatism  to  reduce  the  cognitive 


function  to  the  practical  function  and  knowledge  to 
action  cannot  fail  to  appear  vain  to  the  unprejudiced 
man  who  analyses  the  distinctive  characters  of  the 
two  functions.  Undoubtedly  the  human  mind  is  an 
activity  in  its  every  moment ;  even  in  knowledge  it  is 
not  a  passive  receptacle  of  impressions  which  it  receives 
from  without,  but  is  the  reconstruction  of  reality  in 
accordance  with  its  intimate  laws.  This  must  not, 
however,  lead  us  into  the  mistake  of  confusing  the 
various  forms  of  spiritual  activity,  and  neglecting  the 
specific  differences  which  impart  to  each  of  them  a 
physiognomy  proper  to  itself,  and  an  independent 
value  in  the  life  of  consciousness.  Cognitive  doing  is  ^ 
not  practical  doing,  just  as  it  is  not  artistic  doing :  the 
attitude  assumed  by  us  differs  widely  in  the  three  cases. 
In  the  theoretic  function  it  is  a  fact  that  we  are  conscious 
of  reflecting  upon  something  which  exists  independently 
of  our  subjective  activity,  which  puts  itself  in  opposition 
in  various  ways  to  our  will,  which  is,  in  short,  possessed 
of  a  nature  of  its  own.  The  belief  that  reality  has  / 
nothing  determinate  about  it,  that  it  is  plastic  matter 
which  will  yield  to  our  every  whim,  may  be  useful  in 
so  far  as  it  increases  the  sense  of  our  personal  responsi- 
bility (a  statement  which  is,  however,  open  to  dispute), 
but  is  contradictory  to  human  experience,  which  prag- 
matists  themselves  acknowledge  to  be  the  fundamental 
criterion.66  The  object  is  not  an  amorphous  flux  of 
sensations  which  can  be  segmentated  and  ordered  as  we 
please,  but  is  the  centre  of  a  system  of  reactions  which, 
as  Schiller  himself  admits,  may  sometimes  play  us  false 
and  despatch  us  into  the  other  world.  Our  action  is 
not  always  successful,  but  at  times  meets  with  obstacles 
in  the  outer  world,  which  proves  that  this  world  is  not 
of  an  absolutely  malleable  nature,  and  that,  though  we 
can  modify  it  in  part,  we  cannot  do  so  in  every  direction. 
Facts  do  not  tell  us  that  which  we  would  have  them  say, 
they  are  not  that  which  we  have  made  them,  as  is  alleged 
by  pragmatists,  who  confer  the  rank  of  philosophic 
arguments  on  verbal  quibbles.  Beyond  the  sphere  of 


our  individual  life  there  are  other  active  beings,  some 
like  ourselves,  others  apparently  more  or  less  hetero- 
geneous ;  and  the  facts  of  creation  are  not  merely  a 
creation  of  our  own,  but  also  the  result  of  the  co-operation 
of  extraneous  activities,  even  of  a  non-human  order. 
Even  if  in  some  respect  they  reflect  our  action,  answer 
to  certain  exigencies  of  ours,  and  bear  the  stamp  of 
human  labour,  in  others,  infinitely  numerous,  they 
elude  our  will  and  refuse  to  yield  full  satisfaction  to 
our  desires.  In  short,  our  action  is  one  of  the  factors 
of  reality,  but  not  the  only  one  ;  and  if  by  analogy 
thereto  we  are  to  conceive  of  countless  others  whose 
combination  gives  birth  to  the  life  of  the  universe, 
what  possibility  is  there  of  establishing  dominion  over 
them  if  they  contain  nothing  determinate  ?  A  com- 
plete lack  of  determination  in  events  would  deprive 
our  will  of  all  dominion  whatsoever,  because  our 
caprice  would  be  confronted  by  its  undying  foe,  the 
caprice  of  things,  and  nothing  but  a  miraculous  coin- 
cidence could  enable  our  action  to  divine  the  right 
course  amid  the  arbitrary  succession  of  facts.  The 
success  of  human  previsions,  upon  which  pragmatists 
lay  so  much  stress,  presupposes  in  phenomena  a  certain 
constancy  of  relations  which  we  are  unable  to  modify, 
and  can  merely  imitate  in  our  mental  constructions, 
and  which  is,  on  the  other  hand,  the  necessary  postulate 
of  life.  Does  not  the  development  of  organic  functions, 
the  formation  of  useful  habits  and  of  stable  adapta- 
tions, demand  a  certain  persistency  in  the  conditions 
of  the  environment  ?  Was  it  vital  need  which  forced 
the  world  into  certain  repetitions  of  its  processes  ? 
What  meaning  has  the  struggle  for  existence  in  a  world 
where  there  is  nothing  to  fight,  where  the  plastic  matter 
of  experience  may  be  traversed  in  every  direction  without 
offering  the  least  resistance  to  the  WiUe  zur  Mackt, 
and  the  assertion  of  our  supremacy  ?  Where  nothing 
determinate  exists,  the  words  useful,  opportune,  con- 
venient, so  misused  by  pragmatists  in  their  pseudo- 
explanations  of  the  genesis  of  thought,  become  devoid 


of  all  value,  since  no  idea,  no  means  of  adjustment, 
would  be  more  likely  to  succeed  than  another,  and 
that  which  chanced  to  hit  upon  the  right  course  once 
would  inevitably  be  doomed  to  fail  in  future  experience  ; 
or,  even  if  the  arbitrary  hypothesis  of  absolute  plasticity 
be  granted,  they  would  all  be  of  equal  value  and  all 
equally  successful,  and  every  criterion  of  selection, 
every  possibility  of  distinguishing  between  the  useful 
and  the  useless,  the  true  and  the  false,  would  be  abolished. 
There  can  be  no  meaning  in  any  category  where  deter- 
minate character  does  not  exist.  If  thought  with  its 
durable  and  coherent  structure  were  not  the  reflection 
of  some  order  or  system  of  stable  relations  inherent  in 
the  nature  of  things,  it  would  not  only  be  meaningless 
in  itself,  as  pragmatists  are  never  tired  of  telling  us, 
but  it  would  be  worthless  as  an  organ  of  life.  The] 
evolutionary  theory,  like  all  scientific  conceptions,  in| 
its  explanatory  principles  presupposes  an  organic  struc-  [ 
ture  of  the  real  and  situations  in  the  environment  to, 
which  life  must  adapt  itself  and  which  are  therefore 
not  created  thereby.67  Pragmatism,  which  accepts; 
blindfold  and  dogmatically  the  biological  origin  and 
meaning  of  mental  life,  ends  by  contradicting  its  own 
postulate,  when  it  denies  the  presupposition  of  all 
natural  selection,  that  is  to  say,  the  objective  physical 
order.  Pragmatists  are  indeed  very  enigmatical  on 
this  point :  they  affirm  and  do  not  affirm,  in  order 
not  to  clash  too  violently  with  common  sense.  Dewey 
admits  before  logical  thought  a  more  or  less  organic 
situation,  which  is  not,  however,  the  absolute  absence 
of  determination ;  Schiller  recognises  in  the  external 
world  resistent  factors  capable  of  establishing  a  limit 
to  action,  although  he  proposes  not  to  take  it  into 
account,  and  to  act  so  long  as  no  obstacle  intervenes 
(as  if  the  most  elementary  action  did  not  presuppose 
a  more  or  less  explicit  knowledge  of  these  factors  !) : 
James,  on  the  one  hand,  states  that  sensations  are 
thrust  upon  us,  and  come  from  some  unknown  source, 
and  that  we  have  no  control  over  their  nature,  order, 


v  and  quantity**  on  the  contrary,  he  adds  that  our  beliefs 
1  must  obediently  take  into  account  not  merely  accidental 
'relations,  but  also  those  which  are  essential  and  eternal, 
which  are  based  upon  the  internal  nature  of  terms,  and 
which  are  not  created  by  us,  but  perceived  as  facts ; 
yet  a  few  pages  farther  on  he  affirms  that  the  order  of 
sensations,  and,  in  general,  of  every  determination  of 
them,  depends  upon  us.69  Is  then  the  order  of  sensa- 
tions independent  of  our  action,  or  is  it  created  by  us  ? 
Do  their  intrinsic  and  eternal  relations,  which  are 
immediately  revealed  to  us,  form  something  "  grounded 
on  the  inner  natures  of  their  terms  "  or  not  ?  It  is  then 
not  true  that  the  task  of  moulding  reality  is  entirely 
in  our  hands  :  it  contains  relations  which  we  recognise, 
not  because  it  suits  us  so  to  do,  not  in  so  far  as  they  are 
useful,  but  because  we  are  forced  to  do  so  by  the  nature 
of  things  and  of  our  thought.  The  world  allows  us  to 
modify  it  up  to  a  certain  point,  provided  that  we  in  our 
turn  submit  "  obediently  "  to  it,  recognising  its  universal 
and  eternal  relations.  Things  have  a  nature^  of  their 
own,  their  mode  of  action  is  governed  by  certain  rules 
which  are  not  of  our  making,  but  must  be  sought  and 
recognised  by  our  subjective  activity,  if  we  would  in 
any  way  establish  dominion  over  them.  Natura  non  nisi 
parendo  vincitur,  wrote  Bacon,  the  great  ancestor  of 
modern  empiricists.  We  hold  a  ringer  to  the  fire,  and 
we  feel  it  scorch  us  :  this  common  experience  impels 
us  to  formulate  the  law,  "  fire  burns,"  which  serves 
to  govern  our  future  actions  ;  but  does  this  constant 
relation  between  the  perception  of  the  ringer  in  contact 
with  the  fire  and  the  pain  of  the  burn  exist  only  in  so 
far  as  it  may  aid  us  to  avoid  the  burn  in  future  ?  Did  we 
create  it  ?  Is  our  law  true  because  it  is  useful  to  us,  or 
is  it  not  rather  useful  to  us  because  it  is  true,  i.e.  because 
it  records  in  terms  of  thought  a  relation  between 
objective  facts  ?  Pragmatists  have  a  holy  horror  of 
the  theory  which  regards  knowledge  as  a  copy  or  image 
of  things  and  relations  independent  of  the  act  of  knowing, 
but  must  not  the  idea  in  some  way  reproduce  in  itself 



something  objective,  if  it  would  be  an  efficacious  instru- 
ment of  action  ? 70  It  is  true  that  the  term  copy  or  image 
is  not  a  very  appropriate  definition  of  the  cognitive 
function,  which  is  not  in  the  least  like  a  photograph  or 
picture  of  the  world  :  this  does  not,  however,  do  away 
with  the  fact  that  the  value  of  thought  must  be 
sought  in  its  ability  to  reconstruct  an  ideal  world, 
which,  while  satisfying  its  requirements,  contains  in 
itself  the  largest  possible  number  of  objective  relations. 
In  this  reconstruction,  in  which  thought  may  be  almost 
said  to  remake  consciously  that  which  has  been  made 
by  nature,  creative  activity  is  undoubtedly  manifested, 
but  the  ideal  product  which  results  therefrom  is  not  of 
value  to  us  as  an  action  of  the  mind,  that  is  to  say, 
as  expressing  its  aptitude  to  transfigure  and  direct 
the  content  of  consciousness,  but  derives  its  entire 
significance  from  reference  to  another  real  process,  to 
which  it  must  correspond  in  an  adequate  manner.71 
At  this  point  pragmatists  may  observe  :  Is  not  the 
psychic  content,  which  cognitive  activity  modifies  in 
order  to  attain  its  ends,  part  of  the  general  world  of 
experience,  that  is  to  say,  of  reality  ?  If  we  transform 
our  consciousness,  do  we  not  at  the  same  time  actively 
modify  real  things  ?  The  sophism  here  is  obvious  : 
even  if  we  are  prepared  to  accept  the  epistemological 
absurdity  of  contents  of  consciousness,  colours,  forms, 
sounds,  etc.,  existing  outside  that  individual  and  sub- 
jective context  in  which  experience  presents  them  to 
us ;  even  if  we  are  prepared  to  adopt  the  stand-point 
of  James,  the  relations  between  the  experiences  constitut- 
ing the  psychic  world  still  remain  distinct  from  the 
lations  between  the  experiences  of  the  physical  world.72 
ur  cognitive  activity  can  modify  relations  of  the  former 
kind,  but  cannot,  and  must  not,  change  the  exterior 
relations  of  facts  :  herein  lies  the  difference  between 
the  theoretical  and  practical  attitudes.  I  perceive 
an  increase  of  temperature,  and  see  the  mercury  rise 
in  the  tube  of  the  thermometer :  I  can  in  thought 
transfigure  this  relation  and  imagine,  for  instance,  the 


same  increase  of  temperature  without  the  rise  of  the 
mercury  or  with  a  lowering  thereof,  but  my  activity, 
though  it  may  in  this  way  modify  the  psychic  relation 
between  the  two  facts,  can  exercise  no  influence  over  the 
external  physical  relation,  which  will  always  remain  the 
same.  I  may  devise  as  many  theories  as  I  like,  but 
only  on  condition  that  I  recognise  that  determinate 
sequence  of  phenomena  which  is  not  created  by  me, 
but  forced  upon  me.  My  ideas  are  of  cognitive  value 
only  if  I  restrict  the  sphere  of  my  activity  to  the  interior 
reconstruction  of  these  relations  without  attempting 
to  alter  their  objective  nature,  if  my  action  confines 
itself  to  the  domain  of  consciousness,  and  recognises 
the  independent  reality  of  things  as  an  insuperable 
barrier.  Practical  activity,  on  the  contrary,  bursts  these 
bounds  and  invades  the  sphere  of  objects,  modifying 
not  only  ideas  and  their  relations,  but  things  in  their 
physical  reality.  Human  individuality  is  a  disturbing 
factor  which  must  be  eliminated  from  the  theoretic 
point  of  view  in  order  to  affirm  that  which  exists  in- 
dependently of  subjective  action ;  in  the  moral  act, 
on  the  contrary^  the  personality  of  the  individual  is  an 
essential  factor.  In  spite  of  his  thesis,  Dewey-  has  been 
forced  to  recognise  this,  and  whereas  he  had  started 
with  the  intention  of  demonstrating  the  perfect  analogy 
between  theoretic  and  moral  judgments,  he  ended  by 
owning  that  the  human  element,  which  he  calls  "  char- 
acter," is  of  no  efficacy  in  knowledge.73  Of  course,  even 
in  the  cognitive  function  it  is  impossible  to  prescind 
from  the  subject,  but  this  subject  is  not  the  psychic 
changing  subject,  with  its  individual  needs  and  feelings, 
but  rather  the  epistemological  subject  of  a  thought 
which  is  of  universal  structure.  Knowledge  presupposes 
the  need  of  knowing,  logical  harmony  affords  a  satis- 
faction sui  generis,  herein  we  can  up  to  a  certain  point 
fall  in  with  Schiller's  views,  provided  that  this  need  and 
satisfaction  be  not  taken  in  a  sophistical  sense  in  their 
individual  varieties,  and  the  deduction  made  therefrom 
that  there  is  no  other  logic  but  that  which  Ribot  terms 


the  logic  of  the  feelings.74  Thought  does  not  exist 
apart  from  a  psychological  structure,  which  imparts 
concreteness  thereto,  but  this  does  not  imply  that  its 
intimate  laws  do  not  remain  unchanged  amid  the 
variations  of  the  concrete  content  of  consciousness  in 
which  its  forms  are  actualised :  one  and  the  same  mathe- 
matical demonstration,  for  instance,  may  be  translated 
psychologically  into  auditory,  visual,  or  motor  images, 
according  to  the  type  of  imagination  of  the  subject, 
but  the  meaning  and  value  of  the  deduction  do  not  for 
that  reason  vary  in  the  three  cases.  When  logicians 
speak  of  "  pure  thought,"  they  do  not  in  the  least  mean 
to  return  to  the  Platonic  conception  of  a  world  of  ideas 
severed  from  psychological  reality  and  from  all  concrete 
content ;  tEey  merely  wish  to  affirm  that  it  is  possible 
to  study  thought  apart  from  this  or  that  special  content, 
not  from  all  content  whatsoever,  which  would  be  an 
absurd  hypothesis.  The  norms  of  truth  are  not  dependent 
upon  the  variable  and  contingent  structure  of  the  human 
subject,  although  therein  alone  can  they  make  their 
efficacy  felt  and  enjoy  the  light  of  knowledge.  In  like 
manner  the  fact  that  the  knowledge  of  things  is  realised 
through  the  action  of  concrete  individuals,  and  in  con- 
nection with  certain  vital  needs,  does  not  imply  that 
their  reality  is  created  by  these  subjective  actions  and 
exists  in  that  determinate  form  merely  because  they 
have  constructed  the  needs  of  the  organism  for  their 
own  use  and  consumption.  Things  have  a  nature  of 
their  own,  and  act  according  to  laws  which  are  not 
forced  by  thought  upon  a  flux  of  indeterminate  sensa- 
tions, as  is  believed  by  James,  who  thus  unwittingly 
recrosses  the  threshold  of  Kant's  "  museum  of  anti- 
quities," but  are  revealed  to  us  in  the  relations  of 
experience.  Sensible  data  are  not  absolutely  amorphous, 
they  are  not  adapted  to  assume  any  form  and  every 
form,  but  are  possessed  of  characters  and  needs  of  their 
own,  which  we  are  bound  to  respect.  Sensations  are 
not  indifferent  and  mute,  they  do  not  say  all  we  would 
have  them  say,  but  speak  to  us  in  the  language  of  all 


other  beings,  whether  human  or  non- human,  which 
exist  external  to  our  individuality.  It  is  the  business 
of  thought  to  interpret  these  countless  voices  of  things, 
and  to  understand  their  profound  meaning.  The  publi- 
cation of  the  universe,  to  quote  another  figure  of  speech 
used  by  James,  is  not  yet  completed,  and  awaits  its 
perfecting  from  the  activity  of  man ;  but  how  could 
we  collaborate  in  this  great  work  if  we  did  not  first 
strive  to  decipher  the  numberless  signs  which  the  past 
has  imprinted  on  its  ancient  pages  ?  How  could  we 
understand  that  eternal  language  if  things  were  entirely 
extraneous  to  the  nature  of.  the  intelligence  ?  The 
logical  organism  is  not  an  artificial  arbitrary  mould 
into  which  we  force  a  plastic  and  indifferent  matter 
which  submits  to  all  our  requirements,  but  is  rather 
the  very  structure  of  reality,  whose  ideal  meaning  is 
revealed  in  human  thought. 


1  Pragmatism,  a  New  Name  for  Some  Old  Ways  of  Thinking :  Popular 
Lectures  on  Philosophy  (William  James,  London,  1908).  The  dedication 
of  this  work,  which  is  in  itself  sufficiently  significant,  runs  as  follows : 
"  To  the  memory  of  John  Stuart  Mill,  from  whom  I  first  learned  the 
pragmatic  openness  of  mind  and  whom  my  fancy  likes  to  picture  as  our 
leader,  were  he  alive  to-day." 
1  Op.  cit.  p.  20. 

8  In  his  article,  "  How  to  make  our  Ideas  clear,"  in  the  Popular 
Science  Monthly  (January  1878),  voL  xii.  p.  286,  translated  in  the  Revue 
phihsophique  (January  1879),  voL  vii. 

4  Peirce,  in  Baldwin's  Dictionary  of  Philosophy,  severs  his  responsibility 
from  that  of  James,  stating  that  he  is  unablp  to  follow  him  in  all  the 
conclusions  he  draws  from  his  principle. 

Novum  Organum,  Aph.  24. 

Hume,  Essays  and  Treatises,  voL  iii.,  An  Enquiry  concerning  Human 
Understanding  (London,  1770),  p.  8. 

Op.  cit.  p.  9. 

Op.  cit.  pp.  136-137. 

This  application  has  been  made  not  only  by  Mach  and  Avenarius, 
but  also  by  G.  Simmel,  who  regards  utility  as  the  essential  factor  in  the 
survival  of  our  mental  elements  and  the  only  creator  of  reality.  "  t)ber 
eine  Beziehung  der  Selectionslehre  zur  Erkenntnistheorie,"  Arch.  f. 
system.  Philosophic  (1895),  pp.  39  and  41. 

10  It  would  be  superfluous  for  me  to  quote  the  well-known  works  of 
these  authors.  Of  special  importance  is  Baldwin's  work,  Thought  and 


Things,  vol.  i.  ;  Functional  Logic  or  Genetic  Theory  of  Knowledge  (London, 
1906),  which,  however,  somewhat  modifies  the  "  extravagant  first  hypo- 
theses of  the  pragmatic  revolutionaries  "  (Preface,  p.  viii). 

u  Op.  cit.  p.  57. 

11  The  Will  to  Believe  and  other  Essays  in  Popular  Philosophy  (New 
York,  1897).  Balfour,  in  his  work  Foundations  of  Belief,  had  already 
given  prominence  to  the  action  of  non-intellectual  factors  in  the  foundation 
of  faith. 

13  "  The  Pragmatic  Method,"  Journal  of  Philosophy,  i.  p.  686. 

14  The  Will  to  Believe,  p.  11. 

"  Op.  cit.  pp.  19-20  and  p.  30  ff. 
11  Op.  cit.,  Preface,  p.  vii. 

17  Op.  cit.  p.  12.     The  term  "  Pragmatism  "  was  taken  up  again  by 
James  in  a  speech  made  by  him  at  the  University  of  California,  from 
which  time  its  fortune  was  assured. 

18  Le  Pvoy  distinguished  three  kinds  of  action,  practical,  discursive, 
profound,  and  regards  the  last  named  as  the  criterion  of  philosophy.     The 
mind  must  be  severed  from  practical  life,  and  from  the  illusions  of  speech 
produced  thereby,  if  it  would  withdraw  into  its  deeper  life  (Revue  de 
metaphysique  et  de  morale  (May  1901),  p.  325). 

19  Human  Immortality :  Two  Supposed  Objections  to  the  Doctrine  (Boston, 
1908).     The,  Varieties  of  Religious  Experience  :  a  Study  in  Human  Nature 
(New  York,  1902). 

20  The  first  work  of  James  in  which  the  pragmatic  method  appears  is 
the  article  "  Sentiment  of  Rationality,"  Mind  (1879),  No.  15.     Has  work 
The  Principles  of  Psychology,  published  in  1890,  also  shows  a  method  of 
analysis  of  preception  which  is  essentially  pragmatistic. 

21  Dewey,  in  "  What  does  Pragmatism  mean  by  Practical  ?  "  Journal 
of  Philosophy,  Psychology,  and  Scientific  Method,  voL  v.  pp.  86-99,  distin- 
guishes three  applications  of  the  term  pragmatism,  according  to  whether 
it  refers  to  objects,  ideas,  or  beliefs.    When  applied  to  objects  it  means  the 
future  replies  asked  of  us  by  an  object ;  applied  to  ideas,  it  indicates  the 
changes  effected  by  them,  as  attitudes,  in  things ;    applied  to  truth  or 
belief,  it  implies  the  question  of  value,  of  importance.     Lovejoy  distin- 
guishes no  less  than  thirteen  kinds  of  pragmatism  ("  The  Thirteen  Prag- 
matisms," ibid.  vol.  v.  pp.  5-12,  29-39).     On  this  point  see  Armstrong, 
"  The  Evolution  of  Pragmatism,"  ibid.  voL  v.  p.  645  ff. 

M  Studies  in  Humanism  (London,  1902).  As  early  as  1892  he  had 
unknowingly  followed  the  pragmatic  method  in  his  article,  "  Reality  and 
Idealism,"  Philosophical  Review  (September).  Other  works  by  Schiller 
are  "  Riddles  of  the  Sphinx  "  (London,  1894)  and  "  Axioms  as  Postulates," 
published  in  a  collection  of  essays  by  various  authors  entitled  Personal 
Idealism  (London,  1902). 

23  Humanism,  p.  10  ff. 

*•  The  shaft  is,  of  course,  aimed  at  Bradley's  Appearance  and  Reality. 
Pragmatists  in  England  and  America  have  adopted  a  warlike  attitude 
towards  the  neo-Hegelians. 

M  Op.  cit.  p.  8  ff. 

24  Op.  cit.  pp.  12-14. 

27  Op.  cit.  p.  33. 

28  Personal  Idealism,  p.  123. 

29  Humanism,  p.  59. 

30  Op.  cit.  p.  89  ff.     Here  the  influence  of  Poincare  is  plain. 

31  Op.  cit.  p.  92. 
82  Op.  cit.  p.  104. 



88  Op.  cit.  p.  120. 

84  Op.  cit.  p.  195.     Here,  as  is  obvious,  Schiller  is  defending  the  reality 
of  appearances  against  Bradley. 
"  Op.  cit.  p.  200. 
84  Op.  cit.  p.  203. 

87  Op.  cit.  p.  218.     Schiller  feels  the  influence  of  Ostwald's  energetic 

88  Op.  cit.  p.  227. 

89  Op.  cit.  p.  263. 

40  Logical  Conditions  of  a  Scientific  Treatment  of  Morality  (Chicago, 
1903).    Pragmatists  regard  Dewey  as  a  disciple  of  their  school  of  thought. 
Dewey,  in  his  criticism  of  the  work  of  James  in  the  Journal  of  Philosophy, 
Psychology,  and  Scientific  Method,  for  February  1908,  has  made  reserves 
on  this  count ;   he  admits,  however,  that  his  point  of  view  is  eminently 

41  Op.  cit.  p.  14. 

42  Op.  cit.  pp.  16-20. 

43  Studies  in  Logical  Theory,  by  James  Dewey,  with  the  co-operation 
of  members  and  friends  of  the  department  of  philosophy  (Chicago,  1903), 
p.  14.    James  judges  this  work  to  be  fundamental  for  the  pragmatistic 
theory  (Pragmatism,  p.  8). 

44  Op.  cit.  p.  18. 

46  Op.  cit.  p.  39. 

4*  "  The  restoration  of  a  deliberately  integrated  experience  from  the 
inherent  conflict  into  which  it  has  fallen  "  (op.  cit.  p.  47). 

47  Op.  cit.  p.  52. 

48  Helen  Bradfort  Thomson,  "  Bosanquet's  Theory  of  Judgement,"  in 
Studies  in  Logical  Theory,  p.  111. 

49  Op.  cit.  p.  114.    Cf.  also  in  the  same  volume,  Simon  Eraser,"  Typical 
Stages  in  the  Development  of  Judgement,"  p.  128  ff. ;    Myron  Lucius 
Ashley,  "  The  Nature  of  Hypotheses,"  p.  153  ff. ;    William  Clark  Gore, 
"  Image  and  Idea  in  Logic,"  p.  193 ;   Dewey' s  article,  "  Some  Stages  of 
Logical  Thought,"  Philosophical  Review  (September  1900),  and  that  by 
Rogers  in  the  same  review  (1898),  entitled  "  Epistemology  and  Experience." 

80  "  Does  Reality  possess  Practical  Character  ?  "  in  Essays  Ph\U>~ 
sophical  and  Psychological  in  Honour  of  W.  James  (London,  1908),  p.  80. 

M  "  The  Psychological  Standpoint,"  Mind  (1886),  p.  4  ff. ;  "  Know- 
ledge as  Idealisation,"  Mind  (1886),  p.  86 ;  "  The  Reflex  Arc  Concept," 
Psychological  Review,  voL  iii.  p.  368  ff. 

**  Henry  Waldgrave  Stuart,  "  Valuation  as  a  Logical  Process,"  from 
Studies  in  Logical  Theory,  p.  225. 

M  "  La  Notion  de  conscience,"  Records  of  the  Fifth  International 
Congress  of  Psychology  (Rome,  1905),  p.  148  ff. 

64  Op.  cit.  p.  152. 

**  Pragmatism,  p.  244. 

M  Op.  cit.  p.  247. 

67  Op.  cit.  p.  259.  The  same  conception  will  be  found  in  Schiller: 
"  The  world  is  essentially  0X1?,  it  is  what  we  make  it.  It  is  fruitless  to 
define  it  by  what  it  originally  was  or  by  what  it  is  apart  from  us ;  it  is 
what  is  made  of  it.  Hence  .  .  .  the  world  is  plastic"  (Personal 
Idealism,  p.  60). 

"  Pragmatism,  pp.  251-255. 

**  Op.  cit.  p.  58.  James,  like  all  pragmatists,  accepts  Mach's  economic 
theory  of  science. 

•°  Op.  cit.  p.  64. 


"  Op.  cit.  pp.  170-194. 

61  Strong  has  laid  special  stress  upon  this  process  of  substitution, 
defining  knowledge  as  a  series  of  experiences  which  are  substituted  for 
one  another  in  a  way  satisfactory  to  the  direction  of  conduct.  Cf.  the 
essay  "  Substitution  "  in  Essays  Philosophical  and  Psychological  in  Honour 

W.  James. 

M  Op.  cit.  pp.  208-210. 

M  Op.  cit.  pp.  216-223. 

**  Op.  cit.  p.  15:  "  Truth  is  one  species  of  good,  and  not,  as  is  usually 

iposed,  a  category  distinct  from  good,  and  co-ordinate  with  it." 

66  Cf.  on  the  pragmatistic  notion  of  ti\i)  the  polemic  between  Kallen 
Gifford  in  the  Journal  of  Philosophy,  voL  v.  (1908),  Nos.  4  and  11. 

67  Baldwin,  in  opposition  to  pragmatism,  insists  upon  the  necessity  of 
ognising  the  independent  reality  of  the  environment.      He  remarks 

that  even  reflex  thought  is  never  wholly  autonomous :  reality,  the  fact 
in  itself,  must  be  postulated  as  that  to  which  thought  is  adjusted  in  its 
progressive  movement.  To  deny  this  would  be  equivalent  to  abjuring  the 
pragmatistic  method,  since  it  would  then  be  necessary  to  return  to  the 
idealistic  position,  according  to  which  thought  is  a  teleological  system 
which  is  sufficient  unto  itself  and  develops  of  itself  ("  The  Limits  of 
Pragmatism,"  Psychological  Review  (January  1904),  p.  30). 

M  "  Over  their  nature,  order  and  quantity  we  have  as  good  as  no 
control "  (Pragmatism,  p.  244). 

"  "  By  our  order  we  read  it  in  this  direction  or  in  that  .  .  .  ve  shuffle 
our  perceptions  of  intrinsic  relation  and  arrange  them  just  as  freely.  We 
read  them  in  one  serial  order  or  another  "  (op.  cit.  p.  247). 

70  Strong,   "  Pragmatism   and  its  Definition  of  Truth,"   Journal  of 
Philosophy,  voL  v.  (1908),  p.  256. 

71  Peirce  in  his  article,  which  pragmatists  regard  as  the  programme  of 
their  line  of  thought,  laid  down  as  the  fundamental  postulate  of  the  scientific 
method  the  existence  of  a  reality,  "  whose  characteristics  are  absolutely 
independent  of  the  ideas  we  may  have  of  them  "  (Revue  philosophique,  vi. 
p.  566). 

72  James  himself,  moreover,  says  that  his  conception  of  truth  "  is 
realistic  and  conformable  to  that  dualism  which  in  matter  of  theory  of 
knowledge  constitutes  the  conception  of  common  sense  "  ("  The  Pragmatical 
Account   of   Truth   and   its   Mis-Understanders,"   Philosophical  Review, 
voL  xvii.,  1908).     Cp.  also  "The  Meaning  of  the  Word  Truth,  remarks 
at  the  Meeting  of  the   American  Philosophical  Association "   (Cornell 
University,  December  1907). 

73  Albert    Schinz,    "  Professor    Dewey's    Pragmatism,"    Journal    of 
Philosophy,  Psychology,  and  Scientific    Method,  voL    v.    (1908),  p.  617. 
Cp.  also  the  later  work  of  Schinz,  Anti-Pragmatism  (Paris,  Alcan,  1909), 
p.  72.     Schinz  examines  pragmatism  in  relation  to  the  social  and  religious 
conditions  of  the  American  environment. 

74  The  human  nature  of  which  Schiller  speaks  cannot,  according  to 
Dewey  (Psychological  Bulletin  (September  15,  1904),  p.  336),  be  taken  to 
be  a  purely  subjective  being.     Each  thing  possesses  an  existence- value  only 
in  so  far  as  the  intelligence,  understood  in  the  wide  sense  of  the  word, 
concedes  this  value  to  it. 



1.  The  Philosophy  of  Values  and  the  Primacy  of 
Practical  Reason. — Of  all  the  forms  of  reaction  from 
intellectualism,  the  philosophy  of  values  is  the  one 
which  is  most  directly  related  to  Kant's  doctrine  of  the 
primacy  of  practical  reason,  inspired,  as  it  is,  by  the 
Kritik  der  Urteilskraft.  It,  too,  like  pragmatism, 
reduces  the  true  to  the  good  ;  but,  whereas  pragmatism 
looks  at  the  moral  law  from  the  point  of  view  of  empiri- 
cism, and  sets  up  the  useful,  the  convenient,  and  the 
opportune  as  the  only  criterion  of  truth,  the  philosophy 
of  values,  true  to  the  concept  of  the  categorical  impera- 
tive, sees  in  the  law  of  duty  a  universal  norm,  and  the 
affirmation  of  an  objective  value  in  every  judgment. 

The  doctrine  of  the  primacy  of  practical  reason 
arose  in  the  thought  of  Kant  from  the  need  of  reconciling 
theoretical  exigencies  and  practical  interests,  and  of 
eliminating  the  conflict  between  pure  reason,  which 
forbids  us  to  leave  the  realm  of  phenomena,  and  practical 
reason,  which  impels  us  with  irresistible  force  towards 
the  ultimate  ideas  of  metaphysic.  According  to  Kant, 
it  is  indeed  only  by  suborolinating  theoretic  thought  to 
practical  reason  that  we  can  reach  that  loftier  harmony 
which  would  be  impossible  of  attainment  were  the  two 
functions  placed  on  the  same  level,  or  were  practical 
interests  illegitimately  subordinated  to  speculative 
exigencies,  which,  like  all  forms  of  interest,  are  in 
the  last  analysis  also  included  in  the  sphere  of  practical 



:e.  Kant  failed  to  see  that  the  conflict  was  the  result 
f  his  arbitrary  mutilation  of  knowledge,  which  banished 
om  the  realm  of  true  science  to  that  of  aesthetic  con- 
mplation  all  those  forms  of  judgment  and  all  those 
tegories  of  which  the  physical-mathematical  sciences 
o  not  make  use.  He  regards  these  sciences,  with 
aditional  rationalism,  as  the  true  type  of  all  know- 
ledge ;  everything  which  cannot  be  comprised  in  their 
schemes  is  therefore  not  considered  to  be  true  knowledge  ; 
is  it  not  natural  that  we  should  find  ourselves  face  to 
face  with  insoluble  antinomies,  when  trying  to  exhaust 
all  reality  with  inadequate  categories,  and  applying 
the  conceptual  schemes  created  by  thought  in  order 
to  render  the  physical  world  intelligible,  to  totally 
different  phenomena  ?  Side  by  side  with  the  natural 
sciences  and  above  them,  have  we  not  the  historic  and 
human  sciences,  the  sciences  of  spiritual  values  ?  Have 
we  any  right  to  deny  them  the  name  of  sciences  or 
systems  of  knowledge,  because  their  methods  are  not 
those  of  the  natural  sciences,  because  they  do  not  arrive 
t  mathematical  formulas  ?  Is  it  metaphysical  to  make 
of  the  idea  of  end  in  the  human  world,  in  the  world 
>f  facts  which  are  produced  by  conscious  wills  ?  The 
iccessity  of  integrating  Criticism  with  a  wider  and  more 
mplete  concept  of  knowledge,  comprehending  not 
.erely  the  judgments  of  the  natural  sciences,  but  also 
;he  other  no  less  scientific  forms  of  judgment,  gave 
birth  to  the  philosophy  of  Eickert,  which,  whilst  de- 
veloping certain  fundamental  ideas  which  had  already 
been  unfolded  by  Windelband,  endeavours  to  find  an 
epistemological  basis  for  the  doctrine  of  the  primacy  of 
practical  reason,  placing  himself  in  opposition  on  the  one. 
hand  to  the  metaphysical  development  of  this  doctrine 
attempted  by  Fichte,  Lotze,  and  Renouvier,  and  taken 
up  again  later  on  by  Royce  and  Miinsterberg,  and  on 
the  other  to  the  psychological  interpretation,  which, 
having  been  first  touched  upon  by  Renouvier,  was 
destined  to  become  so  widespread  with  the  advent  of 
pragmatism.  Rickert  indeed  does  not  attempt  to  do 


away  with  the  antinomy  of  pure  reason  and  practical 
reason  by  synthesising  them  in  a  metaphysical  principle, 
conceived  as  an  absolute  will  or  as  a  supreme  Personality, 
the  conscious  creator  of  all  values  ;  neither  does  he 
justify,  like  Dewey  and  Schiller,  the  identification  of 
theoretic  and  practical  judgments  by  a  psychological 
analysis  which  comprehends  them  in  their  empirical  and 
contingent  reality,  and  gives  prominence  to  their  common 
passional  and  utilitarian  character;  he  rather  proceeds 
by  an  essentially  epistemological  method,  and  seeks  the 
ultimate  presuppositions  of  every  judgment  of  truth 
in  the  universal  norms  of  the  Ought.1 

2.  Philosophy  as  the  Science  of  Universal  Values: 
Windelband. — In  this  procedure,  which  starts  from  the 
existence  of  universal  affirmations  in  order  to  reach  the 
conditions  which  make  them  possible,  and  may  be 
considered  a  new  application  of  the  Kantian  method, 
Bickert  develops  the  programme  clearly  outlined  by 
Windelband  in  his  Prdludien.  Windelband  regards 
critical  philosophy 2  as  the  science  of  necessary  and 
universal  values  (Die  kritische  Wissenschaft  von  den 
allgemeingiltigen  Werten)  :  universal  values  are  its 
object,  criticism  its  method.  It  examines  whether 
there  be  a  science  possessing  a  universal  and  necessary 
truth-value ;  whether  there  be  an  art,  that  is  to  say 
an  intuition  and  a  sentiment,  possessing  necessary  and 
universal  beauty- value ;  whether  there  be  a  morality, 
that  is  to  say  a  volition  and  an  action,  possessing 
universal  and  necessary  goodness-value.  A  distinction 
must  be  drawn  between  the  judgments  (Urteile)  in 
which  the  convenience  of  two  representative  contents 
is  expressed,  and  the  other  kind  of  judgments  (Beurtei- 
lungen),  which  express  the  relation  between  the  judging 
consciousness  and  the  represented  object.  There  is  a 
fundamental  difference  between  the  two  judgments, 
"  this  thing  is  white  "  and  "  this  thing  is  good,"  in 
spite  of  the  identity  of  grammatical  form.  In  the 
purely  theoretic  judgment  we  problematically  establish 
a  connection  between  two  presentations  without  giving 


ly  opinion  as  to  their  value  ;  in  the  Beurteilungen, 
)n  the  other  hand,  we  ascribe  or  deny  universal  validity 
to  that  relation.  This  latter  class  of  judgment,  which 
presupposes  a  determinate  end  as  a  unit  of  measure- 
ment, and  is  of  significance  only  to  him  who  recog- 
nises that  end,  and  is  presented  to  us  with  the  two 
fundamental  alternatives  of  pleasing  and  displeasing, 
approving  and  disapproving,  accepting  and  refusing, 
constitutes  the  special  object  of  philosophy,  whose 
business  is  not,  like  the  special  sciences,  to  determine 
the  natural  necessity  of  facts,  their  Miissen,  but  their 
Ought,  the  Sollen,  that  which  all  must  recognise  to  be 
equally  valid,  even  if  it  does  not  exist  in  practice  or  is 
not  actually  a  fact.3  These  valuations  must  be  dis- 
tinguished from  individual  feelings  of  pleasure  and 
L,  since  they  are  not  simple  attractions  or  repulsions 
)f  a  Hedonistic  order,  determined  by  physiological 

mditions,  but  rather  judgments  subject  to  universal 
iorms.4  Some  thinkers  attribute  a  merely  relative 

lue  to  these  judgments,  affirming  them  to  be  a  product 
)f  the  variable  conditions  of  society ;  but  no  one  has 
jver  been  found  to  have  a  serious  belief  in  relativism  ; 
is  a  fable  convenue.  He  who  is  not  content  with 

re  mere  affirmation  of  relativism,  but  strives  to  put 

to  the  test,  will  deny  it,  recognising  universal  norms 
)f  thought.5  Normative  law  differs  widely  from  natural 
ind  causal  law,  which  may  correspond  to  the  norms, 
but  is  often  far  removed  from  them.  This  does  not, 
lowever,  lessen  the  value  of  the  normative  laws  which 

stablish  that  which  ought  to  be,  even  if  it  be  never 

"ly  effected.  The  laws  of  thought,  set  up  by  logical 
consciousness,  are  not  identical  with  the  laws  of  repre- 
sentative association,  but  neither  are  they  something 
entirely  different  from  them  and  opposed  to  the 
mechanism  of  presentations.  True  associative  relations 
are  determined  in  consciousness  by  the  same  natural 
laws  which  determine  false  associations,  and  are  dis- 
tinguished from  these  false  associations  merely  by  their 
conformity  to  ideal  norms.  Truth  is  the  one  white  ball 


amongst  many  black  ones.6  The  psychic  mechanism 
leads  indifferently  to  beauty  and  ugliness,  truth  and 
falsehood,  good  and  evil,  and  is  hence  incapable  of  decid- 
ing their  value.  The  acceptance  of  the  norm  is  forced 
upon  the  empirical  consciousness  by  immediate  evidence 
of  which  no  causal  explanation  can  be  given :  genetic 
psychology  can  merely  tell  us  how  and  to  what  extent 
that  norm  is  actualised ;  it  can  resolve  the  question  of 
fact,  but  is  incompetent  to  decide  the  question  of  right.7 
The  presupposition  of  the  critical  method  is  the  belief 
in  universally  valid  ends,  and  in  the  capacity  of  human 
consciousness  to  recognise  those  ends.  The  historic 
importance  of  Fichte  lies  in  the  stress  laid  by  him  upon 
this  teleological  character  of  the  critical  method ;  but 
he  was  wrong  in  endeavouring  to  deduce  from  the 
determination  of  the  end  the  means  of  its  realisation  as 
well.  Even  if  the  norms  be  not  based  upon  experience 
and  do  not  derive  their  value  therefrom,  it  is  nevertheless 
only  by  means  thereof  that  they  can  become  possessed 
of  clear  consciousness.  The  one  end  of  the  whole 
activity  of  thought  is  the  realisation  of  its  norms  :  that 
which  is  commonly  termed  an  object,  the  copying  of 
which  is  the  task  of  science,  is  reduced,  when  properly 
analysed,  merely  to  a  rule  of  connections  between  repre- 
sentations. We  do  not  need  to  know  whether  this  rule 
correspond  to  an  absolute  and  independent  reality ;  it 
will  suffice  to  observe  that  some  of  our  representative 
associations  are  adjudged  to  be  true,  others  false,  in 
accordance  with  a  norm  which  is  valid  for  them  all.  The 
concept  of  truth  cannot  mean  the  agreement  of  presenta- 
tions and  things,  which  are  two  mutually  incommensur- 
able terms,  but  merely  the  reciprocal  harmony  of  the 
presentations  :  of  secondary  and  primary,  abstract  and 
concrete,  hypothetical  and  sensorial,  theory  and  facts.8 
Immediate  certainty  lies  in  two  points  which  are  dia- 
metrically opposed :  the  sensations  and  the  general 
principles  or  axioms,  according  to  which  the  relations  of 
the  sensations  must  be  apprehended.  All  the  proposi- 
tions established  and  proved  by  the  individual  sciences 


intermediate  products  between  axioms  and  sensa- 
ions.9  In  order  that  knowledge  may  exist,  we  must 
presuppose  the  possibility  of  ordering  the  sensations 
according  to  these  principles — we  must,  that  is,  start 
from  the  postulate  that  the  relations  of  our  sensations 
can  be  logically  ordered.  These  two  factors  of  know- 
ledge are  both  indispensable  :  there  is  no  such  thing  as 
exclusively  deductive  or  exclusively  inductive  know- 
ledge. The  value  of  axioms  is  determined  by  a  universal 
end  for  each  thought,  and  must  be  unconditionally 
recognised,  if  we  would  attain  that  end.  It  is  a  hopeless 
undertaking  to  base  upon  empiric  theory  and  genetic 
research  those  axioms  which  are  the  necessary  presup- 
position thereof.10  The  universal  end  alone  imparts 
meaning  and  value  to  our  knowledge;  only  when  thought 
is  regarded  as  a  moral  duty  can  this  end  be  attained. 
During  the  activity  of  thought  moral  force  restrains 
extraneous  impressions,  personal  interests,  and  the 
temptations  of  the  imagination.11  There  is  no  such 
thing  as  knowledge  of  the  world  sub  specie  aeternitatis  ; 
but  though  our  knowledge  be  limited  to  that  which 
is  transformed  in  time,  the  sentiment  of  that  which  is 
universally  valid  sheds  the  light  of  eternity  abroad  in 
our  minds.  Not  in  science  (Wissen),  but  in  moral 
consciousness  (Gewissen),  does  the  mind  of  man  par- 
take of  the  eternal.  Eternity  will  not  be  known,  but 

3.  Reduction  of  Being  to  the  Ought :  Rickert.— Rickert,13 
following  in  the  footsteps  of  Windelband,  has  endeavoured 
to  prove  that  the  transcendent  object  is  reducible  to  the 
Ought,  the  Sollen.  The  opposition  between  subject  and 
object  may  be  understood  in  three  ways  :  firstly,  as  the 
opposition  of  the  animated  body,  the  psychic-physical 
subject,  to  the  environment ;  secondly,  as  the  opposition 
of  the  world  of  consciousness  with  its  whole  content  to 
that  which  is  external  to  itself  ;  of  the  immanent  to  the 
transcendent ;  thirdly,  as  the  opposition  of  the  conscient 
subject  to  the  content  of  consciousness.14  Correspond- 
ingly, the  word  object  assumes  three  different  meanings  : 


firstly,  the  spatial  world  which  is  external  to  the  body  ; 
secondly,  the  transcendent  object ;  thirdly,  the  object 
immanent  to  consciousness.  The  reality  of  the  immanent 
object  cannot  be  called  in  question ;  the  only  reality 
admitting  of  doubt  is  that  of  the  transcendent  object, 
which  is  not  immediately  certain,  as  is  thought  by  Riehl, 
but  is  merely  an  induction  of  our  own.  Is  this  induction 
legitimate  ?  This  is  the  problem  which  Rickert  would 
fain  solve.  When  the  whole  content  of  consciousness 
is  ascribed  to  the  object  (that  is  to  say,  in  the  third 
method  of  understanding  the  opposition  of  the  two 
terms),  nothing  is  left  of  the  subject  but  mere  conscious 
being  :  consciousness  without  a  name,  of  a  generic, 
impersonal  kind,  which  can  never  become  the  object, 
the  Bewusstsein  uberhaupt,  which  must  not  be  con- 
founded with  the  psychological  individual  subject. 
Everything  which  is  individual  in  the  subject  is  an 
immanent  object  to  consciousness,  hence  it  follows  that 
the  mind  in  its  individuality  cannot  be  regarded 
as  transcendent.  Generic  consciousness  is  neither  an 
immanent  reality  nor  a  transcendent  reality,  but 
merely  a  concept ;  it  only  means  that  which  is  common 
to  immanent  objects,  that  is  to  say,  to  all  contents  of 
consciousness,  that  which  cannot  be  more  nearly 
described  ;  it  is  really  another  name  for  the  only  being 
which  is  immediately  known  to  us,  the  general  concept, 
the  form  or  species  of  this  being,  that  is  to  say,  of  the 
immanent  object,  in  contradistinction  to  that  form  of 
being  proper  to  the  transcendent  object.  Each  im- 
mediately presented  being  is  a  being  in  consciousness, 
an  indubitable  fact,  incapable  of  further  analysis.15 
The  meaning  of  knowledge  is  certainly  based  upon  the 
conviction  that  an  order  independent  of  the  subject 
may  and  should  be  discovered ;  but  we  may  yet  ask, 
Must  this  order  be  an  order  of  transcendent  things,  a 
transcendent  reality  ?  If  knowledge  consists  in  the 
presentment,  it  must  be  compared  with  a  reality  of 
which  it  is  the  sign  or  copy ;  but  this  point  of  view  is 
untenable,  because  presentments,  like  things,  belong 


the  content  of  consciousness,  that  is  to  say,  to  the 
object ;  hence  in  presentments  there  is  no  cognitive 
relation  between  a  subject  and  an  object,  but  only  the 
mutual  relation  of  two  objects.  Now  in  order  to 
recognise  this  agreement,  a  subject  is  required ;  and 
this  knowledge  cannot  be  in  its  turn  a  presentment, 
since  in  that  case  we  should  have  to  recognise  a  fresh 
agreement,  and  the  process  would  go  on  ad  infwitum.™ 
True  knowledge  consists  in  the  judgment,  which  is  not 
a  mere  relation  of  presentments,  but  always  contains 
an  affirmation  or  negation  of  reality.17  Knowledge  is 
an  affirmation  or  a  negation  by  reason  of  its  logical 
essence,  and  belongs  to  the  active  phenomena  of  con- 
sciousness. Affirmation  and  negation  are  but  forms  of 
attraction  or  repulsion,  determined  by  pleasure  or  pain. 
This  practical  nature  of  all  knowledge  distinguishes 
it  sharply  from  pure  presentment :  judgment  is  always 
an  acceptance  or  a  refusal,  an  approval  or  a  disapproval, 
that  is  to  say,  in  ultimate  analysis  the  recognition  of  a 
value.18  Cognitive  value  differs,  however,  from  other 
values  :  whereas  Hedonistic  valuation  is  valid  only  for 
the  individual  at  the  determinate  point  of  time  and 
space  in  which  he  experiences  pleasure  or  pain  ;  in  the 
logical  judgment  something  is  affirmed  which  is  of  value 
to  us  independently  of  that  moment  and  of  those 
determinate  circumstances.19  In  our  judgments  we 
do  not  feel  ourselves  at  liberty  to  deny  or  affirm  in  an 
arbitrary  manner,  but  feel  ourselves  bound  by  a  senti- 
ment of  proof,  we  submit  to  an  extra-individual  power 
which  constrains  us  to  make  that  affirmation  or  negation. 
If  I  hear  a  sound  and  wish  to  pronounce  judgment  upon 
it,  I  am  unconditionally  forced  to  judge  that  I  hear  the 
sound.  This  necessity  (Urteilsnotwendigkeit),  which  is 
not  proper  to  mathematical  judgments  only,  but  is 
common  to  all  judgments  in  which  something  is  affirmed, 
even  to  judgments  which  refer  to  reality  of  experience, 
must  not  be  confounded  with  causal  necessity,  since  it 
is  only  the  logical  reason  of  our  affirmation.20  It  is  not 
a  Miissen,  but  a  Sollen,  an  imperative,  whose  necessity 


in  judgment  we  allow,  and  which  is  accepted  by  our  will. 
The  object  of  our  knowledge  is  not  being  (Sein),  but  the 
Ought  (Solleri),  deriving  its  adhesion  from  a  judgment, 
and  constituting  the  universal  order  which  we  feel  our- 
selves constrained  to  recognise.21  Bickert  agrees  with 
empiric-criticism  in  its  desire  to  confine  the  problem  of 
science  to  the  classification  of  the  contents  of  conscious- 
ness ;  but  this  order  is  not  regarded  by  him  merely  as 
a  convenient  classification,  but  as  an  order  conforming 
to  a  universal  norm,  and  independent  of  the  subject  in 
the  sense  that  it  must  be  valid,  even  were  no  one  to 
recognise  it.22  Its  unconditioned  value  cannot  be  denied 
with  self-contradiction,  because  every  contrary  judgment 
would  imply  the  transcendence  of  that  Ought.  Truth 
does  not  depend  upon  individual  tastes,  as  relativists 
would  have  us  believe  :  he  who  affirms  that  there  is  no 
value  of  absolute  truth  implicitly  contradicts  himself 
when  he  asserts  this  fact  as  a  certainty.  All  human 
judgments  may  be  mistaken :  there  is  only  one  which 
can  never  be  false — the  judgment  that  there  exists  a 
value  of  absolute  truth.  It  is  impossible  to  doubt  the 
transcendent  Ought  as  an  object  of  knowledge,  no  matter 
from  what  point  of  view  it  be  posited,  because  it  is  the 
necessary  condition  of  all  affirmations,  even  of  those  of 
a  sceptical  order.23  That  alone  exists  which  is  judged 
to  do  so.  Hence  not  being,  but  the  Ought  is  the  logically 
original  concept.24  Bickert  terms  his  system  tran- 
scendental idealism  :  idealism,  in  as  much  as  it  recognises 
no  other  immediately  presented  being  than  the  present- 
ment ;  transcendental,  in  as  much  as  it  admits  a  tran- 
scendent object  beyond  the  content  of  consciousness,  a 
Sotten,  an  ideal,  to  which  the  conscient  subject  tends. 
Even  experience,  that  which  is  perceived,  data,  the  fact, 
are  such  only  in  so  far  as  they  are  recognised,  and  hence 
presuppose  from  the  gnoseological  point  of  view 
judgment  and  a  norm.  Every  judgment  is  based  on 
experience  as  far  as  its  content  is  concerned ;  its  form 
is,  however,  related  to  the  Sollen,  which  cannot  be  em- 
pirically presented  ;  in  this  way  the  opposition  between 


empiricism  and  rationalism  is  overcome.26  In  perception 
the  thing  is  presented  as  a  complex  of  qualities,  of 
contents  of  consciousness,  but  these  properties  do  not 
exhaust  the  thing :  it  contains  a  network  of  necessary 
relations,  answering  to  a  transcendent  norm ;  its 
independence  does  not  consist  in  being  independent  of 
the  subject,  but  in  the  necessity  of  the  judgments  with 
which  we  posit  these  relations.  The  thing  in  its  object- 
ivity is  then  reduced  to  a  transcendent  norm  or  rule 
of  the  connections  between  the  presentations,  which 
demands  recognition.27  Even  the  necessary  relations 
of  causality  derive  all  their  objective  value  from  the 
recognition  of  that  ideal  norm.28  There  can  be  no 
opposition  between  the  theoretical  and  the  practical  man, 
between  knowledge  and  volition ;  even  knowledge  i& 
based  upon  a  categorical  imperative,  and  logical  evidence 
is  but  one  case  of  moral  certainty.29  The  antinomy  of 
the  Sollen  and  the  Mussen  is  overcome  when  we  reflect 
that  even  the  form  of  natural  necessity  must  be  founded 
on  the  Sollen,  if  it  is  to  have  objective  significance.30 
In  many  systems  of  philosophy  the  intellectual  values 
were  ranked  above  all  others,  and  moral,  religious,  and 
aesthetic  life  so  debased  or  intellectualised  that  it  lost 
all  meaning  of  its  own.  Contemporary  voluntarism, 
whilst  striving  to  overcome  the  antinomy  between  the 
theoretical  and  the  practical  man,  goes  to  the  other 
extreme,  depriving  knowledge  of  all  foundation  and 
opening  the  door  to  arbitrariness.  Science  naturally 
sees  danger  in  this  intrusion  of  individual  volition  and 
sentiment,  and  is  therefore  impelled  to  combat  the  new 
doctrines ;  on  the  other  hand,  sentiment  and  volition 
cannot  rest  content  with  the  conclusions  arrived  at  by 
science.  Thus  the  theory  of  the  will,  instead  of  eliminat- 
ing strife,  does  but  add  fuel  to  the  flame.31  Only 
epistemological  subjectivism,  which  places  valuation  at 
the  base  of  science,  enables  us  to  do  away  with  the 
antinomy  between  the  intellect  and  the  other  functions 
of  the  mind.  The  recognition  of  truth  also  is  a  categori- 
cal imperative  which  is  unconditionally  forced  upon  us. 


PT.  I 

Every  act  of  cognition  hence  presupposes  an  autonomous 
will  capable  of  conforming  to  an  ideal  norm.  From 
such  a  point  of  view  theoretical  and  practical  activity 
do  not  conflict  with  one  another,  but  we  perceive  them 
to  be  two  different  manifestations  of  the  same  conscious- 
ness of  duty,  in  which  logical  values  find  their  super- 
logical  basis.32  The  consciousness  of  duty,  as  practical 
will,  is  conceptually  antecedent  to  logical  will,  that  is 
to  say,  the  will  to  truth  :  the  tendency  to  truth  pre- 
supposes the  tendency  to  do  one's  own  duty,  because 
the  cognitive  judgment  is  a  special  form  of  practical 
activity.  From  this  is  derived  the  absolute  value  of 
the  conscious  will  to  duty,  as  an  unconditioned  necessity 
even  for  the  theoretical  man,  because  the  recognition 
of  one  particular  value  presupposes  the  recognition 
of  value  in  general.  In  a  reality  which  is  indifferent 
to  duty,  in  a  world  which  is  not  adapted  to  the 
realisation  of  truth-values,  all  judgment  would  become 
meaningless.  The  value  of  knowledge  depends  upon 
the  conviction  that  ethics,  not  logic,  reigns  supreme 
that  the  world  is  guided  in  such  a  way  as  to  bring  the 
realisation  of  the  ends  of  knowledge  within  the  bounds 
of  possibility  ;  it  is  dependent,  that  is  to  say,  upon  faith 
in  the  moral  objective  order  (objective  WeUmacht  des 

4.  Natural  and  Historical  Sciences. — If  human  con- 
sciousness be  thus  placed  in  the  centre  of  the  universe, 
the  cosmic  process  will  no  longer  seem  the  random 
product  of  an  obscure  necessity,  a  decoction  of  mixed 
atoms,34  but  rather  the  progressive  historic  actualisation 
of  the  ideal.  History,  in  as  much  as  it  enables  us  to 
watch  the  realisation  of  universal  values  in  the  world 
of  concrete  consciousness,  thus  becomes  the  fundamental 
organ  of  philosophy.  Historical  science  alone,  interpreted 
in  its  widest  sense,  can  fill  the  gaps  left  by  the  formation 
of  scientific  concepts,  it  alone  can  substitute  reality  in 
the  fulness  of  its  individual  aspects  for  the  empty 
abstractions  of  science.35  Scientific  knowledge  cannot 
consist  in  the  imitation  or  representation  of  single  objects 


their  individuality,  because,  however  large  the  number 
known  objects  may  be,  an  infinite  number  of  others 
remains  still  unknown ;  moreover,  each  object  can  be  re- 
solved into  a  complex  of  relations  and  elements,  which 
become  gradually  more  numerous  as  our  knowledge 
becomes  greater.36  Science  would  not  be  possible  were 
there  no  means  of  overcoming  multiplicity  in  either  form, 
external  and  internal,  extensive  and  intensive  alike. 
This  purpose  is  served  by  the  concept,  which  in  its 
extension  overcomes  extensive  multiplicity,  in  its  con- 
tent intensive  multiplicity.  The  more  perfect  science 
becomes,  the  more  completely  will  the  intuitive  element 
be  eliminated,  and  together  therewith  the  individual 
character  of  things,  that  is  to  say,  that  physiognomy  of 
theirs  which  is  never  repeated  twice  in  the  same  way.37 
We  can  live  and  experience  reality  directly,  but  the 
instant  we  attempt  to  explain  it  by  means  of  science, 
that  which  makes  it  truly  real  will  elude  our  grasp  ; 
the  more  nearly  our  concepts  approach  perfection,  the 
farther  we  shall  go  from  concrete  reality.  If  a  certain 
residuum  of  empirical  reality  still  remain  in  science,  it  is 
an  element  which  science  has  been  unable  to  comprehend, 
to  translate  into  judgments,  or  to  overcome  thoroughly. 
Neither  the  atom  nor  the  simple  sensation  can  be 
regarded  as  an  object  of  knowledge,  but  merely  as  means 
thereto  :  it  would  be  absurd  to  posit  as  the  end  of 
science  the  discovery  of  a  reality  which  cannot  be 
experienced.38  Moreover,  it  is  not  the  business  of 
science  to  copy  reality ;  on  the  contrary,  as  Rickert 
paradoxically  affirms,  the  less  reality  its  concepts 
contain,  the  more  nearly  do  they  approach  perfection.39 
If,  however,  we  must  be  on  our  guard  against  the 
hypostatisation  of  scientific  concepts,  we  must  be  equally 
careful  not  to  go  to  the  opposite  extreme,  by  depriving 
science  of  all  objective  value.  The  place  of  being, 
which  concepts  are  totally  unable  to  represent,  must 
be  taken  by  the  value  which  they  ought  to  have ; 
scientific  concepts  are  not  true  in  so  far  as  they  copy 
real  things,  but  in  so  far  as  they  are  valid  for  reality.40 


Science  then  leaves  external  to  itself  facts  in  their 
individual  concreteness,  which  are  of  no  interest  from  its 
point  of  view  ;  but  the  individual,  though  it  may  not  be 
of  scientific  importance  as  such,  is  of  great  value  to  us 
from  the  aesthetic  and  moral  point  of  view.  The  appre- 
hension of  reality,  in  that  aspect  thereof  which  never 
recurs  twice  in  the  same  way,  is  the  task  of  historical 
knowledge,  understood  in  its  widest  sense,  that  is  to 
say,  as  applying  not  only  to  human  facts,  but  to  all 
events  in  their  individual  physiognomy.41  If  historical 
facts  be  by  their  very  definition  such  as  never  recur 
twice,  not  only  will  it  be  difficult  to  find  historical  laws, 
as  is  commonly  supposed,  but  the  very  concept  of 
historical  law  will  be  a  contradiction  in  terms.  It  is 
commonly  asserted  that  historical  personalities  are  in- 
explicable by  reason  of  the  complexity  of  their  factors  ; 
but  this  applies  to  all  things  in  their  individual  aspect, 
to  a  piece  of  sulphur,  the  leaf  of  a  tree,  etc.,  which  are 
therefore  just  as  inexplicable  as  Goethe  or  Kant.42 
This  distinction  between  the  natural 43  and  the  historical 
sciences  is  of  methodological  value  only,  since  in  reality 
the  two  forms  of  knowledge  are  blended  with  each  other. 
On  the  one  hand,  historical  elements  will  always  be  found 
in  the  sciences,  because  the  sciences,  with  the  exception 
of  mathematics  and  rational  mechanics,  have  not  been 
able  to  free  themselves  entirely  from  the  empirical 
element;  on  the  other  hand,  history  does  not  always  refer 
to  that  which  is  truly  individual,  but  frequently  treats 
of  phenomena  which,  whilst  of  a  generic  character,  are 
relatively  singular.  The  naturalistic  method  may  be 
used  in  that  which  is  relatively  historical,  but  that  which 
is  absolutely  historical,  as,  for  instance,  a  human  person- 
ality with  its  individual  characteristics,  eludes  the  grasp 
of  the  scientific  concept,  unless  the  individual  be  con- 
sidered as  the  type  or  example  of  a  species. 

Though  the  concept  of  law  may  not  be  applicable 
to  historical  facts  in  the  absolute  sense,  it  does  not 
follow  that  these  facts  are  not  determined  by  causes.  A 
distinction  must  be  drawn  between  the  principle  of 


causality,  which  demands  of  a  cause  for  every  fact, 
and  the  causal  law,  according  to  which,  given  the 
same  causes,  the  same  effects  must  be  verified.44  The 
connection  existing  between  an  individual  cause  and 
an  effect  which  is  also  individual,  as,  for  instance, 
between  the  earthquake  of  November  1,  1775,  and  the 
destruction  of  Lisbon,  may  be  termed  an  historical  causal 
connection  ;  that  which  is  common  to  a  group  of  these 
individual  connections  constitutes  the  causal  law,  which 
embraces  that  which  recurs  in  concrete  historical  succes- 
sions. The  opposition  between  nature  and  history  is 
not  an  opposition  between  necessity  and  liberty,  because 
if  law  is  excluded  from  historical  knowledge,  cause  is  not. 
Still  less  can  it  be  said  that  accidental  facts  are  the  object 
of  history ;  if  by  accidental  we  understand  everything 
which  cannot  be  comprised  in  a  general  concept  or  a 
scientific  law,  the  whole  of  concrete  reality  is  a  complex 
of  accidents  subject  to  no  law  whatsoever  :  it  is  a  chance 
that  Saturn  has  a  ring  and  that  the  earth  has  none, 
that  Frederick  the  Great,  won  a  battle  at  Leuthen.  If, 
on  the  other  hand,  we  understand  by  chance,  as  opposed 
to  causal  necessity,  that  which  has  no  cause,  nothing 
in  the  world  is  contingent,  and  everything  is  necessary, 
Saturn's  ring  and  the  victory  of  Frederick  the  Great 
alike.45  Historical  causality  differs,  however,  from 
scientific  causality  :  in  science  it  may  be  stated  that  the 
same  cause  will  produce  the  same  effect ;  in  history 
such  a  statement  is  impossible,  since  there  are  not  two 
equal  causes  and  effects.  Further,  the  principle  of  the 
equivalence  of  cause  and  effect  cannot  be  applied  to 
historical  causality,  because  the  historical  event  is  always 
something  heterogeneous  to  its  cause.46  History  may 
seek  the  influences  of  the  environment  and  of  past 
conditions  upon  the  individual,  but  only  in  so  far  as  the 
environment  and  the  historical  moment  are  considered 
in  their  individuality  ;  if  we  pass  from  these  individual 
complexes  to  generic  concepts  of  the  mind  of  the  people, 
the  spirit  of  the  age,  etc.,  we  forsake  the  historic  point 
of  view  and  adopt  the  attitude  of  naturalistic  treatment.47 


The  individual  elements  of  history  can  be  combined  into 
a  higher  unity  only  by  referring  to  a  universal  value.  It 
is  useless  to  try  to  impart  significance  to  life  and  to 
history  by  taking  up  the  standpoint  of  science,  which 
regards  all  individuals,  as  examples  of  generic  concepts, 
as  being  of  the  same  importance  and  meaning,  and  which 
therefore  recognises  no  difference  in  value.48  If  we  would 
distinguish  the  essential  from  the  non-essential  in  the 
world  of  experience,  in  a  way  which  is  universally  valid, 
we  must  have  a  criterion  of  selection,  an  ideal  norm 
which  will  enable  us  to  eliminate  everything  which  is 
not  of  importance  to  the  attainment  of  that  universal 
end,  and  to  arrange  the  most  important  moments  of 
historical  development  in  a  hierarchical  scale  of  values, 
independent  of  subjective  caprice.49  Historical  thought, 
like  moral  volition,  is  bound  up  with  the  irrationality 
of  the  world,  that  is  to  say,  with  that  element  individual 
which  cannot  be  deduced  from  a  system  of  concepts. 
All  rationalistic  systems,  in  as  much  as  they  presuppose 
that  each  moment  of  development  is  predetermined  in 
an  eternal  idea  beyond  time,  nullify  the  meaning  of 
historical  individuality.  Where  everything  is  logically 
necessary,  as  in  Hegel's  absolute  idealism,  no  distinction 
of  values  is  possible,  because  all  moments  are  placed  on 
the  same  level . M  Empirical  reality  is  absolutely  irrational 
to  us.51 

If  the  concrete  individual  be  true  reality,  and  the  con- 
cept, instead  of  leading  nearer  to  it,  rather  increases  the 
distance  between  us  and  it,  what  is  the  use  of  science  ? 
The  ideal  of  knowledge  is  a  subject  capable  of  embracing 
the  whole  of  past,  present,  and  future  reality  in  a  single 
intuition ;  but  man,  strive  as  he  may  to  increase  his 
knowledge,  by  prolonging  the  series  of  existential  judg- 
ments, can  never  attain  that  ideal,  absolute  knowledge 
of  all  individuals.  He  therefore  requires  a  substitute, 
and  science  is  the  most  complete  compensation  imagin- 
able. It  thus  becomes  of  absolute  value  to  man,  and 
necessary  from  the  human  point  of  view  which  has  but 
a  limited  horizon.  He  who  desires  an  end  must  also 


lesire  the  means  thereto,  hence  the  presupposition  that 
idgments  valid  for  all  instances  may  be  deduced  from 
limited  number  of  facts  must  be  accepted  as  a  necessary 
and  universal  principle.52  Only  by  reference  to  an 
absolute  value  which  ought  to  be,  is  it  possible  to 
explain  the  universal  validity  which  we  attribute  to  law ; 
empiricists  in  their  genetic  researches  are  doomed  to 
move  in  an  eternal  vicious  circle,  presupposing  the 
universality  of  those  principles  which  they  imagine 
themselves  to  be  deriving  from  experience.  When  it 
is  stated  that  repeated  succession  necessarily  produces 
in  each  case  indissoluble  association  of  ideas,  is  not  the 
causal  law  presupposed  ? 53 

Science,  however,  necessary  as  it  is  from  the  human 
point  of  view,  cannot  take  the  place  of  history,  because 
the  scientific  concept,  which  is  but  a  means  of  mastering 
the  infinite  multiplicity  of  things,  cannot  give  us  any- 
thing real.  Historical  knowledge  approaches  more  nearly 
to  the  ideal  than  does  scientific  knowledge  ;  but  it  too 
is  at  bottom  relative  to  the  limitation  of  the  empirical  / 
subject  in  time.  The  total  intuition  of  the  universe  is 
denied  to  the  finite  intellect,  therefore  human  knowledge 
can  only  attain  its  end  discursively  by  means  of  a  series 
of  successive  acts,  which,  seeing  that  they  tend  towards 
an  unconditioned  and  transcendent  end,  and  are  the 
progressive  actualisation  thereof,  in  their  totality  con- 
stitute an  historical  development.  The  process  of  realisa- 
tion of  human  knowledge  cannot  be  known  scientifically, 
but  only  historically,54  this  proves  the  necessity  and 
value  of  historical  knowledge  from  the  point  of  view  of 
the  empiric  subject.55 

5.  Criticism  of  the  Philosophy  of  Values. — The  philo- 
sophy of  values  makes,  like  pragmatism,  the  mistake  of 
trying  to  reduce  the  theoretical  to  the  practical  function, 
positing  as  the  object  of  knowledge  not  that  which  is, 
but  that  which  ought  to  be.  If,  in  fact,  from  the  meta- 
physical point  of  view  there  is  no  doubt  that  we  must 
have  recourse  to  our  moral  experience  in  order  to  under- 
stand fully  both  the  meaning  of  things  and  their  profound 


unity ;   that  no  philosophy  can  afford  us  a  satisfactory 
intuition  of  the  world  without  reference  to  an  end  ;  that 
the  mind  of  man  with  its  universal  values  would  be 
simply   an  inexplicable  monstrosity  in  a  mechanical 
world  wholly  extraneous  to  its  ideals  ;  we  must,  on  the 
other  hand,  recognise  that  the  Ought,  even  if  it  be  not 
derivable  from  being,  yet  finds  its  presupposition  and 
its  necessary  subsistence  therein.     An  end,  a  norm,  a 
value  which  is  not  such  to  any  consciousness  is  incon- 
ceivable, and  consciousness  is  not  merely  valid,  it  is_. 
Bickert  considers  the  priority  of  the  Sollen  over  the 
Sein  to  be  proved  by  the  fact  that  every  form  of  being 
whatsoever,  whether  psychic  or  physical,  real  or  ideal, 
sensible  or  super-sensible,  given  or  inferred,  presupposes 
a  meaning  and  an  objective  value  in  the  judgment 
affirming  such  being.56     But  could  the  judgment  be 
valid,  did  it  not  exist  in  some  way  ?     The  validity  of 
the  judgment  implies  in  its  turn  the  reality  thereof,  and 
of  the  thought  which  judges.     Rickert's  argument  is 
based  upon  the  false  postulate  that  nothing  exists  unless 
it  be  judged  to  do  so',   whereas  we  have  an  experienced 
assurance  of  the  concrete  existence  of  our  thought,  an 
assurance  preceding  any  explicit  recognition  thereof. 
I  feel  that  I  exist,  even  before  I  judge  myself  to  be  in 
existence,  and  my  reality  does  not  depend  upon  the 
value  of  the  judgment  which  recognises  it ;    on  the 
contrary,  the  judgment  is  valid  because  it  is  based 
upon  that  primitive  and  indestructible  fact  which  is 
the  immediate  consciousness  of  the  being  of  my  thought. 
A  Wert  an  sick  absolutely  transcending  consciousness 
is  not  an  intelligible  concept,  and  finds  itself  confronted 
by  the  same  difficulties  as  the  old  idea  of  the  Ding  an 
sick.     How  can  the  value  which  is  in  itself  apart  from 
conscious  being  be  made  one  therewith  in  the  cognitive 
act  ?     How  can  the  transcendent  become  immanent  ? 
Who  will  show  us  how  to  overcome  this  dualism  of  being 
and  meaning,  reality  and  value  ?     To  this  Rickert 67 
replies  that  dualism  is  created  by  the  intelligence,  which, 
in  its  desire  to  explain  facts,  separates  conceptually  that 


hich  is  one  in  origin  :  we  have  immediate  experience 
the  unity  of  meaning  and  being,  in  as  much  as  we  in 
knowing  identify  ourselves  with  truth  :  it  might  be 
said  to  be  that  which  is  best  known,  did  not  knowledge 
already  imply  a  division ;  it  is  inexplicable,  not  because 
it  is  above  all  knowledge,  but  because  it  is  previous  to 
every  conceptual  distinction.  This  inexplicable,  which 
Rickert's  penetrating  mind  finds  at  the  basis  of  his 
conception  of  knowledge,  is  not,  in  my  opinion,  a 
necessary  product  of  intelligence,  but  results  from  his 
arbitrary  concept  of  objective  value,  which  he  defines 
as  being  external  to  every  form  of  being  whatsoever, 
and  hence  also  to  consciousness.  If  value  be  non- 
existent,58 if  it  absolutely  transcend  consciousness,  no 
dialectic  effort  will  enable  me  to  pass  from  the  one  term 
to  the  other  ;  but  this  concept  of  value  in  itself  without 
any  reference  to  a  consciousness  is  not  thinkable  ;  still 
less  is  it  possible  to  think  of  a  value  which  does  not 
exist  either  actually  or  ideally.  Our  thought  refuses 
to  conceive  of  something  absolutely  non-existent,  because 
every  judgment  posits  being  either  implicitly  or  expli- 
citly. The  affirmation  of  being  is  immanent  in  every 
act  of  judgment,  even  in  acts  referring  to  values  ;  I  am 
not  constrained  to  say  "  the  value  is"  by  a  mere  im- 
perfection of  language,  the  very  nature  of  thought  forces 
me  to  do  so.  I  cannot  think  that  something  is  valid, 
and  is  of  intrinsic  worth,  without  implicitly  thinking 
that  it  is  in  some  form  or  other.  A  value  which  is  non- 
existent is  a  meaningless  phrase,  because  nothingness, 
the  absolute  negation  of  being,  is  the  negation  of  thought. 
What  wonder  if,  when  absolute  value  is  defined  in  this 
unintelligible  manner,  it  should  be  impossible  to  conceive 
of  the  transition  from  non-existence  to  existence  ?  It  is 
not  necessary  absolutely  to  break  through  the  relation 
between  value  and  the  object  and  consciousness  in  order 
to  place  knowledge  and  valuation  upon  a  universal  and 
objective  foundation ;  it  will  suffice  for  them  to  be 
independent  of  the  individual  subject,  while  still  in 
relation  to  a  Universal  Consciousness.  The  significance 


of  the  act  of  judgment  goes  beyond  the  empirical  sphere 
of  my  consciousness  and  individual  existence,  and  is 

•  therefore  relatively  transcendent,  but  it  does  not  transcend 
the  sphere  of  consciousness  and  existence  in  the  absolute 
sense.  Things  certainly  contain  a  network  of  laws  and 
relations  which  would  exist  even  had  man  never  been 
born,  and  had  never  known  them ;  but  this  order 
cannot  be  thought  of  as  real  except  in  relation  to  an 

"Absolute  Thought  capable  of  comprehending  universal 
reality  in  the  concreteness  of  its  infinite  Consciousness. 
The  Bewusstsein  uberhaupt,  which  is  an  abstraction  of 
that  which  is  common  to  human  consciousness,  does  not 
of  course  exist  apart  from  them,  and  cannot  therefore 
act  as  the  subject  of  real  relations,  still  less  of  the  uni- 
versal norms  which  existed  previous  to  the  origin  of  man. 
The  consciousness  which  we  must  postulate  in  order  to 
find  a  foundation  for  the  objective  order  and  the 
eternity  of  values  must  not  then  be  an  abstract  concept, 
'  a  pure  logical  fiction,  but  a  living  Personality  with  a 
concrete  content. 

The  identification  of  knowledge  with  practical 
activity,  which  is  the  fulcrum  of  Bickert's  theory,  does 
not  in  the  least  correspond  to  that  which  is  revealed 
to  us  by  our  inner  experience  :  the  attitude  assumed 
by  us  in  the  two  cases  is  very  different.  In  the  cognitive 
function  we  certainly  feel  at  liberty  to  affirm  or  deny 
the  existence  of  a  fact  or  of  a  real  relation,  but  we  are 

,  at  the  same  time  conscious  that  that  fact  and  relation 
exist,  even  if  we  do  not  recognise  them  ;  in  the  practical 
attitude,  on  the  other  hand,  the  reality  of  that  which  is 
willed  seems  to  us  independent  of  our  subjective  action  : 
the  end  will  continue  to  be  of  value,  it  is  true,  even  if  I 
do  not  actualise  it,  but  its  realisation,  its  transition  from 
the  ideal  order  to  the  sphere  of  objective  existence,  is 
dependent  upon  my  free  will.  The  relation  of  the  reality 
to  the  Ego  differs, then, considerably  in  the  two  functions: 
our  mind  is  practical  only  in  so  far  as  it  modifies,  or  at 
all  events  proposes  to  modify,  that  which  exists,  and 
feels  itself  to  be  the  active  cause  of  such  modifications ; 


it  is  theoretical  if  it  recognises  objects  and  relations 
whose  existence  does  not  depend  at  all  upon  its  volition. 
I  do  not  hereby  intend  to  maintain  that  consciousness 
in  the  cognitive  process  reflects  things  passively,  but 
merely  that  the  mind  is  not  active  in  the  theoretical 
function  in  the  same  sense  as  it  is  in  the  practical 
attitude.  That  which  I  perform  and  am  at  liberty  to 
perform  in  knowledge  is  the  act  of  judgment :  this  act, 
not  the  existence  of  the  object  affirmed,  depends  upon 
my  will.  There  is  no  judgment  without  the  will  to 
judge  ;  but  does  it  therefore  follow  that  to  judge  and 
to  will  are  the  same  thing  ?  When  I  affirm  the  reality 
of  a  fact,  I  certainly  feel  the  need  of  affirming  it ;  it 'is 
not,  however,  this  exigency  which  constitutes  the  object 
of  my  judgment :  that  which  I  judge  is  the  existence 
of  the  thing,  not  the  norm  which  governs  my  judgment. 
Rickert  maintains  that  the  affirmation  of  reality  pre- 
supposes the  value  of  the  existential  judgment ;  but,  I 
would  reply,  the  presupposition  is  one  thing,  the  object 
another  :  there  must  be  no  confusion  between  the  two. 
In  the  affirmation  of  existence  the  validity  of  my  judg- 
ment is  implied,  not  the  value  of  the  object  affirmed  ; 
the  existential  judgment  is  valid  just  because  it  recognises 
a  fact  of  which  my  consciousness  gives  me  immediate 
assurance  :  that  is  to  say,  that  my  individuality  does 
not  exhaust  the  sphere  of  being,  that  external  to  myself 
there  exist  other  individuals  and  other  real  phenomena. 
That  which  Rickert  terms  the  immanent  object,  and 
which  he  too  recognises  to  be  beyond  question,  will 
suffice  to  impart  value  to  the  existential  judgment ;  it  is 
enough  that  the  things  and  relation  affirmed  by  me  be 
independent  of  my  inolividual  life,  it  is  not  at  all  necessary 
to  have  recourse  to  an  object  absolutely  transcending 
consciousness.  My  judgment,  "  This  sheet  of  paper 
upon  which  I  am  writing  exists,"  is  valid  in  the  sense 
that  the  sheet  continues  to  exist  even  when  I  no  longer 
perceive  it,  that  is  to  say,  in  the  sense  that  its  being  does 
not  depend  upon  me.  The  same  may  be  said  of  the 
relations  between  the  sensorial  contents,  whose  existence 


we  affirm,  and  which  we  strive  to  reconstruct  in  that 
which  is  objective  about  them,  that  is  which  is  real 
independently  of  this  or  that  individual.  It  is  the 
existence  of  these  relations,  which  are  immanent  in 
the  phenomenal  order,  which  constitutes  the  object  of 
the  scientific  judgment,  which  is  valid,  no  less  than  is  the 
historical  judgment,  not  because  it  refers  to  a  transcend- 
ent norm,  but  in  as  much  as  it  affirms  a  system  of  real 
relations.  In  order  to  comprise  in  the  scientific  concept 
that  which  recurs  in  natural  processes,  this  repetition 
must  exist  in  some  way.  Had  each  individual  moment 
of  the  cosmic  process  nothing  in  common  with  the 
preceding  moments,  were  the  causal  historic  connections 
absolutely  different  from  one  another,  how  could  they 
be  abridged  into  a  law  ?  Are  constant  relations 
artificially  created  by  us,  or  do  they  not  rather  exist 
in  things  ?  Kickert  does  not  even  set  himself  the 
problem,  and  rests  content  with  the  dogmatic  affirma- 
tion that  science  presents  us  with  nothing  real  without 
affording  us  an  explanation  of  its  success. 

The  absolute  distinction  between  natural  and  histori- 
cal sciences,  a  distinction  derived  in  Rickert's  opinion, 
not  from  the  diversity  of  their  matter  which  is  always 
the  varied  and  complex  content  of  experience,  but  from 
the  method  followed  in  its  elaboration  and  from  the 
difference  in  the  proposed  end,  results  in  the  creation  of 

-  an  artificial  dualism  in  the  heart  of  the  cognitive  function 
itself,  which  aims,  on  the  one  hand,  at  a  law,  and,  on 
the  other,  at  an  individual ;  whose  end  in  science  is  the 
concept,  while  in  history  it  uses  the  concept  merely  as  a 

i  means.  Theoretical  activity,  on  the  contrary,  has,  and 
can  have,  but  a  single  end  :  the  comprehension  of  reality 
in  the  fulness  of  all  its  aspects,  the  vision  of  the  fact  in 
the  light  of  the  total  system  of  its  relations.  Its  starting- 
point  is  the  fact  experienced  in  its  individual  physiog- 
nomy, its  goal  neither  is  nor  can  be  other  than  a  concept  in 
which  the  intuitive  moment  loses  nothing  of  its  concrete 
reality,  but  gains  all  those  determinations  which  escape 
immediate  consciousness.  Even  if  we  accept  Rickert's 


definition  of  historical  knowledge,  its  final  goal  will  yet 
in  the  last  analysis  be  a  system  of  concepts  :  when  you 
affirm  that  a  certain  fact  is,  that  it  succeeds  or  precedes 
another  event,  that  it  is  co-existent  with  others,  that 
the  cause  thereof  will  be  found  in  a  certain  anterior 
situation  ;  when  you  determine  its  ideal  value  as  com- 
pared with  that  which  you  regard  as  the  meaning  of 
the  world,  the  individual,  as  such,  considered  in  its  non- 
recurring aspect,  has  ceased  to  be  the  end  of  your  know- 
ledge, which  is  rather  the  individual  sub  specie  aeternitatis, 
not  merely  intuited,  but  above  all  thought.  The  his- 
torian, like  the  scientific  man,  is  not  satisfied  with  merely 
experiencing  the  fact,  but  would  fain  understand  it, 
and,  in  order  to  do  so,  he  must  rise  to  the  concept. 

6.  Historical  Knowledge  in  Miinsterberg^  s  Philosophy 
of  Values. — If  the  end  of  history  be  the  same  as  that  of 
science,  may  not  the  matter  which  is  the  object  of  its 
elaboration  be  different  ?  This  thesis,  the  very  anti- 
podes of  that  propounded  by  Rickert,  has  been  recently 
set  forth  by  Miinsterberg,59  who  proposed  to  give  us 
a  complete  system  of  the  philosophy  of  values,  carrying 
it  back  from  epistemological  criticism  to  Fichte's  meta- 
physical idealism,  a  transformation  necessary  in  the  eyes 
of  any  philosopher  who  was  not  prepared  to  stop  short 
at  the  untenable  position  of  the  pure  norm,  the  absolute 
Ought,  the  transcendent  Sollen,  the  absurd  concept  of  a 
value  in  itself,  divorced  from  every  form  of  existence 
and  consciousness.  Miinsterberg  is  at  one  with  Rickert 
in  the  battle  against  relativism  and  the  subjectivism 
advocated  by  the  new  sophists,  who,  though  they  must 
be  credited  with  forcing  us  to  turn  from  the  artificial 
construction  of  abstract  scientific  knowledge  to  the 
immediate  world  of  consciousness,  yet  fall  into  error 
when  they  profess  to  stop  short  at  this  individual  im- 
mediacy. We  owe  the  vindication  of  historical  reality 
and  practical  activity  against  the  mechanical  ideal  and 
positivism  to  the  empiric -criticists,  intuitionists,  and 
pragmatists ; 60  but  if,  when  we  have  reached  this  point, 
we  would  not  be  forced  to  retreat,  if  concrete  life,  not 


a  sterile  conceptual  scheme,  is  to  be  our  starting-point, 
we  must  go  beyond  the  passing  moment  by  means  of 
affirmations  of  universal  and  eternal  value,  in  order  to 
form  an  intuition  of  the  world.61  But  this  value — and 
on  this  point  Munsterberg  differs  from  Rickert — while 
independent  of  single  individuals,  must  not  be  conceived 
of  as  external  to  all  spiritual  life  whatsoever,  but  in  an 
absolute  will,  an  original  action  (Urtat),  in  the  Supei-Ego 
( Uber-Ich)  which  is  perennial  and  incessant  effort ;  not 
useless  and  painful,  as  Schopenhauer  deemed  it  to  be, 
but  full  of  inexhaustible  joy  in  every  pulsation  of  life, 
which  renews  and  intensifies  the  eternal  will  and  raises 
it  to  a  higher  power.62  The  principle  of  the  world  is 
no  inert  matter,  no  motionless  God,  but  living  activity 
in  perpetual  flux,  which  is  at  once  the  preservation  and 
augmentation  of  itself  (Steigerung  des  Wollens).63  This 
ultimate  basis  of  all  values  is  not  comprehended  either 
by  thought  or  moral  consciousness  or  aesthetic  sentiment, 
which  will  never  enable  us  to  go  beyond  the  finite  Ego, 
but  by  the  philosophical  conviction  that  there  is  a  value 
transcending  human  experience,  in  which  all  empirical 
values  find  their  higher  unity.  We  may  express  such  a 
conviction  in  concepts  and  judgments,  but  by  so  doing 
we  merely  make  use  of  an  auxiliary  means,  which  does 
not  transform  it  into  scientific  knowledge  ;  it  more 
nearly  approaches  religious  belief  than  conceptual 
thought.64  We  cannot  do  without  this  conviction, 
which  is  in  reality  an  action  of  our  own,  because  it  is 
in  this  way  alone  that  our  will  can  be  fulfilled  :  in 
willing  the  unity  of  all  values,  that  is  to  say  of  our  will 
with  itself,  is  concluded  the  universal  action  in  which 
every  exigency  is  satisfied,  every  question  answered, 
every  tendency  completed.  Fidelity  to  oneself  to  all 
eternity  (Sich  selber  treu  sein  in  Eivigkeit)  is  the  action 
ensuring  the  salvation  of  all  the  values  of  the  world.65 

Munsterberg  thus  regards  value  as  identical  with 
that  which  is  willed  by  the  pure  or  super-individual 
will ;  from  the  concept  of  this  ultra-personal  will  which 
urges  us  on  beyond  the  subjective  world,  and  is  ever 


affirming  itself,  he  endeavours  to  derive  all  values  by  a 
process  of  deduction  which  is  a  vicious  circle  from 
Rickert's  point  of  view,66  since  the  existence  of  absolute 
will  presupposes  the  validity  of  the  judgment  affirming 
it.  Miinsterberg  rejects  this  priority  of  the  Sollen, 
which  would  imply  that  value  is  independent  of  the  will, 
whereas  he  considers  that  to  have  value  and  to  be  willed 
form  a  perfect  equation.  If  this  equation  be  assumed,  it 
follows  of  necessity  that  the  will  cannot  choose  the  false, 
ugly,  or  immoral ;  it  is  for  this  reason  that  Munsterberg 
declines  to  accept  Rickert's  view  of  value  as  an  Ought, 
a  norm  to  which  we  submit  of  our  own  free  will,  whilst 
having  it  within  our  power  to  will  the  contrary.  The 
concept  of  the  Sollen,  far  from  elucidating  the  idea  of 
value,  introduces  into  it  a  character  which  is  not  proper 
to  it,  that  is  to  say,  freedom  of  choice  between  ought 
and  non-ought,  without  which  we  cannot  speak  of 
Sollen.67  When  we  desire  to  judge,  we  only  desire  to 
choose  the  truth,  and  there  is  no  question  of  deciding 
between  two  alternatives.  Of  course  error  may  arise, 
but  only  because  we  think  it  to  be  truth,  not  because 
we  choose  the  false  as  such.  Even  in  moral  action, 
although  value  and  the  Ought  may  appear  to  coincide, 
the  Sollen  is  devoid  of  meaning,  because  there  is  no  such 
thing  as  a  will  contrary  to  the  good.  Does  the  highwayman 
steal  because  he  prefers  the  action  of  robbing  ?  Certainly 
not :  at  bottom  he  prefers  that  which  is  right,  and  if  he 
is  induced  to  commit  a  theft,  the  force  impelling  him  to 
do  so  is  the  seduction  of  pleasure,  not  the  will  to  evil. 
Were  he  to  prefer  the  criminal  act,  and  look  upon  it  as 
something  good,  he  would  be  a  moral  lunatic,  not  an 
immoral  man.  Immorality  consists  not  in  willing  that 
which  should  not  be  preferred,  but  in  acting  contrary 
to  that  which  is  and  which  alone  can  be  willed  :  the 
good.68  The  values,  in  the  last  analysis,  whether  they 
be  theoretical,  aesthetic,  ethic,  or  religious,  are  all  alike 
based  upon  the  satisfaction  (Befriedigung)  of  the  pure 
will,  which  must  not  be  confounded  with  individual 
hedonistic  feeling,  since  the  end  of  the  ultra -personal 


will  is  not  pleasure,  but  its  own  indefinite  and  inex- 
haustible development,  the  progressive  intensification 
and  the  preservation  of  itself.69 

There  is  one  act  of  will  which  has  nothing  to  do  with 
our  pleasure  or  pain  :  the  will  that  there  shall  be  a 
world,  that  the  content  of  our  life  shall  be  of  value  not 
merely  to  us  as  life,  but  shall  be  independently  affirmed 
in  itself.  This  original  action,  which  imparts  eternal 
meaning  to  our  existence,  and  without  which  life  would 
be  an  empty  dream,  a  chaos,  a  cipher,  is  neither  a  truth, 
nor  a  beauty,  nor  a  duty,  nor  a  sacred  good,  but  is  the 
fundamental  conviction  from  which  all  these  values  are 
derived.  Such  a  conviction  is  an  absolutely  free  act 
which  cannot  be  enforced  by  any  proof  ;  it  is  impossible 
to  adduce  any  argument  to  the  man  who  refuses  to 
ascribe  value  of  reality  to  his  experience,  and  hence 
to  that  combination  of  facts  which  questions  him,  since 
argument  and  discussion  are  impossible  unless  the 
objective  validity  of  the  world  be  presupposed.  Only 
the  man  who  is  prepared  to  take  this  first  step  can 
receive  the  proof  that  in  this  step  all  other  values 
are  comprised.70  Miinsterberg  presents  us  with  a 
systematic  deduction  of  them,  starting  from  the  single 
principle  of  the  will  that  an  objective  world  shall  exist 
and  thus  imparting  fresh  life  to  the  epic  exploits  of 
speculative  idealism.71 

7.  The  Attempt  to  deduce  all  Values  systematically. — 
If  all  values  originate  in  the  fact  that  we  separate 
experience  from  our  individual  personality  and  consider 
it  as  existing  by  itself,  the  existence -value  must  be 
found  on  the  threshold  of  valuation.  Against  this  it 
might  be  urged  that  the  affirmation  of  the  real  is  not  a 
valuation ;  that  a  judgment  is  valid,  not  that  which 
is  affirmed  therewith ;  this,  however,  results  in  the 
dogmatic  establishment  of  a  dualism  between  the  object 
which  is  recognised  and  the  act  of  recognition,  whereas 
they  are  both  merely  indivisible  aspects  of  the  same 
volition,  whose  end  and  content  is  in  the  end  itself. 
Each  experience  in  its  concreteness  is  an  active  process, 


not    something    passively    endured,   as    the  physicist 
believes,  looking  at  it,  as  he  does,  from  an  abstract 
point  of  view.     Things  are  to  me  originally  ends  and 
means,  objects  of   my  will  and  my  attention  which 
attract  me  or  repel  me  ;   hence  there  is  no  such  thing 
as  an  experience  which  is  not  a  valuation  at  the  same 
time.72    The  proof  of  reality  is  generally  sought  in  the 
confirmation  of  the  experienced  fact  by  means  of  other 
experiences,  either  of  ourselves  or  our  fellow-men,  but 
the  repetition  of  the  same  fact  in  one  individual  and 
the  agreement  with  the  experiences  of  various  persons 
might  both  be  a  pure  accident,  a   mere   coincidence 
of  illusions  ;    hence  it  is  not  an  adequate  foundation 
for  the  existence -values,  whose  ultimate  basis  is  the 
will  that  a  world  shall  exist  for  itself  independently 
of  our  subjective  individuality,  the  exigency  that  the 
content  which  is  present  to  me  at  this  moment  shall  not 
be  an  object  to  me  alone,  but  to  every  other  conscious- 
ness under  the  same  conditions.    Experience,  however, 
though  it  does  not  suffice  to  give  us  the  reality  values, 
yet  serves  as  a  limit  and  guide  to  that  exigency  of 
volition  which  is  their  true  foundation,  weakening  or 
re -enforcing    it    according    as    it   is   opposed   to    the 
facts  or  in  harmony  therewith.    He  who  would  make 
his  dreams  and  imaginings  into  the  contents  of  every 
other  subject  would  meet  with  such  resistance  from 
his  fellow-men  as  to  deprive  him  of  all  power.73    If  the 
objective  existence  of  things  be  derived  from  the  will 
that  the  facts  experienced  by  us  shall  also  be  experiences 
possible  to  other  individuals,  it  is  obvious  that  the 
consciousness  of  the  reality  of  our  fellow  -  men  must 
precede  the  affirmation  of  things.     The  general  belief  is 
rather  that  we  first  perceive  the  bodies  of  other  men,  and 
then  from  the  resemblance  of  their  external  aspect  argue 
to  their  psychic  life  by  a  process  of  induction.     Miinster- 
berg  maintains  that  nothing  can  be  more  false  than 
such  a  conception,  which  is  the  outcome  of  the  habit 
of   considering  reality  naturalistically  and   abstractly. 
We  grasp  the  action  of  our  volition  and  of  the  will  of 


others  in  an  intuitive  and  immediate  manner  which 
precedes  the  knowledge  of  things  ;  we  feel  ourselves 
and  others  directly,  not  as  objects,  but  as  tendencies 
of  attraction  or  repulsion.74  But  why  do  we  not 
attribute  to  the  flower  which  wills  to  be  gathered,  the 
fruit  which  wills  to  be  tasted,  the  line  which  draws  us 
to  follow  it,  the  rhythm  which  urges  us  to  dance,  the 
same  objectivity  which  we  ascribe  to  our  fellow-men 
and  the  higher  animals  ?  Do  they  not  all  alike  make  us 
feel  their  exigencies  directly  ?  Undoubtedly  the  flower, 
the  fruit,  the  line,  and  the  rhythm  all  will  something, 
but  their  volition  is  exhausted  in  the  exigency  experi- 
enced by  us,  whereas  animals  and  other  human  beings 
are  continually  assuming  fresh  attitudes  with  regard  to 
objects.  The  criterion  of  subjective  existence  is  the 
rediscovery  of  the  same  experience  of  will  as  identical 
with  itself  under  new  forms.75  This  intimate  relation  of 
volition  to  itself  constitutes  what  is  commonly  termed 
the  soul.76 

Our  individual  volitions  are  not  merely  limited  by 
exterior  things  and  by  other  subjects,  but  they  also 
recognise  the  existence  above  themselves  of  acts  of  will 
independent  of  any  subjective  caprice  and  possessing 
reality-value  to  us  in  as  much  as  they  always  recur  in 
the  same  way.  These  acts  of  ultra -personal  will  are 
the  absolute  valuations  (die  absolute  Bewertungen)  as 
opposed  to  which  the  volitions  determined  by  necessity 
and  subjective  tendencies  appear  to  us  to  be  accidental 
and  unreal,  as  do  the  products  of  the  imagination  in 
comparison  to  objective  nature  :  only  if  we  will  with  the 
consciousness  that  we  shall  always  will  thus,  shall  we  have 
an  absolute  valuation.  Even  the  existence  of  values, 
like  that  of  subjects  and  objects,  is  based  upon  the  pure 
satisfaction  of  the  will,  which  rediscovers  the  original 
experience  unchanged  in  new  experiences.77 

The  values  of  existence,  which  we  have  thus  deduced 
from  a  single  principle,  constitute  the  world  of  primitive 
experience  in  its  triple  aspect :  external,  internal,  and 
social,  as  it  is  immediately  presented.  To  each  of  these 

wo.  ii  THE  PHILOSOPHY  OF  VALUES  223 

three  kinds  of  values  there  corresponds  a  value  of  culture, 
which  is  discovered  by  reflection  when  the  will  becomes 
conscious  of  its  ends.  We  then  go  beyond  the  bounds 
of  immediate  experience  by  means  of  connections  which 
are  established  between  facts  belonging  to  the  same  order 
of  reality  ;  there  thus  arise  the  various  forms  of  know- 
ledge, whose  objective  validity  we  must  prove  by  keeping 
the  starting-point  of  our  deduction  ever  in  mind,  i.e. 
the  will  which  tends  to  preserve  its  own  identity  amid 
various  experiences.  Everything  which  satisfies  this 
super-individual  will,  each  identity  which  is  discovered 
between  the  different  moments  of  existence,  is  of  in- 
dependent and  absolute  value,  and  is  not  a  mere  act  of 
subjective  thought. 

8.  The  Historic  World  of  Subjective  Witts  and  the 
Mechanical  World  of  Objects. — Seeing  that  every  con- 
nection is  based  upon  identity,  it  is  obvious  that  things 
can  only  be  linked  with  things,  subjects  with  subjects, 
valuations  with  valuations  :  the  first  species  of  connec- 
tion gives  birth  to  the  science  of  nature,  which  is  the 
consideration  of  objects  with  regard  to  that  in  them 
which  remains  identical ;  the  second  to  history,  which 
connects  single  subjective  wills,  thinking  them  in  their 
identity ;  the  third  to  reason,  the  system  of  pure 
valuations  conceived  in  the  unity  of  their  absolute 
principle.78  Science  and  history  have  then  the  same  end, 
and  only  differ  as  to  the  matter  which  they  elaborate  ; 
one  of  them  seeks  the  identity  of  things,  the  other  that 
of  wills,  which,  as  we  have  already  seen,  cannot  be 
reduced  to  objective  contents,  but  are  comprehended 
in  their  immediacy  by  a  peculiar  form  of  experience. 
The  general  law  is  not  the  true  end  of  scientific  know- 
ledge, which  tends  rather  to  connect  phenomena  recipro- 
cally in  such  a  way  that  the  identical  permanence  of 
one  affords  an  explanation  of  the  other ;  it  matters 
little  that  the  two  phenomena  thus  united  are  produced 
but  once,  and  do  not  recur  :  the  formulator  of  a  law 
merely  exacts  that  it  shall  be  possible  to  verify  it  afresh 
in  a  single  case.  The  generic  concept  is  not  a  con- 


stituent  of  science,  but  is,  like  language,  merely  an 
auxiliary  and  extrinsic  means,  a  practical  organ  render- 
ing the  same  service  to  the  scientist  as  the  hand  does  to 
the  painter.79-  The  ideal  of  science  is  not  a  system  of 
laws,  but  a  system  of  things,  such  that  its  preserva- 
tion throughout  time  carries  with  it  all  variations 
perceptible  in  the  outer  world.  Were  it  possible  to 
think  the  whole  natural  series  of  phenomena,  pursued 
ad  infinitum  in  both  directions,  as  a  series  of  atoms  re- 
maining identical  in  their  movements  and  accelerations, 
there  would  be  no  need  to  have  recourse  to  generic  laws, 
but,  since  it  is  impossible  for  each  individual  to  follow 
the  whole  series  in  both  directions  to  the  two  extremes, 
in  order  to  solve  the  problem  definitely  as  nearly  as 
possible,  laws  are  constructed  summing  up  in  themselves 
the  results  of  the  preparatory  work  of  our  predecessors 
in  such  a  way  as  to  avoid  the  necessity  of  beginning 
I  again  at  the  beginning  each  time.80  The  atom  of 
IfTechanics  is  not  a  mere  fiction,  but  is  true  and  existent, 
because,  when  experience  is  reduced  to  mathematical 
properties  only  and  divested  of  all  qualitative  content, 
the  end  of  the  ultra-personal  will  is  realised,  and  that 
pure  satisfaction  is  attained  which  Miinsterberg  regards 
as  the  basis  of  existence- value.  The  physicist  is  there- 
fore within  his  rights  as  long  as  he  confines  himself 
to  affirming  the  reality  of  the  world  conceived  of  by 
him  ;  he  falls  into  error  when  he  makes  nature  a  system 
sufficient  unto  himself  apart  from  that  eternal  act  of  will 
which  can  alone  impart  existential  significance  to  it.81 

Individual  and  subjective  wills,  which  are  eliminated 
by  naturalistic  treatment  in  order  to  construct  an 
independent  world,  constitute  the  matter  proper  to 
historical  knowledge,  which  studies  man  not  as  a  psycho- 
physical  being,  devoid  of  value,  not  as  a  thing  amongst 
other  things,  but  as  a  subject  which  wills  and  values 
freely.  This  world  of  free  wills  escapes  the  law  of 
causality,  because  they  are  external  to  time  in  their 
immediate  life  :  just  as  it  would  be  meaningless  to  ask 
whether  the  will  of  Napoleon  measured  two  or  three 


inches,  whether  it  was  white,  red,  or  green,  so  it  is  non- 
sense to  attribute  duration  to  it :  his  wars  lasted  for 
years,  the  movements  of  his  body  a  few  seconds  only,  but 
the  attitudes  of  his  will  are  not  for  that  reason  limited 
by  time,  which  is  merely  a  property  of  objects.  The  will 
is  wholly  comprehended  if  we  understand  its  ends  :  he 
who  asks  the  cause  of  an  act  of  will  puts  naturalistic 
interest  in  the  place  of  historical  interest.  In  the  immedi- 
ate communication  of  two  subjects,  as,  for  example,  of 
two  friends  who  are  discussing  politics,  one  will  penetrates 
the  other  and  understands  its  meaning  without  setting 
it  up  to  itself  as  an  objective  content,  without  enquiring 
whether  it  precede  or  follow  his  own,  or  be  co-existent 
therewith,  still  less  what  antecedents  have  determined 
it.  It  would  at  first  sight  seem  a  hopeless  task  to  seek 
in  different  individual  wills  that  identity  which  is 
necessary  to  the  attainment  of  a  system  of  historic 
knowledge  ;  but,  when  I  agree  with  the  friend  who  is 
judging  in  his  affirmations  or  negations,  when  I  share 
his  hopes  and  antipathies,  do  I  not  will  his  will  ?  (mit- 
erlebtes,  mitgewolltes  Wollen).82  The  comprehension  of 
a  subject  in  its  historical  existence  involves  the  discovery 
of  the  will  of  other  subjects  in  the  will  of  the  individual, 
and  this  is  attained  by  resolving  that  personality  into  his 
single  political,  judicial,  economic,  scientific,  artistic, 
religious,  and  ethic  volitions,  each  one  of  which  receives 
identically  within  itself  the  will  of  another  individual 
or  group  of  individuals.  Thus  we  shall  say  that  he  is  a 
Darwinist,  a  Wagnerian,  a  Marxist,  etc.,  if  in  his  partial 
volitions  we  find  the  same  theoretic  affirmations  as  in 
Darwin,  the  same  aesthetic  and  musical  preferences  as 
in  Wagner,  the  same  social  and  political  tendencies  as 
in  Marx.  In  historical  elaboration  it  must  not  be 
forgotten  that  every  new  creation  is  also  partially  an 
imitation:  in  history,  as  in  the  world  of  nature,  nothing 
absolutely  new  takes  place.  He  who  desires  something 
new  desires  something  old,  only  he  desires  it  in  a 
different  way.  The  artistic,  ethical,  religious,  political, 
or  scientific  genius  does  but  gather  within  himself  the 



incitations  to  will  which  he  feels  from  a  thousand 
sides  ;  the  only  thing  in  him  which  is  really  new  is  the 
original  synthesis,  and  we  shall  therefore  have  succeeded 
in  understanding  him  historically  if,  when  analysing 
his  will,  we  find  therein  the  wills  of  those  who  have 
exercised  influence  upon  him.83  Things  are  not  entirely 
excluded  from  the  historical  world;  but  they  are  included 
there  in  their  original  reality,  as  means  and  ends  of  the 
will,  not  as  parts  of  nature  :  the  flood  or  earthquake 
which  sweeps  away  a  civilisation  is  of  interest  to  the 
historian  only  in  so  far  as  it  is  'dreaded  by  individual 
minds  ;  the  historical  importance  of  the  boat  which 
carried  Caesar  lies  in  the  fact  that  it  satisfied  his  desire 
to  obtain  news  of  the  fleet.84 

The  normative  sciences  (logic,  ethics,  aesthetics, 
religious  dogma)  differ  from  history  because  the  object 
of  their  search  is  the  identity  not  of  the  subjective  values, 
but  of  the  ultra-personal  valuations,  which  do  not  depend 
upon  the  free  choice  of  individuals.  As  historical  subjects, 
we  may  place  ourselves  at  variance  with  our  valuations  ; 
as  moral  subjects,  on  the  other  hand,  we  will  and  must 
will  in  that  determinate  way  only.  Here,  too,  the 
fundamental  problem  is  the  same  :  given  a  value,  we 
must  find  in  the  current  of  life  a  new  super-individual 
will,  which  shall,  in  spite  of  its  diversity,  prove  identical 
with  the  first.  Just  as  chemistry  can  derive  the  com- 
pound from  the  elements  and  the  elements  from  the 
compound  whilst  preserving  the  same  things  (atoms), 
so  logic  in  the  induction  of  the  single  affirmations  from 
the  ultra-personal  will  passes  to  the  general  valuation, 
and  vice  versa  in  the  deductive  process  derives  the  single 
elementary  valuations  from  the  complex  affirmation, 
always  finding  the  same  fundamental  identity  in  these 
transitions.  The  same  may  be  said  of  all  the  other 
values,  whether  aesthetic,  ethical,  or  religious,  in  which 
the  ultra-personal  attitude  always  remains  identical, 
while  yet  being  realised  and  taking  concrete  form  in 
new  situations  of  life,  in  new  exigencies,  which  set  the 
will  fresh  problems.85 


9.  Criticism  of  Miinsterberg's  Philosophy. — No  great 
amount  of  acumen  is  necessary  to  perceive  the  artificial 
element  in  this  systematic  deduction  of  all  values,  and 
more  especially  of  the  cognitive  function,  from  the 
ultra-personal  will.  The  will  of  which  we  have  all  had 
experience  is  always  the  will  of  an  individual  Ego,  of  a 
concrete  historical  subject ;  volition, even  if  it  be  exercised 
with  the  consciousness  that  it  will  always  will  in  that 
way,  does  not  therefore  cease  to  be  the  action  of  a 
determinate  person.  The  first  artifice  will  then  be 
found  in  the  starting-point  of  the  deduction,  that  is  to 
say,  in  the  concept  of  an  extra-subjective  will,  from 
which  the  subject  is  then  supposed  to  be  derived.  If 
the  existence  of  the  Super  -Ego  be  a  free  conviction 
of  individuals,  their  reality  is  the  presupposition  of  the 
whole  deduction.  It  is  not  the  pure  will  which  imparts 
existence-value  to  the  Ego,  but  rather  the  Ego  which  gives 
a  basis  to  that  as  to  every  other  will.  We  have  immediate 
assurance  of  our  subjective  life,  an  assurance  which 
cannot  be  shaken  by  sceptical  doubt,  whereas  the 
existence  of  an  impersonal  will  is  not  something  which 
all  of  us  are  prepared  to  acknowledge.  In  order  that 
the  reasoning  of  Miinsterberg  may  mean  anything,  we 
must  postulate  that  pure  will  is  of  greater  value  than 
individual  and  momentary  desires  ;  that  the  will  which 
is  always  coherent  with  itself  is  of  greater  value 
than  changing  and  contradictory  volitions  ;  this  pre- 
supposes a  criterion  of  valuation,  a  consciousness  of 
value  which  cannot  be  derived  from  that  pure  will 
itself  without  committing  a  vicious  circle.  Or  shall  we  \ 
say  that  these  contingent  and  individual  values  do  noti| 
exist  ?  Miinsterberg  actually  has  recourse  to  this  arti- 
fice, and,  seeing  that  the  volitions  of  the  historic  subject, 
which  frequently  take  a  direction  contrary  to  the  good, 
the  beautiful,  and  the  true,  cannot  be  reconciled  with 
his  theory  which  identifies  value  with  being  willed, 
he  arbitrarily  banishes  these  actions  from  the  sphere 
of  will.  The  thief  who  commits  a  robbery  really  wills 
the  good ;  does  he  who  denies  that  he  is  guilty  of  a 


crime,  while  well  aware  that  he  has  committed  it,  still 
prefer  the  truth,  in  spite  of  the  fact  that  he  states  the 
false  ?  Here  we  have  the  paradox  to  which  we  are 
forced  to  resort  in  order  to  save  the  equation  :  to  have 
value = to  be  willed,  cost  what  it  may  to  do  so,  an  equation 
contradicting  our  intimate  experience,  which  bears 
witness  that  it  is  possible  to  be  conscious  of  the  good, 
the  true,  and  the  beautiful,  whilst  at  times  not  willing 
them  intensely  enough  to  give  them  the  preference  over 
Hedonistic  and  individual  ends.  The  robber  who 
commits  a  theft  of  his  own  free  will  knows  which  would 
be  the  right  course,  but  pure  volition  is  too  feeble  in 
him  and  is  conquered  by  the  direct  will  to  enjoy.  If 
he  had  really  willed  the  good,  and  the  good  only,  he 
would  not  have  stolen ;  in  appropriating  the  property 
of  another,  he  has  preferred  his  own  pleasure.  For 
him  to  be  termed  immoral,  it  suffices  that  he  is 
conscious  of  the  good ;  it  is  not  necessary,  as  Miinster- 
berg  maintains,  that  he  shall  will  only  the  good.  On 
the  contrary,  were  this  the  case,  we  could  not  accuse 
him  of  being  immoral,  since  he  would  then  be  an  irre- 
sponsible being.  He  who  steals  without  intending  to 
do  so,  like  the  kleptomaniac,  is  ill,  not  guilty.  It  is  one 
I  thing  to  be  conscious  of  the  value  of  an  object,  it  is 
another  to  will  that  object :  they  are  two  widely 
different  moments  which  do  not  always  coincide  in  our 
minds.  He  who  tells  a  lie  in  order  to  avoid  being  sent 
to  prison  still  recognises  the  value  of  truth,  but 
at  the  moment  he  prefers  the  falsehood  which  is  of 
personal  use  to  him.  The  reality  of  the  crime  he  has 
committed  remains  mercilessly  with  him,  even  though 
he  may  repent  and  no  longer  desire  it,  but  may  rather 
strive  to  put  it  out  of  his  mind.  The  past  is  no  longer 
willed,  but  this  does  not  bring  about  its  destruction ; 
we  continue  to  attribute  value  to  the  men  and  the  events 
of  the  past,  even  though  it  may  be  meaningless  to  say 
that  we  still  will  them.  This  is  a  proof  that  that  specific 
reaction  of  our  whole  consciousness,  which  enables  us  to 
feel  the  value  of  things,  is  not  an  act  of  will,  still  less  so 


is  the  affirmation  of  existence,  which,  as  we  have  already 
seen  when  discussing  Eickert's  theory,  has  nothing  to 
do  with  the  apprehending  of  a  value.  My  subjective 
existence  is  not  something  dependent  upon  my  will ;  on 
the  contrary,  my  being  appears  to  me  the  condition  of 
my  will,  not  merely  of  fugitive  and  incoherent  volitions, 
but  of  that  pure  will,  which,  while  acting  sub  specie 
aeternitatis,  never  ceases  to  be  my  will.  To  live  in  spite 
of  oneself,  to  feel  oneself  exist  even  when  one's  own 
individual  life  is  of  no  value  to  one,  even  when  the  will 
to  exist  has  been  shattered  in  oneself,  is  not  this  the 
cruel  despair  of  the  pessimist  ? 

Objective  reality  and  the  assertion  of  it  are  even 
more  obviously  independent  of  the  act  of  will.  Miinster- 
berg  is  correct  in  maintaining  against  the  empiricists 
that  the  evidence  of  objective  being  cannot  come 
to  us  from  without ;  but  he  is  mistaken  in  attribut- 
ing this  recognition  to  the  satisfaction  of  the  pure  will, 
so  that  the  reality  of  the  world  would  be  in  ultimate 
analysis  a  conviction  which  the  individual  is  at  liberty 
to  accept  or  not,  and  which  no  proof  can  force  upon  him. 
It  is  not  will  which  impels  us  to  transcend  the  fugitive 
moment  and  the  sphere  of  individual  life,  but  rather 
thought,  which,  in  its  laws  and  its  function  is  presented 
to  us  as  possessed  of  the  characters  of  necessity  and  uni- 
versality, and  affords  us  the  immediate  and  indestructible 
certainty  that  there  must  be  countless  other  experiences 
beyond  the  limited  sphere  of  our  own  experiences.  If 
identity  within  certain  limits  be  a  sign  of  objective 
existence,  this  is  not  the  case  in  order  that  the  will  may 
be  satisfied,  but  because  it  is  a  law  of  reason,  whence 
we  are  of  necessity  led  to  think  of  nature  in  its  independent 
being  with  that  same  coherency  which  is  proper  to  our 
thought — a  coherency  which  must  not  be,  however, 
understood  as  abstract  identity,  but  as  concrete  unity 
of  the  various  moments  in  time,  which  does  not  exclude 
the  qualitative  multiplicity  of  real  becoming.  Mimster- 
berg,  on  the  contrary,  by  placing  objectivity  in  the 
absolute  permanency  of  the  identical,  turns  nature  into 


a  rigid  and  abstract  system  of  immutable  things,  and 

thus  establishes  another  arbitrary  equation  :    nature  = 

world  of  mathematical  physics,  as  if  independent  existence 

were  reducible  only  to  stereotyped  objects  and  not  to 

evolutionary  processes  as  well ;  as  if  it  were  not  possible 

to  conceive   of  individual   aspects  and  heterogeneous 

qualities  in  things  external  to  our  subjective  life.     The 

new  in  the  objective  world  is  no  less  existent  than  the 

identical ;  on  the  contrary,  it  is  a  necessary  condition  of 

phenomenal   happening,   which   quantitative   formulas 

cannot  entirely  explain.     Is  change  real  only  in  relation 

to  our  subjective  will  ?     Is  the  world  transformed  only 

in  our  immediate  experience  thereof  ?     Certainly  not ; 

science  itself  recognises,  side  by  side  with  the  laws  of 

permanency,  the  irrevocability  of  natural  processes  in 

time.     The  mechanical  world  is  not  the  whole  of  nature, 

but  merely  the  skeleton  thereof — a  skeleton  which  must 

be  clothed  with  muscles,  nerves,  and  blood  if  we  are 

to  be  able  to  think  of  it  as  a  system  of  real  things  and 

events.     The  equation  set  up  by  Miinsterberg  between 

objective  reality  and  identity  of  permanency  is  then  of 

no   greater  value   than  the   others   we   have   already 

discussed  :  in  order  to  affirm  the  independent  existence 

of  a  given  concrete  situation,  I  am  not  in  the   least 

bound  to  recognise  that  it  is  identical  with  another.     If 

we   thus   restore   to   objective   reality   that   incessant 

motion  of  development  of  which  Miinsterberg  arbitrarily 

robs  it,  petrifying  it  into  immovable  things,  it  will  at  once 

be  revealed  to  us  in  its  historical  life,  and  the  artificial 

dualism  of  the  two  forms  of  knowledge  will  be  eliminated. 

Miinsterberg,  while   on  the  one   hand   robbing  nature 

of  all  its  activity,  on  the  other  hand  divests  history  of 

its  every  content,  reducing  it  to  the  mere  abstract 

moment  of  subjective  activity  external  to  time.     Is  it 

however  possible  to  think  of  a  concrete  will  aiming  at 

and  realising  an  end  without  positing  any  temporal 

relation  therein  ?     If  there  be  an  experience  of  which 

time  is  a  constituent  element,  it  is  undoubtedly  the 

experience  of   our  will ;    the  relation  between  present 


and  future  is  essential  to  the  tendency  towards  an  end 
which  ceases  to  be  conceivable  when  duration,  the 
distinction  between  that  which  is  present  to  us  and  that 
which  appears  to  us  as  the  future  goal  of  our  efforts, 
abolished.  It  is  useless  for  Miinsterberg  to  tell  us 
that  this  distinction  of  successive  moments  is  illusory, 
and  that  in  eternal  action  the  will  is  identified  with  the 
willed,  since  we  know  no  will  but  our  own,  and  must 
start  from  our  own  experience  in  order  to  form  a  concept 
of  the  absolute  will.  Further,  according  to  Miinster- 
jrg's  theory,  does  not  history  treat  just  of  subjective 
volitions  ?  We  must  then  determine  the  characters  of 
these  volitions,  not  those  of  absolute  valuations,  by 
lerivation  from  personal  experience.  A  will  in  which 
there  is  no  transition  from  a  state  of  dissatisfaction  to 
me  of  greater  completeness,  from  an  initial  moment  to  a 
final  moment,  is  an  absurdity  not  merely  psychologically, 
but  also  logically.  Were  that  which  we  seek  to  coincide 
with  our  present  condition,  there  would  be  no  such  thing 
as  tendency  ;  desire  ceases  the  moment  it  is  gratified. 
In  short,  we  can  speak  of  will  only  on  condition  that  the 
term  of  the  action  do  not  exist  in  its  completeness  at 
the  point  from  which  we  start ;  if  we  annihilate  this 
interval,  volition  will  disappear  as  a  fact  of  concrete 
experience,  and  cease  to  be  thinkable  even  as  a  concept, 
since  contradiction  would  then  be  implied.  That  which 
is  fully  achieved,  that  which  is  actual  in  its  absoluteness, 
cannot  be  in  course  of  being  done,  since  to  do  means  to 
realise,  and  nothing  can  be  realised  but  something  which 
is  not  as  yet  real.  Even  if  it  be  admitted  that  the  end 
of  the  will  is  another  will,  this  second  will  is  never 
perfectly  identical  with  the  first ;  if  this  were  not  so, 
there  would  be  no  meaning  in  the  action  :  the  intensifica- 
tion of  the  will,  the  raising  thereof  to  a  higher  power, 
assumes  the  existence  in  the  goal  to  be  attained,  which 
imparts  meaning  to  the  volition,  of  something  which  is 
lacking  in  the  initial  moment.  Now,  how  are  we  to 
interpret  this  actualisation  of  ever  loftier  stages  in  the 
cosmic  process  of  the  will,  and  the  distinction  of  absolute 


volition  in  the  single  subjective  tendencies,  unless  we 
understand  them  to  be  a  series  of  successive  terms,  each 
of  which  contains  more  than  its  predecessor  ?  If  you 
attempt  to  suppress  this  succession,  it  is  meaningless 
to  speak  of  will,  which  is  process  developing  in  a 
determinate  direction.  What  will  become  of  the  pro- 
gressive actualisation,  of  which  Minister  berg  speaks, 
the  incessant  becoming  of  the  world,  in  which  each 
volition  tends  towards  a  more  complete  will,  which  is 
in  its  turn  the  starting-point  of  another  act  of  will,  if 
we  place  it  outside  time  ?  That  which  affords  satis- 
faction to  our  will  is  not  another  will,  but  a  perception, 
a  presentation,  a  concept — a  state  of  our  consciousness, 
not  a  new  activity.  We  do  not  desire  another  desire, 
we  do  not  make  efforts  in  order  to  arrive  at  other  efforts, 
we  do  not  act  in  order  to  continue  to  do  so.  Certainly 
there  is  no  such  thing  as  a  will  without  content ;  certainly 
the  end  and  the  activity  directed  thereto  are  fused  in 
consciousness  into  a  concrete  synthesis  ;  it  does  not, 
however,  follow  that  the  content  and  the  action  of  will- 
ing are  absolutely  identical ;  even  if  we  do  not  succeed 
in  separating  them,  we  must  yet  distinguish  between 
them,  since  our  experience,  the  only  source  from  which 
we  can  draw,  if  we  would  know  what  will  is,  always 
presents  them  to  us  as  distinct.  The  statement  that 
consciousness  can  be  wholly  reduced  to  action,  that  the 
subjective  life  is  will  and  nothing  but  will,  merely  because 
every  psychic  phenomenon  contains  a  moment  of  activity, 
is  equivalent  to  reducing  the  whole  of  physical  reality 
to  the  single  property  of  extension,  merely  because  there 
is  no  such  thing  as  a  body  which  does  not  occupy  a 
space.  By  a  similar  train  of  reasoning  the  intellectualist 
in  his  turn  might  reply  that,  since  will  devoid  of  repre- 
sentative or  conceptual  content  does  not  exist,  vague 
and  confused  as  that  content  may  be,  will  is  reducible 
to  presentation  or  concept !  This  is  a  theory  from 
which  Miinsterberg  shrinks  in  holy  horror,  but  which 
is  at  bottom  the  outcome  of  a  sophism  of  the  same 
nature  as  that  which  serves  to  prove  his  voluntarism. 


Moreover,  in  the  concept  of  history  Miinsterberg  in 
the  last  analysis,  speak  as  he  may  of  ends  and  wills, 
has  not  succeeded  in  shaking  off  the  prejudices  of 
traditional  intellectualism,  and  of  abstract  mathe- 
maticism.  Of  what  avail  is  it  to  substitute  the  will 
for  atoms  if  it  be  then  treated  as  if  it  were  the  out- 
come of  a  combination  of  will-particles,  each  one  of 
which  must  be  acknowledged  to  be  identical  with 
any  other  ?  Of  what  avail  is  it  to  vindicate  living  ex- 
perience against  the  schemes  of  the  mechanical  theory, 
if  the  concrete  personality  is  then  to  be  resolved  into 
a  series  of  atomic  wills  in  the  endeavour  to  discover 
identity  between  these  elements  and  the  elementary 
volitions  of  other  subjects  ?  A  system  of  abstract 
equations,  even  though  its  terms  consist  of  volition- 
atoms  instead  of  extended  particles,  a  system  of  identities 
external  to  time  is  the  very  negation  of  history ;  since 
in  such  a  system  there  is  no  meaning  in  speaking  of  that 
development  in  a  determinate  direction  which  is  the 
essential  characteristic  of  the  historical  and  teleological 
process.  In  relations  of  identity  it  is  a  matter  of 
indifference  in  what  order  the  terms  are  placed,  and 
these  terms  can  always  be  inverted ;  hence  it  is  im- 
possible to  decide  which  of  two  elementary  volitions 
which  are  acknowledged  to  be  identical  is  the  original, 
and  which  of  them  is  a  mere  imitation  of  the  other  : 
if,  for  instance,  certain  tendencies  be  found  in  the 
subject  Miinsterberg  which  are  identical  with  those 
found  in  the  subject  Fichte,  it  may  equally  well  be  said 
that  Fichte's  will  lives  again  in  Miinsterberg  or  vice 
versa.  If  we  prescind  from  time  and  confine  ourselves 
to  positing  identity  between  wills,  the  irreversible  order 
of  development  will  vanish,  and  we  have  not  even  a 
criterion  by  which  to  establish  that  hierarchy  of  wills, 
that  progressive  intensification  of  them,  which  Miinster- 
berg maintains  to  be  the  essence  of  absolute  will.  Two 
identical  volitions  are  absolutely  on  the  same  level,  and 
one  cannot  be  regarded  as  the  end  of  the  other  in  such 
a  way  as  to  make  it  allowable  to  place  it  a  degree  higher 


in  the  scale  of  values.  The  system  of  identities  then 
does  not  help  us  to  understand  history,  but  rather 
destroys  it.  That  which  constitutes  the  life  of  historic 
reality,  and  which  we  have  to  reconstruct  and  com- 
prehend, is  the  rise  of  new  ends  and  new  volitions  in 
concrete  consciousnesses  :  even  when  you  succeed  in 
resolving  an  individual  personality  into  certain  volitions 
which  have  been  previously  willed  by  others  (we  may  say 
so,  but  Miinsterberg  could  not  affirm  it  even  from  his 
extra- temporal  point  of  view),  you  have  not  understood 
the  individual  at  all,  because  that  original  imprint  which 
imparts  to  his  will  a  new  physiognomy,  that  cannot  be 
reduced  to  preceding  wills,  has  escaped  your  notice. 
Your  formulas  contain  everything  except  the  conscious- 
ness of  that  subject ;  everything  save  his  history,  which 
does  not  consist,  as  you  maintain,  in  finding  a  will 
identical  to  itself,  but  in  the  knowledge  of  reality  in  its 
development,  and  hence  also  in  those  unique  aspects 
which  can  never  be  identified  with  others.  In  order 
to  affirm  the  independent  existence  of  a  subjective  will, 
it  is  not  at  all  necessary  to  acknowledge  it  to  be  identical 
with  our  own  will  or  with  that  of  another  subject ; 
indeed  the  contrary  is  the  case,  since  we  distinguish 
the  different  subjects  from  ourselves  and  from  one 
another  only  in  so  far  as  they  appear  to  us  possessed 
of  characteristics  irreducible  to  one  another.  Were  we  to 
find  the  same  volitions  in  them  all,  were  we  to  experience 
these  wills  as  we  immediately  experience  our  own,  were 
it  possible  to  identify  them  with  our  own,  all  exteriority 
and  independence  of  the  single  subjects  would  disappear. 
That  which  makes  one  person  a  being  independent  of 
others  is  not  the  universal  identity  which  makes  them 
the  same,  but  the  singularity  which  makes  it  impossible 
to  reduce  them  to  one  another.  I  recognise  the  alter 
external  to  my  ego,  not  because  he  wills  that  which  I 
will,  but  because  his  will,  strive  as  I  may,  refuses  to  be 
identified  with  my  own  will.  Even  if  we  agree,  relatively 
speaking,  if  our  hearts  beat  in  unison,  it  is  impossible 
for  me  to  include  his  will  within  my  consciousness, 


since  it  always  remains  extraneous  to  my  individuality. 
Miinsterberg  in  his  theory  does  not  account  for  the 
wide  difference  between  the  intimate  unity  in  which 
my  volitions  are  bound  together  and  the  identity  which 
may  exist  in  the  ends  willed  by  me  and  another  indi- 
vidual. If  subjective  existence  consisted  in  finding  a  will 
identical,  the  relation  between  my  volition  of  yesterday 
and  my  volition  of  to-day,  both  being  directed  to  the 
same  end,  should  seem  to  me  the  same  as  the  agreement 
between  my  will  and  that  of  another  person.  But  what 
a  profound  difference  there  is  between  the  two  forms 
of  unity!  My  volition  of  this  present  moment  may 
agree  completely  with  the  will  of  another  individual 
and  be  absolutely  contrary  to  that  which  I  willed 
yesterday,  yet  my  two  volitions,  however  contradictory 
they  may  be,  are  far  more  intimately  connected  than 
is  my  will  with  that  of  another.  Even  in  the  case  of 
a  capricious  and  hysterical  subject,  whose  mind  is  con- 
stantly changing,  the  consciousness  of  his  own  identity 
is  never  absent,  because  this  personal  identity  is  not 
derived  from  the  unity  of  the  end,  to  which  the  single 
volitions  may  converge,  but  from  the  common  origin 
from  which  they  irradiate  ;  it  is  an  indefinable  imprint 
due  to  their  origin,  not  to  their  meaning.  Two  wills  may 
be  identical  as  to  their  end,  but  this  is  not  enough  to 
make  them  a  subjective  unity ;  and,  conversely,  the 
individual  does  not  lose  the  identity  of  his  conscious- 
ness, even  though  he  may  change  the  content  of  his 
desires  every  minute ;  neither  do  we  cease  to  recognise 
that  he  is  one  subject,  even  though  we  may  not  succeed 
in  finding  a  constant  meaning  in  his  volitions.  The 
coherency  of  the  will  is  the  criterion  of  judgment  of 
the  moral  character,  not  the  sign  of  subjective  existence. 
We  always  feel  ourselves  to  be  the  same  persons,  even 
though  we  may  not  be  able  to  order  the  volitional  acts 
of  our  whole  lives  in  such  a  way  as  to  enable  us  to  see 
them  as  the  progressive  actualisation  of  the  same  plan 
and  of  an  identical  end.  Inner  experience,  in  which 
we  experience  ourselves  immediately,  must  undoubtedly 


be  distinguished  from  knowledge  of  the  exterior  world  : 
things  affirmed  in  their  independent  reality  are  not 
directly  apprehended  as  is  our  subjective  life.  Miinster- 
berg  would  include  in  the  sphere  of  immediate  experience 
the  knowledge  we  possess  of  other  subjects,  which  are 
hence  supposed  to  be  experienced  in  the  same  way  as 
we  experience  our  own  Ego  :  a  theory  which,  were  it 
true,  would  annihilate  the  unique  distinctive  character  of 
my  own  will  as  opposed  to  that  of  others  ;  because,  if  I 
regard  my  consciousness  as  a  subjective  world  rigidly 
opposed  to  the  consciousness  of  other  individuals,  I  do 
so  by  virtue  of  that  character  of  immediacy  which  is 
found  in  no  other  apprehension  of  reality.  If  the  will 
of  others  were  revealed  to  me  in  the  same  way,  I  should 
be  unable  to  distinguish  it  from  my  own  will ;  this  is, 
however,  not  the  case  :  when  I  have  closed  my  eyes, 
stopped  my  ears,  and  placed  myself  at  such  a  distance 
from  others  that  I  cannot  be  touched,  I  continue  to 
experience  my  own  will,  but  know  nothing  of  the  will 
of  others.  I  can  only  receive  intelligence  of  the  con- 
sciousness of  others  by  means  of  the  sound  of  words, 
the  sight  of  their  features  and  gestures,  and  by  tactile 
and  muscular  sensations  :  that  is  to  say,  mediately,  not 
immediately.  Only  when  these  contents  are  interpreted 
as  signs  of  an  external  reality  do  we  believe  in  the 
existence  of  another  subject ;  an  existence  which  is  not 
admitted  if  these  contents  be  regarded  as  mere  subjective 
images.  When  I  am  convinced  that  the  voice  of 
a  person  which  I  thought  I  had  heard  is  a  hallucina- 
tion of  my  own,  the  existence  of  that  subject  will 
also  become  an  illusion  to  my  mind.  The  existence, 
independent  of  my  will,  of  the  friend  who  is  talking 
politics  with  me  is  a  dream  of  mine  if  I  do  not  actually 
see  and  hear  him  :  the  existence  of  other  subjects  will 
vanish  along  with  the  objective  reality  of  their  contents. 
The  logical  presupposition  of  the  latter  then  will  be  found 
in  the  former,  not  vice  versa,  as  Mtinsterberg  would 
affirm.  That  which  exists  independently  of  me,  no 
matter  whether  it  be  a  thing  or  a  consciousness,  is  never 


apprehended  with  that  immediacy  with  which  I  experi- 
ence my  subjective  facts,  but  is  always  reconstructed 
by  thought  by  means  of  a  more  or  less  conscious  process. 
It  will  not  originate  psychologically  in  a  true  and  exact 
deduction  from  outward  resemblances,  but  it  undoubtedly 
implies  the  more  or  less  clear  concept  of  a  quid  beyond 
the  sphere  of  my  subjective  consciousness.  I  do  not 
apprehend  the  will  of  my  friend  any  more  directly  than 
I  do  his  face  and  his  words  ;  it  exists  for  me,  not  because 
I  will  in  agreement  or  disagreement  with  him  (which  is 
not  always  the  case,  since  it  is  possible  for  me  to  remain 
indifferent  to  his  political  views),  but  because  I  think 
it  and  reconstruct  it  conceptually  in  its  meaning  from 
that  which  he  says  to  me.  Even  if  I  will  the  same  thing, 
I  do  not  on  that  account  experience  his  will  directly, 
I  only  experience  my  own  will  immediately  ;  that  there 
is  in  existence  the  similar  will  of  another  individual, 
having  the  same  end  in  view,  is  a  more  or  less  explicit 
addition  of  thought.  We  then  posit  the  will  in  another 
subject,  not  because  we  experience  it  directly,  but  on 
the  contrary  in  as  much  as  we  think  of  it  as  extraneous 
to  our  consciousness,  and  not  identifiable  with  that 
which  is  directly  grasped  thereby  without  the  help  of 
the  senses.  Miinsterberg's  treatment  of  the  subject 
and  object  of  volition,  of  that  which  is  desired  and 
the  person  who  desires,  gives  rise  to  constant  ambiguity. 
If  it  be  then  admitted  that  history  should  treat  of 
subjects  only  (an  arbitrary  limitation),  its  matter  will 
not  on  that  account  be  presented  to  us  in  a  form  of 
experience  differing  from  that  of  objects.  History 
cannot  be  made  up  of  that  which  is  immediately  experi- 
enced, because  this  does  not  go  beyond  our  own  Ego.  The 
wills  of  other  subjects,  the  ends  they  have  had  in  view, 
the  plans  of  action  which  they  have  realised,  are  thought 
and  reconstructed  by  me  in  their  independent  reality, 
just  in  the  same  way  as  I  think  and  reconstruct  all  the 
other  actions  of  nature.  The  will  of  another  is  appre- 
hended in  a  more  direct  way  than  physical  force,  and 
exists  historically,  because  its  being  is  not  dependent 


upon  my  will,  since  it  is  real  apart  from  the  immediate 
moment  of  my  consciousness.  Spiritual  activity  is 
manifested  as  energy  working  in  the  objective  world, 
which  is  not  motionless  permanency  of  inert  atoms,  as 
Miinsterberg  conceives  it  to  be,  but  concrete  historic 
development.  External  to  history  is  the  world  of 
mathematical  and  mechanical  abstractions,  not  objective 
reality  in  its  entirety.  The  world  which  our  thought 
recognises  to  be  independent  of  individual  subjects,  even 
if  it  be  severed  from  the  wills  of  single  persons,  does  not 
for  that  reason  become  a  dead,  meaningless  thing,  but 
preserves  all  its  value  as  an  activity  directed  towards 
an  end.  Nature  in  its  complete  organisation  and  in  its 
evolutionary  process  is  only  intelligible  as  the  actualisa- 
tion  of  an  end  in  time.  Hence  not  even  teleological 
consideration  can  constitute  a  characteristic  sufficient 
to  exclude  historicity  from  the  objective  world  in 
order  to  confine  it  to  individual  wills  only.  Neither 
can  it  be  urged  in  opposition  that  a  difference  will  always 
remain,  since  in  the  case  of  nature  the  end  is  universal 
and  objective,  whereas  in  history  it  is  personal  and 
subjective,  because,  as  Miinsterberg  himself  maintains, 
historical  reality  does  not  lie  in  the  single  will,  but  in 
the  connections  of  wills  and  in  their  identity.  The 
momentary  desire,  if  it  remain  an  experienced  intuition, 
has  no  historical  existence  ;  in  order  that  it  may  acquire 
such  existence  it  must  be  put  into  relation  with  other 
volitions  in  such  a  way  as  to  give  prominence  to  their 
universal  meaning.  The  will  of  Caesar  becomes  history 
only  when  conceived  with  regard  to  that  which  is  real 
about  it,  not  exclusively  for  me,  not  for  this  or  that 
individual  who  re-experiences  it  in  himself,  but  for  all 
possible  subjects.  The  historian,  no  less  than  the  man 
of  science,  must  eliminate  that  which  is  contingent  in 
the  way  in  which  a  personality  appears  to  different 
individuals  in  order  to  determine  it  in  its  true  existence. 
History  is  altogether  impossible  unless  we  sever,  so  to 
speak,  the  individual  action  from  our  subjective  life 
in  order  to  transfer  it  into  the  objective  process  of  reality. 


In  this  transition  things,  too,  which  Miinsterberg  con- 
siders to  be  matter  for  history  merely  as  means  and  ends 
of  a  given  subject,  are  of  necessity  included  in  the  scheme 
of  nature,  understood,  of  course,  in  its  concreteness,  not 
in  the  schematicism  of  mechanical  science.  In  what 
other  way  can  we  conceive  the  independent  existence 
of  the  processes  serving  as  means  to  the  realisation  of 
certain  individual  ends,  but  through  the  forms  and 
categories  necessary  to  the  construction  of  the  objective 
world  ?  If  we  return  to  pure  primitive  intuition,  to 
immediate  experience  in  which  the  contents  exist  merely 
as  an  integral  part  of  the  subjective  will,  we  cannot 
speak  of  Caesar  as  a  real  individual,  distinct  from  us 
who  compile  history,  still  less  of  the  boat  and  the  night 
voyage,  which  do  not  exist  for  us,  confined  as  we  are 
to  the  experienced  immediacy  of  our  consciousness. 
In  order  to  understand  Caesar's  wish  and  the  satisfaction 
thereof  by  means  of  a  boat,  in  order  to  think  all  this  as 
an  historical  reality,  we  must  conceive  of  the  voyage  and 
the  boat  as  they  were  present  to  Caesar's  mind ;  who 
is  prepared  to  maintain  in  all  seriousness  that,  when 
Caesar  was  on  the  point  of  embarking,  the  movement 
which  was  to  take  him  away  and  the  boat  only  seemed 
to  him  to  be  real  because  they  satisfied  his  desires  ? 
Caesar  might  have  imagined  in  his  consciousness  a  more 
convenient  way  of  going  to  search  for  the  fleet,  but  the 
mere  mental  presentation  would  not  have  satisfied  his 
will ;  the  boat  did  so  just  because  he  recognised  it  as 
an  objective  thing,  independent  of  his  will.  Moreover, 
from  Miinsterberg's  point  of  view  there  would  be  no 
difference  between  Caesar  dreaming  of  embarking  and 
Caesar  embarking  in  reality.  How,  indeed,  are  we  to 
distinguish  between  the  two  contents,  both  of  which 
satisfied  his  subjective  desire,  unless  we  place  in  opposi- 
tion the  real  voyage  and  boat  and  the  imaginary  voyage 
and  boat,  unless  we  think,  on  the  one  hand,  of  a  world 
of  things  existing  independent  of  the  single  subject,  and, 
on  the  other,  of  a  world  only  possessing  the  value  of 
reality  within  that  subject  ?  The  historian  also,  when 


placing  objects  in  relation  to  individual  wills  and  con- 
sidering them  as  means  to  the  actualisation  of  their 
ends,  always  conceives  them  as  real  in  the  externa 
world,  nor  is  it  possible  for  him  to  do  otherwise.  Restore 
all  its  concreteness  to  nature,  all  its  objective  content  to 
history,  and  the  gulf  fixed  by  your  artificial  formulas 
between  the  two  aspects  of  existence  will  disappear 
The  consideration  of  values  and  ends  does  not  preclude 
the  scientific  explanation  of  real  processes,  but  rather 
completes  and  comprehends  it  by  raising  it  to  a  higher 

10.  Miinsterberg's  Super-Ego  and  Royce's  Absolute 
Consciousness. — The  concept  of  the  Super-£^o  which 
supports  all  the  values  and  imparts  a  universal  basis 
thereto  undoubtedly  represents  an  advance  as  compared 
with  Rickert's  Ought,  suspended  in  the  void  of  its  absolute 
transcendence  ;  but  the  conscious  activity  of  the  ultra- 
personal  will,  as  conceived  of  by  Miinsterberg,  external 
to  all  duration,  the  eternal  action  without  any  subject 
is  not  a  principle  which  is  intelligible  in  itself,  still  less 
one  which  can  account  for  the  becoming  of  the  world 
and  our  individual  life  in  time.  To  Josiah  Royce 8* 
must  be  ascribed  the  credit  of  having  placed  the  philo- 
sophy of  values  upon  a  more  solid  speculative  basis,  by 
grafting  it  on  to  the  vigorous  stem  of  English  neo- 
Hegelianism.  Rickert's  Sollen  is  brought  down  by 
him  from  its  transcendent  sphere  in  order  to  be  trans- 
ferred into  the  ideal  order  immanent  in  Green's  Absolute 
Consciousness ;  this  Consciousness  in  its  turn  gains 
from  Rickert's  individual  reality  and  his  concept  of 
history  that  mobile  life  which  enables  it  to  escape  from 
the  universal  system  of  eternal  relations,  the  pan-logism 
of  Hegel,  which  is  powerless  to  resolve  into  itself  the 
concrete  development  of  beings  in  time.  The  idea 
becomes  the  meaning  of  a  will,  and  is  vivified  by  the 
warmth  of  personal  experience.  Thus  in  Royce's  system 
the  different  streams  of  reaction  from  intellectualism, 
whose  course  from  their  common  source  we  have 
endeavoured  to  follow,  as  they  wind  along,  now  far  apart, 


now  close  together,  meet  and  merge  in  a  harmonious 
whole :  voluntarism  and  neo-Hegelianism,  contingentism,  -f- 
and  the  historical  method,  the  philosophy  of  values  and 
pragmatism.  Royce,  like  the  pragmatists,  believes 
that  our  ideas  do  not  consist  of  pure  images,  but  that 
they  always  imply  consciousness  of  the  way  we  propose 
to  act  with  respect  thereto ;  they  are  instruments 
serving  special  ends,  and  must  therefore  be  judged  in 
relation  to  these  ends.87  The  idea  of  a  sword  implies, 
for  example,  the  memory  of  the  appropriate  act,  and 
the  way  of  using  it ;  the  idea  of  friends  differs  from  that 
of  enemies  by  reason  of  the  different  attitude  which  we 
intend  to  assume  towards  them.  Popular  psychology 
regards  understanding  as  a  passive  reception  of  the  truth, 
and  defines  will  as  a  productive  force,  thus  artificially 
severing  the  two  functions,  which  it  afterwards  vainly 
strives  to  unite  ;  but  this  separation  is  false,  since 
experience  shows  us  that  there  is  no  knowledge  without 
the  will  to  know,  that  in  our  intellectual  processes  we 
are  generally  guided  by  those  same  interests  which  are 
commonly  regarded  as  stimulating  the  will ;  on  the  other 
hand,  our  conscious  volition  implies  the  immediate 
knowledge  of  itself.  The  intellect  and  the  will  are  then 
but  two  aspects  of  one  and  the  same  process  ;  when  I 
know,  I  act,  hence  my  theoretical  life  is  also  practical.88 
We  do  not  observe  any  external  fact  without  observing 
at  the  same  time  more  or  less  clearly  our  attitude  with 
regard  thereto,  our  estimate  of  its  value,  our  response 
to  its  presence,  and  our  intentions  with  respect  to  our 
future  relations  to  that  fact.89  Each  thought  is  a  will 
process ;  each  conscious  action  an  idea  visible  and 
tangible  in  its  immediacy.90  But  though  Royce  agrees 
with  the  pragmatists  in  defining  reality  in  terms  of 
action  as  that  which  is  capable  of  satisfying  an  interest, 
a  desire,  or  a  volition,91  he  differs  from  them  in  according 
a  higher  place  to  the  end  and  absolute  fulness  of  the 
Divine  Will,  which  can  never  find  adequate  expression 
in  finite  consciousnesses,  than  to  the  ends  and  relative 
satisfaction  of  human  wills.  Incomplete  and  contingent 


truths  are  thus  subordinated  to  an  eternal  and  absolute 
truth-value,  which  is  not  dependent  upon  any  indi- 
vidual, but  is  based  upon  the  Universal  Consciousness. 
This  affirmation  of  an  objective  will,  which  imparts  a 
common  form  to,  and  imposes  a  categoric  exigency  on 
single  individual  wills  in  spite  of  their  irreducible  variety, 
connects  Royce's  philosophy  very  closely  with  the 
teaching  of  Windelband,  Rickert,  and  Munsterberg.92 
Royce  too  regards  our  recognition  of  facts  as  voluntary 
submission  to  an  Ought  (corresponding  to  Rickert's 
Solleri),  and  the  Ought  is  not  a  force  constraining  from 
without,  but  something  which,  while  in  opposition  to 
the  momentary  impulse,  is  willed  by  us  as  the  most 
complete  expression  of  our  rational  nature.  That  which 
determines  us  to  recognise  one  system  of  special  facts 
as  real  rather  than  another  is  the  Ought  of  recognising 
those  facts  which  at  a  certain  moment  enable  us  to 
actualise  our  will  better  than  we  could  do  were  we  not 
to  recognise  them.93  We  are  not  constrained  thereto 
by  violence  from  without,  but  from  within,  by  the  very 
nature  of  our  will  which  strives  after  a  more  complete 
expression  than  the  present  one  :  the  theoretical  Ouglri 
of  our  judgments  about  facts,  like  the  practical  Ought 
.  of  Ethics,  is  in  the  last  analysis  definable  only  in  terms 
of  what  Kant  called  the  Autonomy  of  the  Will.94  A 
fact  is  generally  conceived  as  something  external  to  our 
power,  as  necessary,  resistant,  extraneous  to  the  will ; 
this,  however,  depends  upon  the  essence  of  our  will  which 
seeks  its  satisfaction  in  an  end,  a  form  of  life,  which  is  in 
its  fulness  external  to  the  actual  moment,  and  is  never 
completely  attained  ;  hence  that  sense  of  limitation 
and  incompleteness  which  makes  the  real  seem  to  us  to 
be  beyond  the  realm  of  our  action.  If  facts  seem  to  us 
to  be  extraneous,  it  is  because  they  imply  aspects  which 
must  at  present  appear  to  us  infinitely  remote  from 
our  fragmentary  consciousness  ;  because  the  end  which 
(•  imparts  the  meaning  of  reality  to  them  is  not  my  human 
1  end  in  its  transitory  aspect,  nor  that  which  I  can  actualise 
1  in  one  moment  of  my  life,  but  that  which  ought  to  be, 


and  which  I  feel  in  my  will  as  an  absolute  exigency,  the 
ultimate  goal  of  my  complete  satisfaction,' even  though 
it  may  be  unattainable  in  the  empirical  process  of  our 
voluntary  actions,  which  develop  in  time.  It  is  due  to 
this  inexhaustibility  that  it  appears  external  to  our 
empirical  consciousness  ;  but  it  is  really  within  us  as  the 
end  of  our  will,  as  the  perfect  expression  of  that  meaning 
to  which  we  never  succeed  in  giving  complete  expression  ; 
it  does  not  absolutely  transcend  consciousness,  but  is 
immanent  in  every  stage  of  its  development,  and  finds 
eternal  satisfaction  in  the  Divine  Will,  which  embraces 
and  completes  the  whole  infinite  series  of  moments  of 
time  and  space  accordingly.  Koyce  thus  puts  aside  the  \ 
absurd  concept  of  the  absolute  transcendence  of  value, 
which,  as  we  have  already  seen,  is  the  bane  of  Kickert's 
system,  and  rightly  maintains,  as  Green  does,  that  no 
absolute  object  is  thinkable  except  in  relation  to  an' 
Absolute  Consciousness.  In  order  to  impart  meaning 
to  our  cognitive  and  practical  life  we  must  transcend 
the  empirical  human  world  ;  but  the  reality  which  is 
the  goal  after  which  we  strive  must  also  be  conceived 
of  as  a  form  of  conscious  experience.95  i 

11.  Reduction  of  the  External  to  the  Internal  Meaning 
of  tlie  Idea. — If  the  truth -value  of  the  idea  be  de- 
pendent upon  the  end  which  it  more  or  less  partially 
actualises,  upon  that  which  Royce  %  terms  the  internal 
meaning,  immanent  in  consciousness  (purpose  embodied 
in  the  idea),  not  transcendent  like  Rickert's  Sinn,  we 
must  reject  the  common  conception  which  considers 
truth  as  consisting  in  a  correspondence  between  the  idea 
and  an  exterior  object,  that  is  to  say,  in  its  external 
meaning.  Against  this  conception,  the  thesis  of  realism, 
Royce  aims  the  shafts  of  his  vigorous  dialectic,  in  order 
to  prove  its  innate  absurdity,  and  thus  to  clear  the 
way  for  the  reduction  of  the  external  to  the  internal 
meaning  of  the  idea.  Realism  views  the  object  as 
that  which  is  absolutely  independent  of  thought, 
which  would  exist  even  were  it  unknown,  and  does  not 
therefore  stand  in  any  necessary  relation  to  conscious- 


ness  :  the  cognitive  relation  is  purely  accidental,  so 
that  even  if  it  be  eliminated,  the  reality  of  the  object 
will  endure.97  Realism  as  a  philosophic  conception  is 
presented  either  in  the  pluralistic  form,  or  in  that  of 
monism,  but  in  both  cases  it  gives  rise  to  insuperable 
difficulties.  In  the  pluralistic  form  the  relations  between 
different  individuals,  whether  they  be  conceived  as 
material  atoms  or  as  spiritual  monads,  remain  inexplic- 
able ;  hence  the  efforts  made  by  philosophers  to  account 
,  for  their  reciprocal  actions  by  means  of  secondary 
!  hypotheses,  frequently  of  a  paradoxical  order,  such  as 
'  pre-established  harmony,  the  accidental  aspect  and  the 
f  like.  In  reality  the  manifold  beings  remain  extraneous 
!'  to  one  another,  and  it  is  not  possible  to  establish  any 
I  link  between  them,  or  to  affirm  any  character  common 
to  them  all  without  implicitly  denying  the  hypothesis 
by  admitting  a  universal  embracing  them  all.  In  order 
to  concerve^aTrelatiorr  between  two  individuals  of  the 
realistic  world  in  time  and  space,  we  must,  if  we  would 
adhere  to  the  hypothesis,  think  of  this  connecting  link 
as  a  third  being,  independent  of  the  first  two,  which 
therefore  cannot  serve  to  connect  them.98  The  realist 
is  thus  forced  to  take  refuge  in  monism,  admitting  a 
single,  internally  complex  being,  whose  various  aspects 
or  moments  are  so  connected  that  nothing  can  change 
or  disappear  without  giving  rise  to  change  in  the  whole. 
Even  this  refuge,  however,  will  fail  realism,  since  from 
its  own  point  of  view  it  is  bound  to  admit  two  independent 
beings  —  the  idea  and  the  object;  and,  if  reality  be 
defined  as  independence,  one  must  be  completely 
extraneous  to  the  other,  and  cannot  stand  in  any  relation 
thereto,  or  have  any  characteristic  in  common  therewith. 
How  can  we  then  maintain  that  it  corresponds  with  the 
object,  or  that  it  represents  it  in  any  way  ? "  The 
realistic  theory  itself  has  nothing  to  do  with  the  world 
which  is  completely  independent  thereof !  It  thus 
contradicts  itself  when,  after  placing  the  real  object 
absolutely  outside  thought,  it  exacts  that  the  idea  shall 
resemble  it  and  correspond  to  it.  Such  an  agreement 


cannot,  moreover,  be  set  up  as  an  absolute  criterion 
of  truth ;  the  resemblance  borne  by  the  idea  to  the 
object  does  not  suffice  to  make  it  true,  if  this  object  be 
not  the  one  purposed  by  the  idea,  and,  conversely,  if 
the  idea  carry  out  adequately  the  plan  it  had  pro- 
posed, it  will  be  true  even  if  it  have  but  a  vague  and 
schematic  resemblance  to  the  external  object.  Agree-^ 
ment  as  such  does  not  constitute  truth,  but  agreement 
which  is  willed  (intended  agreement)  for  certain  special 
ends  :  thus  in  some  cases  a  concrete  representative 
image  may  be  preferable  to  an  abstract  symbol ;  in 
others,  when  we  have  a  different  purpose  before  us,  a 
complex  of  algebraical  symbols  may  be  preferable  as 
a  representation  of  objects  to  the  pictures  thereof. 
Do  you  desire  to  reproduce  a  musical  phrase  ?  Your 
song  will  be  out  of  tune  if  it  fail  to  bear  a  concrete 
resemblance  to  the  series  of  sounds  heard  on  other 
occasions.  Do  you  rather  propose  to  study  acoustics  ? 
It  is  then  no  longer  a  question  of  seeking  a  concrete 
resemblance,  but  rather  of  finding  a  correspondence 
between  certain  abstract  relations,  which  are  mathe- 
matically formulated  in  your  ideas,  and  the  greater  or 
lesser  agreeableness  of  certain  combinations  of  notes.100 
Just  as  it  is  impossible  to  say  in  general  whether  a 
razor  is  better  than  a  hammer,  without  reference  to  the 
use  we  propose  to  make  of  them,  so  these  instruments 
of  a  higher  order — our  ideas — must  be  judged  with  \ 
regard  to  their  specific  end  and  conscious  purpose. 
The  idea  decides  its  own  meaning,  chooses  its~object  ' 
and  the  special  form  of  agreement  or  resemblance  which 
it  desires  to  have  therewith ;  it  assigns  itself  a  task 
and  submits  to  its  plan  of  its  own  free  will.101  The 
external  meaning  of  the  idea  upon  which  realism  lays 
so  much  stress  is  therefore  in  ultimate  analysis  sub- 
ordinated to  the  internal  meaning,  which  alone  decides 
its  truth. 

At  the  very  antipodes  of  realism  we  find  another 
conception  of  being,  which  Royce  regards  as  equally 
impossible  of  acceptance,  although  he  considers  it 


superior  from  the  epistemological  point  of  view :  the 
conception  of  mysticism.  Whereas  the  realist  considers 
the  external  meaning  only,  the  mystic  knows  the  internal 
meaning  alone  and  condemns  all  finite  ideas,  because 
they  fail  to  attain  that  absolute  satisfaction,  that  perfect 
calm  in  which  the  will  finds  its  ultimate  and  adequate 
expression,  the  goal  of  its  desires  and  researches. 
Realism  considers  being  as  mdependentpjjmowledge ; 
mysticism,  on  the  contrary,  defines^it  as~lmmediate 
experience  (immediate  feeling) ;  the  former  says,  Seek 
the  truth  outside  thyself  in  the  outer  world ;  the 
latter,  Seek  the  truth  within  thyself,  withdrawing 
thyself  from  external  and  contingent  facts,  which  never 
satisfy  thy  inmost  will,  into  the  calm  solitude  of  thy 
own  mind.102  The  superiority  of  mysticism  to  realism  lies 
in  its  critical  attitude,  since  it  does  not  dogmatically 
require  that  we  shall  accept  its  definition  of  being,  but 
appeals  to  our  experience  to  determine  that  which  we 
truly  call  real,  and  finds  it  in  full  possession  and  com- 
plete satisfaction.  It  is  a  thoughtful  doctrine,  which 
knows  itself  and  consciously  faces  its  paradoxes  with- 
out ignoring  its  own  contradictions,  as  does  realism.103 
But  if  the  mystic  be  right  in  affirming  that  there  can 
be  no  reality  wholly  independent  of  our  knowledge, 
that  in  ourselves  alone  is  to  be  found  the  criterion  by 
which  to  distinguish  between  the  true  and  the  false, 
the  real  and  the  unreal,  the  eternal  and  the  transient 
contents,  he  is  wrong  in  entirely  repudiating  the  world 
of  facts  and  finite  ideas,  since  the  state  of  Nirvana, 
which  he  proposes  to  attain,  taken  by  itself,  is  nothing, 
and  derives  its  whole  value  from  the  contrast  between  it 
and  that  incomplete  reality  which  is  termed  illusion. 
Now,  if  being  cannot  be  attributed  to  the  first  member 
of  such  a  relation  of  contrast,  the  second  will  disappear 
also.  Annihilation  is  something  only  so  long  as  I  seek 
it,  it  is  a  positive  ideal  only  in  as  much  as  I  strive  to 
attain  it ;  pure  immediacy  has  a  content  only  because 
it  satisfies  the  imperfect  will ;  hence  it  derives  its  whole 
meaning  from  contrast  and  other  relation  with  finite 


facts.    If  our  conscious  ideas  be  nothing,  the  Absolute^ 
is  also  nothing. „• 

Yet  another  inadequate  solution  of  the  problem  of 
reality  is  critical  rationalism,  whose  spiritual  ancestor 
is  Kant,  and  which,  as  opposed  to  the  independent 
individual  of  realism,  identifies  being  with  the  universal 
vahditv  of  the  idea,  with  the  law,  the  type,  tne  common 
form  01  all  possible  experience.104  Physical  and  mathe- 
matical sciences  offer  us  countless  examples  of  these 
universally  valid  truths,  which  always  transcend  the 
sphere  of  our  actual  experience,  and  can  therefore 
never  be  completely  verified.  In  the  physical  and 
mathematical  sciences  alike  consciousness  is  confronted 
by  a  fact  or  empirical  process,  ideally  constructed  in  the 
case  of  mathematics,105  and  presented  by  experience  in 
that  of  physical  science,  but  the  marvellous  thing  in 
both  cases  is  that  the  observation  or  the  experiment 
guarantees  a  universal  affirmation  with  regard  to  an 
infinity  of  objects  which  neither  are  nor  can  be  present 
in  their  totality  to  any  human  being.  How  are  these 
two  aspects  to  be  reconciled  :  on  the  one  hand,  the  em- 
pirical contingent  fact  in  its  transitoriness ;  on  the  other, 
the  affirmation  of  a  universal  validity  ?  What  is  a 
valid  experience  in  the  moment  in  which  it  is  not 
presented  to  me,  but  in  which  I  merely  suppose  it 
possible  ?  What  is  a  valid  truth  when  no  one  verifies 
its  validity  ?  Can  completeness  of  being  be  attributed 
to  the  pure  universals  which  have  not  as  yet  been 
verified  ?  Validity  is  an  ambiguous  term  :  when  it  is 
applied  to  the  ideas  which  we  are  actually  verifying,  it 
means  that  they  are  expressed  in  concrete  in  experience  ; 
when  applied  to  the  whole  realm  of  valid  truth  in  general, 
to  the  world  of  nature  which  is  not  now  under  our 
observation,  or  to  mathematical  truths  which  are  not 
present  to  us,  it  means  that  this  realm  is  in  some  way 
possessed  of  a  character  which  we  cannot  verify  and 
which  is  never  entirely  actual  in  our  human  experience.106 
In  concrete  experience  the  validity  of  ideas  is  presented 
to  us  by  an  individual  fact ;  in  the  realm  of  possible  being 


the  same  validity  appears  as  a  universal,  abstract, 
formal  law.  Now  is  it  possible  to  admit  two  species 
of  beings,  both  of  which  are  known  to  be  valid,  but  of 
which  one  is  individual,  the  other  universal ;  one 
empirical,  the  other  purely  ideal ;  one  present,  the  other 
merely  possible  ;  one  possessed  of  concrete  life,  the 
other  a  pure  form  ?  Must  not  the  same  life  of  concrete 
experience  throb  in  all  beings  ?  Our  will,  which  is  also 
knowledge,  finds  adequate  expression  —  its  full  and 
perfect  determination  —  in  the  individual  alone.  A 
truth  which  remains  purely  valid  fails  to  satisfy  it, 
because  it  does  not  enable  it  to  leave  the  domain  of  the 
indeterminate ;  the  judgment  which  formulates  the 
universal  law  excludes  certain  possibilities,  but  tells  us 
nothing  about  the  positive  content  of  concrete  reality : 
eliminating  little  by  little  the  various  possibilities,  we 
might  go  on  indefinitely  without  ever  reaching  the  end 
of  the  series,  that  unique  experience,  which  is  com- 
pletely determined,  and  leaves  no  other  possible  alterna- 
tive external  to  itself.107  This  defect  of  pure  abstract 
reasoning  in  universal  terms  is  supposed  to  be  remedied 
by  the  appeal  to  experience  ;  but  experience  cannot 
in  a  finite  time  confirm  the  law  in  its  universality.  The 
detailed  judgment  thus  arrived  at,  though  possessed  of 
a  positive  content,  does  not  authorise  us  to  exclude  all 
other  possibilities ;  when  you  define  an  individual 
by  certain  abstract  characteristics,  you  cannot  be  sure 
that  one  individual  alone  corresponds  thereto  in  reality, 
neither  can  human  experience  give  you  absolute  proof 
thereof,  since  it  is  incapable  of  exhausting  the  whole 
sphere  of  existence.  The  presupposition  that  there  is 
no  other  person  identical  with  a  member  of  your  family 
is  one  which  you  may  justify  from  the  metaphysical 
point  of  view,  but  which  it  is  vain  to  ask  experience  to 
confirm.108  To  us  the  individual,  the  complete  deter- 
mination may  be  the  object  of  love  and  hope,  will  and 
desire,  faith  and  action,  but  never  of  present  discovery  ; 
it  can  never  be  defined  either  in  terms  of  generic  con- 
cepts or  as  a  datum  of  finite  experience,  but  only  as 


a  limit  towards  which  are  directed  our  active  researches 
and  our  conscious  will  which  strives  after  complete  satis- 
faction in  a  form  of  experience  at  once  fully  determined, 
unique,  and  exclusive.109 

Criticism  of  the  three  principal  existing  solutions 
of  the  problem  of  reality  thus  leads  us  on  to  the  fourth 
conception  of  being,  which  Royce  regards  as  alone 
capable  of  synthesising  the  others  in  itself,  eliminating 
their  inherent  contradictions  and  reducing  them  to  a 
harmonious  whole.  According  to  this  fourth  conception  v 
the  real  is  the  complete  embodiment  in  individual  form  ( 
and  in  final  fulfilment  of  the  internal  meaning  of  finite] 
ideas. uo  The  object,  the  other,  is  the  full  actualisatioh 
of  our  end  and  of  our  will  which  is  at  present  imperfectly 
incorporated  in  our  ideas  —  the  completion  of  that 
which  we  now  possess  only  in  part  in  our  finite  vision  ; 
it  always  appears  to  us  to  be  out  of  reach  of  our  ideas 
and  finite  experiences  just  because  they  never  succeed 
in  realising  it  in  its  exhaustive  and  individual  concrete- 
ness.111  It  is  true  in  a  certain  sense,  as  is  asserted  by 
realism,  that  the  object  exercises  authority  over  the 
finite  idea,  since  the  idea  can  only  seek  that  which  it 
consciously  intends  to  seek,  that  which  demands  the 
determination  of  its  will  for  singularity  and  that  final 
expression  for  which  nothing  can  be  substituted,  and 
must  therefore  be  in  subjection  to  its  own  plan  ;  but 
this  authority  exercised  by  the  object  over  the  idea  must 
not  be  transformed  into  an  absurd  independence.  Thus/ 
Royce  and  the  mystic  alike  consider  that  in  that  final 
stage  the  world  and  the  Ego  are  absolutely  identical,! 
but  the  nescio,  nescio  of  the  mediaeval  mystic  merely 
serves  to  express  the  present  inability  of  the  transient 
idea  to  actualise  the  end  in  full,  not  the  essential 
nature  of  true  being ;  the  satisfaction  of  the  will, 
fragmentary  though  it  be,  will  be  found  in  earth,  not 
in  heaven.  Critical  rationalism  gives  us  the  universal 
essence  of  the  object,  and  the  characteristics  which  it 
possesses  in  common  with  our  present  idea,  and  the 
experiences  of  the  moment  in  which  we  define  it,  but 


it  leaves  undetermined  precisely  the  being  of  the  object 
as  other,  as  different  from  the  finite  idea.  The  fourth 
.concept  of  being  embraces  everything  which  is  true  in 
the  three  former  views  and  corrects  the  false  elements 
contained  in  them :  being  exercises  authority  over 
finite  ideas,  as  is  asserted  by  realism ;  it  is  valid,  in 
conformity  with  the  demands  of  critical  rationalism ; 
it  is  identical  with  the  true  internal  meaning,  as  is 
affirmed  by  mysticism,  but  its  reality  is  not  external  to 
the  idea,  as  in  the  realistic  conception  ;  and,  as  opposed 
to  the  assertions  of  the  mystic,  its  imperfections,  its 
incompleteness,  its  struggles,  and  its  strivings  in  time 
are  also  real,  as  an  integral  and  constituent  part  of 
the  Absolute,  which  is  not  a  mere  law  of  abstract 
validity,  as  is  affirmed  by  the  rationalistic  theory,  but 
rather  a  will  embodied  in  a  concrete  life,  a  life  giving 
full  expression  to  that  meaning  which  each  passing 
moment  of  human  consciousness  actualises  only  partially 
and  which  is  the  object  of  its  ideal  aspirations.112 

A  sceptic  might  say,  "  I  admit  the  existence  of 
nothing  beyond  human  experience,  there  is  no  experience 
which  is  more  complete  and  more  perfect "  ;  but  in 
making  this  assertion,  he  would  admit  that  the  present 
content  of  his  consciousness  is  perfectly  adequate  to 
his  idea  of  being,  that  is  to  say,  that  this  experience  is 
not  of  a  transient  nature,  but  is  an  experience  at  once 
absolute,  individual,  and  definitive.113  Moreover,  even 
the  sceptic  must  admit  the  existence  between  different 
subjects  of  relations  whose  reality  can  only  be  conceived 
in  a  Consciousness  which  is  able  to  embrace  in  one 
inclusive  act  all  single  consecutive  processes  together 
with  their  relations.  If  everything  which  is  real 
exists  merely  as  a  known  fact,  the  actualisation  of  a 
conscious  end,  there  can  be  no  reality  in  the  distinction 
between  different  known  beings  and  their  reciprocal 
actions  except  in  so  far  as  they  satisfy  a  conscious 
will.  This  Supreme  Knower  of  the  universe,  who  is  not 
an  empty  unit  external  to  time,  but  includes  all  temporal 
processes  in  their  infinite  variety,  and  all  the  manifold 


meaning  of  our  minds  in  the  inexhaustible  riches  of  his 
content,  must  be  conscious  of  himself,  since,  were  his 
own  being  and  his  spiritual  unity  to  escape  him,  he 
could  (according  to  Royce)  be  real  only  to  some  other 
consciousness  to  which  his  internal  meaning  was  present ; 
but  this  cognitive  relation,  like  all  relations,  could  in  its 
turn  only  exist  as  a  fact  present  to  the  Absolute  Conscious- 
ness, which,  since  it  must  be  aware  of  its  relation  to  the 
other  consciousness,  must  know  each  one  of  the  terms, 
and  hence  also  itself.114  Everything  then  which  develops 
and  lives  in  time  exists  in  God  ;  it  is  neither  absorbed 
nor  destroyed,  but  is  rather  preserved  in  its  individual 
physiognomy  ;  finite  consciousness,  just  as  it  exists  in 
ourselves,  with  its  strivings  and  defeats,  its  mistakes, 
its  temporality  and  limitations,  is  all  present  from  the 
absolute  point  of  view  ;  but  it  is  seen  together  with  the 
solution  of  its  problems,  the  attainment  of  its  ends,  the 
overcoming  of  its  defeats,  the  correction  of  its  mistakes, 
the  final  completion  of  temporal  processes,  the  perfecting 
of  that  which  is  faulty  in  us.U5  The  Absolute  knows 
everything  we  know,  and  as  we  know  it ;  our  experience 
is  not  transmuted  or  reduced  in  some  ineffable  way  in 
order  that  it  may  become  one  with  the  Divine  Life,  but 
persists  in  that  Life  wearing  the  same  concrete  aspect 
which  it  does  in  us.  Even  our  pain  exists  in  God,  since  / 
the  full  triumph  of  eternity  can  only  be  attained  through 
the  sorrows  of  time ;  in  struggle  with  pain,  conflict 
with  suffering,  victory  through  striving,  will  be  found  the 
loftiest  fulfilment  of  the  life  of  the  mind.  Were  God 
ignorant  of  pain,  He  could  not  know  the  sublimity  of 
victory  ;  just  as  there  is  no  courage  without  conquered 
fear,  so  in  the  life  of  suffering  there  is  no  conscious 
heroism  without  present  tribulation.116  Thus  Royce,  as/ 
opposed  to  Bradley,  resolutely  affirms  the  reality  of  finite  ( 
experience  and  of  its  becoming,  replacing  the  purely 
logical  and  static  concept  of  reality,  as  a  harmonious 
system  by  a  dynamic  interpretation  of  it  in  terms  of 
conscious  will.  The  reality  of  time  is  from  such  a  stand- 
point a  condition  necessary  to  moral  life,  and  to  the 


actualisation  of  the  Absolute  Will,  which  would  be  incon- 
ceivable without  development.117  Within  the  duration 
of  His  present  God  embraces  the  infinite  series  of 
successive  moments,  which  forms  an  individual  whole 
in  its  single  and  definitive  meaning.  It  is  this  unity  of 
plan  that,  determining  as  it  does  the  position  of  each 
moment  in  the  irreversible  process  of  time,  which  has 
the  form  of  a  well-ordered  series,  defines  it,  and  thus 
renders  it  thinkable  as  a  present  totality.  The  error 
fallen  into  by  critics  of  the  actual  infinite  lies  in  the  belief 
that  the  place  of  each  term  in  the  series  must  be  found 
by  means  of  empirical  counting,  whereas  in  reality  the 
definition  of  the  series  predetermines  at  one  stroke  the 
successive  order  of  its  elements.  When  we  say  that) 
the  series  is  present  in  its  completeness,  we  do  no 
mean  that  there  is  a  last  term  which  can  be  reachec 
by  passing  its  members  in  review  one  after  another  in 
a  land  of  roll-call,  but  that  these  elements  are  seen 
together  in  a  total  experience,  all  at  once,  with  the 
place  pertaining  to  each  in  the  system,  just  as  the 
definition  determines  them  in  their  individuality,  their 
unique  and  irreplaceable  meaning.118 

12.  Error. — If  our  every  presentation  and  our  every 
thought  exist  in  the  Absolute  Consciousness,  if  truth  b 
dependent  upon  the  idea  itself  which  selects  its  object 
task,  and  meaning,  does  not  the  existence  of  error 
become  inexplicable  ?    If  all  be  real  in  God,  how  can 
we  affirm  the  existence  of  anything  false  ?     If  it  be  th 
idea  which  says,  "  I  will  mean  this  or  that,"  how  is  it 
possible  for  facts  to  give  it  the  he  ?     If  the  object  be 
that  which  the  idea  freely  wills  it  to  be,  how  can  it  place 
itself  in  opposition  thereto,  and  be  out  of  harmony 
therewith,  thus  giving  rise  to  that  which  is  commonly 
called  error  ?     This  question  is  the  rock  on  which  al 
pantheistic  systems  are  doomed  to  split,  and  Koyce's 
philosophy  shares  the  fate  of  the  rest.    He  does  not 
attempt  to  avoid  it  by  means  of  dialectical   devices 
but  faces  it  boldly.    Green's  panlogism,  which  absorbs 
and  dissolves  the  individual  into  the  system  of  eterna 


relations  which  are  present  to  the  Absolute  Conscious- 
ness, affords  no  explanation  whatsoever  of  the  possibility 
of  error,  which  it  regards  as  no  less  real  than  that  which 
we  commonly  call  truth,  though  existing  in  a  different 
order  of  relations.  He  certainly  distinguishes  between 
variable  and  arbitrary  relations  and  the  eternal,  un- 
changeable system  of  relations,  which  acts  as  our  ob- 
jective criterion,  and  which  we  place  in  opposition  to  our 
subjective  life,119  but  this  individual  variability  together 
with  everything  changeable  and  contingent  in  the  history 
of  the  world  finds  no  adequate  justification  in  his  system. 
Bradley's  doctrine  of  degrees  of  truth  goes  more  deeply 
into  the  problem  than  does  Green,  though  he  too  is 
very  far  from  affording  a  solution  of  it.  Bradley 
regards  everything  in  the  realm  of  human  thought  as 
appearance  ;  hence  there  is  error  in  everything,  but 
every  error  contains  a  certain  amount  of  truth,  just  as 
every  truth  contains  a  certain  amount  of  error ;  it  is 
therefore  possible  to  distinguish  various  degrees,  accord- 
ing as  the  appearance  must  be  subjected  to  a  greater 
supplementation  or  rearrangement  in  order  that  it  may 
be  transformed  into  absolute  experience.  Bradley  does 
not,  however,  afford  us  any  explanation  of  the  existence 
of  error,  which,  partial  as  it  may  be,  is  always  a  deviation 
from  the  absolute  system  ;  he  does  not  explain  why  the 
severance  of  the  what  from  the  that,  the  beginning  of 
so  much  evil,  takes  place,  and  he  leaves  us  in  an  uncertain 
sceptical  position.  If  human  experience  be  illusory,  why 
and  how  does  this  great  illusion  exist  ?  Are  appearances 
necessary  for  the  constitution  of  the  reality  of  the 
Absolute  which,  as  you  yourselves  admit,  is  nothing 
apart  from  them,  or  are  they  not  ?  Bradley  replies 
that  they  are  not  all  necessary  to  the  same  degree  ;  but 
if  we  divest  appearances  of  that  which  is  true  in  them, 
that  is  to  say,  of  that  part  which  is  necessary  in  order 
to  give  a  concrete  content  to  Universal  Consciousness, 
for  whom  and  in  what  way  does  the  residue  exist  ?  It 
is  not  necessary  to  the  life  of  the  Absolute,  which  could 
be  manifested  in  its  perfection  without  them ;  it  does 


not  exist  in  the  experience  of  the  Absolute,  which  would 
in  that  case  become  contradictory  ;  why  and  where  then 
does  it  originate  ?  Does  anything  exist  external  to  the 
Absolute  Consciousness  or  not  ?  If  there  be  no  subject 
distinct  therefrom,  where  did  and  does  the  separation 
take  place  between  the  what  and  the  that,  the  idea  and 
the  fact  ?  Bradley  stops  short  at  this  problem,  and 
proclaims  the  inadequacy  of  the  human  intellect,  thus 
turning  us  away  on  the  threshold  of  mystery  with  our 
difficulties  unsolved.  Royce,  on  the  contrary,  does 
not  refuse  us  an  explanation  of  that  transitory  and 
imperfect  element  which  marks  the  distinction  between 
human  and  divine  experience,  and,  whilst  accepting 
the  theory  of  degrees  of  truth,  does  not  take  up  Bradley's 
purely  negative  position,120  but  endeavours  to  make 
clear  to  us  the  reason  for  the  existence  of  these  different 
degrees,  and  determines  the  vague  concept  of  supplemen- 
tation by  means  of  a  more  exact  idea  of  the  relations 
between  finite  thought  and  the  infinite  Consciousness, 
explaining  to  us  the  nature  of  that  greater  completeness 
which  our  soul  finds  in  God.  That  which  Green  and 
Bradley  treat  as  an  inexplicable  accident  is  to  Royce 
a,  necessary  moment  hTWe  life  of  the  Absolute,  whose 
will  can  only  attain  to  perfect  satisfaction  through 
incompleteness.  The  will,  that  is  to  say,  the  idea  bounded 
by  time,  never  attains  this  fulness  of  individual  life  ; 
it  is  never  able  to  express  its  definitive  meaning ;  in  the 
process  of  actualising  the  will  we  can  therefore  dis- 
tinguish various  stages  (corresponding  to  the  different 
degrees  of  truth),  each  one  of  which  is  more  or  less 
distant  from  the  end  and  embodies  the  internal  meaning 
of  the  idea  in  a  more  or  less  adequate  manner.  The  end 
is  not  always  clearly  present  to  consciousness ;  we  pass 
from  a  vague,  indeterminate  state  of  restlessness  to 
a  definite  state  of  will  and  resolution  ;  before  arriving 
at  it  we  ask  ourselves,  "  What  do  I  desire  ?  What 
is  my  real  end  ?  "  and  the  answer  to  such  a  question 
may  make  large  demands  upon  our  time,  and  may  be 
erroneous  as  regards  intelligence  of  our  end.121  The 


unique,  unambiguous  expression  capable  of  fully  de- 
termining our  will  may,  when  our  will  has  not  yet 
reached  its  goal,  differ  from  that  which  at  the  present 
moment  seems  to  us  to  be  the  meaning  of  the  idea. 
Here  we  have  the  explanation  of  the  possibility  of  error, 
which  lies  in  the  inadequacy  of  the  present  stage  of  the 
volitional  process  to  express  its  true  end.  The  object 
which  may  conflict  with  my  partial  and  fragmentary  will, 
that  is  to  say,  with  my  will  not  as  yet  fully  realised, 
and  may  to  a  certain  extent  contradict  it,  is  not  an 
external  thing,  an  obstacle  to  my  conscious  activity, 
but  rather  my  will  itself  in  its  phase  of  complete 
actualisation,  my  final  intention,  my  total  meaning 
determinately  and  definitely  expressed.122  In  the  last 
analysis  that  which  decides  whether  an  idea  be  true 
or  false  is  the  object  which  it  has  predetermined 
and  the  plan  which  it  has  proposed  to  carry  out.  The 
idea  chooses,  so  to  speak,  the  game  it  will  play,  but, 
coherently  with  itself,  it  cannot  change  it  arbitrarily 
or  alter  the  rules,  thus  failing  to  fulfil  its  task :  thus, 
for  instance,  if  it  proposes  to  find  its  complete 
determination  in  a  group  of  sensorial  experiences  (as 
occurs  in  the  verification  of  physical  theories),  these 
experiences  exercise  authority  over  it  and  demand  its 
full  submission ;  but  this  is  in  reality  not  the  exercise 
of  extrinsic  force,  since  it  is  the  idea  itself  which  has 
freely  determined  to  find  the  agreement  with  facts.  It 
is  possible  that  it  may  fail,  but  to  what  else  can  this 
failure  be  ascribed  than  the  end  proposed  by  it,  that  is 
to  say,  to  the  object  and  form  of  correspondence  which 
it  has  chosen  as  its  term  of  reference  ? 123  If  it  then  be 
contradicted,  it  is  so  of  its  own  free  will,  just  as  the 
lover  who  is  rejected  by  his  lady  owes  this  repulse 
to  his  desire  to  possess  her,  a  repulse  which  he  would 
not  have  had  to  endure  had  he  not  chosen  just  this 
particular  woman  as  the  object  of  his  adoration.124 
There  can  be  no  doubt  that  facts  can  resist  our  momentary 
desire,  but  at  bottom  it  is  the  will  that  recognises  these 
limits,  which  are  objective  in  the  sense  that  they  differ 


as  more  complete  expressions  from  that  which  is  now 
present  to  us.  Even  in  appearing  extraneous  to  me, 
nature  embodies  my  will,  since  I  recognise  that  my 
conscious  activity  is  limited  and  controlled  only  in  so 
far  as  it  can  attain  the  desired  completion  through  these 
limitations  and  this  control.125 

13.  The  World  of  Science  and  the  World  of  Valuation. 
—Belief  in  the  reality  of  the  external  world  is  not  forced 
upon  us  from  without  and  is  not  justified  by  the  resist- 
ance met  with  by  muscular  effort,  as  some  philosophers 
have  thought,  but  is  guaranteed  from  motives  of  a 
social  order,  and  makes  itself  felt  by  us  as  the 
requirement  of  a  duty.  The  physical  world  is  that 
part  of  human  experience  which  is  common  to  all 
men,  which  enables  them  to  understand  one  another, 
and  thus  acts  as  the  basis  of  their  co-operation  ;  failure 
to  recognise  it  would  therefore  be  equivalent  to  cutting 
oneself  off  from  civilised  society.126  The  existence  of  our 
kind  is  then  the  presupposition  of  the  reality  of  nature, 
not  vice  versa,  as  is  usually  affirmed  when  our  belief  in 
the  inner  life  of  other  men  is  explained  by  an  induction 
by  analogy  based  upon  likeness  of  features  and  objective 
physical  manifestations.  We  are  social  beings  primarily 
by  reason  of  hereditary  instincts  ;  we  instinctively  love, 
fear,  and  watch  our  fellow-men,  who  are  therefore  real 
to  us  as  immediate  objects  of  desire  or  repulsion,  in  so 
far  as  they  supply  us  with  that  which  we  lack,  complete 
our  fragmentary  meanings,  answer  our  questions,  and 
render  our  experience  and  consciousness  of  our  ends 
more  perfect.127  In  this  direct  penetration  of  minds 
and  their  internal  meanings  which  causes  us  to  feel 
ourselves  part  of  a  single  Ego  is  found  the  world  of 
valuation,  the  most  profound  of  truths  in  its  concrete 
history ;  the  external  mechanical  aspect,  the  world 
of  scientific  description,  is  but  an  inadequate  symbol, 
necessary  to  the  empirical  communication  of  finite 
individuals  in  time  and  space,  a  common  scheme 
formed  by  eliminating  the  variable  subjective  element, 
in  order  that  all  men  may  be  able  to  establish  an 


understanding  amongst  themselves  in  their  practical 

To  civilised  man  the  difference  between  the  mind 
and  material  objects  is  so  great  not  by  virtue  of  any 
experience  conferring  upon  him  the  right  to  assert  it 
positively,  but  by  virtue  of  the  fact  that  our  relations 
to  the  physical  world  are  possessed  of  a  social  meaning 
which  tends  to  contrast  more  and  more  strongly  with 
our  practical  relations  to  living  man.  Owing  to  this 
contrast  more  and  more  prominence  is  given  to  that 
aspect  of  nature  which  enables  us  to  have  dominion 
over  it,  and  to  which  the  success  of  practical  life  is  due, 
the  unbending,  uniform,  mechanical  aspect,  whereas 
the  increase  in  the  common  heritage  of  civilisation 
raises  the  importance  of  our  fellow-men  in  our  eyes.129 
This  sharp  distinction,  which  is  a  mere  artifice  whose 
existence  is  justified  by  reasons  of  a ,  practical  order, 
must  not,  however,  lead  us  into  the  mistake  of  making 
a  dualistic  separation  between  the  two  forms  of  reality. 
If  we  compare  with  the  life  of  consciousness,  not  the 
abstractions  with  which  mechanical  science  presents  the 
physical  world  to  our  notice,  but  rather  physical  pro- 
cesses in  their  concrete  complexity,  the  apparent  contrast 
will  vanish  and  that  which  is  common  to  both  nature  and 
the  mind  will  take  the  prominent  place  which  is  its  due.130 
Both  are,  as  a  matter  of  fact,  subject  to  an  irreversible 
becoming,  though  the  process  of  transformation  in 
nature  is  considerably  slower ;  in  both  we  see  the 
tendency  to  form  habits,  which  are  not,  however, 
absolutely  fixed,  but  form  rhythms  of  temporary 
duration  which  are  finally  dissolved  by  the  perturbing 
action  of  irrevocable  change.  The  slowness  of  natural 
processes  prevents  our  consciousness  adapting  itself 
to  the  rhythm  of  that  psychic  life  which  lies  at  their 
base  ;  hence  the  erroneous  opinion  which  classes  them 
as  unconscious  phenomena.  In  reality  they,  too,  form 
part  of  a  finite  consciousness,  embracing  millions  and 
millions  of  years  in  the  duration  of  its  present.  There 
is  nothing  against  our  conceiving  other  consciousnesses 



whose  relation  to  time  differs  from  ours,  which  have  a 
different  time-span.1*1  Single  animals  and  objects  can- 
not each  be  possessed  of  consciousness,  but  they  form 
part  of  a  conscious  process  which  embraces  them  in  its 
vast  present ;  just  in  the  same  way  as  human  individuals 
with  their  inner  life  are  included  in  other  finite  experi- 
ences, of  which  the  phenomena  of  racial  memory  and 
instincts  are  indications.  The  birth  and  death  of  a 
man  are  not  the  beginning  and  end  of  a  conscious 
life,  but  a  mere  change  in  this  consciousness  with  a 
longer  time-span.™2  Royce  then  does  not  agree  with 
Berkeley  in  regarding  matter  as  something  illusory,  he 
rather  considers  it  to  be  real  in  the  same  sense  as  our 
fellow-men  are  real :  it  is  a  finite  consciousness  which 
is  identified  with  the  life  of  the  Absolute  in  the  same 
degree  as  our  individual  mind  is  identified  therewith.188 
Each  consciousness  can,  whilst  preserving  the  unity  of 
its  plan,  form  part  of  a  vaster  plan  of  conscious  experi- 
ence, and  is  not  enclosed  within  itself,  and  external 
to  all  other  consciousnesses,  as  are  the  monads  of 
Leibnitz.  The  relations  of  communication  of  finite 
individuals  are  an  indication  of  their  unity  in  the 
Absolute,  which  embraces  them  all  as  moments  in  a  con- 
scious process  having  an  ultimate  and  single  meaning.134 
That  which  characterises  and  distinguishes  different 
individuals  is  not  the  plurality  of  substances  which  are 
inconceivable  in  their  realism,  but  the  unique  nature 
of  the  plan  which  each  one  of  them  actualises  in  his 
consciousness  and  the  originality  of  the  end  which  he 
embodies.  I  place  myself  in  opposition  to  others, 
because  my  life  is  possessed  of  a  unique  meaning 
which  even  in  the  Absolute  remains  distinct  from  the 
ends  of  other  persons.135  In  this  originality,  this 
unique  imprint  preserved  by  our  will  in  the  Divine 
Consciousness  in  which  each  one  of  us  gives  perfect 
expression  to  his  meaning,  lies  the  essence  of  human 
liberty.  My  will,  though  a  moment  of  the  Absolute 
Personality,  is,  in  as  much  as  it  is  possessed  of  a  unique 
physiognomy,  determined  by  nothing  but  itself  :  that 


which  I  will  is  still  willed  by  me  even  in  God.136  My 
experience  is  not  absorbed,  transmuted  or  reduced  in 
some  ineffable  way,  but  exists  in  the  Eternal  Mind  just 
as  it  does  in  myself  with  all  its  imperfections  and  all  its: 
errors.137  Eternity  does  not  annihilate  the  succession 
of  time,  but  embraces  it  all  within  itself  in  its  infinite) 
present,  just  as  we  distinguish  the  various  moments  or 
a  rhythmical  measure  with  its  successive  notes,  while 
yet  grasping  it  as  a  whole  in  our  consciousness.138 

14.  Criticism  of  Royce's  Philosophy. — In  Koyce's 
philosophy  the  reaction  from  intellectualism  reaches  its  4, 
speculative  acme  in  a  system  grandly  architectural  in 
its  monumental  lines.  Eoyce  does  not  attempt  to 
evade  the  great  problems  which  have  baffled  the  mind 
of  man  throughout  the  ages,  but  rather  faces  them  with 
a  vigour  of  thought  born  of  genius.  Liberty,  im- 
mortality, the  existence  of  evil  and  error  all  find  their 
metaphysical  justification  in  his  system,  a  justification 
which,  though  it  may  fail  to  satisfy  us  wholly,  is  yet  the 
most  momentous  attempt  ever  made  to  solve  these 
problems  by  means  of  pantheistic  intuition  of  an  ethical 
and  religious  order.  As  we  have  already  seen,  Royce 
-considers  that  the  existence  of  error  is  due  to  the  fact 
that  the  true  meaning  of  the  idea,  as  an  act  of  will,  is 
never  fully  actualised  :  before  the  complete  satisfaction 
of  the  will  is  attained,  a  series  of  stages  must  be  passed 
through  in  which  the  end  is  not  present  in  its  full  deter- 
mination. The  transition  from  dissatisfaction  to  satis- 
faction is  the  very  essence  of  the  volitional  life,  and 
hence  also  of  knowledge,  which  Royce  regards  as 
identical  therewith.  Truth  is  that  which  I  will,  that 
which  I  propose  to  do,  my  plan  of  action  ;  and,  should , 
I  ejr,  I  do  so,  not  because  there  is  something  external! 
to  myself~which  sets  itself  in  opposition  to  my  idea,  but  ] 
because,  though  the  meaning  of  my  thought  depends  1 
upon  myself  and  myself  alone,  I  have  no  clear  conscious- 
ness thereof  at  the  initial  and  intermediary  stages  of 
the  volitional  process.  From  the  first  I  have  no 
determinate  knowledge  of  my  true  end ;  in  that  case, 


however,  we  would  ask  Royce  how  it  is  possible  to  state 
that  this  end  is  dependent  on  myself  alone,  that  I  have 
selected  it,  if  it  is  not  that  which  was  present  to  my 
consciousness.     If  the  result  attained  by  the  process 
of  my  research  differ  from  that  of  which  I  am  conscious 
at  a  certain  moment  (and  it  is  just  this  difference  to  which 
the  possibility  of  error  is  due),  am  I  justified  in  affirm- 
ing that  this  ultimate  result  was  the  one  which  I  had 
proposed,  and  that  the  contradiction  which  facts  so 
frequently  present  to  my  ideal  hypotheses  is  dependent 
upon  my  will  ?     To  take  an  example  :  a  scientific  man 
might  conceive  the  notion  that  the  motion  of  falling  bodies 
is  uniform,  but  he  is  unable  to  actualise  this  idea,  or  to 
impart  to  it  the  intensity  and  concrete  determination 
of  experience  ;   does  this  failure  depend  upon  himself  ? 
How  can  he  seriously  maintain  that  this  contradiction 
is  due  to  the  internal  meaning  of  the  idea,  if  the  experi 
enced  fact  of  the  constant  increase  in  velocity  were  no 
the  end  of  his  researches  ?     He  had  neither  foreseen 
nor  chosen  it :   his  will  was  directed  towards  a  total! 
different  end,  and  he  was  fully  conscious  of  this  interna 
meaning.     That  which  contradicts  it  was  not  willed  by 
him;    hence  it  cannot   be    regarded  as  the   interna 
meaning  of  the  will  of  that  individual  Ego.    Neither  can 
it  be  said  that  the  end  proposed  by  the  student  was  thi 
constant  acceleration  of  motion,  although  he  was  no 
aware   of  it,  since    it    is  not    allowable    to   consider 
that  as  being  willed  which  was  not  present  to  the  con 
sciousness  of  the  individual,  and  which  is  therefore 
times  the  very  opposite  of  the  desired  end.    If  the  idea 
[be  not  aware  of  its  true  meaning,  how  can  it  be  main- 
Itained  that  this  is  the  free  choice  of  the  idea  ?      Is 
it  possible  to  will  without  knowing  what  one  wills  ? 
In  reality,  the  assumption  by  our  idea  of  individua 
concrete  form  never  appears  to  us  to   be  dependent 
upon  the  idea  itself,  even  when  the  idea  is  confirmed  by 
experience  :  the  transition  from  the  abstract  hypotheses 
to  the  determinate  form  of  perception  is  not  due  merely 
to  the  will  to  actualise  that  idea.     In  the  cognitive 



function  we  are  conscious  that  this  transition  is  not 
due  to  our  will  alone,  and  that  it  depends  upon 
something  external  to  our  will,  so  much  so  that  it  is 
sometimes,  as  in  the  case  of  error,  a  hindrance  to  the 
realisation  of  our  idea.  Metaphysics  may  even  conceive 
the  other,  which  is  external  to  my  will,  to  be  the  actualisa-  . 
tion  of  a  Higher  Will,  but  this  Will  is  not  my  individual 
will.  Koyce's  argument  is  entirely  based  upon  the 
confusion  of  these  two  wills,  which  he  postulates  as 
being  identical,  thus  making  the  volitionary  process 
in  man  into  a  stage  of  a  wider  process.  Such  an  in- 
clusion of  consciousness  in  one  another,  of  the  mind  of 
man  in  the  mind  of  the  species,  and  of  this  mind  of  the 
species  in  the  consciousness  of  matter,  and  of  them  all 
in  the  Absolute  Will  is,  however,  inconceivable.  It  is  an 
undeniable  fact  of  experience  that  each  finite  Ego  presents 
an  impenetrable  front  to  other  individuals,  and  that, 
strive  as  it  may,  it  can  never  apprehend  the  phenomena 
of  consciousness  in  others  with  that  immediacy  with 
which  it  apprehends  the  processes  of  its  own  conscious- 
ness. To  this  impossibility  of  fusion,  not  to  singularity 
of  plan,  is  due  the  fact  that  each  mind  places  itself 
in  opposition  to  the  rest,  refusing  to  regard  as  its  own 
those  feelings,  thoughts,  and  acts  of  will  of  which  it 
can  have  no  immediate  experience  within  itself,  and 
can  only  reconstruct  indirectly,  and  by  analogy.  In 
our  criticism  of  Miinsterberg's  system  we  have  already 
observed  that  the  unity  of  the  Ego  cannot  be  reduced 
to  the  unity  of  the  end  :  the  consciousness  of  oneself 
is  one  thing,  moral  character  another.  The  unification 
of  the  various  stages  in  the  life  of  an  individual  in  such 
a  way  that  he  always  feels  himself  to  be  the  same  is  so 
little  the  work  of  a  plan  developed  by  that  life  that  there 
exist  individuals  whose  plans  are  both  incoherent  and 
unstable,  but  who,  nevertheless,  do  not  lose  conscious- 
ness of  their  own  personal  identity.  From  the  ethical 
point  of  view  it  is  absolutely  impossible  to  co-ordinate 
their  actions  in  such  a  way  as  to  make  them  appear  the 
expression  of  a  single  design,  yet  we  continue  to  look 


upon  them  as  persons  who  are  conscious  of  themselves : 
and  vice  versa,  different  individuals  may  at  times  work 
towards  the  same  end  without  on  that  account  feeling 
themselves  to  be  a  single  Ego.  It  is  no  argument  to  say 
that  each  of  them  works  towards  it  in  an  original  way, 
since,  even  in  the  case  of  a  single  individual,  the  various 
moments  of  life,  though  directed  towards  one  and  the 
same  end,  each  give  expression  thereto  in  a  different  way 
at  each  period  of  time,  so  that  each  individual  would 
need  to  be  split  up  into  as  many  persons  as  there  are 
moments  in  his  life.  If  the  personality  be  determined  by 
the  original  method  of  expressing  a  meaning,  then  each 
single  act  of  will,  seeing  that  it  cannot  be  reduced  to  the 
•  rest,  would  constitute  a  mind.  In  short,  from  Eoyce's 
standpoint  it  is  impossible  to  distinguish  between  the 
processes  of  consciousness  of  a  single  individual  and  those 
of  different  individuals  ;  at  bottom  the  ultimate  meaning 
is  the  same  in  them  all  while  the  expression  of  it  is 
singular  in  each.  Experience,  on  the  contrary,  shows 
us  that  the  psychic  facts  of  one  consciousness  are  related 
in  a  peculiar  way,  differing  entirely  from  the  extrinsic 
relation  which  may  connect  the  phenomena  of  different 
consciousnesses.  Metaphysical  speculation  should  ex- 
plain and  not  destroy  the  indubitable  data  of  our  ex- 
perience. If  we  hold  these  data  firmly,  what  would 
take  place  in  the  Absolute  Personality  were  it  obliged 
to  live  our  conscious  life  in  itself  just  as  we  ourselves 
live  it  ?  Each  of  us,  even  in  the  Divine  Consciousness, 
would  feel  himself  to  be  impenetrable  to  the  rest,  hence 
the  various  simultaneous  and  successive  moments  of  that 
supreme  spiritual  life  would  continue  to  be  extraneous 
to  one  another,  and  God  would  feel  Himself  to  be  a 
different  person  from  one  moment  to  the  next.  He 
might  indeed  regard  our  single  lives  as  different  expres- 
sions of  one  and  the  same  meaning,  but  this  would  not 
cause  Him  to  feel  Himself  to  be  the  same  in  each  one  of 
us ;  He  would  be  in  the  same  position,  as  far  as  His  self- 
consciousness  is  concerned,  as  a  victim  of  hysteria  in 
whom  duplication  of  personality  has  taken  place.  If, 


on  the  other  hand,  we  admit  that  the  various  self-con- 
sciousnesses of  single  individuals  lose  this  characteristic 
of  incommunicabihty  in  the  Absolute  Mind,  we  con- 
tradict Koyce's  thesis  from  another  side,  since  in  that 
case  it  ceases  to  be  true  that  our  experience  remains 
unchanged  in  God.  Moreover,  on  this  last  hypothesis 
we  should  cease  to  feel  ourselves  to  be  distinct  persons. 
In  short,  the  inclusion  of  human  consciousness  in  the 
divine  consciousness  only  becomes  possible  if  one  or 
the  other  lose  the  characteristic  of  personality — self- 
consciousness.  If  we  would  preserve  this  characteristic 
in  both  of  them,  we  must  give  up  the  absolute  imman- 
ence of  the  will  of  man  in  the  Will  of  God.  Every 
personality  in  its  self -consciousness  is  in  its  very  nature 
transcendent  with  regard  to  other  persons.  Seeing  then 
that  my  Ego  must  be  distinguished  from  other  Ego's, 
and  from  the  Absolute  Ego,  that  which  in  the  act  of 
cognition  appears  to  me  beyond  the  bounds  of  my 
will  may  certainly  be  regarded  as  the  expression  of 
a  will,  but  this  will,  far  from  being  identifiable  with 
my  own  will,  is  a  transcendent  object  as  far  as  I 
am  concerned.  That  which  is  experienced  by  other 
individuals  in  the  intimacy  of  their  consciousness  is  a 
real  life  transcending  the  sphere  of  my  will :  who  would 
venture  seriously  to  assert  that  other  minds  exist  only 
in  so  far  as  they  express  the  internal  meaning  of  an  idea 
of  mine,  and  embody  a  plan  of  my  devising  ?  Reduce 
all  reality  to  conscious  wills,  and  it  will  be  no  less  true 
that  each  consciousness  is  a  transcendent  object  with 
regard  to  every  other  consciousness.  Is  the  existence 
of  other  Ego's  dependent  upon  me  ?  Assuredly  not ! 
Then  if  I  think  this  existence,  may  it  not  be  an  external 
meaning  with  respect  to  my  idea  ?  Are  my  friends,  and 
those  who  are  dearest  to  me,  real  only  in  so  far  as  they 
satisfy  my  desire  ?  Or  do  they  rather  exist  in  them- 
selves in  the  intimacy  of  their  consciousness,  an  intimacy 
which  I  cannot  directly  penetrate  ?  Does  this  existence 
of  theirs  in  themselves  differ  from  my  thought  which 
takes  it  as  its  object  or  not  ?  The  idealist,  finding 


himself  in  such  a  strait,  takes  refuge  in  the  Universal 
Mind,  a  subterfuge  which  avails  him  nothing,  since, 
even  if  the  immanence  in  God  of  my  thought  and 
of  the  other  consciousness  thought  by  me  be  granted, 
my  thought  will  still  remain  something  distinct  from 
the  person  whom  I  think.  For  instance,  I  conceive 
the  reality  of  the  individual  named  Royce,  and  even 
supposing  my  concept,  and  the  consciousness  of  Royce 
to  form  part  of  one  and  the  same  spiritual  life,  my  idea 
with  its  internal  meaning  on  the  one  hand  and  the 
subject  Royce  on  the  other  will  nevertheless  remain 
two  distinct  things  which  cannot  be  fused  into  one 
unless  the  consciousness  of  the  great  American  philo- 
sopher be  annihilated. 

But  if  being  be  thus  placed  outside  the  idea,  will 
not  an  insuperable  dualism  be  the  result  ?  No ;  because 
we  say  that  the  two  terms  must  be  kept  distinct,  but 
do  not  assert  that  one  is  entirely  independent  of 
the  other,  so  that  reality  would  remain  unchanged, 
even  if  thought  be  eliminated.  Consciousness  is  not 
indifferent  to  being ;  the  bond  between  reality  and 
thought  is  not  a  mere  accident  which  might  actually  be 
dispensed  with,  but  an  essential  relation.  Nature  and 
the  human  mind  are  moments  of  one  and  the  same 
evolutionary  process,  a  process  which  is  the  actualisation 
of  an  ideal  plan,  and  their  organic  unity  affords  sufficient 
justification  of  the  cognitive  relation.  Such  a  teleo- 
logical  unity  undoubtedly  implies  an  Absolute  Conscious- 
ness which  thinks  it,  but  does  not  require  that  the  two 
terms  and  their  relation  shall  exist  only  in  that  Eternal 
Thought.  The  physical  world  and  the  human  mind  are 
objects  of  the  Divine  Mind,  but  do  not  exist  merely  as 
His  ideas.  This  distinction  between  finite  beings  in 
their  spontaneous  activity,  and  the  Absolute  Ego,  whilst 
it  is  the  only  way  of  accounting  for  the  possibility  of 
error,  does  not  isolate  them  in  such  a  way  as  to  render 
their  relations  inconceivable,  and,  more  especially,  pre- 
serves in  every  stage  of  their  immanent  development 
that  ideal  meaning  which  is  the  profound  reason  of  their 


existence.  Each  centre  of  spontaneous  life  bears  within 
itself  the  stamp  of  the  common  origin,  and  the  close  tie 
uniting  it  to  others  in  the  solidarity  of  the  eternal  plan 
which  is  carried  into  effect  throughout  the  infinite 
vicissitudes  of  history.  Nature,  as  a  necessary  moment 
of  this  process  which  embodies  an  ideal  plan  in  its 
objectivity,  though  the  result  of  a  combination  of 
actions  which  are  independent  of  our  Ego,  is  nevertheless 
not  extraneous  to  those  ends  which  constitute  the 
deepest  essence  of  our  mind.  Thus  when  we  invest 
it  with  the  forms  of  consciousness  and  interpret  it  in 
terms  of  our  thought,  we  do  not  falsify  it,  but  rather 
express  its  true  meaning. 

15.  Ward  on  the  Realm  of  Nature  and  the  Realm  of 
Ends. — Nothing  but  a  spiritualistic  view  of  the  world 
can,  without  encountering  the  difficulty  of  absolute 
idealism,  afford  an  intelligible  explanation  of  the  unity 
of  nature  and  thought,  and  the  universal  teleology  of 
the  ought  to  be,  which  the  philosophy  of  values  regards 
as  controlling  the  evolutionary  movement  of  experience. 
If  the  universe  be  not  a  brute  mechanism,  but  the 
realm  of  ends  and  of  history,  the  outcome  of  the  inter- 
weaving of  spontaneous  individual  activities  whose 
goal  is  the  actualisation  of  the  ethical  order,  only  a 
iheistic  conception  will  enable  us  to  comprehend  it.  The 
logical  completion  of  the  philosophy  of  values  can  only 
be  found  in  a  form  of  spiritualism,  and  to  James  Ward 
belongs  the  credit  of  having  frankly  recognised  this  fact. 
Ward,  who  in  his  Gifford  Lectures  waged  a  glorious 
warfare  against  agnostic  naturalism,  sees,  like  Koyce, 
Miinsterberg,  and  Rickert,  in  the  historical  and  concrete 
aspect  of  the  world  its  true  reality  as  opposed  to  the ' 
abstract,  mechanical  fictions  of  science.  The  cognitive 
attitude  which  endeavours  to  describe  the  world  as  it 
exists  independently  of  our  subjective  activity,  presents 
us  merely  with  an  abstract  fragment  of  reality,  because  it 
neglects  its  ties  with  the  subject,  whereas  in  the  practical 
attitude,  in  which  things  are  conceived  as  objects  of 
attraction  and  repulsion,  as  means  and  ends  of  our 


spontaneous  activity,  we  have  the  fulness  of  reality 
without  any  abstraction  whatsoever,  and  the  whole  _of 
experience  in  its  double  aspect,  both  subjective  and 
objective.139  Whereas  the  cognitive  attitude  entirely 
fails  to  take  into  account  the  subjective  factor  of 
experience,  which  is  therefore  subjected  to  a  process  of 
mutilation,  the  attitude  of  valuation  will  not  allow  us 

I  to  neglect  the  object,  since  our  life  really  consists  in 
an  exchange  of  actions  therewith.  Science,  as  has  been 
proved  by  the  criticisms  of  Mach,  Boltzmann,  Kirchhoff, 
and  Pearson,  gives  us  but  a  symbolic  description  of 
phenomena,  and  symbols  are  abstract  by  their  very 
nature  ;  physical  science  with  its  mechanical  schemes,  no 
less  than  arithmetic  and  geometry,  "is  incompetent  to 
furnish  a  concrete  presentment  of  a  real  and  living  world. 
Its  essentially  formal  character  has  become  increasingly 
evident  with  every  improvement  in  its  methods."  14°  We 
are  now  very  far  removed  from  the  time  in  which  our 
psychic  experiences  were  thought  to  be  a  vain  appearance 
of  the  movements  of  material  masses,  which  were  re- 
garded as  absolute  reality  :  the  terms  are  now  inverted. 
:'  What  we  see  and  fee],  the  facts  of  perception,  become 
the  real  phenomena.  Instead  of  the  states  of  conscious- 
ness supervening  upon  certain  motions  of  mass-points 
or  some  peculiar  complex  of  ethereal  vortices,  these 
motions,  etc.,  prove  to  be  but  ideal  conceptions  super- 
imposed upon  phenomena  by  the  mind,  that  seeks  to  con- 
nect them  in  respect  of  their  quantitative  relations." ltt 
History,  not  science,  can  show  us  reality  in  its  concrete- 
ness  ;  this  reality  is  not  an  eternal  repetition  of  necessary 
motions,  but  rather  "  the  intercourse,  the  co-operation  " 
of  individual  subjects  which  tend  freely  and  sponta- 
neously to  their  preservation  and  their  perfecting.142 
All  beings  are  animate,  though  in  different  degrees  : 
in  proportion  to  the  growth  of  our  knowledge  will  be 

*  the  disappearance  of  the  artificial  barrier  between  the 
psychic  and  the  physical,  mind  and  nature,  the  world 
of  liberty  which  gives  rise  to  actions  which  cannot  be 
foreseen  and  the  world  of  necessity  which  admits  of 


mathematical  calculation.  He  who  contemplates  the 
world  in  its  historical  aspect  regards  the  constant 
uniformity  of  physical  laws  merely  as  the  result  of  an 
average  in  which  variations  in  opposite  senses  have 
been  eliminated  by  summation.  May  not  the  same 
thing  take  place  in  the  case  of  free  human  actions, 
which  are  sometimes  disguised  by  the  apparent  uni- 
formity of  statistic  averages  ? 143  The  contingency  which 
Ward  recognises  in  the  world  is  not  "  that  of  chance, 
but  that  of  freedom,"  which  consists  in  conformity  to  - 
what  ought  to  be.  Absolute  conformity — the  complete 
actualisation  of  the  realm  of  ends — is  an  ideal  for  us ;  but 
little  by  little  in  the  course  of  evolution  we  shall  see  the 
harmony  of  free  co-operation,  together  with  the  elimina- 
tion of  conflicts,  being  realised  more  and  more  nearly.144 
This  order  and  harmony  lead  us  perforce  to  the  theistic 
hypothesis,  which  alone  can  make  us  understand  how 
it  is  possible  for  the  many  to  co-ordinate  their  actions 
in  systematic  unity.  Ward  rejects  not  only  the  dualism 
of  matter  and  mind,  but  also  that  of  subject  and  object : 
there  is  but  one  living  experience :  that  which  we 
call  objective  reality  is  merely  experience  itself  in  that 
part  thereof  which  is  common  to  all  subjects.  The 

i  separation  of  subject  and  object  is  due  to  the  exchange 
of  action  amongst  different  subjects  by  means  of  that 
process  which  Avenarius  termed  "  introjection."  145  In 
like  manner  there  exists  no  absolute  distinction  between 
sensibility  and  reason,  since  sense,  no  less  than  under- 
standing, gives  us  something  objectively  real,  and  the 
universal  world  of  reason  is  at  bottom  but  the  individual 
world  itself  in  so  far  as  it  is  brought  into  harmony  with 
the  contents  of  experience  of  other  conscious  beings  living 
in  society.  Ward  therefore  looks  upon  knowledge  not 
as  a  passive  reflection  of  an  external  reality  by  means  of  - 
a  special  faculty  called  intellect,  but  rather  as  an  active 

(,  expansion  of  experience  into  a  larger  sphere  of  life  by 
means  of  that  tendency  to  preserve  and  perfect  which 
lies  at  the  root  of  all  being.     Theoretical  activity  is  in  ~ 
ultimate  analysis  but  a  form  of  practical  life  :   there  is 


no  cognition  the  impulse  to  which  will  not  be  found  in 
determinate  needs,  and  the  whole  scientific  construction 
is  at  bottom  but  a  means  for  the  extension  of  the  sphere 
of  our  power.  Ward  regards  conation,  not  cognition,  as 
"  the  central  feature  of  experience." 146  Thus  he  conceives 
everything  as  subordinate  to  human  ends,  and  as  bearing 
the  imprint  of  the  activity  of  our  mind  and  our  subjective 
selection,  and  ultimate  reality  too  as  formed  in  the 
likeness  of  our  intimate  experience.  Is  this  anthropo- 
morphism ?  Ward  replies  with  truth  that  "  in  a  sense 
we  are  always  anthropomorphic,"  since  we  can  never 
divest  ourselves  of  our  consciousness  ;  hence  not  only 
spiritualistic  intuition  but  the  very  mechanical  inter- 
pretation of  the  universe,  which  in  the  last  analysis 
derives  its  concepts  from  our  human  experience,  is  of 
an  anthropomorphic  nature.147 

Whilst  we  fully  agree  with  Ward  in  his  spiritualistic 
conclusions,  we  are  not  equally  ready  to  accept  the 
concept  of  the  value  of  science  and  of  the  theoretical 
function  in  general  in  its  relations  to  practical  life  which 
he  derives  from  empiric-criticism,  and  which  we  have 
already  discussed  at  length.  On  the  other  hand,  we 
fail  to  see  how  his  idealistic  theory  of  knowledge,  which 
would  annihilate  the  dualism  of  subject  and  object,  of 
internal  and  external  experience,  can  be  reconciled  with 
pluralism.  If  other  beings  do  not  exist  merely  in  so 
far  as  I  think  them,  but  exist  also  in  themselves  in  their 
spiritual  intimacy,  my  experience  of  them  from  without 
is  of  a  different  order  from  the  experience  which  each 
one  of  them  enjoys  of  itself  from  within.  When  I  think 
another  individual,  his  being  as  present  to  himself  and 
the  idea  of  him  formed  by  me  constitute  an  irreducible 
duality.  The  existence  of  anything  outside  thought 
may  be  denied,  but  in  that  case  we  must  also  deny 
the  truth  of  pluralism  which  regards  each  individual  as 
existing  outside  the  consciousness  of  other  individuals. 
The  plurality  of  subjects  and  their  existence  even 
outside  the  Divine  Mind,  which  must  be  granted  in 
the  theistic  hypothesis,  leads  perforce  to  realism.148 



I  In  the  Preface  to  the  second  edition  of  his  book,  Der  Gegenstand  der 
Erkenntnis  (Tubingen  und  Leipzig,  1904,  p.  vi.),  Rickert  insists  upon  the 
epistemological  character  of  his   method :  " .  .  .  Meine  Schrift  will  nur 
Erkenntnistheorie  und  nicht  Psychologie  oder  Metaphysik  geben,   d.h. 
sie  will  das  entwickeln,  was  auch  fur  den  Psychologen  und  den  Meta- 
physiker  Voraussetzung  ist  und  daher  nicht  gut  Object  psychologischer 
oder  metaphysischer  Untersuchungen  sein  kann." 

2  Prdludien  (Freiburg,  1884),  p.  28  ff. 

3  Op.  cit.  p.  36  ff. 

4  Here  the  contrast  with  the  teaching  of  pragmatism  is  obvious. 

5  Op.  cit.  p.  43. 

6  Op.  cit.  pp.  221-224. 

7  Op.  cit.  p.  227. 

8  Op.  cit.  p.  130. 

9  Op.  cit.  p.  251  ff. 

10  Op.  cit.  pp.  256-261. 

II  Op.  cit.  p.  210. 

12  Op.  cit.  p.  320  ff. 

13  Der  Gegenstand  der  Erkenntnis.    Einfuhrung  in  die  Transzendental- 
philosophie  (Tubingen  und  Leipzig,  1904,  second  edition,  p.  vi.     The  first 
edition  was  published  in  1892). 

14  Op.  cit.  p.  12  ff. 

15  Rickert  here  shows  the  influence  of  Schuppe's  philosophy  of  imman- 
ence :  Erkenntnistheoretische  Logik  (Bern,  1878) ;  Grundriss  der  Erkenntnis- 
theorie und  Logik  (Berlin,  1898).     Schuppe  regards  subject  and  object  as 
two  aspects  of  the  only  reality, — consciousness,  external  to  which  nothing 
exists.     The  Ego  is  not  a  substance,  but  merely  consciousness  of  oneself. 
The  different  consciousnesses  possess  one  part  which  differs  from  other 
consciousness  and  which  constitutes  their  individuality,  and  one  which  is 
common  to  them  all  ("  gattungsmassiges  Ich  "),  which  constitutes  objective 
reality.     To  the  latter  belong  abstract  concepts,  which  are  presented  to 
us  as  elements  of  perception  (Grundriss,  p.  31  ff.,  p.  90  ff.). 

16  Rickert,  op.  cit.  pp.  78-84 . 

17  Op.  cit.  p.  97. 

18  "  Erkennen  ist  anerkennen  oder  verwerfen.  .  .  .  In  jeder  Erkenntnis 
wird  ein  Wert  anerkannt  "  (op.  cit.  pp.  108-110). 

19  Op.  cit.  p.  112.     Note  also  here  the  difference  between  the  philosophy 
of  values  and  pragmatism. 

20  Op.  cit.  pp.  111-114. 

21  Op.  cit.  pp.  115-123. 

22  Op.  cit.  p.  124  ff. 

23  Op.  cit.  p.  141. 

24  Op.  cit.  p.  157. 

25  Op.  cit.  p.  165. 
28  Op.  cit.  p.  185. 

27  Op.  cit.  p.  199. 

28  Op.  cit.  p.  197  ff. 

29  Op.  cit.  p.  234. 
80  Op.  cit.  p.  240. 

31  Die  Grenzen  der  Naturwissenschaftlichen  Begriffsbildung  (Tubingen 
und  Leipzig,  1896-1903,  p.  695  ff.). 


«  Op.  cit.  p.  697  ff. 

»  Op.  cit.  pp.  737-739. 

84  Windelband,  Prdludien,  p.  75. 

34  Rickert,  op.  cit.  p.  24. 

84  Op.  cit.  p.  34  ff. 

87  Op.  «/.  pp.  230-237. 

88  0p.  ci/.  p.  244. 

39  Op.  cti.  p.  246. 

40  Op.  cit.  p.  247. 

41  Op.  ci<.  p.  256. 

42  Op.  c&.  pp.  258-260. 

43  It  should  be  noted  that  by  nature  Rickert  does  not  mean  merely  the 
physical  world,  but  in  general  that  which  recurs  in  the  psychic  world  as 
welL      Windelband  had  already  replaced  the  old  distinction  between 
natural  and  moral  sciences  by  that  between  the  sciences  of  events  ("Ereignis- 
wissenschaften  ")  and  sciences  of  laws  ("Gesetzeswissenschaften"),  applying 
the  term  idiographisch  to  the  method  of  the  former,  and  nomothetisch  to 
that  of  the  latter  (Geschichte  und  Naturwissenschajt,  Strassburger  Rek- 
toratsrede,  1894).      Xenopol  too,  in  his  Les  Principes  fondamentaux  de 
Fhistoire  (Paris,  1899),  makes  a  similar  division,  distinguishing  the  fails 
de  repetition  from  the/atte  de  succession.     The  first  suggestion  of  a  division 
of  the  kind  occurs  in  Humboldt's  Cosmos,  but  Cournot  was  the  first  to 
determine  it  clearly  and  to  extend  it  to  all  the  sciences  (Consideration  sur 
la  marche  des  idees  et  des  evenements  dans  les  temps  modernes,  Paris,  1872, 
Preface,  p.  4).     Hermann  Paul,  who  was  not  acquainted  with  Cournot's 
work,  draws  a  distinction  in  his  Principien  der  Sprachgeschichte  (Halle,  1880) 
between  the  Gesetzwissenschaft  and  the  Geschichtewissenschaften. 

44  Op.  cit.  pp.  412-414. 

45  Op.  cit.  p.  416  ff. 
44  Op.  cit.  p.  422. 

47  Op.  cit.  p.  428. 

48  Op.  cit.  p.  622. 

4»  Op.  cit.  pp.  641-649. 

M  Op.  cit.  pp.  650-653. 

61  "  Die  empirische  Wirklichkeit  fur  uns  absolut  irrazional  ist " 
{op.  cit.  p.  511). 

«  Op.  cit.  p.  680. 

68  Op.  cit.  p.  685. 

64  Op.  cit.  p.  687. 

68  Op.  cit.  voL  ii.  p.  98. 

*•  "  Zwei  Wege  der  Erkenntnistheorie  "  (from  Kantetudien,  vol.  xiv. 
Xo.  2),  published  separately  in  Halle,  1909,  p.  37. 

57  Op.  cit.  p.  57  ff. 

M  "  Unter  Sollen  verstehen  wir  gerade  das,  was  nicht  ist  oder  nicht 
existiert  "  (op.  cit.  p.  16). 

M  Philosophic  der  Werte,  Grundzuge  einer  Weltanschauung  (Leipsig, 
1908).  Mtinsterberg  had  already  sketched  the  first  outlines  of  this 
conception  in  his  earlier  works :  Psycliology  and  Life,  1899 ;  Grundzuge. 
der  Psychologie,  voL  i.  1900  ;  Science  and  Idealism,  1906. 

•°  "  Die  Geschichte  tritt  wieder  in  ihr  Recht.  Der  wollende  Mensch 
wird  zum  Ausgangspunkt  und  der  psychophysische  Mechanismus  ver- 
schwindet  endlich  aus  der  Metaphysik.  Dem  Positivismus  folgt  der 
Voluntarismus "  (Philosophie  der  Werte,  p.  36). 

41  Op.  cit.  pp.  29-38. 

41  Op.  cit.  p.  39  ff.,  pp.  449-481. 


63  "  Das  eine  also  wissen  wir :  am  Anfang  war  die  Tat "  (p.  456) ;  "  Die 
Welt  ist  lebendige  Tat "  (p.  476). 

64  Op.  cit.  pp.  438-481.     "  Diese  Bewertung  der  Ganzheit  ist  also  eiii 
Wert    sonderer   Art,   ein    metaphysischer   Uberzeugungswert,   der   vom 
logischen    Zusammenhangswert  grundsatzlich    zu    trennen  ist  und    der 
aufs  engste  mit  dem  religiosen  Glaubenswert  zusammengehort "  (op.  cit. 
p.  444). 

86  Op.  cit.  p.  481. 

68  "  Deshalb  lassen  sich  auch  die  theoretischen  Werte  nicht  aus  einem 
iiberindividuellen  Willen  ableiten.  Der  Wille  ist  als  etwas  Feindes  dem 
Sinn  gegeniiber  immer  Sekundar "  (Zwei  Wege,  der  Erkenntnistheorie, 
p.  50). 

67  Miinsterberg,  op.  cit.  p.  53  ff. 

68  Op.  cit.  p.  57  ff. 

69  Op.  cit.  p.  60  ff.,  p.  461  ff. 

70  Op.  cit.  p.  74  ff. 

71  We  shall,  of  course,  confine  our  explanation  to  the  theoretical  values, 
and  omit  the  others  which  are  not  comprised  in  our  subject. 

72  Op.  cit.  pp.  85-89. 

73  Op.  cit.  pp.  94-97. 

74  "  Der  Wille  trifft  unmittelbar  den  Willen  "  (op.  cit.  p.  106). 

75  Op.  cit.  p.  110  ff. 

78  Op.  cit.  pp.  112-114. 

77  Op.  cit.  pp.  115-117. 

78  Op.  cit.  pp.  120-122. 

79  Op.  cit.  p.  131. 

80  Op.  cit.  pp.  134-139. 

81  Op.  cit.  p.  130. 

82  Op.  cit.  pp.  150-165. 

83  Op.  cit.  pp.  167-169. 

84  Op.  cit.  p.  170. 

85  Op.  cit.  pp.  174-181. 

86  Our  exposition  of  Royce's  thought  is  based  upon  his  chief  work, 
The  World  and  the  Individual  (New  York,  1901). 

87  "...  your  intelligent  ideas  of  things  never  consist  of  mere  images 
of  the  things,  but  always  involve  a  consciousness  of  how  you  propose  to 
act  towards  the  things  of  which  you  have  ideas  "  (The  World  and  the 
Individual,  vol.  i.  p.  22).     "  Ideas  are  like  tools.     They  are  there  for  an 
end  "  (ibid.  p.  308).     Royce  quotes  Stout's  Analytic  Psychology  (vol.  ii. 
pp.  114,  124),  in  which  ideas  are  regarded  as  "  plans  of  action." 

88  "  When  I  know,  I  am  acting.     My  theoretical  life  is  also  practical  " 
(op.  cit.  p.  27). 

89  Op.  cit.  p.  434  ff. 

90  Op.  cit.  p.  153. 

91  "  The  conscious  expression  of  an  interest,  of  a  desire,  of  a  volition  " 
(op.  cit.  p.  41).     Royce  himself,  in  a  communication  made    by  him  to 
the  third  International  Congress  of  Philosophy,  "  The  Problem  of  Truth 
in  the  Light  of  recent  Research,"  has  termed  his  system   "  absolute 

92  As  early  as  1881,  in  an  article  published  in  the  Journal  of  Speculative 
Philosophy,  entitled  "  Kanfs  Relation  to  Modern  Philosophical  Progress," 
Royce  insisted  upon  the  active  character  and  ethical   meaning  of   the 
recognition  of  facts,  to  which  Rickert  and   Miinsterberg,   acting  inde- 
pendently of  Royce,  called   attention   later.      Thus,  before  reading  the 
works  of  Rickert  and  Miinsterberg,  he  arrived  at  the  distinction  between 


PT.  I 

the  world  of  valuation  and  the  world  of  description,  which  he  compares 
for  the  first  time  in  his  book,  Spirit  of  Modern  Philosophy  (Boston,  1892). 
He  acknowledges,  however,  the  influence  exercised  by  the  works  of  these 
writers  upon  the  final  form  assumed  by  his  system  (op.  cit.  vol.  ii.  Preface, 
p.  6ff.).  These  coincidences  are  not,  however,  purely  accidental,  but  are 
due  to  a  common  source :  Windelband,  with  whom  Royce  was  un- 
doubtedly acquainted,  and  more  remotely  to  Lotze. 

98  Op.  cit.  voL  ii.  pp.  32-41. 

94  "  And  the  theoretical  Ought  of  our  judgments  about  facts,  like  the 
practical  Ought  of  ethics,  is  after  all  only  definable  in  terms  of  what  Kant 
called  the  Autonomy  of  the  Will "  (op.  cit.  voL  ii.  p.  32). 

»5  Op.  cit.  voL  ii.  p.  24. 

86  Op.  cit.  voL  i.  p.  24  ff. 

97  Op.  cit.  voL  i.  p.  62  ff. 

98  Op.  cit.  voL  i.  p.  128. 

99  Op.  cit.  vol.  i.  p.  134  ff. 

100  Op.  cit.  voL  i.  pp.  306-308. 

101  Op.  cit.  voL  i.  pp.  318-319. 

102  Op.  cit.  voL  i.  pp.  176-179. 

103  Op.  cit.  voL  i.  p.  185  ff. 

104  Op.  cit.  vol.  i.  p.  204  ff. 

105  Royce,  who  is  a  diligent  student  of  mathematical  logic,  and  believes 
that  metaphysic  can  profit  largely  by  modern  researches  ("  The  metaphysic 
of  the  future  will  take  fresh  account  of  mathematical  research,"  op.  cit. 
voL  i.  p.  527),  applies  it  freely  in  his  system.     As  regards  mathematical 
procedure  he  follows  the  theory  set  forth  by  Peirce,  according  to  which 
abstract  reasoning  consists  in  a  process  of  experiment  upon  an  artificial 
object  constructed  by  the  mathematician  and  observed  by  him  in  his  own 
consciousness,  just  in  the  same  way  as  one  observes  an  external  object, 
».e.  in  that  which  Mach  has  termed  "  Gedankenexperiment "   (op.  cit. 
voL  i.  p.  225). 

1M  Op.  cit.  voL  i.  p.  260  ff. 

107  Op.  cit.  voL  L  p.  280  ff. 

108  Op.  cit.  voL  i.  p.  293  ff. 
1W  Op.  cit.  voL  L  p.  297  ff. 

uo  «  What  is,  or  what  is  real,  is  as  such  the  complete  embodiment  in 
individual  form  and  in  final  fulfilment  of  the  internal  meaning  of  finite 
ideas  "  (op.  cit.  voL  i.  p.  339). 

111  Op.  cit.  voL  i.  p.  346. 

118  Op.  cit.  voL  i.  pp.  353-366. 

118  Op.  cit.  voL  i.  p.  373. 

"«  Op.  cit.  voL  i.  p.  391-400. 

us  Op.  cit.  voL  ii.  p.  302. 

"•  Op.  cit.  voL  ii.  pp.  408-410. 

U7  Op.  cit.  voL  ii.  p.  122  ff.,  p.  344. 

"«  Op.  cit.  voL  i.  pp.  581-584. 

119  Green,  Prolegomena  to  Ethics,  pp.  28-30. 
1M  Royce,  op.  cit.  voL  i.  p.  419. 

181  Op.  cit.  voL  i.  p.  327. 

»*  Op.  cit.  voL  L  p.  389. 

113  Op.  cit.  voL  i.  pp.  334  and  389. 

1M  Op.  cit.  voL  ii.  p.  31. 

m  Op.  cit.  voL  ii.  p.  41  ff. 

118  Op.  cit.  voL  ii.  p.  186. 

127  Op.  cit.  voL  ii.  pp.  170-174. 


1!8  The  Spirit  of  Modern  Philosophy,  Part  ii.  p.  398.     Royce  refers  to 
Kirchhoff  and  Mach  for  this  conception  of  science. 
129  The  World  and  the  Individual,  voL  ii.  p.  181  ff. 
180  Op.  cit.  vol.  ii.  p.  217  ff. 

131  Op.  cit.  vol.  ii.  p.  228  ff. 

132  Op.  cit.  vol.  ii.  p.  233. 

133  Op.  cit.  vol.  i.  p.  236. 

134  Op.  cit.  vol.  ii.  p.  238. 

135  Op.  cit.  vol.  ii.  pp.  276-286. 

136  Op.  cit.  vol.  ii.  p.  330. 

137  Op.  cit.  vol.  ii.  p.  408. 

138  Op.  cit.  voL  ii.  p.  142. 

139  Ward,  The  Realm  of  Ends,  or  Pluralism  and  Theism  (Cambridge, 
1911),  p.  430  ff. 

140  Naturalism  and  Agnosticism  (London,   1899),    voL   i.    p.   82  sq., 
p.  151  ff.,  p.  179  ff. 

141  Op.  cit.  vol.  ii.  p.  103. 

142  The  Realm  of  Ends,  p.  20  ff.,  p.  431  ff. 

143  Ibid.  p.  5. 

144  Op.  cit.  p.  434. 

145  Naturalism  and  Agnosticism,  voL  ii.  p.  182  ff. 

146  Op.  cit.  voL  ii.  p.  134  and  p.  232  ff. 

147  Op.  cit.  vol.  ii.  p.  257. 

148  There  are  already  signs  in  contemporary  philosophy  of  a  return  to 
epistemological  realism  ;  it  will  suffice  to  quote  Kiilpe's  book,  Die  Realisie- 
rung  (Leipzig,  1913),  and  the  works  of  Meinong  and  Russell  to  which  we 
shall  refer  later  on.     Of  importance  is  the  work  entitled  The  New  Realism  ; 
Co-operative  Studies  in  Philosophy,  by  Edwin  B.  Holt,  Walter  T.  Marvin, 
William  Pepperell  Montague,  Ralph  Barton  Perry,  Walter  B.  Pitkin,  and 
Edward  Gleason  Spaulding  (New  York,  The  Macmillan  Company,  1912). 




1.  Traditional  Geometry  and  the  New  Theories  of  Gauss, 
Lobatchewsky,  and  Bolyai. — Until  the  beginning  of  the 
nineteenth  century  Euclid's  geometry  had  seemed  to 
be  the  perfect,  unchangeable  model  of  all  scientific 
certainty  :  Cartesian  rationalism,  inspired  by  Kepler's 
words,  Ubi  natura,  ibi  geometria,  had  placed  it  at 
the  foundation  of  all  knowledge  of  things  idealised  in 
pure  extension,  and  had  finally  in  the  teaching  of 
Spinoza  claimed  to  establish  an  Ethica,  more  geometrico 
demonstrata.  The  keen  analyses  of  Berkeley  and  the 
bold  criticism  of  Hume  were  alike  powerless  to  shake 
this  ancient  faith,  because  in  Kant's  Transcendental 
Aesthetic  the  ideality  of  the  pure  intuition  of  space 
achieved  a  triumph  over  nominalism  and  empirical 
scepticism.  Only  at  the  beginning  of  last  century  did 
the  construction  of  a  different  geometry  begin  to  seem 
possible ;  and  about  fifty  years  later  these  new  specu- 
lations formed  the  subject  of  lively  discussions  and 
polemics  in  the  world  of  philosophy  by  reason  of  the 
consequences  which  were  supposed  to  be  deducible  from 
them  against  the  a-priority  of  space. 

The  failure  of  the  many  attempts  to  deduce  the  axiom 
of  parallels  directly  from  the  other  axioms  2  induced 
Gauss,3  Lobatchewsky,4  and  Bolyai 5  to  make  use  of  a 
bolder  method,  a  kind  of  reductio  ad  absurdum.*  If  the 
axiom  of  parallels  could  be  logically  derived  from  the 
others,  by  denying  it  while  retaining  the  rest,  one  should 
arrive  at  contradictory  results ;  but  the  three  mathe- 



maticians,  while  denying  it,  reached  a  geometry  which 
was  logically  consequent,  and  drew  the  conclusion 
therefrom  that  this  axiom  was  logically  independent  of 
the  rest  and  essential  only  to  the  Euclidean  system. 
Lobatchewsky  substitutes  the  following  proposition 
for  Euclid's  axiom  :  "  In  relation  to  a  straight  line, 
all  the  other  straight  lines  in  the  same  plane  may  be 
divided  into  two  classes  :  those  which  intersect  the 
given  line,  and  those  which  do  not  intersect  it :  a  line 
which  forms  the  limit  between  these  two  classes  is 
termed  parallel  to  the  given  line  ;  for  each  point  external 
to  the  line  there  exist  two  parallels,  which  are  symmetri- 
cal in  relation  to  the  perpendicular  drawn  from  that 
point."  From  these  premisses,  and  by  means  of  the 
Euclidean  synthetical  method,  he  deduces  a  series  of 
propositions,  of  which  the  following  is  the  most  im- 
portant :  :'  The  sum  of  the  internal  angles  of  a  triangle 
is  either  always  less  than,  or  always  equal  to,  two  right 
angles  :  in  the  latter  case  the  whole  system  becomes 

2.  The  Empiricism  of  Riemann  and  Helmholtz,  and 
the  Dispute  with  the  Neo-Kantians. — The  new  geometrical 
speculations  failed  at  first  to  excite  philosophic  interest, 
but  after  Riemann  and  Helmholtz  had  turned  to  them 
for  proof  of  Stuart  Mill's  empiricism,  the  dispute  began 
between  the  meta- geometricians  on  the  one  hand  and 
the  neo-Kantians  on  the  other.  Riemann  7  subordinates 
the  concept  of  space  to  the  more  general  concept  of 
magnitudes  having  manifold  extension  (der  allgemeine 
Begriff  mehrfach  ausgedehnter  Grossen) :  in  order  to 
determine  how  many  kinds  of  space  are  logically  possible, 
we  must  first  find  out  in  how  many  ways  magnitude  can 
have  manifold  extension.  When  the  number  of  spatial 
varieties  which  are  conceptually  possible  has  thus  been 
fixed,  it  is  the  work  of  experience  to  determine  which 
of  them  is  represented  by  our  space,  that  is  to  say,  by 
the  space  in  which  the  world  with  which  we  are  acquainted 
is  situated.  After  having  determined  the  general  con- 
cept of  space  as  a  continuous  manifold  of  points,  each 


of  which  is  dependent  upon  algebraic  values,  and  having 
posited  as  its  fundamental  property  constant  curvature  8 
which  is  a  necessary  condition  of  the  free  mobility  of 
figures,  Riemann  reduces  the  number  of  dimensions  to 
three,  and  proves  that  in  this  species  of  space  three 
varieties  are  possible,  according  as  the  value  of  the 
constant  of  curvature  is  positive,  negative,  or  null,  i.e. 
spherical,  pseudo-spherical,  and  flat  or  homaloidal  space.9 
The  last  named  corresponds  to  Euclidean  space  ;  the 
second  to  that  of  Lobatchewsky ;  the  first  is  a  new 
variety  introduced  by  Riemann.  In  spherical  three- 
dimensional  space  no  line  passes  through  a  point  external 
to  a  straight  line  which  does  not  meet  this  latter  ;  two 
points  do  not  always,  as  in  Euclidean  geometry,  deter- 
mine one  straight  fine  only,  and  the  sum  of  the  angles 
of  a  triangle  is  greater  than  two  right  angles.  This 
geometry  is  termed  spherical,  because  for  the  case  of  two 
dimensions  it  is  identical  with  the  geometry  of  the 
surface  of  the  sphere,  in  which  the  arc  of  maximum 
circumference  plays  the  part  of  a  straight  line. 

Helmholtz10  arrives  at  the  same  conclusions,  but 
follows  a  different  procedure  in  the  transition  from 
the  manifold  of  n  dimensions  to  Euclidean  space,  de- 
ducing from  certain  hypotheses  on  the  movement  of 
bodies  the  analytic  function  of  the  space-constant,  which 
Riemann  takes  as  his  starting-point.  Of  w-dimensional 
manifolds  he  takes  into  consideration  those  contain- 
ing non-deformable  and  mobile  systems  ;  he  further 
imagines  the  movement  of  a  perfectly  free  solid  and 
restricts  the  concept  of  the  spatial  manifold  by  the 
condition  that  if  n  +  1  points  of  a  system  be  fixed,  it 
must  return  to  the  initial  position.  Of  the  spaces  thus 
defined  he  then  determines  Euclidean  space,  assuming 
the  number  of  the  dimensions  to  be  equal  to  three,  and 
admitting  the  dimensions  of  a  point  to  be  capable  of 
indefinite  increase. 

Riemann  and  Helmholtz  agree  in  thinking  that  the 
possibility  of  conceiving  other  systems  of  geometry 
proves  the  empirical  origin  of  axioms.  Riemann  thinks 


it  possible  that  these  axioms  are  not  valid  in  the  case 
of  the  infinitely  small  which  does  not  admit  of  observa- 
tion ;  as  a  matter  of  fact  the  empirical  concepts  upon 
which  spatial  measures  are  based — i.e.  the  concepts  of 
the  rigid  body  and  the  luminous  ray — do  lose  their 
validity  in  the  infinitely  small ;  it  is  therefore  perfectly 
conceivable  that  the  relations  of  spatial  magnitude 
cease  to  correspond  therein  to  the  presuppositions 
of  geometry ;  hence  we  must  grant  this  hypothesis, 
which  enables  us  to  give  a  simpler  explanation  of 
phenomena.  Helmholtz  also  endeavoured  to  prove  that 
all  the  axioms  are  empiric,  basing  his  conclusions  on 
meta-geometry  as  well  as  upon  the  results  of  psycho- 
physiological  research.  To  the  objections  of  Land, 
Krause,  Becker,  and  others  who  defended  Kant's  position, 
affirming  that  even  if  it  be  possible  to  conceive  of  other 
spaces,  there  can  be  no  intuition  but  that  of  Euclidean 
space,  Helmholtz  replied  u  that  the  representation  of 
non-Euclidean  spaces  is  difficult  because  we  are  not 
accustomed  to  it,  but  not  actually  impossible,  and 
that  Kant's  arguments,  even  were  they  formally  valid, 
would  not  prove  the  a-priority  of  Euclidean  space  in 
particular,  but  merely  that  of  space  in  general,  which 
embraces  both  Euclidean  and  non-Euclidean  spaces. 
The  a-priority,  in  short,  does  not  imply  a  preference  for 
certain  spatial  relations  over  others,  but  is  independent 
of  the  relations  affirmed  in  the  axioms  of  geometry  which 
constitute  the  matter  of  the  idea  of  space  and  can  there- 
fore only  be  justified  by  experience.  In  order  to  prove 
the  possibility  of  rendering  non-Euclidean  space  in- 
tuitive, Helmholtz  makes  use  of  the  work  of  Beltrami,12 
who  had  endeavoured  to  impart  an  intelligible  Euclidean 
sense  to  Lobatchewsky's  plane  geometry,  showing  all 
the  propositions  established  by  this  mathematician  in 
plane  geometry  to  be  valid  in  ordinary  Euclidean  space 
on  the  surfaces  of  constant  negative  curvature,  which 
Beltrami  terms  pseudo-spherical.  The  dispute  between 
Helmholtz  and  the  pure  neo-Kantians  turned  more 
especially  on  the  possibility  or  impossibility  of  repre- 


senting  such  a  surface  intuitively.  Helmholtz,  in  order 
to  prove  his  thesis,  defines  imaginability  as  the  ability 
to  form  a  complete  representation  of  the  sensible  im- 
pressions which  the  object  makes  upon  us  according 
to  the  known  laws  of  our  organs  of  sense ; 13  and 
endeavours  to  enumerate,  in  conformity  to  this  defini- 
tion, the  series  of  sensible  impressions  which  the  pheno- 
mena of  pseudo-spherical  space  makes  upon  us.14  An 
observer,  having  sight  and  a  criterion  of  judgment  like 
our  own,  would,  on  first  entering  the  pseudo-sphere, 
continue  to  see  luminous  rays  or  lines  of  vision  as  straight 
lines,  just  as  in  plane  space,  and  as  they  are  in  reality 
in  the  spherical  representation  of  pseudo-spherical  space. 
The  visual  image  of  the  objects  of  the  pseudo-sphere  will 
then  make  the  same  impression  upon  him  as  if  he  were 
in  the  centre  of  Beltrami's  representative  sphere.  More 
remote  objects  will  appear  to  surround  him  at  a  finite 
distance  (about  a  hundred  feet,  for  instance),  but  if  he 
approaches  them,  he  will  see  them  expand  before  him— 
and  that  more  in  depth  than  superficies — and  contract 
behind  his  back,  and  will  realise  the  error  of  judgment 
committed  by  his  eyes.  If  he  have  seen  two  straight 
lines  which  appear  to  him  to  run  parallel  for  a  distance 
of  100  feet,  at  which  point  the  world  comes  to  an 
end  for  him,  he  will  recognise,  as  he  approaches  more 
closely,  that  this  dilation  causes  objects  to  become 
more  and  more  remote  the  farther  he  advances  ;  behind 
him,  on  the  contrary,  their  distances,  which  in  the 
former  position  appeared  to  intersect  one  another  at 
one  identical  point  only,  will  appear  in  the  new  position 
behind  him  with  the  same  intersection  at  100  feet,  and, 
approach  as  he  may,  he  will  never  reach  the  point  of 

Land15  objects  that  Helmholtz's  description  is 
couched  in  conceptual  terms,  and  is  therefore  no  proof 
of  the  possibility  of  intuiting  the  new  space  ;  moreover, 
as  Stallo  truly  remarks,16  it  is  not  enough  to  ask  our- 
selves what  would  be  the  nature  of  the  impressions 
produced  upon  us  by  the  objects  of  that  fantastic  world; 


we  must  also  ask  whether  they  can  be  imagined  together 
in  the  spatial  order  and  the  required  form,  in  conformity 
to  the  known  laws  of  the  representative  faculty.  The 
perception,  as  conceived  of  by  Beltrami,  of  points,  lines, 
and  surfaces  of  pseudo- spherical  space  in  the  interior 
of  an  ordinary  spherical  surface,  whose  points  correspond 
to  the  infinitely  remote  points  of  pseudo-spherical  space, 
does  not  enable  us  actually  to  represent  that  space,  since 
it  is  one  thing  to  intuit  the  projection  and  another  to 
imagine  the  projected  figure,  which  will  only  be  present 
to  our  intuition  if  we  have  already  known  it  in  some 
other  way.  The  projection  of  a  solid  on  a  plane  does 
not  in  itself  enable  us  to  form  a  mental  image  of  that 
three-dimensional  figure  ;  if  we  succeed  in  imagining 
it,  we  do  so  because  we  already  possess  intuitive  know- 
ledge of  the  solid  in  question.  In  like  manner,  a  figure 
of  plane  space  wi]l  never — let  Klein 17  say  what  he  will — 
enable  us  to  imagine  a  figure  of  pseudo-spherical  space 
projected  upon  it.  The  vocabulary18  which  brings  the 
elements  of  the  pseudo  -  sphere  into  correspondence 
with  those  of  Euclid  is  of  an  artificial  nature  :  nothing 
but  a  convention  can  assimilate  Beltrami's  geodesies  to 
the  straight  lines  of  the  plane  ;  and  his  calculi  take  us 
very  far  from  intuition  into  the  realm  of  pure  analysis, 
in  which  symbols  and  equations  still  keep  the  names 
of  lines,  surfaces,  figures  situated  on  the  superficies, 
lengths  of  lines,  displacements  of  figures,  merely  by 
virtue  of  their  literal  resemblance  to  the  cases  which 
directly  recall  these  intuitive  forms.19  The  geometrician 
may  be  driven  to  reduce  the  entities  of  his  geometry 
to  certain  analytical  properties  which  can  be  expressed 
in  algebraic  language,  assuming  as  their  definition 
the  fact  of  correspondence  to  certain  equations ;  but 
he  thus  renounces  the  intuitive  form  of  the  figures,  whose 
equations  merely  express  certain  abstract  relations ; 
if  these  relations  be  transformed,  he  neither  can  nor  may 
assert  that  his  formulas  still  correspond  to  intuitive 

3.  Intuition  and  Concept  in  Geometry. — The  dispute 


between  the  empiricists  and  the  neo-Kantians  as  to 
the  possibility  of  representing  non  -  Euclidean  space 
intuitively  took  its  rise  in  the  prejudice  that  mathe- 
matical space  and  figures  can  be  the  object  of 
immediate  intuition.  It  is  obvious  that  there  thus 
arises  a  confusion  between  the  spatial  forms  of  bodies, 
as  perceived  and  represented  in  their  concreteness,  and 
the  ideal  types  conceived  by  the  mathematician.  No 
geometrical  space  or  figure,  be  it  Euclidean  or  non- 
Euclidean,  is  representable  in  the  strict  sense  of  the 
word.  The  triangle  on  which  the  mathematician  reasons 
is  not  the  triangle  which  is  drawn  on  the  paper  or 
mentally  imagined,  but  the  triangular  entity  which  he 
has  defined,  that  is  to  say,  the  concept,  not  the  intui- 
tion of  the  triangle.  The  same  may  be  said  of  space 
in  general :  perfect  continuity,  unlimited  divisibility, 
absolute  homogeneity,  the  number  of  dimensions,  the 
degree  of  curvature,  etc.,  are  conceptual  determinations 
which  may  be  formed  on  the  occasion  of  an  experience 
or  the  image  of  one,  but  were  not  given  therein  as  such. 
When  Helmholtz  affirms  that  congruence,  that  is  to  say, 
the  possibility  of  displacing  a  geometrical  figure  without 
deformation,  is  drawn  from  experience  of  mechanical 
rigidity,  he  fails  to  perceive  that  he  is  moving  in  a 
vicious  circle,  since,  in  order  to  prove  that  a  body  has 
not  changed  in  form,  we  must  have  recourse  to  measure- 
ment, which  presupposes  the  homogeneity  of  space. 
But,  if  experience  fail  to  give  us  the  figures  of  mathe- 
matical space,  may  not  these  figures  be  revealed  to  pure 
intuition  ?  Investigation,  however  accurate  it  may 
be,  of  the  mental  functions  does  not  afford  proof  of  the 
existence  of  any  such  mysterious  faculty.  The  repre- 
sentation is  subject  to  the  same  limitations  and  the  same 
inaccuracies  as  the  sensorial  perception ;  thought  alone 
with  its  concepts  can  complete  and  perfect  it  in  such 
a  way  as  to  make  it  the  starting-point  of  rigorous  de- 
ductions. Intuition,  as  such,  can  merely  give  us  some- 
thing individual  and  contingent :  the  represented  circle 
always  remains  this  or  that  particular  circle,  and  our 


observations,  or,  if  you  will,  our  mental  experiments,  on 
it  will  be  valueless  for  all  other  cases,  unless  there  be 
behind  the  intuition  the  thought  that  all  which  we 
deduce  is  derived,  not  from  the  properties  of  the  single 
figure  which  is  present  to  us,  but  from  the  characteristics 
which  it  possesses  in  common  with  others  of  the  same 
kind.  Now  a  figure  considered  in  the  abstract  as  the 
type  of  a  class  is  no  longer  an  intuition,  but  a  concept. 
The  existence  of  geometry  is  in  itself  the  inconfutable 
proof  of  the  falsity  of  nominalism  and  empiricism. 
It  is  not  true,  as  Stuart  Mill  asserts,  that  figures  existing 
in  the  thought  of  the  mathematician  are  mere  copies 
of  those  given  to  us  in  experience,  and  are  hence 
imperfect :  unless  the  ideal  type  of  the  figure  were 
present  to  our  mind,  how  could  we  judge  of  the  in- 
accuracy of  the  sensorial  data  ?  "  It  is  true  that  this 
type  cannot  be  represented ;  this  does  not,  however, 
imply  that  it  cannot  be  thought :  the  mistake  made  by 
Stuart  Mill,  and  earlier  by  Berkeley  and  Hume,  lies  in 
the  identification  of  thought  and  representation. 

4.  Tannery  on  the  Contingency  of  Geometrical  Truths. 
— If,  then,  we  cannot  speak  of  pure  a  priori  intuition, 
because  the  exactness  of  mathematical  concepts  passes 
the  bounds  of  imagination,  is  there  nothing  of  an  a 
priori  nature  about  space  and  mathematics  ?  Is  the 
possibility  of  constructing  different  systems  of  geometry 
an  argument  against  this  a-priority  ?  Must  we  not 
rather  modify  the  conception  of  the  a  priori,  and  define 
its  limits  more  exactly  ?  Tannery  has  chosen  the 
former  alternative,  affirming  that  geometry  contains 
nothing  necessary :  Riemann's  analyses  and  later 
studies  have  proved  that  the  mathematical  concept  of 
space  is  formed  by  associating  different  notions,  which 
are  absolutely  distinct  from  one  another  (magnitude, 
continuity,  dimension,  triplicity,  measure,  identity  of  the 
unit  of  measurement  in  different  dimensions,  distance, 
analytical  law  relative  to  the  distance  of  two  points, 
etc.),  and  that  there  is  nothing  subjectively  necessary 
in  the  association  of  these  notions.  Tannery  considers 


that  there  is  no  doubt  that  the  laws  of  our  thought  are 
at  work  in  the  construction  of  these  concepts,  but  they 
do  not  help  to  determine  in  a  necessary  way  their 
associative  links,  which  may  be  inverted,  ordered  and 
connected  in  every  possible  way,  without  going  beyond 
the  bounds  of  logic.  Every  proposition  on  space  is  then 
subjectively  contingent,  and  in  no  way  different  in  this 
respect  from  the  other  propositions  which  formulate 
the  laws  of  external  phenomena.21 

5.  The  General  Geometry  of  Calinon  and  Lechalas.— 
Others,  while  recognising  the  impossibility  of  defending 
Kant's  position,  hold  that  though  the  geometry  of 
Euclidean  space  may  not  be  a  priori,  the  a-priority  of  a 
more  general  geometry  should  be  granted.22  This  thesis, 
which  was,  as  we  have  seen,  propounded  by  Helmholtz, 
who  had  confined  the  characteristic  of  a-priority  to  this 
more  general  geometry,  only  leaving  to  experience  the 
task  of  selecting  the  series  of  axioms  which  are  valid  for 
our  space,  has  been  taken  up  again  and  developed  by 
Calinon,23  who  has  elaborated  the  essential  definitions 
capable  of  serving  as  the  basis  of  a  geometry  of  three- 
dimensional  spaces,  of  which  Euclidean  geometry  would 
be  but  a  particular  instance.  Taking  these  definitions 
as  a  starting-point,  we  thus  create  by  a  series  of 
logically  deduced  theorems  a  general  geometry  depend- 
ing upon  a  parameter  whose  value  must  be  fixed  by 
experience,  not  by  thought.  This  geometry  is  a  purely 
rational  construction,  devoid  of  postulates,  based  upon 
a  priori  definitions  and  wholly  created  by  thought : 
experience  only  intervenes  later  to  act  as  a  practical 
guide  in  the  choice  of  the  parameter  best  suited  to 
transcribe  the  phenomena  of  our  experience.  Whereas 
Helmholtz  over-depreciates  the  formal  task  of  the  mind, 
reducing  it  to  a  vague  notion  devoid  of  any  particular 
space  -  relation,  and  thus  departing  very  far  from 
Kantian  idealism,  Calinon,  while  divesting  Euclidean 
geometry  of  its  a  priori  character,  leaves  the  mind  not 
only  the  power  of  forming  the  concept  of  a  space  without 
content,  but  also  that  of  creating  a  complete  geometry 


capable  of  indefinite  development.  At  first  sight  it 
would  appear  that  in  this  construction  the  fundamental 
elements  of  our  geometry  are  derived  from  rational 
notions  posited  from  the  first  with  a  series  of  necessary 
restrictions ;  in  reality,  however,  they  are  not  deduced 
but  are  the  outcome  of  the  habitual  elements  of  our 
intuition.  Calinon  presents  three-dimensional  spaces  as 
a  generalisation  of  the  surfaces  of  ordinary  geometry,  and 
derives  all  his  definitions  without  exception  by  general- 
isation or  simply  by  analogy  from  the  properties  of  the 
plane,  the  straight  line,  and  the  surface.  The  concrete 
materials  which  have  guided  thought  in  the  construction 
of  definitions  are  always  present.  "  There  are  sur- 
faces," says  Calinon,  "  such  as  the  plane  and  the  sphere, 
in  which  the  figures  can  be  moved  without  changing 
their  form ;  we  will  call  these  surfaces  identical  with 
themselves ;  in  like  manner  we  will  give  the  name  of 
spaces  identical  with  themselves  to  those  spaces  in 
which  figures  can  be  displaced  without  deformation, 
as  in  Euclidean  space."  Calinon  endeavours  to  prove 
that  general  geometry,  as  defined  by  him,  is  well 
defined  and  presents  the  maximum  of  generalisation 
possible  to  the  mind  of  man  without  leaving  the  realm 
of  intuition  :  he  does  not  admit  geometries  having  more 
than  three  dimensions,  because  they  take  us  entirely 
away  from  intuition,  and  can  be  reduced  to  the  mere 
analytical  aspect  of  formulas  to  which  no  geometrical 
meaning  can  be  attached  :  since  we  have  no  idea  of  a 
figure  having  more  than  three  dimensions,  there  is  not 
only  correspondence,  but  absolute  identity,  between 
this  figure  and  the  equation  representing  it.  This 
statement  does  not,  however,  hold  good  of  the  various 
three-dimensional  spaces  of  general  geometry,  because 
these  spaces  are  either  but  little  removed  from  Euclidean 
space,  or,  if  the  difference  from  it  be  considerable,  they 
can  always  be  resolved  into  infinitely  small  elements, 
differing  very  little  from  Euclidean  elements,  so  that, 
though  we  may  not  conceive  a  space  of  this  kind  as  a 
whole,  we  can  readily  conceive  each  of  its  elements.*4 


Milhaud  s  rightly  remarks  that  this  intermediate  position 
cannot  be  accepted  ;  we  can  only  assume  two  attitudes 
with  regard  to  intuition :  we  must  either  accept  it 
in  all  its  exigencies,  or  dispense  with  it  altogether. 
Calinon,  like  Helmholtz,  aims  at  the  ideal  creation  of 
an  intuition  differing  from  our  own,  made  up  of  elements 
taken  from  Euclidean  space ;  but  this  artificial  con- 
struction has  nothing  to  do  with  true  intuition,  and 
cannot  endow  analytical  formulas  with  geometrical 
meaning.  We  may  make  a  figure  of  Euclidean  space 
correspond  to  a  certain  formula,  but  such  a  proceeding 
is  a  mere  arbitrary  convention,  which  might  be  equally 
well  applied  to  a  space  having  more  than  three  dimen- 
sions, in  contradiction  of  Calinon's  assertion.  Renouvier 
and  Broglie  have  also  drawn  attention  to  the  fact  that 
even  general  geometry  cannot  dispense  with  a  number 
of  postulates  in  its  primary  propositions,  and  Lechalas,26 
in  order  to  defend  Calinon's  thesis  against  this  objection, 
has  proved  a  series  of  theorems  on  identical  surfaces 
and  their  geodesies  without  enunciating  any  postulates  ; 
but  he  constantly  has  recourse  to  intuitive  data,  intro- 
ducing, for  instance,  in  the  course  of  the  deduction  the 
notions  of  superficies,  line,  point,  figure,  displacement, 
etc.,  without  saying  what  they  are,  and  arguing  thereon 
as  if  they  had  a  logical  meaning  and  the  methods  of 
association  were  legitimate.  Who  can  fail  to  see  that 
a  whole  series  of  postulates  is  thus  taken  for  granted  ? 
Lechalas,  on  the  contrary,  asserts  that  general  geometry 
can  be  based  solely  on  the  axioms  of  magnitude,  which 
he  regards  as  purely  analytical,  and  that  all  its  theorems 
can  be  deduced  from  them  with  the  principle  of  contra- 
diction as  the  only  criterion. 27  These  theorems  would  thus 
possess  an  apodictic  value,  although  the  space  of  our 
real  world  is  contingent  like  every  other  phenomenon. 
General  geometry,  being  devoid  of  postulates,  has  the 
universal  and  necessary  value  of  analysis,  of  which 
it  is  an  application ;  whereas  Euclidean  geometry, 
which  is  merely  a  branch  of  it,  is  based  upon  postu- 
lates of  an  essentially  synthetic  nature,  designed  to 


define  and  specify  the  particular  space  to  which  they 

6.  Criticism  of  these  Theories  :  the  a  priori  Properties 
of  Space. — The  fundamental  error  of  the  rationalistic 
construction  of  Calinon  and  Lechalas  is  the  same  as 
that  lying  at  the  root  of  Riemann's  philosophy  of  space, 
i.e.  the  alleged  possibility  of  deriving  the  determinations 
peculiar  to  space  from  pure  relations  of  magnitude.28 
Were  the  a  priori  element  reducible  only  to  the  analytical 
combination  which  can  be  deduced  from  the  general 
axioms '  of  magnitude,  we  should  merely  have  an 
algebra,  never  a  general  geometry  of  universal  and 
necessary  a  priori  validity.  Calinon  and  Lechalas 
apparently  succeed  in  constructing  their  geometry  by 
purely  rational  methods,  because  they  derive  from 
experience  and  spatial  intuition  the  constituent  elements 
of  space,  namely,  those  properties  which  distinguish  it 
from  other  magnitudes  and  which  make  geometry  a 
branch  of  science  distinct  from  a  pure  algebraic  calculus. 
If  this  content  be  eliminated  from  space,  nothing  is  left 
of  it,  and  it  is  an  arbitrary  proceeding  to  give  the  name 
of  geometry  to  the  science  which  results  therefrom. 
The  diversity  of  positions,  which  constitutes  the  quali- 
tative content  of  space,  and  is  irreducible  to  mere  rela- 
tions, is  that  which  is  empirical  in  it ;  but  if  this  hetero- 
geneity of  spatial  elements  be  a  posteriori,  space,  as 
conceived  by  the  mathematician,  is  a  priori  in  the  sense 
that  it  is  a  means  of  making  experience  intelligible. 
Homogeneity,  continuity,  and  infinity  are  a  priori 
characteristics  of  geometrical  space,  in  as  much  as  they 
represent  that  which  thought  has  infused  of  its  own 
into  the  manifold  of  positions,  filling  up  the  gaps  left 
by  experience,  and  leading  it  on  to  its  ideal  perfection  in 
order  to  satisfy  its  demand  for  rationality.  Everything 
in  space  which  is  intelligible  is  a  pure  construction  of 
thought.  Dimensions  are  not  given,  but  are  a  product 
of  the  analysis  made  by  thought  of  indistinct  spatial 
experience  in  order  to  translate  that  experience  into 
intelligible  quantitative  relations.  The  number  of 


dimensions  consequently  is  also  a  priori.  It  is  not  true 
that  it  is  only  possible  to  determine  that  number  by 
having  recourse  to  experience  ;  it  is  not,  moreover,  easy 
to  understand  how  our  hypothesis  could  be  verified 
by  experience  when  once  a  dimension  ceases  to  be  a 
datum,  and  is  taken  to  be  a  complex  of  ideal  relations 
constructed  by  thought.  If  by  the  a  priori  we  are 
to  understand  the  condition  indispensable  to  the  intel- 
ligibility of  experience,  it  is  obvious  that  we  must 
attribute  to  geometrical  space  such  a  number  of  dimen- 
sions as  is  necessary  and  sufficient  for  the  transcription 
of  our  spatial  experience  into  intelligible  terms.  Now 
no  one  will  deny  that  three  dimensions  answer  perfectly 
to  this  requirement :  one  or  two  would  not  be  enough  to 
exhaust  the  whole  content  of  our  empirical  space  ;  four 
or  more  would  be  superfluous,  since  there  are  no  spatial 
data  which  are  not  comprised  within  three-dimensional 
geometry.  If  we  posit  four  spatial  co-ordinates  instead 
of  three,  the  position  of  a  point  will  be  no  better  defined ; 
four-dimensional  space  is  not  more  extensive  than  that 
having  but  three,  so  as  to  comprise  it  within  itself  as  the 
superficies  does  the  line,  but  coincides  with  it,  however 
widely  the  analytical  description  may  differ.  Three 
dimensions  exhaust  the  whole  of  empirical  space,  nothing 
is  left  to  be  determined  by  another  dimension  ;  a  fourth 
dimension  may  then  be  excluded  a  priori,  since  it  does 
not  render  more  intelligible  any  aspect  of  our  experience, 
the  only  experience  of  which  we  can  speak,  unless  we 
propose  to  write  a  scientific  romance.  We  might  apply 
an  old  aphorism  and  say :  "  Dimensiones  non  sunt  multi- 
plicandae  praeter  necessitate™,." 

7.  Vain  Attempt  at  an  a  priori  Deduction  of  Three- 
dimensional  Space :  Cohen,  Natorp. — We  do  not  mean 
hereby  that  the  three  dimensions  of  space  can  be  deduced 
a  priori  from  a  pure  rational  exigency  :  if  thought  has 
constructed  mathematical  space,  and  has  done  so  in 
that  determinate  form,  it  is  due  to  the  fact  that  experience 
demanded  this  construction  in  order  that  it  might  be 
transcribed  in  intelligible  terms.  If  we  do  not  take  the 



special  characteristics  of  the  empirical  data  into  account, 
we  shall  not  see  why  reason  has  been  forced  to  construct 
the  category  of  space  with  just  that  number  of  dimen- 
sions. The  attempt  made  by  Natorp,29  following  in  the 
footsteps  of  Cohen,30  to  deduce  space  with  all  the  other 
determinations  of  nature  from  the  pure  activity  of 
thought  is  undoubtedly  a  failure.  In  ultimate  analysis 
Natorp's  proof  does  but  show  that  without  space  and  just 
this  form  of  space  we  could  never  attain  to  the  complete 
univocal  determination  of  the  object  of  thought.  But 
is  space  necessary  to  the  thought  of  a  completely  deter- 
mined and  individualised  existence  ?  Do  we  not  con- 
ceive the  unique  reality  of  our  consciousness,  and  of 
the  consciousness  of  others  in  its  concrete  determina- 
tion without  being  obliged  to  make  use  of  spatial  co- 
ordinates ?  The  characteristic  of  reversibility,  which 
differentiates  spatial  from  temporal  series,  is  so  far  from 
necessary  to  the  requirement  of  complete  individualisa- 
tion  that  certain  philosophers  (Royce  amongst  others) 
who,  regarding  as  the  end  of  knowledge  complete  in- 
dividuality exclusive  of  every  other  alternative  (much  as 
does  Natorp),  consider  its  principal  characteristic  to  be 
the  irreversible  process  of  time,  i.e.  a  series  developing  in 
a  single  order  in  a  determinate  sense.  The  possibility  of 
inverting  this  order,  the  abstract  homogeneity  of  space, 
which  allows  us  to  make  the  two  opposite  directions 
issuing  from  one  and  the  same  point  coincide  by  rotat- 
ing one  of  them  in  the  plane  round  this  point,  would, 
according  to  these  philosophers,  remove  us  farther  from 
univocal  determination.  Is  not  reality  sufficiently 
individualised  as  a  irreversible  series  of  moments  ? 
Why  add  to  the  single  direction  of  time  the  infinite 
multiplicity  of  directions  contained  in  the  concept  of 
space  ?  Do  we  thus  gain  in  determination  ?  I  do  not 
think  so.  Try  as  you  may,  you  will  never  succeed  in 
deriving  from  the  demand  for  an  ultimate  determination, 
which  leaves  nothing  undetermined,  the  necessity  of  an 
infinite  number  of  directions  issuing  from  a  point,  and 
of  their  connection  in  a  continuous  and  homogeneous 


system,  which  is  the  fulcrum  of  your  proof  of  the 
three-dimensional  nature  of  space.  What  Natorp 
regards  as  necessitating  a  new  dimension  is  the  logical 
exigency  of  the  continuity  of  the  transition  from  one 
direction  to  the  opposite  :  thus  the  second  dimension 
of  the  plane  is  necessary  in  order  to  allow  of  the  con- 
tinuous transition  from  one  direction  issuing  from  a  point 
to  the  opposite  direction  ;  a  third  dimension  is  necessary 
in  order  to  conceive  the  continuous  rotation  of  the  semi- 
plane  on  one  of  its  axes  in  such  a  way  as  to  come  to 
coincide  with  the  opposite  semiplane.  We  do  not  require 
more,  because  with  three  dimensions  only  the  rotation 
of  the  plane  can  be  inverted  and  the  transition  made 
continuously  from  one  direction  to  the  opposite.  Hence 
Euclidean  space  is  necessary  and  sufficient  for  the 
production  of  a  homogeneous  and  continuous  system 
of  spatial  determinations,  such  as  is  required  by  the 
concept  of  existence.31  In  this  proof  of  his  Natorp 
postulates  two  propositions  :  first,  that  one  direction 
only  developing  in  an  irreversible  order,  as,  for  example, 
the  series  of  instants  of  time,  would  suffice  for  the  uni- 
vocal  determination  of  reality ;  second,  that  opposite 
directions  are  necessary,  and  the  order  of  the  elements 
of  the  series  must  always  be  reversible,  because,  were  it 
not  so,  there  would  be  a  sudden  saltus  from  one  direction 
to  the  opposite  one,  whereas  thought  by  the  law  of 
continuity  exacts  a  gradual  transition  from  one  to  the 
other,  that  is  to  say,  a  series  of  intermediate  directions.32 
Now  with  regard  to  the  first  proposition,  we  note  that 
from  a  logical  point  of  view  an  existence  completely 
determined  in  an  irreversible  series  is  very  far  from 
inconceivable ;  if  our  thought  constructs  an  opposite 
direction,  and  other  intermediate  ones  of  all  senses, 
it  does  so  because  the  series  of  tactile,  visual,  and  kin- 
aesthetic  sensations  cannot  be  ordered  in  one  sense  only, 
and  the  data  of  sensible  experience  could  not  be  exhausted, 
much  less  understood,  with  the  temporal  direction  alone. 
Three-dimensional  space  remains  unexplained,  unless  the 
exigencies  peculiar  to  its  data,  together  with  their  special 


characteristics,  be  taken  into  account  as  well  as  the 
exigencies  of  thought.  As  to  the  second  proposition, 
it  may  be  observed  that  if  the  continuous  transition  from 
one  order  of  elements  to  the  opposite  order  were  really 
necessary  to  thought,  this  exigency  should  be  satisfied 
not  only  in  the  case  of  the  opposite  senses  of  the  plane 
with  reference  to  any  one  of  its  straight  lines,  but 
also  in  that  of  the  opposite  orders  of  three-dimensional 
space  with  reference  to  any  place  dividing  it  into  two 
parts.  In  the  case  of  space  also  it  should  be  possible 
to  conceive  a  continuous  transition  between  the  two 
opposed  senses,  a  rotation  leading  by  degrees  to  the  in- 
version of  the  order  of  the  elements  with  reference  to  the 
plane.  Now  it  is  well  known  that  in  three-dimensional 
space  rotation  of  such  a  nature  as  to  lead  to  the  coincidence 
of  symmetrical  solid  figures  is  not  always  possible. 
Must  we  conceive  a  fourth  dimension,  as  has  been  argued 
by  some  philosophers  ?  Natorp  stops  short  at  three ; 
but  in  that  case  can  opposite  orders  exist  for  thought 
without  a  continuous  transition  from  one  to  the  other  ? 
If  this  be  so,  why  not  stop  short  at  the  plane,  or  even 
at  the  straight  line  ?  The  truth  is  that  it  is  not  the  part 
of  pure  thought  to  exact  three  dimensions  and  three  only 
for  real  existence,  but  that  the  epistemological  justifica- 
tion of  such  a  determinate  number  of  dimensions  must 
be  sought  in  the  fact  that  it  is  necessary  and  sufficient 
to  exhaust  and  make  intelligible  the  series  of  sensorial 
data  with  their  characteristics  which  are  immediately 
experienced  by  us. 

8.  Impossibility  of  an  Experimental  Proof  of  Eudidean 
Geometry :  Stallo,  Poincare,  Couturat. — The  limitation 
of  the  number  of  dimensions  to  three  thus  appears  to  us 
justifiable  a  priori  as  the  only  adequate  solution  of  the 
problem  which  spatial  experience  has  set  to  thought. 
Can  the  same  be  said  of  the  postulate  of  parallels 
Most  metageometricians  are  agreed  in  affirming  that) 
experience  alone  can  decide  between  the  Euclidean  and 
non-Euclidean  systems,  a  thesis  which  has  been  subjected 
to  special  criticism  by  Stallo,  Poincare,  and  Couturat. 


Supposing,  says  Stallo,33  an  astronomer  turns  his 
telescope  on  to  a  star  in  order  to  determine  its  parallax, 
and  that  he  finds  this  parallax  to  be  of  appreci- 
ably higher  value  than  that  of  less  distant  stars ; 
supposing,  in  other  terms,  the  angle  of  intersection 
between  the  straight  lines  of  his  sight  to  differ  from  that 
required  by  the  laws  and  facts  known  to  astronomy  and 
optics  :  to  what  conclusion  will  he  come  ?  We  may 
safely  say  that  no  one  would  attempt  to  explain  this 
anomaly  of  the  parallax  by  a  pseudo  -  sphericity  of 
space  ;  he  would  rather  try  to  find  the  physical  cause 
producing  it,  like  Bradley,  who,  having  discovered 
during  the  first  half  of  the  eighteenth  century  that  the 
apparent  displacement  of  the  star  7  of  the  constella- 
tion of  the  Dragon,  due  to  the  revolution  of  the 
earth,  differed  in  direction  and  amount  from  that 
resulting  from  calculation,  was  led  after  many  hypotheses 
to  explain  this  anomaly  by  the  aberration  of  light. 
Couturat M  draws  attention  to  the  fact  that  in  astro- 
nomical triangles  the  three  vertices  are  not  accessible, 
so  that  it  is  impossible  to  measure  the  three  angles 
directly,  and,  if  one  of  them  be  calculated  by  means  of  the 
others,  the  proposition  is  postulated  which  ought  to  be 
proved.  How  are  we  to  make  sure,  then,  that  the  sides 
of  the  triangle  are  straight  lines  ?  By  means  of  the 
definition  of  the  straight  line,  in  virtue  of  which  not 
more  than  one  such  line  can  pass  through  two  given 
points  ;  this  is,  however,  an  axiom  which  permits  of 
exceptions  in  Riemann's  spherical  space,  and  still  more 
in  Klein's  elliptic  space,  and  which  Russell  regards  as 
being  of  empirical  value  only.  Those  who  maintain  that 
Euclidean  geometry  can  be  verified  by  means  of  measure- 
ment implicitly  assume  that  our  space  has  a  constant 
curvature,  and  that  our  measuring  instruments  therefore 
remain  invariable  in  their  displacement.  Now  Poincare 35 
has  proved  that  hypothetical  beings  living  in  a  non- 
isogeneous  space  would  of  necessity  be  led  to  conceive  of 
it  as  isogeneous,  because  their  measuring  instruments 
would  vary  proportionately  to  the  bodies  to  be  measured 


and  to  their  own  bodies,  and  the  relation  of  measure 
would  therefore  remain  constant.  Lechalas  tried  to 
evade  this  objection S6  by  considering  rays  issuing  from 
the  same  centre  and  falling  upon  a  rectilinear  base  at 
different  angles  :  these  rays,  which  will  meet  in  a  point 
in  isogeneous  space,  will  not  do  so  in  a  non-isogeneous 
space,  and  this  would  afford  an  empirical  criterion  by 
which  to  verify  the  isogeneity  of  space.  Couturat,  how- 
ever, does  not  regard  this  reply  as  decisive,37  because 
Lechalas  attributes  the  form  of  Euclidean  straight  lines 
to  the  second  series  of  rays,  forgetting  that  in  Poincare's 
non-isogeneous  space  the  index  of  refraction  is  inversely 
proportionate  at  every  point  to  the  absolute  temperature, 
i.e.  to  the  linear  dilatation  at  that  point.  The  luminous 
rays  will  not  then  be  rectilinear  and  can  therefore  con- 
verge until  they  meet  in  spite  of  the  deformation 
of  the  base,  since  they  in  their  turn  would  undergo  a 
deformation.  The  isogeneity  of  space  cannot  be  verified, 
because  all  measurement  presupposes  it,  by  postulat- 
ing the  constancy  of  the  unit.  The  experimental 
verification  of  the  Euclidean  axioms  thus  revolves  in  a 
vicious  circle.  Moreover,  as  was  already  pointed  out 
by  Calinon,38  we  know  only  the  tangents  of  the  lumin- 
ous rays  emitted  by  the  stars  at  the  point  where  they 
strike  our  eye ;  it  is  therefore  possible  that  the  rays 
are  not  rectilinear,  but  that  they  are  subject  to  two 
conditions :  each  of  them  must  be  determined  by  two 
points ;  all  of  those  emanating  from  the  same  star 
must,  no  matter  what  their  form  may  be,  meet  at 
a  point,  which  is  the  real  position  of  the  star,  as  if 
they  were  rectilinear.  Any  geometry  can  be  applied 
to  the  real  world  through  the  medium  of  a  suitable 
hypothesis  as  to  the  path  of  luminous  rays.  Klein89 
gives  utterance  to  a  similar  thought,  regarding,  as  he 
does,  all  forms  of  space  as  equally  compatible  with  our 
experience  :  by  far  the  larger  part  of  the  universe 
is  indeed  only  known  to  us  by  means  of  sight  or  per- 
spective, that  is  to  say,  through  its  projective  properties; 
hence  it  can  be  constructed  indifferently  in  any  one 


of  the  metrical  geometries  which  are  protectively  equi- 

Poincare40  has  subjected  the  alleged  experimental 
proof  of  Euclidean  geometry  to  further  criticism. 
Experiences  merely  teach  us  the  relations  of  bodies  to 
each  other  ;  neither  of  them  either  does  or  can  tell  us  any- 
thing about  the  relations  of  bodies  to  space  or  about  the 
mutual  relations  of  the  different  parts  of  space.  Russell 
affirms  that  dynamics  would  cease  to  be  possible  without 
Euclidean  geometry ;  now  it  is  obvious  that  if  we 
forsake  Euclid's  geometry  for  that  of  Lobatchewsky 
we  should  be  forced  to  modify  the  enunciations  of  all 
the  laws  of  dynamics,  which  could  not  exist  without  a 
language  to  express  them,  and  which  are  modified  along 
with  this  language,  but  this  does  not,  however,  imply  that 
the  verification  of  one  of  these  laws  proves  the  truth 
of  this  or  that  special  expression.  The  human  mind 
frames  with  the  help  of  its  own  resources  alone  a  system 
of  signs  or  symbols  suited  to  represent  the  system  of 
relations  which  we  term  experience  ;  and,  since  signs 
are  of  their  very  nature  conventional,  it  can  construct 
an  infinite  number  of  equivalent  systems,  which  can  be 
translated  into  one  another,  just  like  different  languages. 
Euclidean  geometry  is  but  one  of  countless  others  which 
we  might  equally  well  have  chosen,  and  we  give  it  the 
preference,  not  because  it  gives  a  more  faithful  reflection 
of  objective  reality  and  is  imposed  on  us  by  experience, 
but  because  we  regard  it  as  a  more  convenient  language 
than  the  rest.41  Geometrical  axioms  are  neither 
synthetic  a  priori  judgments  nor  experimental  facts, 
but  conventions.  The  choice  we  make  among  all 
possible  conventions  is  guided  by  experimental  facts, 
but  it  is  free  and  is  limited  by  nothing  but  the  necessity 
of  avoiding  all  contradiction.  Thus  the  postulates  can 
be  rigorously  true,  though  the  experimental  laws  which 
have  determined  their  adoption  are  of  a  merely  approxi- 
mative nature.  In  other  words,  the  axioms  of  geometry 
are  but  disguised  definitions  ;  hence  there  is  no  sense 
in  asking  whether  Euclidean  geometry  be  true  or  false. 


Such  a  question  amounts  to  the  same  thing  as  asking 
whether  the  metric  system  be  true  and  the  older 
measures  false  :  one  geometry  cannot  be  possessed  of 
a  greater  degree  of  truth  than  another  ;  it  can  merely 
be  more  convenient,  because  it  is  simpler.42  Euclidean 
and  non-Euclidean  geometry  rest  upon  a  common  basis, 
i.e.  a  continuum  of  three  dimensions,  which  is  the  same 
for  all,  and  differs  only  as  to  the  figures  delineated 
therein,  and  as  to  the  method  of  measuring  them 
adopted.43  Either  of  the  two  spaces  may  then  issue 
from  this  amorphous  continuum,  just  as  either  a  straight 
line  or  a  circle  may  be  drawn  upon  a  blank  sheet  of  paper 
at  will.  We  are  acquainted  in  space  with  rectilinear 
triangles  in  which  the  sum  of  the  angles  is  equal  to  two 
right  angles,  but  we  also  know  curvilinear  triangles  in 
which  the  sum  of  the  angles  is  less  than  two  right 
angles  ;  if  we  call  the  sides  of  the  first  straight  lines,  we 
are  adopting  Euclidean  geometry ;  if  we  apply  that  name 
to  those  of  the  second,  our  geometry  is  non-Euclidean. 
Neither  experience,  nor  intuition,  which  may  equally 
well  represent  the  Euclidean  and  the  non-Euclidean 
triangle,  can  decide  the  question  ;  the  Euclidean  straight 
line  is  merely  preferable  to  the  rest,  because  it  differs 
but  little  from  certain  natural  objects  from  which  the 
non-Euclidean  straight  line  differs  very  considerably. 
In  like  manner  we  confine  the  number  of  dimensions 
to  three  for  reasons  of  a  practical  order,  which  have 
worked  for  centuries  in  the  psychological  genesis  of 
space  in  such  a  way  as  to  constitute  a  mental  habit. 
We  do  not  know  from  experience  that  space  has  only 
three  dimensions,  it  is  merely  more  convenient  to 
attribute  three  to  it,  because  our  sensations  are  thus 
more  simply  ordered.  The  number  of  dimensions  is  not 
then  an  a  priori  necessity,  but  is  suggested  by  practical 
reasons :  usually  we  place  the  muscular  sensations 
imparted  to  us  by  movements  of  accommodation  and 
convergence  in  the  same  series,  because  the  members 
thereof  correspond  exactly  to  one  another,  so  that  they 
can  be  regarded  as  depending  upon  a  single  variable ; 


but  were  we  to  distinguish  between  the  sensations  of 
convergence  and  those  of  adjustment,  we  should  have  a 
four-dimensional  space ;  if  in  touch  we  were  to  dis- 
tinguish between  the  various  series  of  sensations  to  which 
movements  of  different  kinds  give  rise,  we  should  con- 
struct a  space  having  as  many  dimensions  as  there  are 
muscles.44  It  is  not  beyond  the  bounds  of  possibility 
to  conceive  of  physical  phenomena  in  a  space  having 
more  than  three  dimensions :  Hertz's  system  of  mechanics 
gives  us  an  example.  Hertz,  in  order  to  eliminate  the 
idea  of  force,  supposed  visible  material  points  to  be 
subject  to  certain  invisible  bonds  connecting  them  with 
other  invisible  points,  and  that  which  we  term  force  to  be 
the  effect  of  these  ties.  Suppose  a  system  to  be  formed 
of  n  material  points  either  visible  or  invisible  :  we  shall 
then  have  3n  co-ordinates  in  three-dimensional  space ; 
Hertz,  however,  thinks  it  would  be  more  convenient  to 
regard  them  as  the  co-ordinates  of  a  single  point  in  a 
space  having  3n  dimensions.  The  ties  of  which  we  have 
already  spoken  will  force  this  point  to  remain  on  a 
superficies  (having  any  number  of  dimensions  smaller 
than  3w),  and  in  order  to  pass  from  one  point  to  another 
on  this  surface  it  will  always  take  the  shortest  way. 
The  whole  of  mechanical  science  can  thus  be  simply 
and  elegantly  summed  up  with  the  help  of  this  single 
principle.  Be  the  value  of  this  hypothesis  what  it  may, 
the  fact  that  Hertz  was  able  to  conceive  it  as  more 
convenient  than  the  habitual  hypothesis  proves  that 
three-dimensional  space  is  not  irresistibly  imposed  upon 

Russell,46  in  reply  to  the  criticisms  of  Couturat  and 
Poincare,  has  insisted  upon  the  possibility  of  an  experi- 
mental proof  of  Euclidean  geometry.  It  is  commonly 
stated  that  the  inaccuracy  of  the  measurement  of 
astronomical  angles  leaves  the  question  undecided ;  it 
is  not,  however,  essential  to  our  purpose  that  the  line 
with  which  we  experiment  should  be  absolutely  straight 
or  that  the  bodies  should  be  absolutely  rigid ;  it  will 
suffice  to  know  the  limit  within  which  the  lines  deviate 


from  the  straight  and  the  bodies  from  absolute  rigidity, 
the  bounds  within  which  the  spatial  constant  must  neces- 
sarily be  found.  Even  if  a  formal  demonstration  be  not 
possible,  our  proof  will  suffice  from  an  empirical  point  of 
view.  We  are  unable  to  determine  accurately  that  our 
space  is  Euclidean,  just  as  we  are  unable  to  give  a  rigor- 
ous proof  of  the  law  of  gravitation  ;  on  the  other  hand, 
however,  no  theoretical  limit  can  be  assigned  to  the  degree 
of  approximation  of  which  such  a  proof  is  susceptible. 
In  short,  the  Euclidean  axioms  are  susceptible  of 
empirical  proof  in  the  same  sense  as  other  scientific  laws, 
that  is  to  say,  it  can  be  shown  that  they  constitute  the 
simplest  hypothesis  for  the  explanation  of  facts,  although 
it  is  possible  to  imagine  other  facts  of  which  a  slightly 
non-Euclidean  space  would  afford  a  simpler  explanation. 
The  empirical  nature  of  these  axioms  does  not,  however, 
imply  that  they  may  any  moment  become  false  or  that 
the  fourth  dimension  may  be  discovered  in  some  other 
country  or  planet :  be  the  nature  of  space  what  it  may, 
we  cannot  admit  that  it  is  capable  of  varying  with  time. 
It  is  in  the  last  analysis  permissible  to  doubt  whether 
space  be  three-dimensional,  but  only  in  so  far  as  we 
throw  doubt  upon  truths  of  fact  and  the  data  of  the 
senses.  Finally,  the  Euclidean  axioms  are  not  pro- 
positions relative  to  our  sensibility,  imposed  by  a  priori 
intuition,  but  are  as  certain  as  any  truth  of  fact  can  be. 
9.  Euclidean  Geometry  more  Rationally  Complete 
than  the  Rest. — Russell's  thesis 47  does  not  appear  to  me 
wholly  acceptable  because  it  fails  to  explain  how  human 
thought  came  to  ascribe  a  greater  degree  of  evidence  to 
the  axioms  of  Euclid  than  to  the  laws  derived  from 
experience.  Is  this  a  mere  illusion  ?  Or  is  it  based 
upon  a  characteristic  peculiar  to  the  science  of  space? 
In  my  opinion  the  latter  alternative  should  be  chosen, 
and  we  must  therefore  determine  wherein  lies  the  dis- 
tinctive character  of  geometrical  truths.  We  have 
already  seen  that  pure  intuition  cannot  act  as  the  basis 
of  the  Euclidean  axioms,  because  no  such  faculty  exists 
1  among  the  functions  of  consciousness.  Strive  as  we 


may  to  extend  and  correct  our  representation,  we 
remain  very  far  from  the  perfection  and  ideal  limits  of 
the  mathematician :  it  is  not  possible  to  imagine  an 
infinite  straight  line  or  two  parallel  lines  in  their  geo- 
metrical precision.  If  we  are  unable  to  prove  the  axioms 
by  means  of  perception,  still  less  can  we  do  so  by  means 
of  imagination  which  is  subject  to  the  same  limits  of  the 
threshold  and  the  same  errors  as  perception;  because, 
whereas  in  external  measurements  exact  instruments 
afford  us  the  means  of  reducing  the  errors  of  sensorial 
data,  and  of  transcending  limits,  and  thus  approximat- 
ing to  the  ideal  set  up  by  mathematics,  the  psycho  - 
physiological  structure  of  the  organism  sets  insuperable 
bounds  to  our  imagination  of  geometrical  forms  and 
dimensions.  Thought  alone  with  its  concepts  is  capable 
not  only  of  transcending  the  limits  of  subjective 
representation,  but  of  being  more  accurate  than  any 
measurement  made  with  objective  instruments.  The 
character  of  necessity  and  universality  pertaining  to 
geometrical  concepts  is  derived  from  the  ideal  nature  of 
those  concepts.  But,  we  might  here  observe,  does  not 
non-Euclidean  geometry  contradict  Euclidean  ?  Is  it 
not  then  absurd  to  pretend  that  they  are  both  equally 
necessary  and  universal  ?  The  contradiction  is,  in  my 
opinion,  only  apparent,  and  arises  from  an  abuse  of 
terminology.  Euclid's  triangle  is  not  the  same  figure 
as  that  of  Lobatchewsky  or  Biemann,  hence  it  is  not 
surprising  that  that  which  can  be  proved  of  the  one 
should  not  be  applicable  to  the  other.  If  you  call  that 
a  straight  line  which  has  hitherto  been  called  a  curve, 
it  is  only  natural  that  you  should  arrive  at  different 
conclusions  ;  just  as  the  anatomy  of  the  dog  would 
cease  to  be  the  same  if  by  this  name  you  understand 
another  animal  such  as  the  horse.  If  by  a  straight  line 
we  understand  that  defined  by  Euclid  and  by  a  triangle 
the  rectilinear  triangle,  the  sum  of  the  internal  angles 
is  equal  to  two  right  angles  ;  this  does  not,  however, 
prevent  the  sum  of  the  angles  of  a  triangle  whose 
sides  are  not  straight,  but  correspond  to  what  Euclid 


PT.  n 

calls  a  curve,  being  greater  or  less  than  two  right 

Euclidean  geometry  does  not  exclude  these  curvi- 
linear triangles,  but  affirms  with  justice  that  they  are 
not  the  only  ones  in  existence,  and  that  it  is  possible 
to  conceive  of  others  the  sum  of  whose  angles  is  equal 
to  two  right  angles.  Such  an  assumption  is  not  only 
allowable  but  necessary,  unless  we  would  cause  an 
arbitrary  interruption  of  the  continuity  of  the  process 
of  thought.  Euchd's  rectilinear  triangle  may  be  regarded 
as  the  limit  of  the  series  of  the  triangles  of  the  so-called 
spherical  spaces  and  of  the  series  of  triangles  of  the 
pseudo-sphere,  in  which  the  degree  of  curvature  of  the 
sides  gradually  decreases.  There  is  no  sense  in  asking 
whether  this  limit  reatty  exists,  that  is  to  say,  whether  it 
exists  in  empirical  space  :  the  essential  thing  is  that  it 
shall  exist  ideally,  and  that  it  shall  be  impossible  to  avoid 
conceiving  it,  if  we  would  not  interrupt  the  continuous 
transition  from  a  positive  to  a  negative  degree  of 
curvature.  Little  by  little,  as  the  degree  of  curvature 
decreases,  the  sum  of  the  angles  will  approach  more  and 
more  closely  to  two  right  angles  and  will  be  identical 
therewith  in  the  passage  to  the  limit.  Though  the 
various  systems  of  geometry  may  reach  different  con- 
clusions, they  do  not  contradict  one  another,  because 
their  axioms  and  theorems  refer  to  different  figures. 
The  concept  of  three-dimensional  space  in  its  infinite 
homogeneity  remains  unchanged  in  them  all,  the  only 
things  which  undergo  change  are  the  figures  drawn 
in  space  and  depending  upon  the  value  of  the  spatial 
constant.  The  difference  between  the  three  geometries 
may  be  stated  as  follows  :  whereas  Euclidean  geometry 
does  not  exclude  the  existence  of  triangles  other  than 
the  rectilinear  triangle,  but  merely  distinguishes  them 
and  calls  them  by  another  name,  the  two  other  geometries 
banish  true  rectilinear  triangles  and  take  nothing  but 
curvilinear  triangles  into  consideration.  They  are  not 
false,  but  defective  in  so  far  as  they  are  partial,  they 
fail,  that  is  to  say,  to  exhaust  all  the  figures  and  rela- 


tions  of  figures  which  can  be  conceived  in  ideal  space.48 
Euclidean  geometry  hence  appears  to  us  to  be  the  most 
complete,  in  as  much  as  it  can  transcribe  the  figures  of 
the  other  geometries  into  terms  of  its  own  figures  by 
means  of  a  mere  change  of  language  ;  whereas  the  other 
two,  excluding  as  they  do  from  the  first  by  means  of  an 
artificial  hypothesis  the  possibility  of  certain  figures, 
give  us  but  a  fragment  of  three-dimensional  geometrical 
space.  Thus  if  we  are  asked :  Which  of  the  three 
geometries  is  true  ?  we  have  no  hesitation  in  replying 
that  all  three  are  true,  in  as  much  as  they  refer  to 
different  figures  ;  at  the  same  time,  from  the  episte- 
mological  point  of  view,  we  feel  justified  in  stating  that 
Euclidean  geometry  more  nearly  fulfils  the  demand  for 
the  complete  intelligibility  of  space  than  the  others  do, 
since  it  alone  is  capable  of  exhausting  the  whole  of  its 
ideal  existence. 

Though  figures  and  geometrical  space  exist  only 
ideally  in  thought,  they  are  not  mere  fictions  or  convenient 
signs  upon  which  no  judgment  of  truth  or  falsehood  can 
be  passed,  as  Poincare  asserts.  Even  with  reference  to 
applied  geometry  it  is  certain  that  if  no  figure  fulfils 
perfectly  the  conditions  laid  down  by  mathematicians, 
an  indefinite  approximation  to  this  ideal  type  is  possible, 
and  we  observe  that  the  more  nearly  these  conditions 
are  verified,  the  more  perfectly  do  we  encounter  the  pro- 
perties which  are  of  necessity  connected  therewith  in 
our  thought.49  We  should  not  find  our  geometry  more 
convenient  than  any  other  were  the  space  of  experience 
not  more  naturally  transcribed  into  certain  conceptual 
terms  than  into  others  :  experience  is  not  absolutely 
indifferent,  it  is  not  capable  of  assuming  any  spatial 
order  whatsoever,  it  rather  suggests  to  thought  the 
direction  in  which  the  process  of  idealisation  should  be 
accomplished  ;  it  shows  us,  for  instance,  that  the  more 
nearly  the  degree  of  curvature  of  the  sides  of  the  triangle 
approximates  to  zero,  the  more  closely  will  the  sum  of 
the  angles  approximate  to  two  right  angles,  so  that, 
continuing  conceptually  the  process  which  in  experience 


PT.  n 

and  intuition  can  be  pursued  only  up  to  a  certain 
point,  we  conclude  by  passing  to  the  limit  that  in  the 
rectilinear  triangle  the  sum  of  the  internal  angles  is  equal 
to  two  right  angles.  This  conclusion  of  ours  is  legitimate, 
because  the  empirical  data  are  arranged  in  regular  series, 
which  point  out  to  us  the  road  we  ought  to  take,  and 
thought,  once  started  on  this  road,  arrives  at  the  ideal 
limit  by  a  law  inherent  in  its  very  nature.  The  concept 
which  results  therefrom  with  all  its  properties  is  not  a 
fiction  depending  upon  our  caprice,  but  rather  the  one 
and  only  and  necessary  conclusion  at  which  it  is  possible 
to  arrive,  given  those  empirical  or  intuitive  data,  and 
given  the  nature  of  our  thought ;  in  this  way  alone  is 
it  possible  to  make  the  data  of  experience  intelligible, 
by  a  transformation  of  empirical  into  ideal  space.  The 
possibility  of  arriving  within  certain  limits  at  various 
systems  of  geometry  is  due  to  the  fact  that  one  and  the 
same  order  of  concepts  can  be  translated  into  different 
languages,  which  rob  science  of  none  of  its  universal 
value,  unless  we  would  by  an  absurd  nominalism 
identify  the  concept  with  the  symbol  expressing  it.  Is 
not  the  possibility  of  translating  one  system  of  signs 
into  another,  and  non- Euclidean  geometries  into 
Euclidean  terms  and  vice  versa,  as  Poincare  himself 
maintains,  a  proof  that  equivalent  symbols  express  one 
and  the  same  concept  ?  A  dictionary  is  only  possible 
when  the  different  terms  correspond  to  the  same  idea 
which  is  thought  universally  by  all  men,  though  they 
give  expression  to  it  in  different  ways.  In  like  manner 
the  system  of  analytical  signs  and  their  relations  is 
capable  of  infinite  variations,  because  it  depends  upon 
certain  conventions  ;  this  does  not,  however,  change  the 
concept  of  geometrical  space,  which  is  universally  recog- 
nised, because  it  is  the  only  one  which  meets  the  demand 
for  perfect  intelligibility. 


1  A  complete  bibliography  of  the  works  on  these  new  geometrical 
speculations  has  been  published  by  Halstead  ("  Bibliography  of  Hyperspace 


and  non-Euclidean  Geometry,"  American  Journal  of  Mathematics,  vol.  i. 
p.  261  ff.  ;  voL  ii.  p.  65  ff.).  For  the  history  of  non-Euclidean  geometry 
see  Klein,  Vorlesungen  uber  nicht  -  euclidischen  Geometrie  (Gottingen, 
1893) ;  Russell,  An  Essay  on  the  Foundations  of  Oeometry  (Cambridge  and 
London,  1897). 

8  For  the  history  of  these  attempts,  of  which  that  of  Legendre  in  1833 
was  the  last,  see  Stackel  and  Engel,  Die  Theorie  der  Parallellinien  von 
Euclid  bis  auf  Gauss  (Leipzig,  Teubner,  1895). 

*  "  Disquisitiones  generates  circa  seriem  infinitam,"  Comm.  recent. 
Soc.  GStt.  2  (1811-13);  "Theoria  residuorum  biquadraticorum,"  ibid.  7 

4  Lobatschewsky  first  published  his  results  in  Russian  in  the  Proceedings 
of  the  University  of  Kazan  (1829-30),  but  they  remained  unknown  until 
he  translated  them  into  French :  "  Geometrie  imaginaire,"  Journal  de 
Crelle  (1837),  voL  xvii. 

s  His  results  first  appeared  as  an  appendix  to  a  work  of  his  father's : 
Appendix,  scientiam  spatii  absolute  veram  exhibens,  a  veritate  aut  falsitate 
axiomatis  XI.  Euclidei  (a  priori  haud  unquam  decidenda)  independenteni  ; 
adiecta  ad  casum  falsitatis  quadratura  circuli  geometrica  (translated  into 
French  by  Hougl  in  1868,  repubUshed  by  Hermann,  Paris,  1896). 

6  The  method  had  been  suggested  almost  a  century  previously  by  the 
Italian  Saccheri,  whose  work,  Euclides  ab  omni  naevo  vindicatus  (Mediolani, 
1733),  remained  unknown  till  Beltrami  discovered  it. 

7  "  Uber  die  Hypothesen,  welche  der  Geometrie  zu  Grande  liegen." 
This  dissertation,  which  was  read  by  Riemann  before  the  faculty  of  philo- 
sophy of  the  University  of  Gottingen,  was  published  after  the  death  of 
the  author  in  1866  (Abhand.  d.  Kgl.  Gesellschaft  der  Wissenschafl  zu  Got- 
tingen, voL  xiii.  p.  133  ff.). 

8  Note  that  the  curvature  of  an  w-dimensional  manifold  is  a  purely 
analytical  expression  having  a  merely  symbolic  affinity  with  ordinary 
curvature.     Russell,  in  order  to  avoid  misunderstanding,  makes  use  of  the 
term  "  space-constant." 

9  Klein  calls  these  three  species  of  space  elliptic,  parabolic,  and  hyper- 
bolic   ("Uber   die    sogenannte   nicht  -  euclidischen    Geometrie,"    Mathe- 
matische  Annalen,  vol.  iv.  p.  577).     Klein's  elliptical  space  is  not,  however, 
absolutely  identical  with  spherical  space,  since  while  in  the  latter  the 
geodesic  lines  may  have  two  points  in  common,  they  cannot  have  more 
than  one  point  of  intersection  in  elliptic  space. 

10  "  Uber  die  Thatsachen,  die  der  Geometrie  zu  Grande  liegen,"  Nach- 
richten    der    Kgl.   Gesellschaft  der   Wissenschaft  zu  Gottingen  (3  giugno, 

11  Cp.  his  polemic  with  Land  in  Mind,  vols.  ii.  and  iii. 

11  "  Teoria  fondamentale  degli  spazi  di  curvatura  costante,"  Annali 
di  mathematica,  voL  ii.  (1868-69);  "  Saggio  d'  interpretazione  della 
geometria  non-euclidea,"  Giornale  di  matematica,  voL  vi.  (1868). 

13  Vortrdge  und  Reden,  voL  ii.  p.  237. 

14  "  Los  Axiomes  geometriques,"  Revue  scientifique  (June  1877). 
16  Mind,  voL  ii.  p.  45. 

18  La  Matiere  et  la  physique  moderne,  p.  191  ff. 

"  Op.  cit.  p.  573. 

18  Klein,  Poincare,  and  Lie  have  constructed  analytical  developments 
which  contain  the  series  of  theorems  of  the  three  systems  of  geometry 
corresponding  to  the  three  different  hypotheses.  A  special  vocabulary 
has  been  formed  allowing  of  the  translation  of  the  enunciations  of  non- 
Euclidean  geometry  into  Euclidean  terms. 


19  Milhaud,  Essai  sur  les  conditions  et  les  limites  de  la  certitude  logique, 
p.  167. 

80  Pasch  (Neuere  Geometric,  Leipzig,  1882)  endeavoured  to  construct 
a  geometry  by  strictly  empirical  methods,  maintaining  the  object  of  this 
science  to  be  not  types  of  ideal  figures,  but  things  themselves  in  their 
material  form  !  Thus  he  regards  a  point  as  a  corpuscle  which  cannot  be 
further  divided  into  parts  within  the  limits  of  our  observation  !  Even 
Pasch,  however,  is  forced  to  abandon  the  empirical  method  when,  for  instance, 
he  assumes  the  penetrability  of  solids,  which  is  not  a  matter  of  experience, 
and  the  motion  of  them  without  deformation,  as  he  does  in  the  definition 
of  the  congruence  of  two  figures.  Of  a  more  moderate  order  is  the  empiri- 
cism of  Freycinet,  De  ^experience  en  geometrie  (Paris,  1903),  who,  while 
maintaining  that  geometrical  axioms  are  experimental  truths,  resulting 
from  observation  of  the  outer  world,  yet  introduces  a  process  of  purification 
and  idealisation. 

21  Revue  philosophique,  voL  iii.  p.  574. 

"  It  should  be  remembered  in  this  connection  that  Kant  himself 
conceived  the  idea  of  a  general  geometry :  "  Eine  Wissenschaft  von  alien 
diesen  moglichen  Raumsarten  ware  unfehlbar  die  hochste  Geometrie, 
die  ein  endlicher  Verstand  unternehmen  konnte,"  Gedanken  von  der 
wahren  Schdtzung  der  kbendigen  Krafte  (1747),  p.  10. 

28  "  Les  Espaces  geometriques,"  Revue  philosophique  (1889,  1891),  2 ; 
"  Sur  Pindetermination  geometrique  de  Punivers,"  ibid.  (1893),  2. 

u  "  Les  Espaces  geometriques,"  Revue  philosophique,  voL  xxxii. 
p.  375. 

25  Op.  cit.  p.  192. 

26  Introduction  a  la  geometrie  generate  (Paris,  1904) ;  Etude  sur  FEspace 
et  le  temps,  2nd  ed.  (Paris,  1909),  p.  68  ff. 

27  Veronese  must  be  credited  with  having  recognised  that  in  order  to 
speak  of  a  geometry  with  more  dimensions  it  will  not  suffice  to  prove  that 
it  is  possible  to  find  an  analytic  expression  for  it,  but  that  it  is  also 
necessary  to  show  that  we  are  dealing  with  real  true  geometrical  beings. 
He  therefore  endeavours  to  construct  spaces  having  more  than  three 
dimensions  with  the  help  of  the  ordinary  intuitive  elements.     Given  space 
of  three  dimensions  and  a  point  outside  it,  he  constructs,  e.g.,  space  of  four 
dimensions,  and  the  others  analogously  by  the  synthetic  method.     This, 
of  course,  presupposes  the  conceivability  of  a  point  external  to  our  space, 
which  is  decidedly  problematic,  since,  whatever  efforts  we  make,  the  point 
thought  of  will  always  remain  in  three-dimensional  space. 

28  The  same  error  will  be  found  in  Erdmann  (Axiome  der  Geometrie, 
1877),  who,  like  Riemann,  claims  to  deduce  space  from  the  concept  of 
magnitude.     In  order  to  define  space  as  magnitude  he  starts  from  its  two 
most  obvious  properties,  continuity  and  the  three  dimensions ;   but,  since 
these  two  properties  are  also,  according  to  Erdmann,  common  to  the 
manifolds  of  sounds  and  colours,  to  distinguish  space  from  these  manifolds 
it  is  necessary  to  add  that  in  space,  though  not  in  sounds  and  colours,  the 
dimensions  are  homogeneous  and  permutable.     In  the  more  general  case 
the  manifold  is  n  times  determined  (»-bestimmt) ;  in  space  it  is  n  times 
extended  (n-ausgedehnt). 

29  System   der  Philosophic,  pt.   i.,    "Logik  der  neuen  Erkenntnis" 
(Berlin,  1902),  p.  162  ff. 

80  Die  logischen  Grundlagen  der  exakten  Wissenschaflen  (Leipzig,  1910), 
p.  303  ff. 

81  Op.  cit.  p.  306  ff. 

82  Op.  cit.  p.  326. 


»  Op.  cit.  pp.  179-181. 

84  Revue  de  metaphysique  et  de  morale  (May  1898),  p.  371  S. 

38  Revue  generate  des  sciences  pures  et  appliques  (January  30,  1892). 

38  fitudes  sur  Fespace  et  le  temps,  2nd  ed.  pp.  181-197. 

37  Revue  de  metaphysique  et  de  morale,  voL  iv.  (1896),  p.  648. 

38  "  L'Indetermination  geometrique  de  1'univers,"  Revue  philosophique 
(1893),  vol.  xxxvi.  pp.  595-607. 

39  Zur  ersten  Verteilung  des  Lobatchewsky  Preises,  p.  20. 

40  "  Des  Fondaments  de  la  geometric  a  propos  du  livre  de  M.  Russell," 
Revue  de  met.  et  de  mor.,  p.  251  ff. ;  "  Reponse  a  M.  Russell,"  ibid.  p.  79 
(January  1900). 

41  Science  et  hypothese,  p.  65  ff. 

42  Ibid.  p.  90  ff. 

43  La  Valeur  de  la  science,  p.  61. 

44  Science  et  hypothese,  p.  72  ff.  ;  La  Valeur  de  la  science,  p.  103  ff. 
48  La  Valeur  de  la  science,  p.  126  ff. 

46  "  Les  Axiomes  propres  a  Euclide  sont-ils  empiriques  ?  "  Revue  de 
met.  et  de  mor.  (November  1898),  p.  760 ;   "  Sur  les  axiomes  de  la  geo- 
metrie, ibid.  (November  1899),  p.  685  ff. 

47  Note  that  Russell  is  here  speaking  of  applied  geometry  ;  in  the  next 
chapter  we  shall  see  what  view  he  takes  of  pure  geometry. 

48  The  non-Euclidean  systems  of  geometry  exclude,  for  instance,  the 
possibility  of  similar  figures.     Delbceuf  regards  this  as  the  main  argument 
against  non-Euclidean  geometry,  since  the  impossibility  of  enlarging  the 
figure  without  changing  the  form  thereof  appears  to  him  to  contradict  the 
perfect  homogeneity  of  space  ("  L'ancienne  et  les  nouvelles  geometries," 
Revue  philosophique,  voL  xxxvii.  p.  380  ff.  ;   cp.  also  Megamicros,  ou  les 
effete  sensibles  d?une  reduction  proportionnelle  des  dimensions  de  Vunivers 
(Paris,  Alcan,  1893). 

49  Poincare's  objection  that  it  is  impossible  to  separate  in  the  experi- 
ment that  which  is  due  to  physical  actions  from  that  which  depends  upon 
the  special  structure  of  space  is  valueless,  since  we  can  cause  the  spatial 
conditions  to  vary  while  keeping  the  physical  conditions  unchanged,  and 
vice  versa,  thus  effecting  a  relative  separation  between  the  effects  of  the 
one  and  those  of  the  other. 



1 .  Fusion  of  Logic  with  Mathematics  towards  the  Middle 
of  the  Nineteenth  Century.  —  Until  the  middle  of  the 
nineteenth  century  mathematics  and  logic  had  remained 
apart  in  spite  of  the  attempts  made  by  Jungius  and 
Leibnitz  to  bring  them  together,1  but  during  the  second 
half  of  the  century  mathematicians  were  seized  by 
logical  scruples  unknown  to  their  predecessors,  and 
began  to  analyse  all  the  methods  of  proof,  to  verify 
the  concatenation  of  their  theorems,  to  investigate  the 
hypotheses  and  postulates  which  crept  surreptitiously 
into  their  arguments,  and  to  give  prominence  to  the 
axioms  or  principles  which  were  the  starting-point  of 
their  deductions,  and  upon  which  their  theories  depended. 
The  infinitesimal  calculus,  which  had  till  then  preserved 
something  paradoxical  and  mysterious  in  its  principles, 
found  its  strict  basis  in  the  theory  of  limits  ;  the  theory 
of  functions,  over  which  notions  of  intuitive  origin  had 
long  held  sway,  was  refined  and  deepened ;  geometry 
and  mechanics,  freed  as  far  as  possible  from  intuition, 
became  hypothetical  deductive  systems,  based  upon  a 
certain  number  of  axioms  and  postulates,  from  which 
everything  else  is  logically  deduced.  Mathematicians, 
in  laying  bare  the  foundations  upon  which  their  science 
rested,  were  thus  led  to  form  two  new  theories  which 
were  destined  to  serve  as  the  basis  of  all  others  :  the 
theory  of  assemblages  and  that  of  groups,  that  is  to 
say,  the  science  of  multiplicity  and  that  of  order. 



Moreover,  the  science  of  number  and  magnitude  began 
to  be  regarded  merely  as  a  small  division  of  a  more  far- 
reaching  science  based  upon  notions  about  which  there 
was  nothing  quantitative,  a  view  opposed  to  that  of  the 
school  of  Weierstrass,  which  claimed  to  reduce  the 
content  of  analysis  and  of  pure  mathematics  as  a  whole 
to  the  single  idea  of  number,  in  its  endeavour  to 
"  arithmeticise  mathematics,"  as  Klein  expresses  it.2 
Logic,  on  the  other  hand,  strove  to  extend  its  domain, 
which  had  previously  been  limited  to  the  relations  of  I 
inclusion  of  concepts,  and  to  discover  new  forms  of 
deduction.  Formal  logic,  borrowing  the  method  and 
symbolism  of  algebra,3  established  itself  under  the  two- 
fold form  of  the  calculus  of  classes  and  the  calculus  of 
propositions,  finding  surprising  analogies  between  these 
two  branches,  and  enlarged  its  borders  till  it  became 
a  general  logic  of  all  relations 4 ;  since,  moreover,  the 
simplest  and  most  elementary  relations  are  to  be  found  in 
mathematical  theories,  it  was  only  natural  that  it  should 
apply  itself  to  analysing  and  verifying  the  concatena- 
tion of  the  propositions,  and  to  proving  mathematical 
axioms  by  reducing  them  to  purely  logical  principles. 
Thus  the  gulf  between  logic  and  mathematics  was 
bridged  over :  the  calculus  of  classes  presented  itself 
as  the  most  elementary  part  of  the  theory  of  assem- 
blages, and  the  logic  of  relations  as  the  indispensable 
basis  of  the  theory  of  groups  and  the  theory  of  functions. 
This  fusion  of  logic  and  mathematics,  which  began 
during  the  past  century  in  the  bary-centric  calculus  of 
Mobius  (1827),  the  calculus  of  equipollences  of  Bellavitis 
(1832),inGrassmann's  theory  of  extension  and  Hamilton's 
method  of  quaternions,  became  an  accomplished  fact  in 
the  works  of  Peano,  Fieri,  Whitehead,  and  Russell. 

2.  Peano' s  Logistic  and  its  Application  to  Arithmetic 
and  the  Geometrical  Calculus. — Peano  was  not  content 
merely  to  apply  logical  symbolism  to  arithmetic,  which 
he  formulated  into  a  strict  deductive  system,5  but  also 
developed  a  geometrical  calculus,  in  which  he  makes 
use  of  the  notation  contained  in  Grassmann's  Aits- 


dehnungslehre,  a  work  which  had  hitherto  remained 
almost  unknown  owing  to  the  elevation  and  abstruseness 
of  its  concepts.6  The  geometrical  calculus  in  general 
consists  of  a  system  of  operations  carried  out  upon 
geometrical  entities,  analogous  to  those  of  algebra  on 
numbers,  and  enables  us  to  express  the  results  of  geo- 
metrical constructions  in  formulas,  to  represent  geo- 
metrical propositions  by  means  of  equations,  and  to 
substitute  a  transformation  of  equations  for  an  argument. 
This  calculus,  while  presenting  certain  analogies  with 
analytical  geometry,  differs  from  it  in  that,  whereas 
in  analytical  geometry  calculations  are  made  on  the 
numbers  which  determine  the  geometrical  entities,  in 
this  new  science  the  calculations  are  made  on  the 
entities  themselves.  Fieri,7  in  a  series  of  interesting 
articles,  has  contributed  largely  to  the  new  logical 
elaboration  of  geometry,  whose  goal  is  the  establishment 
of  an  accurate  distinction  between  primitive  and 
indefinable  geometrical  entities  and  those  derived  from 
them  by  definition,  between  the  properties  which  must 
be  postulated  and  propositions  drawn  therefrom  by 
means  of  a  pure  deductive  calculus.8 

3.  Geometry  as  a  Hypothetico  -  Deductive  System : 
Fieri. — Fieri  considers  that  geometry  in  all  its  branches 
should  be  increasingly  affirmed  and  consolidated  as  the 
study  of  a  certain  order  of  logical  relations,  shaking  off 
little  by  little  the  somewhat  feeble  bonds  between  it  and 
intuition,  and  assuming  in  consequence  the  form  of  an 
ideal  science  of  a  purely  deductive  and  abstract  order. 
From  this  point  of  view  we  are  led  to  acknowledge  with 
Pasch  that  if  geometry  is  really  to  be  a  deductive  science, 
its  arguments  must  not  depend  upon  the  intuitive 
meaning  of  geometrical  concepts,  but  must  be  based 
on  those  relations  only  which  are  imposed  on  those 
concepts  by  postulates  and  definitions.  The  primitive 
entities  of  any  deductive  system  whatsoever  (the 
geometrical  point,  for  instance)  must  lend  themselves 
to  arbitrary  interpretations  within  certain  limits 
assigned  by  the  primitive  propositions,  so  that  each 


mathematician  is  at  liberty  to  attach  what  meaning  he 
pleases  to  the  words  and  signs  representing  those  entities, 
provided  that  this  meaning  be  compatible  with  the 
general  properties  laid  down  by  the  postulates  and 
definitions.  Geometry  thus  becomes  a  hypothetical 
science  whose  object  is  not  the  space  of  experience,  but 
merely  an  assemblage  of  abstract  entities,  created  by 
our  mind,  upon  which  an  act  of  our  will  imposes 
certain  arbitrary  properties  expressed  in  the  postulates. 
Nominalism  thus  achieves  a  victory  over  the  old  realistic 
conception  of  geometry.9 

4.  Whitehead's  Universal  Algebra. — Whitehead 10  •  in 
his  universal  algebra,  which  admits  of  very  extensive 
application,  has  realised  the  idea  of  a  "  universal 
characteristic  "  conceived  by  Leibnitz.  This  universal 
algebra  embraces  not  merely  geometry  and  kinematics, 
but  also  mechanics  and  mathematical  physics,  because 
it  lends  itself  to  the  representation  of  matter  with  its 
various  qualities,  and  hence  of  all  physical  phenomena. 
The  power  and  fruitfulness  of  the  new  algorithm  are 
due  to  the  fact  that  it  shakes  off  the  yoke  of  arithmetic, 
and  freely  defines  new  combinations  having  but  a  formal 
and  partial  analogy  with  arithmetical  operations,  instead 
of  confining  itself,  as  did  analytical  geometry,  to  dis- 
covering everywhere  the  properties  of  the  addition  and 
multiplication  of  numbers,  and  admits  different  rules  of 
calculation  suited  to  every  application,  instead  of  confin- 
ing itself,  as  did  classical  algebra,  to  treating  its  symbols 
according  to  the  laws  of  numerical  calculation.  This 
algorithm  offers  immense  advantages  in  geometry, 
because,  instead  of  introducing  three  parallel  and 
simultaneous  equations  relative  to  the  three  axes,  which 
repeat  the  same  geometrical  fact,  relation,  or  construction, 
it  expresses  in  a  single  formula  the  one  fact,  no  longer 
dismembered  into  its  three  projections,  but  with  its 
nature  and  physiognomy  undef ormed  and  without  the 
intervention  of  extraneous  quantitative  concepts,  thus 
delivering  us  from  the  arbitrary  element  contained  in 
every  system  of  co-ordinates.  While  in  analytical 


geometry  the  letters  always  represent  numbers  and 
indirectly  the  magnitudes  measured  by  these  numbers, 
in  the  calculus  of  extension  the  letters  are  a  direct 
representation  of  geometrical  elements  (points,  lines, 
planes),  which  not  only  have  nothing  in  common  with 
numbers,  but  are  not  magnitudes  either  (at  least  not 
primarily),  and  the  formulas  are  a  direct  transcription 
of  geometrical  constructions.  This  allows  of  the  applica- 
tion of  the  new  algebra  to  the  geometry  of  position  and 
enables  it  to  give  us  a  faithful  translation  of  projective 
constructions  without  having  recourse  to  the  notions 
of  number  and  measure.  The  algebraic  symbols,  which 
represent  the  positions,  have  a  co-efficient  expressing 
the  intensity  of  that  point ;  and  this  intensive  magnitude, 
from  which  geometry  makes  abstraction  by  assuming  it 
to  be  always  equal  to  1,  is  of  great  use  to  mechanics  and 
physics,  since  it  makes  it  possible  to  treat  by  means  of 
universal  algebra  those  physical  qualities  of  matter 
which  are  susceptible  of  various  degrees  of  intensity. 
Thus  mathematics  is  no  longer  the  science  of  number 
and  magnitude,  but  becomes  the  science  of  all  the  types  of 
formal  and  deductive  reasoning.  That  a  certain  assem- 
blage of  objects  of  thought  should  verify  the  principles 
of  such  an  algebra  will  be  the  sufficient  condition  that 
it  should  also  of  necessity  verify  perforce  all  the  pro- 
positions derived  from  them  :  in  short,  the  starting-point 
alone  is  hypothetical,  but  once  it  has  been  verified, 
everything  else  follows  of  deductive  necessity.11 

5.  Russell  on  the  Identity  of  Logic  and  Mathematics.— 
This  work  of  the  logical  systematisation  of  mathematics 
was  completed  in  Russell's  book,12  the  aim  of  which  is 
to  prove  the  fundamental  identity  of  logic  and  mathe- 
matics, by  showing  all  mathematical  propositions  to  be 
based  upon  eight  indefinable  notions  and  twenty  un- 
demonstrable  principles,  which  are  also  the  primitive 
notions  and  principles  of  logic  itself.  Pure  mathe- 
matics thus  assumes  an  exclusively  logical  character,  and 
its  necessity  becomes  hypothetical,  depends,  that  is 
to  say,  upon  certain  conditions  ;  the  theorem  is  true  if 


such  and  such  an  hypothesis  be  true.  Russell 13  defines 
pure  mathematics  as  the  totality  of  propositions  having 
the  form,  p  implies  q,  in  which  p  and  q  are  propositions 
containing  the  same  variables,  and  containing  none 
but  logical  constants ;  that  is  to  say,  it  is  a  class 
of  formal  implications  which  are  independent  of  | 
any  and  every  content,  hence  the  paradox :  "  Mathe- 
matics is  a  science  in  which  we  never  know  what  we 
are  speaking  of,  or  whether  what  we  say  is  true."  14 
In  applied  mathematics,  which  endows  these  formal 
implications  with  a  material  content,  the  theses  of  the 
theorems  become  true  only  in  the  degree  and  measure 
in  which  their  hypotheses  are  verified  by  these  data. 
Geometry  in  so  far  as  it  refers  to  space  and  to  the  real 
world  is  the  arithmetic  of  concrete  numbers ;  that  is  to 
say,  all  its  applications  to  the  numeration  of  objects 
and  the  measuring  of  real  magnitudes  belong  to  applied 

In  order  to  reconstruct  pure  mathematics  Russell 
makes  use  of  Peano's  logistic  ;  he  begins  by  determining 
the  laws  of  the  calculus  of  propositions,  of  classes,  and 
of  relations,  which  constitute  a  logical  basis  able  to 
support  the  whole  edifice.15  If  we  take  these  elements 
as  our  starting-point,  we  can  define  all  the  other  notions 
and  prove  all  the  other  propositions  of  pure  mathematics. 
In  this  particular,  Russell 16  modifies  the  theory  of 
Peano's  school,17  which  admits  a  special  group  of 
indefinables  for  every  branch  of  mathematics ;  of  the 
three  forms  of  definition  considered  by  Peano,  nominal 
definition,  definition  by  postulates,  and  definition  by 
abstraction,  he  recognises  the  first  only.  An  object  x 
is  nominally  defined  by  an  equivalence  having  the  form 
x  =  a,  in  which  a  is  an  expression  formed  with  the  elements 
already  known.  It  is  merely  the  bestowal  of  a  new 
name,  an  abbreviation,  which  is  not  theoretically 
necessary,  however  convenient  and  practically  indis- 
pensable to  the  progress  of  science  it  may  be.  Every 
defined  sign  or  word  may  therefore  be  suppressed 
provided  that  its  value  be  substituted  for  it ;  should 


such  a  substitution  not  be  successful,  the  definition  is 
not  complete.18  Such  an  explicit  definition  is  not  always 
possible  ;  in  such  a  case,  if  we  would  define  a  complex 
of  notions,  we  must  have  recourse  to  an  assemblage  of 
relations  verified  by  it ;  but  this  group  of  postulates 
only  defines  those  entities  to  a  certain  degree,  and  may 
leave  their  value  undetermined,  like  a  system  of  equa- 
tions with  several  unknowns.  The  definition  by  ab- 
straction is  also  imperfect :  this  definition  consists  in 
stating  in  which  cases  a  mathematical  or  logical  function 
is  equal  to  itself  for  different  values  of  the  variable. 
These  forms  of  definition  can  be  but  provisional  and  must 
be  transformed  into  nominal  definitions  in  a  strictly  de- 
ductive system ;  it  should,  however,  be  borne  in  mind 
that  even  in  this  more  perfect  stage  a  definition  is  merely 
a  convention  of  language  and  must  not  therefore  be 
regarded  either  as  a  principle  or  as  a  source  of  truth  ; 
strictly  speaking,  it  is  neither  true  nor  false,  because 
the  only  thing  responsible  for  the  consequences  is  the 
existential  judgment  which  must  accompany  and  justify 
it  by  a  theorem  or  postulate  affirming  the  compatibility 
of  the  concepts  constituting  the  meaning  of  the  new 
symbol,  that  is  to  say,  the  existence  of  at  least  one 
individual  verifying  all  these  properties.19 

6.  Ordinal  and  Cardinal,  Finite  and  Infinite  Number. 
— Arithmetic  is  the  first  branch  of  pure  mathematics 
to  be  presented  to  logical  elaboration.  Weierstrass 
considers  that  the  whole  of  analysis  can  be  constructed 
with  the  idea  of  number  alone,  but  Russell,  while 
recognising  the  utility  of  the  work  performed  under  his 
influence,  since  to  it  is  due  the  exclusion  of  intuition 
from  the  domain  of  mathematics,  regards  the  reduction 
of  the  primitive  ideas  of  mathematics  to  the  concept 
of  number  alone  as  arbitrary.  In  the  theory  of  groups 
and  substitutions,20  the  essential  idea  is  that  of  order, 
hence  this  idea  too  must  be  admitted  to  be  primitive  side 
by  side  with  that  of  number.  Certain  mathematicians 
have  maintained  that  of  the  two  forms  of  numbers,  ordinal 
and  cardinal,  the  first  named  alone  is  irreducible  and 


a  priori ;  this  view,  however,  is  not  accepted  by  Russell 
and  Couturat,21  who  affirm  the  idea  of  order  to  be  less 
primitive  and  simple  than  that  of  number.  Number  ' 
may  be  defined  in  a  purely  logical  way,  by  use  of 
the  notion  of  class  alone.  Two  classes  have  the  same 
cardinal  number  when  a  univocal  and  reciprocal  corre- 
spondence can  be  established  between  their  elements, 
that  is  to  say,  a  one-to-one  relation,  or,  to  put  it  briefly, 
when  they  are  equivalent.  Each  number  defined  in  this 
way  is  regarded  as  the  name  of  a  class  :  the  class  of  the 
apostles,  for  instance,  is  one  of  the  classes  whose  number 
is  twelve  or,  in  more  common  parlance,  is  a  dozen.  In 
short  the  cardinal  number  of  a  class  u  would  be  the 
assemblage  of  the  classes  equivalent  to  u.  Thus  each  of 
the  cardinal  numbers  is  defined  independently  of  the 
others,  and  no  order  is  assigned  to  them  :  in  ultimate 
analysis  mathematical  equality  is  reducible  to  logical 
equality,  that  is  to  say,  to  the  identity  of  a  concept. 
Thus  even  arithmetical  operations  can  be  defined  without 
the  intervention  of  the  idea  of  order ;  arithmetical 
addition,  for  instance,  is  defined  by  means  of  logical 
addition  :  the  arithmetical  sum  of  two  cardinal  numbers 
a  and  6  (corresponding  to  two  classes  a  and  6)  is  the 
cardinal  number  of  the  logical  sum  of  the  classes  a 
and  b,  conditionally  on  these  classes  being  disjuncted, 
that  is  to  say,  on  their  having  no  element  in  common. 
By  means  of  the  logic  of  relations  Whitehead  has  given 
a  general  proof  of  the  associative  law  for  addition  and 
multiplication,  and  of  the  distributive  law  of  multi- 
plication in  relation  to  addition ;  he  has  defined  the 
powers  of  a  cardinal  number,  the  combinations  and 
permutations  of  any  number  of  objects  whatsoever,  and 
has  proved  the  principal  theorems  relating  to  these 
notions,  as,  for  instance,  the  generalisation  of  the 
binomial  formula.  Thus  Russell  and  Whitehead,  taking 
purely  logical  principles  as  their  starting-point,  have 
succeeded  in  giving  formal  proof  of  all  the  propositions 
of  the  theory  of  assemblages  discovered  by  Cantor, 
and  thus  in  confirming  the  logical  validity  of  this 


theory  by  divesting  it,  as  they  do,  of  any  appeal  to 

The  cardinal  definition  of  number,  given  above, 
is  preferable  to  that  of  Dedekind,22  who  begins  by 
defining  numbers  as  simple  ordinals,  which  are  supposed 
to  become  possessed  of  their  cardinal  meaning  when 
they  are  applied  to  the  enumeration  of  concrete  classes  ; 
because,  whereas  the  cardinal  definition  extends  to  all 
numbers,  finite  and  infinite  alike,  the  ordinal  definition 
is  applicable  only  to  a  part  of  them,  i.e.  to  those  which 
are  obtainable,  starting  from  0  by  repeated  additions  of 
1,  and  for  which  the  principle  complete  of  induction  is 
valid.  This  principle  is  not  a  synthetic  a  priori  principle, 
as  was  maintained  by  Poincare,23  but  merely  a  property 
characterising  finite  numbers  and  forming  part  of  their 
definition.  It  is  not  valid  of  the  transfinite  classes  defined 
by  Cantor,24  as  those  assemblages  which  are  equivalent  to  a 
proper  part  of  themselves.  The  class  of  all  whole  numbers 
(which  Cantor  indicated  by  the  number  a>)  is  equivalent 
to  that  of  all  even  numbers  which  forms  a  part  of  it, 
because  each  term  of  the  one  can  be  made  to  correspond 
with  a  term  of  the  other,  and  vice  versa.25  If  in  com- 
paring the  classes  we  also  take  the  order  of  elements 
into  account,  we  shall  arrive  at  the  concept  of  ordinal 
number.  The  two  well-ordered  series  M  and  N  belong 
to  the  same  type,  or  are  like  one  another  if  they  can  be 
made  to  correspond  univocally  and  reciprocally  in  such 
a  way  that,  m  and  m'  being  two  elements  of  the  one, 
and  n  and  n'  the  corresponding  elements  of  the  other, 
the  relation  of  position  of  m  and  m'  is  the  same  as 
that  of  n  and  n'.  An  ordinal  number  is  then  nothing 
but  the  abstract  concept  of  a  type  of  order  common  to 
like  classes,  and  is  thus  defined  without  having  recourse 
to  intuition,  because  the  idea  of  order  is  in  its  turn 
definable  by  the  pure  logic  of  relations.  The  linear  order 
of  an  open  series,  for  instance,  is  reducible  in  the  last 
analysis  to  a  transitive,  asymmetrical  relation ;  that 
is  to  say,  to  a  relation  between  the  terms  x,  y,  z  of  the 
class,  such  that  if  it  exist  between  x,  y  and  y,  z,  it  also 


exists  between  x  and  z,  but  cannot  be  inverted ;  that 
is  to  say,  the  two  relations  xRy  and  yRx  exclude  one 
another  reciprocally. 

7.  The  Continuum. — The  continuum  may  be  defined 
by  means  of  pure  relations  of  order  without  having 
recourse  to  spatial  intuition.  The  ordinal  definition 
of  the  continuum,  which  was  formulated  for  the  first 
time  by  Enriques  26  and  Cantor,27  has  been  simplified 
by  Whitehead  as  follows  :  "  A  series  is  continuous, 
(1)  when  it  has  a  first  and  last  term,  and  when  all  its 
segments  (upper  and  lower  alike)  have  a  limit ;  (2)  when 
it  contains  a  denumerable,  compact  series,  such  that  a 
term  of  this  latter  series  will  be  found  between  any  two 
terms  of  the  former  series."  a  The  idea  of  magnitude 
does  not  enter  into  this  definition,  but  only  that  of 
order,  because  the  concepts  of  segment  and  limit  can 
be  defined  by  means  of  pure  ordinal  relations.  A 
segment  of  a  series  E  is  an  assemblage  S  containing 
some,  but  not  all,  of  the  terms  of  E,  not  containing  a  last 
term,  and  containing  all  the  terms  of  E  which  precede 
some  term  of  S.  A  term  x  is  the  limit  of  a  series  S,  if  all 
the  terms  of  S  be  anterior  to  x,  and  if  every  term  which  is 
posterior  to  all  the  terms  of  S  be  posterior  to  x.  Cantor  ^ 
has  shown  that  all  continua  are  equivalent,  whatever 
be  the  number  of  their  dimensions  ;  that  is  to  say,  it  is 
possible  to  establish  a  one-to-one  correspondence  between 
them,  so  that  nothing  distinguishes  them,  from  the  point 
of  view  of  the  number  of  their  elements.  There  are  as 
many  points  in  a  rectilinear  (or  curvilinear)  segment, 
as  in  a  square  or  cube  ;  this  paradoxical  truth  has  been 
illustrated  by  Peano,  who  has  invented  a  curve  which 
fills  a  square,  that  is  to  say,  which  passes  through  all 
the  points  of  the  square.  Couturat  ^  regards  this  a 
manifest  proof  of  the  incompetence  of  intuition  in 
matters  of  geometry.  Continua  of  a  different  number 
of  dimensions  are  not  equivalent  and  indiscernible 
except  from  the  point  of  view  of  the  cardinal  number 
of  their  elements ;  but  they  are  distinguished  from 
one  another  by  their  ordinal  properties.  A  segment,  a 


square,  a  cube,  do  not  differ  from  one  another  as  classes 
of  points,  but  only  as  regards  the  order  and  arrange- 
ment of  these  points,  that  is  to  say,  in  ultimate  analysis 
as  regards  the  relations  set  up  between  them,  since 
every  order  consists  in  a  system  of  relations.  That 
which  constitutes  the  continua  having  several  dimen- 
sions, no  less  than  the  linear  continuum,  is  not  an 
assemblage  of  points,  but  an  assemblage  of  asym- 
metrical relations ;  space  is  not  a  simple  manifold,  but 
an  ordered  manifold.  A  one-dimensional  assemblage  is 
a  simple  series  whose  terms  are  absolute  individuals, 
i.e.  not  relations ;  a  two-dimensional  assemblage  is  a 
double  series  whose  terms  are  themselves  simple  series, 
i.e.  a  relation  of  relations ;  a  three-dimensional  assem- 
blage is  a  triple  series  whose  elements  are  double  series, 
i.e.  a  relation  whose  terms  are  relations  of  relations, 
and  so  on.31 

8.  Geometry  as  a  Hypothetico- Deductive  System. — 
Fieri 32  constructs  the  whole  of  protective  geometry 
with  nothing  but  the  two  notions  of  point  and  of  the 
connecting  fine  between  two  points,  defining  straight 
lines  as  relations  of  a  certain  type,  and  points  as  the  prob- 
lematic terms  of  these  relations.  In  such  a  hypothetico- 
deductive  system,  there  ceases  to  be  any  such  thing 
as  a  primitive,  undemonstrable  proposition,  because  all 
the  postulates  form  part  of  the  definition  of  projec- 
tive  space  and  constitute  its  hypothetical  properties. 
No  one  of  them  is  categorically  affirmed ;  it  is  merely 
stated  that  if  a  space  be  possessed  of  certain  properties 
enunciated  in  its  definition,  it  will  also  be  possessed  of 
the  others  which  are  enunciated  in  the  theorems.  Thus 
projective  geometry  is  reduced  to  the  form  of  a  vast 
implication,  and  is  therefore  included  in  pure  mathe- 
matics, which  knows  no  other  principles  than  those  of 
logic  ;  the  same  may  also  be  said  of  descriptive  geometry. 

Metrical  geometry  is  historically  anterior  to  the 
geometry  of  position  ;  it  is,  however,  logically  posterior 
thereto,  since  it  of  necessity  implies  relations  of  position 
(for  the  most  part  unnoticed  or  neglected)  upon  which 


relations  of  magnitude  are  superposed  ;  it  is  not  the  most 
elementary,  but  the  most  complex  part  of  geometry. 
The  most  elementary  truth,  "  two  points  determine1 
a  straight  line,"  which  is  commonly  regarded  as  the 
definition  of  the  straight  line,  implies  a  large  number  of 
postulates.  Neither  Euclid  nor  his  imitators  can  give 
us  any  demonstration  which  is  logically  exact,  and  does 
not  imply  an  appeal  to  intuition.  Couturat  pronounces 
the  rigid  accuracy  of  Euclidean  geometry  to  be  but  a 
legend  w ;  for  proof  of  this  statement  it  will  suffice  to 
take  into  consideration  the  numerous  errors  which 
Russell  w  has  pointed  out  in  the  first  twenty-six  pro- 
positions of  Euclid.  It  is  only  in  our  day  that  mathe- 
maticians have  begun  to  take  into  account  all  the 
postulates  implied  in  the  elements  of  geometry,  and, 
subsequently  to  the  enunciation  of  these  postulates,  the 
whole  of  geometry  has  been  reconstructed  in  a  purely 
analytical  manner,  taking  as  the  starting-point  certain 
primitive  notions,  which  Peano  **  considers  to  be 
reducible  to  the  point  and  distance.  Others  on  the 
contrary  assume  the  primitiveness  of  the  notion  of 
congruence,  which  is  the  presupposition  of  the  possibility 
of  super-position,  because  two  figures  are  not  congruent 
when  they  can  coincide,  but,  vice  versa,  in  order  to 
coincide,  they  must  first  be  congruent ;  and  Pasch 
postulates  congruence  between  figures  of  any  descrip- 
tion ;  Hilbert,  between  segments  and  angles  ;  Veronese, 
between  segments  only.36  Pieri,37  on  the  other  hand, 
regards  motion  and  the  point  as  primitive  concepts ; 
but  this  is  at  bottom  merely  a  mere  intuitive  way 
of  representing  the  relation  of  congruence,  since  in 
geometry  we  do  not  take  into  consideration  the  con- 
tinuous series  of  intermediate  positions  of  the  moving 
point,  but  only  the  initial  and  final  positions.  Metrical 
geometry,  like  that  of  position,  is  reducible  to  a  purely 
logical  form,  if  the  postulates  be  transformed  into  a 
definition  of  metrical  space  :  we  give  the  name  metrical 
space  (Euclidean  or  non-Euclidean)  to  an  assemblage 
endowed  with  the  properties  enunciated  in  the  postu- 


lates.38  Metrical  geometry,  or  rather,  each  of  the  metrical 
geometries,  then  assumes  the  form  of  a  vast  implica- 
tion :  if  a  certain  assemblage  of  entities  verify  the  funda- 
mental properties  enunciated  in  the  postulates,  it  will 
verify  all  the  theorems  of  the  corresponding  geometry. 
Thus  geometry,  or  to  express  it  more  accurately, 
the  geometries,  are  no  longer  based  upon  primitive,  un- 
demonstrable  propositions,  and  are  no  longer  possessed 
of  axioms  of  their  own  differing  from  the  general  axioms 
of  logic.  This  transformation  is  legitimate,  since  so  long 
as  we  are  constructing  pure  geometry,  we  speculate  on 
ideal  spaces  whose  real  existence  we  do  not  affirm ; 
therefore  we  can,  and  indeed  should,  divest  postulates 
of  their  categorical  character,  in  order  to  reduce  them 
to  mere  hypotheses  problematically  posited ;  it  is 
necessary  because,  in  order  to  reason  on  a  space,  we  must 
define  that  space,  and  we  can  only  define  it  by  enunciat- 
ing its  characteristic  properties,  from  which  all  the 
others  are  logically  derived.39  The  definition  of  a  space 
is  the  totality  of  the  conditions  which  are  necessary 
and  sufficient  for  the  determination  of  all  its  properties. 
Now  a  postulate  must  either  belong  to  this  totality 
of  conditions,  in  which  case  it  ceases  to  be  a  postulate, 
and  becomes  an  integral  part  of  the  definition,  or  it 
does  not  belong  to  it,  in  which  case  it  is  a  theorem, 
which  can  and  therefore  must  be  proved.  There  is  no 
room  in  a  logically  constructed  geometry  for  postulates 
of  any  description ;  in  short,  as  has  been  pointed  out 
by  Poincare,  postulates  are  but  disguised  definitions,  or 
rather,  parts  of  a  definition  :  Euclid's  famous  postulate, 
for  instance,  is  a  mere  complement  of  the  definition  of 
the  straight  line,  and  of  Euclidean  space.  Geometry 
thus  ceases  to  be  an  autonomous  science  having  its 
special  principles,  and  based  upon  synthetic  a  priori 
judgments,  and  becomes  a  series  of  formal  deduc- 
tions, dependent  upon  a  definition  from  which  logical 
consequences  are  derived  ad  infinitum.  Geometry  no 
longer  has  primitive  notions  of  its  own,  just  as  it  has 
ceased  to  possess  primitive  propositions ;  in  fact  the 


primitive  notions  in  all  the  systems  upon  which  we  have 
touched  may  be  reduced  to  two :  a  class-concept, 
which  is  termed  point,  and  a  notion  of  relation 
(order,  congruence,  motion),  which  sometimes  appears 
in  the  guise  of  a  class-concept  (straight  line,  segment, 
vector),  when  the  analysis  is  not  followed  out  to  its 
conclusion.  Now  the  notion  of  point  does  not  enter  into 
the  logical  structure  of  geometry :  points  have  ceased  to 
be  anything  but  the  elements  of  certain  assemblages,  or 
rather  the  terms  of  certain  relations :  they  are  objects 
of  which  we  know  one  thing  only,  viz.:  that  if  certain 
fundamental  relations  subsist  between  them  (i.e.  the 
relations  which  are  enunciated  in  the  axioms)  all  the 
theorems  logically  derived  therefrom  will  be  verified.40 
Thus  pure  geometry,  like  a  system  of  implications,  affirms 
nothing  with  regard  to  points  :  strictly  speaking,  it 
neither  knows  them  nor  has  need  of  them.  On  the  other 
hand,  the  relations  constituting  the  second  primordial 
datum  of  the  various  systems  are  no  longer  indefinable, 
because  the  logic  of  relations  permits  of  their  definition 
by  means  of  their  formal  properties.  Mathematics 
disregards  the  intrinsic  nature  of  objects  in  order  to  take 
into  consideration  nothing  but  their  relations,  so  that 
if  two  assemblages  of  objects,  of  a  totally  different 
nature,  verify  the  same  relations,  they  will  be  submitted 
to  the  same  theory ;  a  proceeding  of  which  mathe- 
matical physics  affords  us  many  examples.  But,  if 
mathematics  be  an  abstract  science,  it  is  not  such  because 
it  disregards  the  properties  of  the  objects  of  experience, 
as  is  believed  by  empiricists,  but  because  it  has  ceased 
to  be  a  science  of  objects  at  all,  and  has  become  a  pure, 
formal  science,  dealing  only  with  the  form  of  object 
and  their  relations.  This  explains  why  mathematical 
truths  are  of  a  priori  universality  and  necessity  :  their 
objectivity  is  due  to  the  fact  that,  while  they  refer  to  no 
object  in  particular,  they  are  applicable  to  all  possible 
objects,  like  the  laws  of  logic,  whose  characteristics 
they  possess,  and  of  which  they  are  the  necessary  con- 
sequence. Geometry  is  distinguished  from  logic  and 


the  other  branches  of  mathematics,  because  it  studies 
multi-dimensional  series,  i.e.  ordered  multi-dimensional 
assemblages,  whereas  arithmetic  studies  a  series  having 
but  one  dimension,  the  natural  series  of  numbers.41 
Pure,  wholly  a  priori  geometry  is  an  implication  of 
the  form,  if  A  be  true,  B  is  true  :  applied  geometry, 
which  is  an  empirical  science,  says :  A  is  true,  there- 
fore B  is  true,  affirming  the  existence  of  A  and  B 
in  actual  objective  space,  whereas  pure  geometry  con- 
fines itself  to  affirming  their  logical,  ideal  connection. 
Intuition,  which  is  absolutely  excluded  from  pure 
geometry,  prevails  in  applied  geometry,  because  it  is  indis- 
pensable to  give  a  direction  and  a  support  to  the  primitive 
notions,  and  for  the  verification  of  the  primitive  pro- 
positions (postulates)  from  which  all  the  rest  are  derived. 
Whereas  pure  geometry,  for  instance,  ignores  points, 
and  must  ignore  them,  applied  geometry  has  to  determine 
in  real  and  objective  space  those  elements  to  which  it 
will  give  the  name  of  points,  and  their  various  rela- 
tions, straight  lines,  plane,  etc.,  because  it  is  only 
when  this  condition  is  fulfilled  that  geometrical  pro- 
positions acquire  a  real  sense  and  become  capable  of 

9.  The  Analytic  Character  of  Mathematical  Truths 
according  to  Cowturat. — Russell  regards  pure  mathe- 
matics as  being  identical  with  logic  from  the  standpoint 
of  form,  in  as  much  as  it  proceeds  by  logical  principles 
from  logical  definitions,  and  is  distinguished  there- 
from merely  by  the  special  content  of  the  relations  it 
studies  ;  hence  its  character  of  necessity,  which  renders 
it  possible  to  say  with  Benjamin  Peirce  :  Mathematics 
is  the  science  which  draws  necessary  conclusions.*2 
Mathematics  thus  assumes  an  analytical  character  as 
opposed  to  the  Kantian  thesis  which  would  turn  it  into 
a  system  of  synthetic  a  priori  judgments.  That  which 
distinguishes  the  analytical  and  synthetical  attributes  of 
a  concept  is  the  purely  logical  fact  that  they  do  or  do 
not  form  part  of  the  definition  of  that  concept :  every- 
thing which  is  contained  in  the  definition  of  a  concept 

CH.  n       ELABORATION  OF  PURE  MATHEMATICS         321 

or  is  logically  deduced  therefrom  is  of  an  analytical 
character ;  everything  which  is  added  thereto  for 
reasons  of  extra  -  logical  necessity  is  of  a  synthetic 
nature.43  It  is  a  mere  matter  of  words  whether  a 
definition  be  termed  analytical  or  synthetical ;  in  reality 
all  mathematical  definitions  are  purely  nominal,  that 
is  to  say,  they  consist  in  the  determination  of  the  mean- 
ing of  a  new  term,  supposed  to  be  unknown,  as  a  function 
of  old  terms  whose  sense  is  already  known  ;  it  is  a  con- 
vention as  to  the  use  of  a  simple  sign  which  is  substituted 
for  a  combination  of  signs  ;  it  can  therefore  in  no  way 
influence  the  analytical  or  synthetical  character  of  the 
propositions  deduced  from,  or  rather  deduced  by  means 
of,  it.44  The  concept  of  the  sum  of  7  and  5 
does  not,  according  to  Kant,  contain  anything  more 
than  the  union  of  these  two  numbers,  which  does  not 
at  all  imply  the  thought  of  the  single  number  :  analyse 
the  concept  of  this  sum  as  much  as  you  will,  you  will  fail 
to  find  the  number  12,  hence  you  must  transcend  this 
concept  and  have  recourse  to  intuition,  by  counting  on 
your  ringers  for  instance.  Now  Couturat K  regards  this 
as  a  gratuitous  affirmation ;  the  sum  of  7  and  5, 
for  the  very  reason  that  it  implies  the  union  of  the 
two  numbers,  or,  to  put  it  more  accurately,  that  of 
their  units  in  a  single  number,  contains  this  very 
number,  in  as  much  as  it  determines  it  univocally  ; 
there  is  not  merely  equality  but  absolute  identity 
between  7  +  5  and  12,  as  can  be  proved  by  recourse 
to  the  definition  of  numbers,  according  to  which  each 
is  equal  to  its  predecessor  plus  1,  and  to  the  equation 
a  +  (b  +  !)  =  («  +  6)  +  1,  which  is  derived  from  the 
definition  of  sum.  Kant's  error  is  explained  by  his 
conception  of  logic,  a  conception  both  too  restricted 
and  too  simple.  We  may,  he  says,  turn  and  turn  our 
concepts  as  much  as  we  please  without  ever  succeeding 
in  rinding  the  sum  by  merely  resolving  our  concepts  into 
their  component  parts.  Couturat,  however,  observes 46 
that  Kant  starts  from  the  false  presupposition  that  all 
concepts  are  composed  of  partial  concepts,  so  that  it 


will  suffice  to  resolve  them  into  their  component  parts 
in  order  to  discover  all  their  properties.  Concepts 
of  number  cannot  be  defined  per  genus  proximum  et 
differentiam  specificam,  or  be  resolved  into  logical 
factors ;  this,  however,  merely  proves  the  inadequacy  of 
classical  logic,  and  does  not  give  us  the  right  to  conclude 
that  arithmetical  addition  is  beyond  the  grasp  of  true 
logic,  since  it  can  and  must  be  defined  by  means  of  the 
logical  sum  of  the  classes  a  and  6 :  the  sum  of  7  and  5 
is  the  number  of  the  collection  formed  by  uniting  the 
two  collections  represented  by  7  and  5.  Intuition  may 
even  be  necessary  as  a  psychological  help  ;  this  does  not, 
however,  alter  the  fact  that  the  concept  of  7  +  5  must 
by  its  very  definition  contain  that  of  12,  or  rather  is 
identical  with  it.  The  synthetic  character  of  judg- 
ments does  not  depend  either  upon  the  nature  of  the 
concepts  or  upon  their  origin  and  mode  of  formation  ; 
it  is  possible  to  form  analytic  judgments  upon  empirical 
concepts  which  are  the  product  of  an  intuitive  synthesis.47 
Not  even  geometrical  judgments  are  synthetic  ;  that  is 
to  say,  the  judgment  that  the  straight  line  is  the  shortest 
distance  between  two  points  is  not  an  axiom,  but  a 
theorem  which  can  be  proved  by  means  of  the  definition 
of  inequality  and  of  the  sum  of  segments  and  angles. 
Kant  regards  the  fact  that  in  the  course  of  mathematical 
demonstrations  we  are  frequently  forced  to  have  recourse 
to  auxiliary  constructions  as  affording  proof  of  the  syn- 
thetic character  of  geometrical  truths.  These  auxiliary 
constructions  are,  however,  either  merely  aids  to  the 
imagination,  corresponding  to  elements  which  have 
already  been  analytically  determined,  or  useless,  since 
they  are  not  indispensable  in  the  demonstration.48 
Neither  is  the  existence  of  symmetrical  figures  an 
argument  in  favour  of  the  synthetic  character  of 
geometry,  since  this  merely  proves  the  impossibility  of 
reducing  space  to  its  metrical  properties  only.  It  is 
not  true  that  two  symmetrical  figures  are  absolutely 
equal ;  they  are  so  merely  as  regards  the  relations  of 
magnitude,  but  differ  as  to  the  relations  of  order  which 


may  be  defined  by  means  of  the  logic  of  relations  :  in 
the  end  two  inverse  orders  correspond  to  inverse 
relations,  and  the  conversion  of  relations  is  a  logical 

10.  Intuition  in  Mathematics.  —  The  new  logical 
elaboration  of  pure  mathematics  may  be  regarded  as 
a  return  to  the  rationalism  of  Leibnitz  as  opposed  to 
the  intuitionism  of  Kant.  Mathematicians  do  not  all, 
however,  agree  in  placing  an  absolute  ban  upon  intuition. 
Felix  Klein,50  after  distinguishing  three  classes  of 
mathematicians — the  logical,  the  formalist,  and  the 
intuitive — vindicates  the  rights  of  intuition  in  the  con- 
struction of  mathematics,  and  emphasises  its  usefulness 
and  even  necessity  in  every  sphere  thereof,  even  in 
the  realm  of  abstract  number,  thus  rehabilitating 
geometrical  intuition,  which  had  been  over-depreciated 
and  neglected  by  the  excessive  rigour  and  exclusive 
purism  of  mathematicians  of  the  formal  and  logical 
schools.  He  shows,  for  instance,  that  a  very  simple 
geometrical  representation  serves  to  interpret  the 
equivalence  of  binary  quadratic  forms  in  the  theory  of 
numbers,  and  to  illustrate  Kummer's  conception  of  ideal 
numbers  in  algebra.  It  is  not  possible  to  base  mathe- 
matics solely  upon  logical  axioms,  and  intuition  must  do 
its  share.51  Poincare,  too,52  maintains  the  legitimacy 

<  of  intuition,  affirming  that  the  two  different  types  of 
mathematicians,  the  intuitive  (with  whom  he  ranks 
Klein,  Bertrand,  Riemann,  and  Lie)  and  the  logical  (such 

!  as  Meray,  L'Hermite,  Weierstrass,  and  Kowalevski), 
are  equally  necessary  to  the  advance  of  science  since 
analysis  and  synthesis  alike  have  their  allotted  task 
to  fulfil.  Analysis  gives  us  single  parts  but  not  a 
general  view ;  logic  and  intuition  are  then  both  necessary, 
the  former  affords  us  strict  certainty  and  is  the  instru- 
ment of  proof,  the  latter  is  the  organ  of  discovery. 
There  are  discoverers  in  the  ranks  of  the  analysts ;  they 
are,  however,  but  few  in  number  :  sensible  intuition  is 
the  more  usual  tool  of  discovery.53  To  the  accusation 
of  barrenness  brought  against  logistic  by  Poincare  and 


other  critics,  Couturat  has  with  justice  replied  that 
logistic  does  not  claim  to  be  an  instrument  of  discovery.54 
Only  a  crass  ignoratio  elenchi  can  place  the  psychological 
fact  of  discovery  in  opposition  to  logistic,  since  it  is 
not  its  business  to  inspire  or  explain  discovery,  but 
merely  to  control  and  verify  it.  Would  you  reproach 
the  science  of  metre  or  harmony  with  failing  to  create 
poetical  or  musical  genius  ?  Poincare's  analysis  of  the 
two  opposite  types  of  mathematicians  is  undoubtedly 
extremely  interesting  from  the  psychological  point  of  view 
all  the  more  since  a  similar  difference  exists  amongsl 
men  of  science  in  the  realm  of  physics  with  regard  to 
their  concrete  procedure  of  discovery  and  their  mode  oj 
thought,  and  of  setting  forth  their  theories — a  difference 
which  has  given  rise,  as  we  shall  see  later,  to  two  opposite 
schools.  We  must,  however,  beware  of  confusing  the 
psychological  question  with  the  epistemological  problem, 
and  must  draw  a  distinction  between  that  which  is 
dependent  upon  the  individual  structure  of  the  thinker 
and  upon  his  type  of  imagination,  and  that  which  is 
essential  to  all  thought  whatsoever,  given  the  nature 
of  his  branch  of  knowledge. 

The  criterion  by  which  to  gauge  the  necessity  of 
intuition  cannot  be  derived  from  psychological  observa- 
tion ;  in  order  to  be  entitled  to  affirm  that  a  science 
cannot  dispense  therewith,  we  must  prove  that  it  is 
impossible  for  the  pure  activity  of  logical  thought  to 
establish  its  principles,  and  to  draw  all  the  con- 
clusions from  those  principles.  Now  as  long  as  we 
confine  ourselves  to  the  realm  of  abstract  relations,  as 
studied  by  the  new  mathematical  logic,  and  to  that  of 
pure  quantity,  the  object  of  arithmetic  and  of  algebraic 
analysis,  there  is  no  need  to  appeal  to  intuition  in  order 
to  define  the  supreme  concepts  upon  which  these  sciences 
are  based,  and  to  deduce  all  the  theorems  from  them. 
The  fact  that  it  is  possible,  within  certain  limits,  for 
mathematical  calculus  and  logical  theory  to  become 
fused  and  to  pervade  one  another,  affords  proof  of  the 
profound  affinity  between  the  two  orders  of  knowledge 


which  are  the  outcome  of  the  reflections  of  thought  upon 
its  own  function,  and  hence  exclude  all  consideration 
of  intuitive  matter.     Number  is  a  product  of  the  analytic  -t- 
and  synthetic  activity  exercised  by  thought  upon  itself, 
associating  its  single  acts  in  complex  units  and  resolving 
the  units  which  had  previously  been  undivided  into 
elementary  acts.     The   human  mind   finds   it   within 
itself   like  a  law  of  its  nature,  an  intrinsic  necessity, 
of   which   it  cannot  divest  itself   without  denying  its 
own  very  nature.      The  existence   of   cardinal    num- 
ber  is   not   something   hypothetical,   as    the   logistics 
would  affirm,   but  rather  an  axiomatic  truth  which 
thought  discovers  by  reflection  upon  its  own  acts,  and 
recognises  immediately  as    the  necessary  presupposi-    • 
tion  of  its  function.     There  is  no  concept  without  the 
possibility  of  distinguishing  a  whole  in  its  parts,  and  of ) 
recombining  them  into  a  synthetic  unity  :  the  ability 
to  grasp  the  one  in  the  many,  and  the  many  in  the 
one  is  the  very  essence  of  human  thought,  which  is 
therefore  by  its  own  activity  implicitly  led  to  presuppose 
the  existence  of  number.    Dura  lex,  sed  lex.    We  may 
seek  to  escape  from  this  law  by  living  with  Bergson 
in    the  fantastic   world    of    creative    and    indivisible ; 
intuition,  but  if  we  thus  deny  number,  we  deny  dis-  ? 
cursive  thought  at  the  same   time,  and  with  it  the 
whole   science    of   logic.      We  are   as  certain  of  the  J 
existence  of  number  as  we  are  of  that  of  our  own  logical 
thought,  since  thinking  is  potential  numeration. 

11.  Irreducibility  of  Mathematics  to  Logistic. — If 
such  be  the  nature  of  cardinal  number,  it  will  at  once 
be  obvious  that  all  attempts  to  define  it  with  the  help 
of  pure  logical  constants  must  of  necessity  move  in  a 
vicious  circle.  We  cannot  therefore  be  surprised  that 
Poincare 55  and  various  other  critics  have  discovered 
in  the  alleged  definitions  a  more  or  less  explicit  use 
of  numerical  concepts  and  terms  or  of  a  word  in  the 
plural,  which  naturally  presupposes  that  which  is  to 
be  defined.  Thus  Couturat  defines  zero  as  the  number 
of  the  elements  of  the  null  class,  i.e.  of  the  class  con- 


taining  no  element,  or  again  as  the  number  of 
objects  fulfilling  a  condition  which  is  never  fulfilled, 
and  1  as  the  number  of  the  elements  of  a  class  of  which 
any  two  elements  are  identical.  Couturat56  replies 
that  the  logistical  definition  of  1  does  not  in  the  least 
imply  that  of  2,  but  means,  properly  speaking,  that  "  1  is 
the  class  of  the  classes  u,  not  being  null,  such  that  if  a;  be 
a  u,  and  y  be  a  u,  x  is  identical  with  y,  whatever  x  and  y 
may  be  ";  hence,  in  the  place  of  x  and  y  we  may  put  an 
indeterminate  plurality  of  terms,  provided  that  they  all 
be  identical.  But,  it  may  be  urged,  does  not  plurality, 
however  indeterminate  it  may  be,  presuppose  the  idea 
of  number  ?  When  you  define  the  cardinal  number  of  a 
class  u  as  the  totality  of  the  classes  which  are  equivalent 
to  u,  and  add  that  two  classes  have  the  same  cardinal 
number  when  a  univocal  and  reciprocal  correspondence 
can  be  established  between  their  elements,  that  is 
to  say,  when  these  elements  can  be  made  to  correspond 
term  for  term,  or  to  put  it  more  briefly,  when  the  two 
classes  are  similar,  you  appeal  to  the  logical  calculus, 
which  is  in  its  turn  impregnated  with  numerical  concepts. 
Even  if  we  put  aside  explicit  numeral  terms  (as,  for 
instance,  in  the  definition  of  the  logical  product  or  sum 
of  two  or  more  propositions)  which  could  be  disguised 
by  saying  x,y  instead  of  2,  x,y,z  instead  of  3,  and  so  on, 
it  is  an  undoubted  fact  that  the  simplest  logical  pro- 
position cannot  be  formulated  without  establishing  a 
relation,  that  is  to  say,  without  implicitly  positing  a 
multiplicity  synthetised  into  unity  :  the  logical  con- 
stants, by  whose  means  number  is  supposed  to  be  defined, 
already  contain  number  within  themselves  as  their 
necessary  presupposition.  How  is  it  possible  to  conceive 
the  relation  of  a  term  to  a  class  of  which  it  is  a  member, 
without  at  the  same  time  positing  the  concept  of 
multiplicity  of  terms  upon  any  one  of  which  we  fix  our 
thoughts  ?  What  meaning  can  be  attached  to  the  word 
class,  if  you  do  not  presuppose  the  concept  of  a  plurality, 
which  may  be  as  indeterminate  as  you  will,  but  which 
is  still  a  plurality  of  logical  individuals  ?  Does  not  the 


notion  of  any  and  every  term  too,  imply  the  thought  of 
a  multiplicity  of  terms,  composing  one  and  the  same 
class,  belonging,  that  is  to  say,  to  one  and  the  same 
conceptual  synthesis  ?  While  we  recognise  with 
Kussell 57  that  the  class  may  be  defined  intensionally,  that 
is  to  say,  by  means  of  the  comprehension  of  the  concept 
determining  it,  without  having  recourse  to  the  actual 
enumeration  of  its  terms,  that  is  to  say,  to  its  extension,  % 
it  is  certain,  on  the  other  hand,  that  in  the  logical  calculus 
we  are  continually  forced  to  leave  the  pure  consideration 
of  the  intension  in  order  to  refer  to  the  entities  belonging 
to  these  classes.58  Thus  when  we  define  the  logical  pro- 
duct of  the  classes  a  and  b  as  the  assemblage  of  the  values 
of  the  variable  x,  which  are  at  the  same  time  a  and  b,  we  do 
not  by  the  expression  assemblage  of  the  values  of  x  mean 
the  intension  of  the  concept  x,  but  rather  the  extension 
thereof.  Is  not  this  assemblage  of  values  a  numerical 
plurality  ?  Thus  when  we  define  the  equality  of 
numbers  by  means  of  the  similarity  of  classes,  and  say 
that  one  term  and  one  term  only  of  the  one  must  corre- 
spond to  one  term  of  the  other,  we  are  already  taking 
for  granted  the  thought  of  the  class  as  a  collection  of 
terms,  that  is  to  say,  we  regard  it  as  being  composed  of 
a  certain  number  of  terms. 

The  attempt  to  give  a  logical  definition  of  the  idea  of 
linear  order  will  also  end  in  a  like  petitio  principii. 
Russell  and  Couturat  define  linear  order  as  an  asym- 
metrical relation,  and  this  is  in  its  turn  defined  as  a  rela- 
tion which  can  never  be  inverted ;  that  is  to  say,  that 
the  two  relations  xRy  (i.e.  the  relation  between  x  and  y), 
and  yRx  (i.e.  the  relation  between  y  and  x)  are  mutually 
exclusive.  Is  it,  however,  possible  to  define  the  inverse 
of  a  relation  without  presupposing  the  concept  of  order  ? 
The  intuitive  assistance  afforded  by  the  succession  of 
terms  in  the  schemes  xRy  and  yRx  enables  you  to  avoid 
the  use  of  the  word  "  order  "  in  the  definition  of  inverse 
relations,  and  deceives  you  into  thinking  that  you  have 
succeeded  in  avoiding  a  vicious  circle,  but,  were  you 
asked  to  give  an  abstract  definition  of  the  inverse  of  a 


relation  without  making  use  of  the  signs  x  and  y,  you 
could  only  say  that  a  relation  is  converted  when  the 
order  of  the  two  terms  is  changed.  The  existence  of 
non-invertible  series  is  not  a  mere  hypothesis,  or  an 
arbitrary  convention,  but  rather  an  axiomatic  truth 
which  we  derive  from  reflection  upon  our  acts  of  thought, 
together  with  the  primitive  and  indefinable  general 
concept  of  order.  Analysis  of  the  logical  function, 
which  brings  to  our  notice  cases  in  which  our  thought 
is  capable  of  passing  from  the  truth  or  falsity  of  one 
proposition  to  that  of  another,  without,  however,  being 
able  to  make  the  inverse  deduction,  affords  us  immediate 
and  apodictic  certainty  of  the  existence  of  non-invertible 

•  relations,  and  hence  of  series  of  acts  of  thought  develop- 
ing in  a  determinate  order.    We  cannot,  moreover,  con- 
ceive of  this  series  as  limited  without  at  the  same  time 
placing  a  limit  to  the  function  of  logical  thought,  which 
by  its  very  character  of  universality  transcends   all 
limitations.     From  this  point  of  view  the  proposition 
that  each  number  has  a  successor  ceases  to  appear  an 
arbitrary  convention,  a  mere  hypothesis  set  up  by  us 
in  the  definition  of  number,  as  logisticians  would  have 
us  believe,  and  becomes  a  law  which  our  mind  recognises 
in  the  series  of  its  denumerable  acts,  refusing  to  conceive 
of    a   last    term   to    its    function    beyond   which   no 
further  act  of  thought  is  possible.     It  would  be  absurd 
to  conceive  such  a  term,  since  to  do  so  would  be  tanta- 

•  mount  to  contradicting  that  value  of  universality  which 
thought  apprehends  immediately  in  the  affirmation  of 
its  principles. 

In  geometry  the  impossibility  of  defining  all  mathe- 
matical concepts  with  the  help  of  logical  constants  only 
becomes  still  more  apparent.  If  we  consider  the 
hypothetico  -  deductive  systems  attentively,  we  shall 
at  once  see  that  their  definitions  refer  to  conceptual 
entities,  having  nothing  geometrical  about  them,  and 
if  they  recall  spatial  figures  and  relations  to  a  certain 
extent,  they  do  so  because  the  terms  commonly  used  to 
indicate  certain  intuitive  properties  are  introduced  into 


the  definitions.  Thus  when  we  say  :  "  An  assemblage 
of  one  dimension  is  a  series  whose  terms  are  absolute  in- 
dividuals, that  is  to  say,  are  not  relations  ;  an  assemblage 
having  two  dimensions  is  an  assemblage  whose  terms  are 
themselves  relations,  that  is  to  say,  a  relation  of  relations; 
an  assemblage  having  three  dimensions  is  a  relation  whose 
terms  are  relations  of  relations,"  and  so  on ;  our  definition 
does  not  determine  anything  spatial,  and  if  we  think 
of  the  straight  line,  the  plane,  and  ordinary  space,  we 
do  so  because  the  word  dimension  suggests  intuitive 
extension  to  our  minds.  Thus  when  in  projective 
geometry  we  enunciate  the  postulates  relative  to  the 
point  and  say  that  points  form  a  class,  that  there  exists 
at  least  one  point,  and  that  if  a  be  a  point,  there  exists 
a  point  differing  from  a,  the  word  point  is  an  appeal  to  -|— 
intuition  and  imparts  a  geometrical  meaning  to  these 
postulates  which  otherwise  would  have  none,  seeing  that 
they  can  refer  to  any  individuals  composing  a  class.  In 
like  manner,  when  we  say  that,  given  the  two  points  a 
and  b,  there  is  an  entity  which  we  call  the  straight  line  ab, 
which  is  a  class  of  which  every  individual  is  a  point,  etc., 
if  the  words  straight  line  and  point,  which  recall  geo- 
metrical entities  to  our  minds,  be  removed,  these 
formulations  would  apply  to  any  class  of  individuals 
verifying  all  those  properties.  Neither  do  we  determine 
anything  really  spatial  in  the  postulates  of  metrical 
geometry  when  we  say  that  the  point  and  motion  are 
generic  and  class  concepts,  that  every  assemblage  of 
points  is  termed  a  figure,  that  two  figures  are  identical 
when  they  are  composed  of  the  same  points,  etc.  ;  since, 
if  the  words  points,  figure,  etc.,  be  eliminated,  proposi- 
tions will  remain  which  are  valid  in  the  case  of  certain 
assemblages.  In  short,  hypothetico-deductive  systems 
do  not  succeed  in  individualising  geometrical  entities 
in  their  definitions,  but  treat  of  generic  relations  of 
assemblages  and  classes,  which  only  apply  to  the  specific 
case  by  a  mental  restriction,  due  to  the  terms  of  common 
geometry  and  to  the  spatial  intuition  which  is  associated 
with  them.  In  ultimate  analysis,  when  we  formulate 


these  systems,  we  either  fail  to  create  a  geometry,  and 
merely  create  a  logic  of  classes,  assemblages,  and  rela- 
tions, since  that  which  we  enunciate  does  not  refer  to  the 
point,  the  straight  line,  the  figure,  etc.,  bu.t  to  any  entity 
which  is  a  term  of  those  relations,  and  to  any  assemblage 
of  like  entities ;  or,  if  we  succeed  in  individualising  these 
concepts,  and  in  determining  them  specifically,  so  as 
to  impart  a  geometrical  sense  to  them,  our  success  is 
due  to  the  fact  that  we  recall  intuition  by  the  use  of 
corresponding  terms,  and  derive  therefrom  the  properties 
expressed  by  the  definitions  and  postulates.  The  new 
systems  bear  the  same  relation  to  the  science  of  space 
as  a  genus  to  its  species  :  it  is  true  that  they  differ 
from  the  old  analysis,  since  they  treat  of  relations  which 
cannot  be  reduced  to  mere  relations  of  magnitude,  but 
they  possess  in  common  with  it  the  characteristic  of 
being  reducible  to  a  pure  logical  calculus,  which,  though 
it  may  be  applicable  to  geometry,  is  not  for  that  reason 
geometry,  just  in  the  same  way  as  general  logic  is  not 
the  science  of  space,  although  the  properties  of  con- 
cepts, and  the  deductive  laws  formulated  thereby,  are 
necessarily  valid  of  geometrical  figures  also. 

12.  Criticism  of  the  Hypothetico- Deductive  Systems. — 
The  new  logical  elaborations  claim  to  divest  mathe- 
matical truths  of  their  categorical  character,  and  to 
transform  them  into  hypothetical  judgments,  but  this 
interpretation  of  the  value  of  mathematical  knowledge 
is  thoroughly  vitiated  by  the  empiristic  preconception 
that  geometrical  and  arithmetical  principles  and  de- 

•  ductions  require  to  be  legitimatised  by  experience.     If 
this  prejudice,  which  contrasts  forcibly  with  the  ideal 
character  of  mathematical  constructions,  be  put  aside, 
there  ceases  to  be  any  sense  in  speaking  of  hypotheses. 
Geometrical  and  arithmetical  concepts  exist  of  necessity 

*  in  our  thought,  and  are  of  universal  value,  in  as  much 
'  as  experience  would  not  be  intelligible  without  them  ; 

they  are  not  mere  arbitrary  fictions,  which  may  or  may 
not  be  verified  by  empirical  facts,  but  are  conditions 
indispensable  to  the  intelligibility  of  the  facts.  A  non- 


denumerable  reality,  or  a  reality  which,  while  denumer- 
able,  did  not  conform  to  the  laws  which  our  mind  recog- 
nises as  necessary  in  the  various  forms  of  calculus,  would 
be  an  absurdity  baffling  the  intelligence.  To  say  :  If 
experience  verify  our  definition  of  number,  it  will  verify 
all  the  theorems  which  follow  therefrom,  has  as  little 
sense  as  to  say  :  If  experience  verify  logical  axioms, 
our  arguments  are  applicable  to  it !  The  same  thing 
holds  good  of  geometrical  concepts,  which,  whilst  they 
are  not  a  product  of  the  simple  reflection  of  thought  upon 
itself,  since  they  derive  their  content  from  intuition, 
yet,  in  as  much  as  they  represent  the  only  adequate 
means  of  translating  the  empirical  data  of  space  into 
intelligible  terms,  appear  to  us  to  be  equally  universal 
and  necessary.  Even  in  the  case  of  geometrical  truths 
there  is  no  sense  in  the  hypothesis  :  "If  an  entity  exist 
which  verifies  these  relations,"  since  that  entity  does  and 
must  exist  ideally,  and  this  is  enough,  since  geometry 
neither  does  nor  should  take  empirical  existence  into 
consideration.  When  logisticians  define  or  claim  to 
define  a  geometrical  entity  by  means  of  a  certain  number 
of  properties,  they  of  course  assume  that  a  concept 
corresponds  to  that  complex  of  symbols,  that  is  to  say, 
that  that  entity  is  thought  in  some  way  or  other.  When 
it  is  stated  that  all  mathematical  definitions  are  nominal, 
says  Couturat,59  it  is  not  meant  that  mathematical 
concepts  are  reducible  to  names,  in  accordance  with  the 
thesis  of  nominalism,  but  that  they  can  all  be  logically 
and  explicitly  defined  in  terms  of  certain  primitive 
notions,  and  may  therefore  be  regarded  as  names  given 
to  certain  combinations  of  those  notions.  Thus  even 
this  new  sign  must  correspond  to  the  concept  resulting 
from  the  synthesis  of  the  primitive  notions.  More- 
over, continues  Couturat,60  in  order  to  reason  later  on 
this  concept  and  invoke  its  properties,  it  must  be 
possible  to  affirm  that  individuals  of  the  class  exist, 
that  is  to  say,  that  the  conditions  defining  it  are  not 
logically  incompatible  ;  each  definition  must  therefore 
be  accompanied  by  a  theorem  or  a  postulate,  affirming 


the  existence  of  the  object  defined.  Then,  we  ask,  what 
becomes  of  the  hypothetical  character  of  mathematics 
the  moment  that  its  concepts  have  and  must  have  an 
ideal  existence  ?  When  such  an  existence,  which  is 
essential  to  ulterior  deductions,  has  been  proved  or 
recognised  in  some  other  way,  we  shall  have  the  right 
to  affirm  categorically  :  "  An  entity  exists  in  our  thought 
which  is  endowed  with  those  properties." 

The  demand  that  the  object  denned  shall  be  thought 
and  recognised  as  existing  cannot  be  satisfied  in  the 
realm  of  geometry  without  having  recourse  to  intuition 
which  has  been  idealised  and  purified  by  thought.  How 
indeed  are  we  to  prove  by  means  of  logistic  alone  that  the 
notions  and  relations  with  which  we  define  a  geometrical 
entity  are  mutually  compatible  ?  61  Only  two  ways 
are  open  to  us  :  we  must  either  prove  that  none  of  the 
possible  consequences  of  those  premisses  contradict  one 
another ;  a  never-ending  process  of  verification,  which 
could  therefore  never  afford  us  perfect  certainty  ;  or 
we  must  show  by  an  example  that  there  exists  a  class 
of  individuals  verifying  all  those  properties.  "  If,"  says 
Fieri,62  "A, B,C,  be  propositions  belonging  to  a  deductive 
system  F,  their  compatibility  may  be  said  to  be  proved 
if  in  some  domain  A  an  interpretation  can  be  found  of 
the  primitive  ideas  of  F  manifesting  all  the  properties 
enunciated  by  the  propositions  A,  B,  C,  provided  that 
such  a  domain  do  not  embrace  any  one  of  those  proposi- 
tions amongst  its  premisses,  and  that  the  consistency  of 
its  principles  be  already  established  or  granted  a  priori.'' 
In  other  words,  the  justification  of  one  system  is  sought 
from  another  system,  and  of  course  we  must,  unless  we 
would  continue  the  process  ad  infinitum,  stop  at  one 
of  those  systems  which  posits  the  ideal  compatibility 
of  its  primitive  propositions  by  means  of  an  axiom 
or  a  postulate.  Fieri  is  forced  to  acknowledge  that, 
"  it  will  never  be  possible  to  afford  deductive  proof  of 
the  truth  and  consistency  of  the  whole  system  of  logical 
premisses." 63  For  geometry  the  proof  of  the  ideal 
existence  of  an  entity  verifying  all  these  properties 


lies  in  the  concept  of  the  figure  in  which  we  find  the 
verification  of  all  these  properties  and  relations.  We 
may  amuse  ourselves  by  forming  countless  combinations 
of  logical  constants  and  relations  ;  but  these  com- 
binations are  not  all  possessed  of  geometrical  meaning, 
that  is  to  say,  they  do  not  all  determine  an  object 
existing  in  ideal  space.  Logicians  choose  from  all 
possible  combinations  those  which  are  endowed  with 
geometrical  sense,  but  in  this  selection  they  are  in  the 
end  guided  by  the  old  intuitive  notions.  Moreover,  the 
ideal  existence  of  these  entities,  which  in  formal  com- 
binations64 remains  a  mere  hypothesis  which  cannot 
be  translated  into  our  intuitive  notions  of  space,  becomes 
an  axiomatic  truth  when  these  notions  are  present,  • 
because  the  certain  verification  of  all  the  postulates 
afforded  us  directly  by  thought  in  the  concept  of  the 
figure  transforms  the  hypothetical  judgment  into  a 
categorical  one. 

13.   A  priori  Synthesis  in  Mathematics.  —  Though 
the  truths  of  mathematics  are  necessary  and  a  priori, 
this  does  not  imply  that  they  are  purely  analytical,  as 
Couturat  maintains  :  it  is  erroneous  to  believe,  as  David 
Hume  did,  that  thought  is  synthetical  only  in  empiric  - 
knowledge,  when  it  derives  its  materials  from  experience,  \ 
and  that  a  priori  deduction  never  affords  us  anything 
new.    Even  in  abstract  calculation  mathematical  thought 
is_  essentially  inventive   and  constructive,   and  every 
analysis  presupposes  the  synthesis  completed  in  the  act  of 
definition.    In  so  far  as  you  can  derive  the  rules  of  arith- 
metical operations  from  the  rules  of  the  logical  calculus, 
your  thought  has  already  formed  in  the  eight  indefinable 
notions  and  twenty  undemonstrable  principles  the  con- 
ceptual synthesis  necessary  for  all  the  following  analyses. 
Modern  logic  differs  from  the  older  form  in  that  it  conO 
denses  and  absorbs  within  itself  in  a  more  generic  form  \ 
principles  and  definitions  which  were  previously  scattered  • 
throughout  the  different  branches  of  mathematics ;  so 
that,  whereas  in  the  old  constructions  the  foundations 
were  laid  little  by  little  as  the  need  for  them  became 


apparent  in  order  that  the  process  of  deduction  might 
be  continued,  and  the  single  synthetic  acts  were  carried 
out  case  by  case,  in  the  new  logical  edifice  the  whole  basis 
is  constructed  from  the  very  first  and  the  particular 
syntheses  are  condensed  into  one  wider  synthesis. 
This  form  of  systematisation  of  pure  mathematics  may 
also  be  preferable  to  the  older  one,  in  as  much  as  it 
saves  useless  repetitions  of  analogous  synthetic  acts 
in  the  individual  sciences,  and  in  their  different  depart- 
ments, and  gives  prominence  to  the  logical  unity 
of  mathematical  knowledge ;  it  does  not,  however, 
eliminate  the  synthesis  which  is  merely  shifted,  con- 
centrated, and  disguised  in  the  definitions  and  initial 
principles.  Moreover,  the  work  of  constructive  activity 
is  not  wholly  excluded  even  in  successive  deductions  ; 
this  activity  manifests  itself  in  the  combination  of  the 
elements  originally  defined  into  new  products,  which 
are  not  merely  a  juxtaposition  of  entities  and  principles, 
admitted  from  the  first,  but  organic  syntheses  of  them. 
Each  new  notion  is  denned  by  a  complex  of  properties, 
and,  although  these  properties  may  have  been  known 
already  through  the  definitions,  the  thought  of  the 
whole  is  always  something  new;  even  if  it  be  merely 
thought  of  as  possible,  at  all  events  we  must  have  a 
concept  of  it.  Neither  can  it  be  said  to  be  but  a  new 
name,  since  in  the  hypothetical  judgment  it  is  implicitly 
admitted  that  an  objective  entity  can  exist  which 
verifies  all  the  properties  at  one  and  the  same  time  ; 
this  entity  is  certainly  not  the  word,  but  that  which 
is  symbolised  by  the  word,  that  is  to  say,  that  which  is 
thought  by  its  means.  The  Kantian  doctrine  which 
would  derive  the  synthetic  character  of  mathematics  from 
its  intuitive  nature  does  not  hold  good  of  the  calculus, 
to  which  intuition  is  not  essential,  but  the  activity  of 
thought  in  its  a  priori  deductions  is  none  the  less 
fruitful  in  new  products,  which,  constructed  as  they 
are  in  accordance  with  its  intimate  laws,  bear  the 
imprint  of  universality  and  necessity. 

14.  Russell    on    the    Philosophical    Consequences    of 


Mathematical  Logic. — Russell  has  considered  himself 
entitled  to  draw  certain  important  philosophical  con- 
clusions from  his  logico-mathematical  theories.65  The 
theory  which  resolves  the  continuum  into  an  infinite 
number  of  distinct  elements  without  any  contradiction 
has  robbed  of  their  value  the  idealistic  doctrines  of  space 
and  time  which  were  based  upon  the  alleged  antimonies 
of  the  actual  infinite.  Realism  is  thus  restored  to  its 
place  of  honour.  Mathematics  further  teaches  us  that 
there  are  certain  fundamental  and  irreducible  con- 
cepts (the  logical  constants),  and  certain  primitive 
undemonstrable  propositions,  which  enable  us  to  con- 
struct a  system  of  truths,  recognised  by  us,  in  their 
deductive  relations,  without  the  need  of  an  appeal 
to  experience.  Every  general  proposition  transcends 
the  bounds  of  sensible  knowledge,  which  is  limited 
to  the  particular  case,  and  never  authorises  us  to 
formulate  a  principle  having  universal  extension. 
Induction  is  at  bottom  but  a  deduction  based  upon  a 
certain  premiss,  i.e.  upon  the  principle  of  induction, 
which  cannot  be  derived  from  experience  without 
a  vicious  circle,  and  must  therefore  be  recognised  as  an 
a  priori  truth.  Empiricism  is  then  false,  but  no  less 
false  is  the  idealism  which  believes  that  the  salvation 
of  the  universality  of  a  priori  truths  lies  in  reducing 
those  truths  to  subjective  forms  of  the  mind.  If  general 
truths  were  merely  the  expression  of  psychological  facts 
we  could  not  be  sure  of  their  constancy  or  legitimately 
make  use  of  them  in  order  to  deduce  one  fact  from 
another,  because  they  would  not  connect  facts,  but 
only  our  ideas  about  facts.  Mathematical  logic  then 
forces  us  to  admit  a  species  of  realism  in  the  Platonic 
and  scholastic  sense,  to  conceive,  that  is  to  say,  a  world 
of  universals  having  a  reality  of  its  own  external  to  space, 
time,  and  the  mind  of  man.  This  world  must  subsist, 
though  it  may  not  exist  in  the  same  sense  as  that  in' 
which  particular  facts  exist.  We  have  direct  knowledge 
by  acquaintance  of  universals,  just  as  we  have  of  sensible 
data ;  of  material  objects  on  the  other  hand,  existing  in 


time  and  space,  independently  of  our  subjective  percep- 
tions, we  can  only  have  indirect  knowledge  by  description, 
by  making  use  of  a  combination  of  universal  ideas  and 
sensible  experience.  Such  knowledge  is,  however,  always 
far  from  perfect,  whereas  our  immediate  intuition  of  the 
eternal  relations  constituting  in  their  ideal  combinations 
the  system  of  mathematical  logic,  is  extremely  perfect. 

15.  The  New  Realism. — Closely  connected  with  this 
Platonising  tendency  of  the  Cambridge  school,  of  which 
the  chief  representatives  are  Bertrand,  Russell,  and 
George  Moore,  is  the  new  realism,  which  has  recently 
been  the  subject  of  so  much  discussion  in  England  and 
America.66  This  new  realism  is  based  upon  the  mathe- 
matical theory  of  the  externality  of  relations  set  forth 
by  Russell,  according  to  which  terms  are  in  no  way 
altered  by  the  relation  established  between  them,  so 
that  one  and  the  same  entity  may  be  a  constituent  of 
many  different  complexes.  Knowledge  itself  is  an 
external  relation :  the  object,  when  known,  remains 
the  same  object  which  existed  outside  the  relation 
with  the  subject.  It  therefore  follows  that  everything 
which  we  perceive  or  imagine  exists  objectively  also  just 
as  it  is  presented  to  our  consciousness.  The  new  realism 
differs  from  the  older  realism  in  that  it  does  not  admit 
that  the  things  external  to  thought  are  different  from 
the  contents  present  to  our  consciousness,  that  is  to  say, 
in  its  "  epistemological  monism"  which  identifies  the 
real  object  with  that  which  is  immediately  present  to  us 
in  the  act  of  perception.  On  this  point  the  new  realism 
disagrees  with  Russell,  who  maintains  that  "  if  there  are 
to  be  public  neutral  objects,  which  can  in  some  sense 
be  known  to  many  different  persons,  these  objects  are 
not  identical  with  the  private  and  particular  sense- 
data  which  appear  to  various  people." 

In  my  opinion  the  fundamental  error  of  the  new 
realism  will  be  found  in  its  starting-point,  that  is  to 
say,  in  the  theory  of  the  externality  of  relations  applied 
to  the  cognitive  relation.  Relations  are  external  only 
in  abstract  mathematics,  in  which  the  terms  can  be 

en.  ii      ELABORATION  OF  PURE  MATHEMATICS         337 

ranged  side  by  side,  and  united  by  a  sign  which  sym- 
bolises their  relation,  without  in  any  way  modifying 
them.  The  number  8,  for  instance,  will  always  remain 
the  same  number  in  all  the  relations  in  which  it  can  be 
placed  to  other  numbers  :  8  x  4,  8  +  3,  8  -  5,  8 > 2,  etc. 
But  if  we  leave  the  world  of  abstractions  for  the  realm 
of  concrete  reality,  it  is  a  matter  of  common  experience 
that  things  are  subjected  to  physical  changes  by  the"] 
action  of  other  things  standing  in  certain  determinate 
relations  to  them.  It  has  been  rightly  observed  thaV 
the  new  realism  fails  to  afford  an  adequate  explana- 
tion of  the  production  of  illusions  and  hallucinations,  ^ 
all  of  which  should  correspond  to  objects  existing 
outside  consciousness  just  in  the  same  way  as  they  are 
imagined.  The  new  realism  cannot  turn  to  the  physio- 
logical action  of  the  organism  for  an  explanation  of 
illusion,  since  by  doing  so  it  would  deny  its  doctrine  of  f 
the  externality  of  relations  :  if  the  object  appears  in 
different  ways  according  to  the  different  organisms 
with  which  it  enters  into  relations,  it  is  obvious  that 
these  relations  are  not  external.  The  illusory  appearance 
is  a  real  fact,  but  it  is  so  only  in  that  particular  context 
of  psycho -physiological  relations;  and  every  other 
content  of  sensation  is  real  in  the  same  sense ;  but  to 
admit  that  this  content  remains  identical  even  when 
Hhe  relations  are  changed  is  to  contradict  our  most 
!  certain  experiences. 

16.  Meinong's  Theory  of  Objects. — Russell's  mathe- 
matical realism  has  manypoints  of  contactwith  Meinong's 
theory  of  objects.67  As  opposed  to  empirical  sciences 
!  (Wirklichkeitswissenschaften)  which  deal  with  existing 
reality  (the  Daseiri),  the  theory  of  objects  is  the  science 
of  the  Sosein,  the  rational  essence,  which  can  be 
elaborated  a  priori  independently  of  any  considera- 
tion of  existence  (WirMichJceitsfreie  oder  Daseinsfreie 
Wissenschaft).  We  have  an  example  thereof  in 
mathematics,  whose  object  is  not  the  real,  but  the 
ideal,  that  which  subsists  (besteht),  although  it  may 
not  exist  as  do  the  phenomena  studied  by  the  empirical 



sciences.  In  addition  to  the  facts  immediately  ex- 
perienced, such  as  colours,  sounds,  desires,  etc.,  we 
must  admit  objects  of  a  higher  order,  such  as  like- 
nesses, equalities,  diversities,  complexes,  etc.,  upon 
which  we  pronounce  a  priori  judgments.  AccorcLing 
to  Meinong,  the  theory  of  objects  embraces  not  only 
the  study  of  these  relations,  but  also  that  of  a  series  of 
objects  which  of  their  very  nature  are  not  comprised 
within  the  field  of  any  of  the  sciences  hitherto  known, 
and  which  Meinong  terms  homeless  objects  (heimadose 
Gegenstande).  Sensorial  contents,  for  instance,  cannot 
be  the  object  of  the  psycho -physiology  of  the  senses, 
which  does  not  treat  of  these  contents  in  themselves 
and  in  their  relations,  but  only  of  the  way  in  which 
they  are  subjectively  apprehended  in  relation  to  the 
organism ;  nor  yet  that  of  physics  whose  task  it  is  to 
study  the  objective  stimuli  of  sensations,  for  instance, 
vibrations  of  the  air  or  of  ether,  not  sounds  and 
colours.  Another,  as  yet  unexplored  field  of  research, 
is  that  of  impossible  objects,  as,  for  instance,  the  round 
square,  non-extended  matter,  etc.  Russell M  has  re- 
marked that  these  objects  would  divest  the  principle 
of  contradiction  of  its  universal  validity,  but  to  this 
Meinong &  has  replied  that  this  principle  is  valid  of 
objects  which  are  possible  and  real,  not  of  those  which 
are  impossible,  and  that  the  round  square,  non-extended 
matter,  etc.,  are  not  reducible  to  mere  flatus  vocis,  mere 
complexes  of  letters,  since  these  complexes  exist  psycho- 
logically, which  is  not  the  case  with  impossible  objects. 
The  delicate  subtleties  of  Meinong's  arguments  can- 
not, however,  invest  this  alleged  theory  of  impossible 
ob j  ects  with  meaning.  How  can  you  rationally  elaborate 
that  which  is  contradictory,  or  apply  the  laws  of 
thought  to  that  which  is  constructed  in  antagonism  to 
those  laws  ?  With  regard  to  sensorial  contents  which 
Meinong  considers  should  be  studied  by  the  new  theory, 
his  assertion  that  research  into  them  is  not  within  the 
province  either  of  physics  or  psychology  does  not  appear 
to  me  to  be  accurate.  When  Meinong  states  that  the 


object  of  physics  is  not  colours  and  sounds,  but  rather  the 
vibrations  of  ether  and  air,  it  is  clear  that  he  is  confusing 
the  object  of  science  with  the  explanatory  theory ; 
you  might  equally  well  say  that  chemistry  does  not  study 
metals,  salts,  acids,  etc.,  but  the  relations  of  atoms.  If 
sensorial  contents  be  thus  eliminated  from  the  theory  of 
objects,  nothing  will  remain  but  relations  and  complexes, 
which  Meinong  regards  as  having  no  existence,  hence 
the  name  science  of  the  non-existing,  which  distinguishes 
the  theory  of  objects  from  the  empirical  sciences.  Now 
it  seems  to  me  that  an  artificial  division  is  thus  made 
between  the  two  forms  of  knowledge  which  renders  their 
interpenetration  in  the  concrete  fife  of  science  impos- 
sible of  explanation.  Were  a  priori  deduction  merely 
the  instrument  of  knowledge  of  the  non-existent,  it 
would  be  an  abuse  to  make  use  of  it  in  the  science  of  the 
existent.  How,  too,  could  this  illegitimate  transition 
jattain  success  ?  How  could  mathematical  deduction, 
the  organ  of  knowledge  unfettered  by  existence,  enable 
us  to  make  previsions  concerning  existence  ? 

17.  Criticism  of  Russell's  Theory. — Russell's  theory 
partly  escapes  these  criticisms,  because  it  regards  the 
.deal  world  as  subsisting,  if  not  existing  ;  it,  too,  however, 
has  made  the  grave  mistake  of  setting  up  an  insuperable 
barrier  between  sensible  cognition  and  rational  know- 
.edge.  This  new  form,  of  realism  raises  once  more  the 
-self-same  difficulties  which  perplexed  the  mind  of 
Plato,  and  which  were  already  emphasised  by  Aristotle. 
The  doctrine  of  the  exteriority  of  relations  accentuates 
the  want  of  agreement  between  the  two  worlds,  and 
rjurns  the  process  of  knowledge  into  an  incomprehensible 
nystery.  On  the  one  side,  in  fact,  we  have  eternal 
relations ;  on  the  other,  things  in  time  and  space ;  and  in 
addition  to  and  external  to  them  both,  human  conscious- 
less.  Each  relation  is  external  to  every  other,  each 
:hing  external  to  all  others,  each  consciousness  external 
ind  impenetrable  to  the  rest.  We  may  now  ask,  How 
ind  by  what  miraculous  means  is  that  union  of  the  ideal 
ind  the  real  brought  about  which  is  necessary  to  the 


cognitive  act  ?  The  subject,  reduced  to  a  mere  mirror 
which  is  to  reflect  external  relations  on  the  one  hand 
and  the  facts  of  experience  on  the  other,  while  itself 
remaining  unaltered,  will  certainly  not  be  equal  to  such 
a  task  of  mediation,  because  even  with  regard  to  it  and 
in  it  the  universal  idea  and  immediate  experience  will 
remain  outside  each  other.  It  is  useless  to  turn  to 
an  exterior  relation  between  the  idea  and  immediate 
experience,  first,  because  in  the  world  of  objective  things 
constructed  by  science  the  concept  and  the  fact  do 
not  remain  external  to  each  other,  but  pervade  one 
another  in  a  synthesis  which  transfigures  both  of  them ; 
and  further,  because  the  external  relation  between  the 
idea  and  the  phenomenon  would  not  resolve  the  problem, 
but  would  merely  add  another  eternal  relation  to  the 
others  which  the  mind  must  receive  from  without.  Of 
this  new  relation,  in  turn,  the  question  might  once  more 
be  asked,  "  How  is  its  union  with  the  sensible  world 
possible  ? " 

We  are  confronted  by  still  more  serious  difficul- 
ties in  the  conception  of  the  relation  of  the  subject  to 
these  real  entities.  How  can  the  revelation  of  them 
to  consciousness  be  possible  ?  Does  not  consciousness 
undergo  a  certain  modification  in  the  act  of  intuiting 
ideas  through  this  very  act  ?  Or  are  we  to  grant,  in 
order  to  save  the  theory  of  the  externality  of  relations, 
that  the  subject  thinking  the  principle  of  inclusion,  for 
instance,  is  the  same  subject  as  that  to  whose  conscious- 
ness it  was  not  present  before  ?  Does  not  sensible 
experience  modify  the  subject  to  a  certain  extent  ? 
Do  subject  and  object  remain  external  to  each  other  in 
that  experience  also  ?  Or  is  that  experience  a  purely 
subjective,  individual  fact,  not  due  to  the  action  of 
external  reality  ?  In  that  case  by  what  right  do  you 
make  use  of  it,  as  well  as  of  the  idea,  in  order  to  gain 
indirect  knowledge  of  real  things  ?  How  do  eternal 
relations  make  their  way  into  the  consciousness  ?  How 
is  a  relation  set  up  between  thought  and  that  which 
is  thought  ?  If  this  relation,  too,  be  an  external  one, 


we  return  to  our  starting-point,  since  we  must  explain 
how  such  a  relation,  which  you  affirm  to  be  real,  can 
become  the  object  of  your  mind,  that  is  to  say,  how  it 
can  enter  into  relation  therewith.  In  the  incoherent 
dust-storm  of  facts  and  external  relations  we  shall  vainly 
seek  that  synthetic  principle  which  shall  account  for 
the  possibility  of  knowledge,  and  that  organic  unity  of 
thought  and  reality  which  alone  can  render  knowledge 


1  Leibnitz  was  conscious  of  the  need  for  the  extension  of  mathematics, 
and  conceived  a  geometrical  calculus  which  could  be  directly  applied  to 
figures  without  the  mediation  of  numbers  and  express  situs  directly,  as 
algebra  does  magnitude*  (Lettre  a  Huygens,  September  8,  1679).     "  Datur 
.  .  .  analysis  geometriae  sublimior  per  proprios  characteres,  qua  multa 
pulchrius  breviusque  quam  per  algebram  praestantur"  (De  scientia  uni- 
versali  sen  calculo  philosophico,  1684).      Cp.  Couturat,   "  L'Algebre  uni- 
verselle  de  Whitehead,"  Revue  de  met.  et  de  mor.,  May  1910  ;  Les  Principes 
de  mathematiques  (Paris,  1905),  pp.  1-2. 

2  "  Sur  1'arithmetisation  des  mathematiques,"   Nouvelles  Annales  de 
mathematiques,  March  1807. 

3  The  first  suggestion  of  this  "  scriptura  universalis  "  will  be  found  in 
Leibnitz,  "  Logicae  inventionis  semina,"  Math.  Schriften,  voL  v.     Logistic 
assumed  a  specially  scientific  form  through  the  works  of  De  Morgano, 
Formal  Logic  (London,  1847) ;    Boole,  An  Investigation  of  the  Laws  of 
Thought  (London,  1854) ;   Schroeder,  Der  Operationskreis  der  Logikkalkuls 
(Leipzig,    1872) ;    Algebra    der    Logik   (Leipzig,    1890-95) ;    and    Peano, 
Formulaire  de  mathematique  (Turin,  Bocca,  1894-1906). 

*  This  extension  is  mainly  due  to  Russell,  "  Sur  la  logique  des  relations 
avec  des  applications  a  la  theorie  des  series,"  Sevista  di  matematica  del 
Piano,  vol.  vii.  (Turin,  1902),  pp.  115-147. 

5  Arithmetices  principia,  nova  metodo  exposita  (Turin,  1889). 

6  Calcolo  geometrico    secondo  I'    Ausdehnungslehre    di  H.   Grassmann, 
preceduto  dalle  operazioni  della  logica  deduttiva  (Turin,  1888),  Preface,  pp.  5-6. 

The  following  are  examples  of  these  geometrical  notations :  If  the 
volume  ABCD  indicate  a  tetrahedron,  the  formula  ABCD=O  means 
that  the  points  ABCD  are  situated  in  the  same  plane ;  if  A  be  a  point 
and  a  be  a  plane,  Aa=O  (i.e.  tetrahedron  Aa  is  nothing)  indicates  that  the 
point  A  is  situated  in  the  plane  a  ;  if  a,  b  be  two  lines,  ab  =  0  means  that 
the  lines  a,  b  are  situated  in  the  same  plane,  i.e.  either  that  they  meet  or 
are  parallel  (op.  cit.  p.  33). 

7  Peano,  /  Principii  di  geometria  hgicamente  esposti  (Torino,  1889),  p.  3. 

8  "  I  Principii  della  geometria  di  posizione  composti  in  sistema  logico 
deduttivo,"  Memorie  della  R.  Accademia  delle  Scienze  di  Torino,  serie  xi. 
voL  xlviii.,  1898  ;    "  Nuovo  Metodo  di  svolgere  deduttivamente  la  geo- 
metria proiettiva,"  Rendiconti  del  R.  Istituto  Lombardo,  voL  xxxi.,  1898  ; 
"  Della  geometria  elementare  come  sistema  ipotetico  deduttivo.     Mono- 


grafia  del  punto  e  del  moto,"  Memorie  della  R.  Accademia  delle  Scienze  di 
Torino,  serie  ii.  voL  xlix.,  1900. 

'  Fieri,  "  Snr  la  geometrie  envisagee  comme  un  systeme  purement 
logique,"  Bibliotheque.  du  Congres  International  de  Philosophic  (Paris,  1901), 
voL  iii.  pp.  268-377. 

"  A  Treatise  on  Universal  Algebra  (Cambridge,  1898). 

u  Couturat,  Article  quoted  in  Rev.  de  met.  et  de  mor.,  May  1900,  p. 
259  ff. 

11  The  Principles  of  Mathematics,  voL  i.  (Cambridge,  University  Press, 

u  "  Pure  mathematics  is  the  class  of  all  propositions  of  the  form  '  p 
implies  q,'  where  p  and  q  are  propositions  containing  one  or  more  variables, 
the  same  in  the  two  propositions,  and  neither  p  nor  q  contains  any  constants 
except  logical  constants."  The  logical  constants  according  to  Russell 
are  :  implication,  the  relation  of  a  term  to  a  class  of  which  it  is  a  member, 
the  notion  of  such  that,  the  concepts  of  relations,  of  prepositional  function 
and  of  class,  the  notion  of  denoting  and  of  any  or  every  term  (op.  cit. 
p.  3  e  p.  106). 

14  Russell,  "  Recent  Work  on  the  Principles  of  Mathematics  "  (Inter- 
national Monthly,  voL  iv.  No.  1,  p.  84). 

w  Russell,  Principles  of  Mathematics,  pp.  13-32.  We  cannot  here  set 
forth  the  whole  development  of  these  calculi :  we  merely  give  a  few 
examples  in  order  that  the  reader  may  be  able  to  form  a  general  idea 
of  them.  In  the  calculus  of  propositions  the  logical  product  of  two  pro- 
positions means  that  both  propositions  are  true  at  one  time,  and  the 
commutative  law  applies  thereto  (if,  for  example,  p  be  true  together 
with  q,  q  is  true  together  with  p),  as  do  also  the  associative  law  (if  p  be 
true  together  with  the  simultaneous  affirmation  of  q  and  r,  the  simultaneous 
affirmation  of  p  and  q  is  true  together  with  r) ;  the  principle  of  simplifica- 
tion (the  simultaneous  affirmation  of  p  and  q  implies  the  affirmation  of  p) ; 
and  the  principle  of  composition  (if  p  imply  q  and  p  imply  r,  p  implies  the 
simultaneous  affirmation  of  q  and  r).  The  logical  sum  of  two  proposi- 
tions is  defined  as  the  proposition  which  is  implied  in  each  of  them  and 
implies  every  proposition  implied  in  each  of  them.  In  the  calculus 
of  the  propositions  is  enunciated  amongst  others  the  principle  of  the 
hypothetical  syllogism  ;  if  p  imply  q  and  q  imply  r,  p  implies  r.  In  the 
calculus  of  classes  a  prepositional  function  is  defined  as  a  logical 
function  which  becomes  a  proposition  for  every  value  attributed  to  the 
variable  or  variables :  the  totality  of  values  verifying  the  prepositional 
function  constitutes  a  class.  An  axiom  of  the  calculus  of  classes 
is  that  if  two  prepositional  functions  be  equivalent,  the  correspond- 
ing classes  are  equal  The  logical  product  of  the  classes  a  and  b  is  the 
totality  of  the  values  of  the  variable  x,  which  are  at  the  same  time  a 
and  b ;  the  logical  sum  of  the  classes  a  and  b  is  the  totality  of 
the  variables  x,  which  are  either  a  or  6.  The  calculus  of  relations  deals 
with  the  relations  of  equivalence,  implication,  etc.,  in  general  One 
of  the  axioms  of  this  calculus  is  that  every  relation  can  be  inverted,  that  is 
to  say,  that  if  the  relation  R  exist  between  any  two  terms  x  and  y,  a  relation 
also  exists  between  y  and  x,  which  is  termed  the  inverse  of  R.  Another 
axiom  is  that  every  relation  has  its  negative  which  is  also  a  relation.  It 
can  be  proved  that  the  inverse  of  the  negative  is  identical  with  the  negative 
of  the  inverse.  If  there  exist  a  relation  R  between  the  individuals  x  and  y, 
and  a  relation  S  between  y  and  z,  there  will  exist  between  x  and  z  another 
relation  which  is  termed  the  relative  product :  the  relative  product  of 
two  relations  is  also  a  relation :  the  relation  of  uncle,  for  instance,  is  the 

en.  ii       ELABORATION  OF  PURE  MATHEMATICS         343 

relative  product  of  the  relations  of  brother  and  father.  Relative  multiplica- 
tion in  general  is  not  commutative ;  for  instance,  my  brother's  father  is 
not  my  uncle. 

18  Op.  cit.  p.  112. 

17  "  Les  Definitions  mathematiques,"  Bibliotheque  du  Congres,  vol.  iii. 
p.   279  ;    Burali-Forti,   "  Sur  les  differentes  methodes  logiques  pour  la 
definition  du  nombre  reel,"  ibid.  p.  289 ;    Padoa,   "  Essai  d'une  theorie 
algebrique  des  nombres  entiers,  precede  d'une  introduction   logique   a 
une  theorie  deductive  quelconque,"  ibid.  p.   309 ;    Burali-Forti,  Logica 
matematica  (Milan,  1894),  pp.  120-130. 

18  Peano,  op.  cit.  p.  288. 

19  Couturat,  Principes  des  mathematiques,  p.  39  ff. 

20  The  theory  of  substitutions  was  originated  by  Galois.    The  name  sub- 
stitution is  applied  to  the  transition  from  one  arrangement  of  objects,  that  is 
to  say,  from  one  permutation  to  another.     An  assemblage  of  substitutions 
of  n  objects  form  a  group  if  the  result  obtained  by  effecting  successively 
two  substitutions  of  this  assemblage  can  be  obtained  with  a  single  sub- 
stitution of  the  assemblage  ;  in  other  terms,  if  the  product  of  two  substitu- 
tions be  equivalent  to  a  single  substitution  of  the  assemblage.    In  particular, 
all  the  possible  substitutions  of  n  objects  form  a  group.     The  notion  of 
group  is  very  general  and  can  be  applied  not  only  to  substitutions,  but  also 
to  all  arithmetical  operations  and  to  analytical  transformations  of  all  kinds. 
Thus  the  labours  of  Sophus  Lie  have  made  the  theory  of  groups  of  trans- 
formations into  a  method  of  marvellous  extension  and  fruitfulness. 

21  Russell,  op.  cit.  pp.  111-120 ;  Couturat,  "  Sur  une  definition  logique 
du  nombre,"  Revue,  de  met.  et  de  mor.,  January  1900,  p.  21  ff.  ;   "  Sur  les 
rapports  du  nombre  et  de  la  grandeur,"   ibid.,  July  LM'M,  p.  422  ff.  ; 
Russell,   "  On  the  Relations  of   Number  and   Quantity,"   Mind,  N.S., 
vol.  vi.  No.  23. 

22  Was  sind  und  was  sollen  die  Zahlen  ?  (Brunswick,  1887). 

23  Science  et  hypothese,  p.  20  ff. 

24  "  Qrundlagen  einer  allgemeinen  Mannigfaltigkeitslehre "   (Leipzig, 
1883),  Math.  Ann.  voL  xxi. 

26  See  what  has  already  been  said  in  Chapter  II.  Part  I.  on  this  apparent 
paradox  a  propos  of  Renouvier's  criticism  of  the  infinite. 

28  "Sui    fondamenti     della     geometria    proiettiva,"     postulate    vii., 
JRendiconti  del  R.  Istituto  Lombardo,  serie  ii.  vol.  xxix.,  1897. 

27  "  Beitrage  zur  Begriindung  der  transfiniten  Mengenlehre,"   Math. 
Annalen,  vol.  xlvi.,  1895,  and  vol.  xlix.,  1897. 

28  Russell,  op.  cit.  p.  299  ;  Couturat,  op.  cit.  p.  95  ;   "  Sur  la  definition 
du  continu,"  Rev.  de  met.  et  de  mor.  vol.  viii.  pp.  157-168. 

29  Math.  Annalen,  vol.  xxxvi.  pp.  157-160. 

30  Op.  cit.  p.  132. 

31  It  is  superfluous  to  remark  that  the  relations  in  question  are  non- 
symmetrical  and  transitive,  like  those  characterising  linear  order.    Russell, 
op.  cit.  p.  374  ff.  ;  Couturat,  op.  cit.  p.  134. 

32  In  the  two  articles  already  quoted  :   "I  Principii  della  geometria  di 
posizione,  etc.,"  and  "  Nuovo  modo  di  svolgere  deduttivamente  la  geo- 
metria proiettiva."     In  the  latter,  Pieri  constructs  projective  geometry 
with  primitive  entities  (projective  point  and  homography)  and  postulates 
differing  from  those  of  the  first  article.   These  two  hypothetical  and  parallel 
developments  are  an  extremely  interesting  example  of  equivalent  systems, 
i.e.  such  as  permit  of  the  primitive  entities  of  the  one  being  defined  by  those 
of  the  other,  and  the  primitive  propositions  of  the  one  being  deduced  from 
the  postulates  of  the  other.     This  proves  the  choice  of  indefinable  entities 


and  of  primitive  propositions,  which  are  not  capable  of  proof,  to  be 
arbitrary  (Rendiconti  del  R.  Istituto  Lombardo  di  Scienze  e  Lettere,  aerie  ii. 
vol.  xxxi.  p.  797). 

**  Op.  tit.  p.  82. 

84  Op.  cit.  pp.  404-407. 

**  "  La  Geometria  basata  sull'  idea  di  punto  e  di  distanza,"  Atti 
della  R.  Accademia  delle  Scienze  di  Torino,  1902. 

«•  Enriques,  Questioni  riguardanti  la  geometria  elementare  (Bologna, 
1900),  Article  3,  ''  Della  congruenza  e  del  movimento." 

17  In  the  Article  already  quoted,  "  Delia  geometria  elementare  come 
sistema  ipotetico  deduttivo." 

38  The  following  are  some  of  the  postulates  laid  down  by  Fieri  (M emorie 
della  R.  Accademia  delle  Scienze  di  Torino,  serie  ii.  vol.  xlix.  p.  179  ff.) 
as  the  basis  of  metrical  geometry:  —  (1)  The  point  and  motion  are 
generic  and  class  concepts.  (2)  At  least  one  point  exists.  (3)  If  p  be  a 
point,  there  exists  a  point  differing  from  p.  Every  assemblage  of 
points  shall  be  termed  a  figure.  Two  figures  are  identical  (or  coincide) 
when  they  are  composed  of  the  same  points.  Two  points  are  identical 
(or  coincide)  when  every  figure  containing  one  of  them  contains  the  other 
also.  (4)  Every  motion  is  a  bi-uniform  correspondence  of  two  figures  ; 
this  means  that  identical  points  correspond  to  identical  points,  and  different 
points  to  different  points,  etc. 

*•  Couturat,  op.  cit.  p.  204. 

40  Op.  cit.  pp.  205-207. 

41  Russell,  op.  cit.  p.  372. 

**  American  Journal  of  Mathematics,  vol.  iv.,  1881,  p.  97  ff. 

48  Couturat,  op.  cit.  pp.  242-246 ;  cp.  also  Frege,  Grundgesetze  der 
Arithmetik  begriffschafilich  abgeleitet  (Jena,  1893-1903),  in  two  volumes. 
In  this  work  the  whole  of  arithmetic  is  constructed  analytically. 

44  Couturat,  op.  cit.  p.  250. 

48  Op.  cit.  p.  253. 

«•  Op.  cit.  p.  257. 

47  Op.  cit.  p.  267. 

48  Op.  cit.  pp.  279-285. 

49  Op.  cit.  p.  293. 

80  Conferences  sur  les  mathematiques  (Paris,  1895),  Lecture  VIII. 

81  Op.  cit.  p.  45. 

M  La  Valeur  de  la  Science,  p.  11  ff. 

83  Both  Borel  in  "  La  Logique  et  1'intuition  en  mathematique,"  Revue 
de  met.  et  de  mar..  May  1907,  and  Lucas  de  Peslouan  in  Les  Systemes 
logiques  et  la  logistique  (Paris,   1909),  p.   13  ff.,   p.  220,  also  place  the 
necessity  of  intuition  for  the  discovery  of  mathematical  truths  in  opposi- 
tion to  logistic. 

84  "  Pour  la  logistique,"  Rev.  de  met.  et  de  mor.,  March  1906,  p.  214  ff. 
u  "  Les  Mathematiques  et  la  logique,"  Revue  de  met.  et  de  mor.,  November 

1905,  pp.  215-835 ;  January  1906,  pp.  17-36  ;  May  1906,  pp.  294-317. 
"A  propos  de  la  logistique,"  ibid.,  1906,  pp.  866-868.  See  also  the 
criticisms  of  Winter,  Borel  (ibid.,  May  1907),  and  Reymond,  Logique  et 
mathematiques  (Paris,  1908),  p.  133  sq.  These  criticisms  have  been  replied 
to  by  Russell :  "  Sur  la  relation  des  mathematiques  et  de  la  logistique," 
Revue  de  met.  et  de  mor.,  November  1905,  pp.  906-917  ;  "  Les  Paradoxes 
de  la  logique,"  ibid.,  September  1906,  pp.  627-650 ;  Couturat,  "  Pour  la 
logistique,"  ibid.,  March  1906,  p.  208  sq. ;  Pieri,  "  Sur  la  Compatibility 
des  axiomes  de  1'arithmetique,"  ibid.,  March  1906,  p.  196  ff. 

*•  "  Pour  la  logistique,"  Revue  de  met.  et  de  mor.,  March  1906. 


67  Op.  cit.  p.  69. 

68  Couturat  (op.  cit.  p.  51)  writes  as  follows :   "  It  is  certainly  not  for- 
bidden to  think  of  concepts  and  their  relations  through  their  intensions, 
but  they  only  enter  into  our  formulas  by  their  extension,  and  their  relations 
in  extension  are  those  which  form  the  basis  of  the  logical  calculus." 

69  Op.  cit.  p.  36. 

60  Op.  cit.  p.  39. 

61  Poincar6  lays  special  emphasis  upon  this  point  in  his  polemic  against 
the  logisticians  (Article  already  quoted). 

62  See  Article  quoted  above. 

63  Fieri  in  his  more  recent  utterance  (Uno  Sguardo  al  nuovo  indirizzo 
logico-mathematico  dette  scienze  deduttive  (Catania,  1907),  p.  51  ff.,  observes 
that  Russell's  logical  constants,  though  sufficient  for  the  construction  of 
numerical  and  geometrical  entities,  are  insufficient   to  assure  us  of  their 
existence.     He  considers  that  the  following  existential  judgment  should  be 
included  among  our  logical  premisses :  "  There  exists  at  least  one  infinite 
class  of  entities,"  to  deduce  the  existence  of  the  whole  numbers  from  them. 
From  this  it  would  then  be  possible  to  derive  the  existence  of  any  other 
mathematical  entity  we  choose. 

64  Besides,  Russell  too  recognises  the  necessity  of  having  recourse  to 
intuition,  "  Les  Paradoxes  de  la  logique,"  Revue  de  met.  et  de  mor.,  September 
1906,  p.  630  S. 

85  "  L' Importance  philosophique  de  la  logistique,"  Revue  de  met.  et  de 
mor.,  1911,  p.  283  ff. ;  The  Problems  of  Philosophy  (London,  1912); 
"  The  Basis  of  Realism,"  Journal  of  Philosophy,  Psychology,  and  Scientific 
Methods,  vol.  viii.  p.  158  ff. 

66  "  The  Programme  and  first  Platform  of  six  Realists,"  Journal  of 
Philosophy,  Psychology,  and  Scientific  Method,  voL  vii.  p.  393  ff. ;    The 
New  Realism ;  Co  •  operative  Studies  in  Philosophy,  by  Edwin  B.  Holt, 
Walter  T.  Marvin,  William  Pepperell  Montague,  Ralph  Barton  Perry, 
Walter  B.  Pitkin,  and  Edward  Gleason  Spaulding  (New  York,   1912). 
Dewey,  "The  Short  Cut  to  Realism  examined,"  Journal  of  Philosophy, 
Psychology,    and    Scientific    Method,    voL    vii.    p.    553   ff.  ;     Spaulding, 
"  Realism,  a  Reply  to  Professor  Dewey,"  ibid.  voL  viii.  p.  63  ff. ;   Dewey 
"  Rejoinder  to  Dr.  Spaulding,"  ibid.  voL  viii.  p.  77  ff. ;    Drake,  "  The 
Inadequacy  of  Natural  Realism,"  ibid.  vol.  viii.  p.  365  ff. ;  •  Dewey,  "  Brief 
Studies  in.  Realism,"  ibid.  vol.  viii.  p.  393  ff. ;  p.  546  ff.,;    Calkins,  "  The 
Idealist  to  the  Realist,"  ibid.  vol.  viii.  p.  449  ff.  ;   Love  joy,  "  Reflections 
of  a  Temporalist  on  the  New  Realism,"  ibid.  vol.  viii.  p.  58  ff. ;    "  On  some 
Novelties  of  the  New  Realism  and  Subjectivism,"  ibid.  vol.  x.  p.  43  ff.  ; 
Cohen,    "  The  New   Realism,"    ibid.   vol.   x.   p.  197   ff. ;    Perry,   "  Some 
disputed  Points  in  neo-Realism,"  ibid.  vol.  x.  p.  449 ;    Pratt,  "  Professor 
Perry's  Proofs  of  Realism,"  ibid.  vol.  ix.  p.  573  ff. 

67  "  tiber  die  Stellung  der  Gegenstandstheorie  im  System  der  Wissen- 
schaften,"   Zeitschrift  fur  Philosophic  und  philosophische  Kritik,  October 
1906,  p.  48  ff. ;  January  1907,  p.  105  ff. ;   April  1907,  p.   1  ff. ;    Unter- 
suchungen  zur  Gegenstandstheorie  und  Psychologic  (Leipzig,  1904),  which 
in  addition  to  the  first  article  by  Meinong,  entitled  "  Uber  Gegenstands- 
theorie,"  contains  papers  by  his  followers,  Ameseder,  Mally,  Frankel, 
Benussi,  Liel,  and  Saxinger. 

68  Mind,  vol.  xiv.,  1905,  p.  533. 

69  "  Uber  die  Stellung  der  Gegenstandstheorie,"  Article  1,  p.  63  ff. 



1.  Traditional  Mechanism. — From  the  Renaissance  until 
the  middle  of  the  nineteenth  century  scientific  thought 
was  dominated  by  the  concept  that  the  key  to  all  natural 
phenomena  was  to  be  sought  in  mechanics.  In  the  re- 
action from  the  Scholasticism  which  saw  in  every  new 
phenomenon  the  working  of  some  new  occult  quality, 
and  had  no  hesitation  in  multiplying  the  number  of  these 
qualities  ad  absurdum,  the  science  of  the  Renaissance 
was  inspired  by  the  ruling  idea  that  the  true  essence 
of  physical  reality  is  to  be  found  in  quantitative 
relations.  If,  as  Kepler  affirms,  mundus  participat 
quantitate,  what  but  mechanics,  which  Leonardo  da 
Vinci  terms  "  the  paradise  of  the  mathematical  sciences," 
can  serve  as  the  foundation  upon  which  all  experimental 
science  is  to  be  mathematically  built  up  ?  The  master 
mind  of  Galileo  regarded  the  book  of  nature  as  written 
in  mathematical  characters,  and  the  geometrical  pro- 
perties of  bodies,  figure,  magnitude,  rest,  and  motion 
as  the  first  and  real  accidents,  which  exist  objectively, 
whereas  other  qualities  only  exist  in  relation  to  the  organ 
of  sense.1  In  like  manner  Descartes,  reducing  matter 
to  extension  only  and  making  all  variations  of  bodies 
dependent  upon  motion,  absorbs  physics  into  mechanics 
and  mechanics  into  geometry.2 

In  spite  of  the  criticisms  of  Berkeley  and  Hume,  the 
division  between  primary  and  secondary  qualities,  taken 
up  by  Hobbes  and  Locke,  is  accepted  as  a  dogma  by  all 



those  scientists  the  tendency  of  whose  researches  enables 
them  to  say  with  Descartes :  Terram  totumque  hunc 
mundum  instar  machinae  descripsi,  and  the  dream  of  a 
universal  system  of  mechanics  is  realised  in  Huygen's 
undulatory  theory  of  light,3  Bernouilli's  kinetic  theory 
of  gases,  and  Mayer's  mechanical  theory  of  heat.  Just, 
however,  when  the  great  work  seemed  to  be  accomplished 
with  the  inclusion  in  the  same  system  of  the  mechanical 
laws  of  the  great  revolutions  of  the  planets  and  the 
imperceptible  motions  of  atoms,  and  the  hope  had 
dawned  that  it  might  be  possible  to  comprise  even  the 
phenomena  of  life  within  these  universal  formulas, 
the  first  doubts  as  to  the  value  of  mechanical  explana- 
tions began  to  arise. 

In  the  first  part  of  this  book  we  have  studied  the 
general  causes  of  a  philosophical  order  which  brought 
about  the  critical  revision  of  science  and  a  new  episte- 
mological  valuation  of  it  towards  the  end  of  the  nine- 
teenth century ;  we  shall  therefore  now  confine  our- 
selves to  pointing  out  the  scientific  reasons  which  led 
physicists  to  reconstruct  their  theories  upon  new  bases.4 

The  supreme  principles  of  energy,  undoubtedly  the 
greatest  triumph  of  the  last  century  in  the  realm  of  theo- 
retical physics,  did  much  to  undermine  faith  in  traditional 
mechanism.  The  principle  of  conservation  of  energy 
appeared  at  first  sight  to  confirm  the  mechanical  theory  : 
Helmholtz,  Clausius,  and  Kelvin,  indeed,  took  Mayer's 
discovery  of  the  equivalence  of  heat  and  work  to  be  a 
proof  of  the  possibility  of  reducing  all  forms  of  energy 
to  kinetic  energy ;  an  interpretation  which  was  not 
legitimate.  Mayer's  experiments  merely  proved  that 
it  was  possible  to  transform  one  form  of  energy  into 
another,  that  a  determinate  quantity  of  one  such  form 
always  corresponded  to  a  determinate  quantity  of 
another  ;  it  did  not,  however,  afford  any  authority  for 
regarding  one  form  of  energy,  i.e.  the  kinetic,  as  the 
basis  of  all  other  forms.  We  should  be  equally  entitled 
to  conclude  that  heat,  light,  motion,  and  chemical  affinity 
are  but  different  manifestations  of  the  same  electrical 


energy.  As  Ostwald  correctly  observes,  the  equivalence 
of  afl  forms  of  energy,  far  from  authorising  us  to  reduce 
one  of  these  forms  to  another,  places  them  all  on  the 
same  level.  In  any  case  the  principle  of  conservation, 
if  it  could  not  be  adduced  in  support  of  the  mechanical 
theory,  since  it  rather  impelled  thought  to  transcend 
that  theory  and  to  comprehend  it  as  a  special  instance 
in  a  wider  theory,  based  upon  the  general  laws  of  ener- 
getic transformations,  did  not,  on  the  other  hand,  con- 
stitute a  decisive  argument  against  it. 

2.  Carnofs  Principle. — The  heaviest  blow  to  the 
mechanical  theory  was  dealt  by  the  other  principle— 
that  of  Carnot.  Mechanics,  as  ordinarily  understood, 
is  the  study  of  reversible  phenomena :  if  to  the 
parameter  representing  time,  which  has  acquired  in- 
creasing values  in  the  course  of  the  development  of 
the  phenomenon,  we  assign  decreasing  values  which 
cause  its  inversion,  the  whole  system  must  once  more  go 
through  just  the  same  stages  as  it  has  already  traversed. 
Now  Carnot 5  and  Clausius 6  have  shown  (the  latter  even 
more  plainly  than  the  former)  that  this  is  not  verified 
in  the  transition  from  thermal  to  kinetic  energy  :  if  a 
determinate  quantity  of  work  be  expended  in  order 
to  raise  the  temperature  of  a  body,  we  cannot  return 
exactly  to  the  initial  stage  of  the  process  by  inverting 
the  cycle  :  however  perfect  the  machine  may  be,  we  shall 
never  obtain  from  the  lowering  of  the  thermal  level  the 
same  amount  of  work  as  we  have  employed  :  there  will 
always  be  a  portion  of  the  thermal  energy  which  is  not 
transformed  into  work,  which  is,  as  it  is  commonly 
expressed,  lowered  or  degraded.  This  irrevocability, 
which  is  a  general  characteristic  of  the  physical  world, 
and  this  evolution  of  nature  in  a  determinate  direction 
do  not  admit  of  explanation  by  the  mechanical  theory. 
Were  physical  phenomena  exclusively  due  to  the  motions 
of  atoms,  whose  mutual  attraction  depended  upon 
nothing  but  distance,  they  should  be  reversible  :  when 
all  the  initial  velocities  are  reversed,  the  atoms  subjected 
to  the  action  of  the  same  forces  should  pursue  their 


trajectories  in  the  contrary  sense,  just  in  the  same 
way  as  the  earth  would  describe  in  a  retrograde  sense 
the  same  elliptic  orbit  which  it  describes  in  a  direct 
sense,  were  the  initial  conditions  of  its  motion  in- 
verted. The  attempts  which  have  been  made  to 
reconcile  Carnot's  principle  with  traditional  mechanics 
have  failed  to  give  satisfactory  results  :  it  has  almost 
always  been  necessary  in  the  course  of  the  deduction 
to  introduce  some  new  hypothesis,  independent  of  the 
fundamental  principles  of  mechanics,  and  equivalent 
in  reality  to  one  of  the  postulates  upon  which  the 
ordinary  enunciation  of  the  second  law  of  thermo- 
dynamics is  based.7  Helmholtz  has  endeavoured  to 
include  Carnot's  principle  in  the  principle  of  least 
action ;  this  does  not,  however,  eliminate  the  diffi- 
culties involved  in  the  mechanical  interpretation  of 
the  irreversibility  of  phenomena.  Gibbs,8  Boltzmann,9 
and  Planck  have  advanced  extremely  interesting  ideas 
on  this  point :  they  consider  that  the  principle  indi- 
cates that  a  given  system  tends  to  the  configuration 
offering  the  maximum  probability  :  thus  two  different 
gaseous  masses,  placed  in  two  separate  receptacles, 
will,  when  communication  is  opened  between  the  two 
receptacles,  become  diffused  into  one  another,  and 
it  is  extremely  improbable  that  in  the  course  of  the 
reciprocal  shocks  the  two  kinds  of  molecule  will  assume 
a  distribution  of  velocity  bringing  them  back  to  the 
initial  state  by  a  spontaneous  phenomenon.  Carnot's 
principle  would  then  merely  express  a  law  of  probability  : 
an  extraordinary  concurrence  of  circumstances  would 
be  required  in  order  to  render  phenomena  reversible. 
The  return  to  the  primitive  state  demands  a  very  great 
interval  of  time,  but  is  not  absolutely  impossible.  This 
attempt  at  reconciliation  is  undoubtedly  sufficiently 
ingenious  :  at  bottom  it  does,  however,  but  oppose  the 
possibility  of  a  fact  to  a  phenomenon  proved  by  experi- 
ence, though  this  procedure  does  not  answer  to  the  rules 
of  scientific  method.  Physical  theories  must  formu- 
late the  laws  of  observed  phenomena,  not  of  those  which 


are  more  or  less  probable.  It  is  better  to  seek  another 
theory  which  affords  a  more  satisfactory  explanation 
of  the  phenomena  which  have  been  hitherto  observed 
than  to  speculate  upon  mere  possibilities,  in  the  hope 
of  saving  the  mechanical  hypothesis  at  all  costs. 

3.  Evolutionary  Genesis  of  Chemical  Elements. — In 
the  realm  of  chemistry  also  the  new  discoveries  have 
led  science  to  abandon  the  old  concept  of  the  in- 
destructible atom  and  to  substitute  an  energetic  con- 
ception for  the  old  atomic  theory.  As  early  as  1815 
Prout,  starting  from  the  hypothesis  that  the  atomic 
weights  of  all  simple  bodies  were  exact  multiples  of  the 
weight  of  hydrogen,  had  maintained  the  unity  of  com- 
position of  the  elements,  regarding  them  as  formed  by 
successive  condensations  of  hydrogen.  The  periodic 
law,  first  suggested  by  Newlands  in  1864,  and  elaborated 
by  Mendelejeff  in  1869,  according  to  which  the  chemical 
and  physical  properties  of  elements  are  periodic  functions 
of  their  atomic  weights,  confirmed  the  hypothesis  of  the 
unity  of  composition  of  the  elements ;  so  that,  when 
William  Crookes,  in  a  discourse  on  "  The  Genesis  of  Ele- 
ments," 10  given  at  the  Royal  Institution  on  February  18, 
1887,  and  in  his  presidental  address  to  the  Chemical 
Society  in  the  following  year  on  "  Elements  and  Meta- 
Elements," u  proving  the  falsity  of  the  belief  that 
chemical  elements  have  existed  ab  aeterno  as  we  now 
observe  them,  and  cannot  be  subjected  to  change  or 
decomposition,  maintained  that  these  elements  are 
neither  simple,  nor  primordial,  nor  created  all  at  once, 
but  that  they  are  the  result  of  evolution,  he  did  in  reality 
but  formulate  an  idea  which  had,  if  I  may  so  put  it, 
already  been  for  long  in  the  air  of  science.  Crookes, 
however,  must  be  credited  with  having  placed  the 
evolutionary  hypothesis  in  chemistry  upon  an  experi- 
mental basis  by  analysing  the  spectra  of  certain  metals 
belonging  to  the  series  of  rare  earths,  such  as  yttrium, 
samarium,  thorium,  etc.  If  one  of  these  metals,  yttrium, 
for  example,  be  subjected  to  a  long  and  tedious  process 
of  fractionisation,  and  the  parts  thus  obtained  become 


phosphorescent  by  the  action  of  the  induction-spark  in 
tubes  with  the  rarefaction  of  a  millionth  part  of  an  atmo- 
sphere, different  spectra  will  be  obtained,  revealing  the 
existence  of  specifically  distinct  substances.  The  con- 
clusions thus  reached  by  Crookes  have  been  corroborated 
by  Lockyer's  long  and  painstaking  spectral  analyses,12 
which  prove  the  erroneousness  of  the  theory  that 
each  chemical  element  has  but  one  spectrum.  The 
application  of  a  higher  degree  of  temperature  than  had 
previously  been  employed  led  Lockyer  to  admit  the 
existence  of  component  parts  of  a  still  more  subtle  nature 
in  substances  which  had  been  regarded  as  simple.  The 
same  element  will  present  different  spectra  if  it  be 
exposed  to  different  degrees  of  temperature :  certain 
lines  in  the  spectra  of  iron,  calcium,  and  magnesium  are 
not  visible  at  a  low  temperature,  but  become  more  intense 
when  the  temperature  is  raised — a  proof  that  the  atoms 
composing  these  substances  are  not  immutable  and  in- 
divisible, but  are  subject  to  change  and  dissociation.13 

The  recent  discoveries  of  cathode  rays,  X-rays,  and 
radio-active  bodies  such  as  uranium  and  radium,  and 
the  proof  that  radio-activity  does  not  belong  to  certain 
bodies  only,  but  constitutes  a  general  property  of  matter, 
have  corroborated  from  another  point  of  view  the 
hypothesis  of  the  evolutionary  formation  of  elements 
and  of  their  dissociation  ;  since  such  radiations, 
according  at  all  events  to  Le  Bon's  theory,14  which  is 
based  upon  numerous  experiments,  are  but  the  product 
of  the  dematerialisation  of  atoms,  which  thus  restore 
by  means  of  a  slow  process  of  dissipation  the  energy 
stored  up  in  them  during  the  period  of  cosmic  formation. 
Energy  and  matter  are  at  bottom  but  two  forms  of  one 
and  the  same  thing ;  one  is  a  stable,  the  other  an  un- 
stable form  of  intra-atomic  energy ;  when  the  atoms 
are  dissociated,  that  is  to  say  when  matter  is  de- 
materialised,  the  stable  form  of  energy,  which  is  termed 
matter,  is  merely  transformed  into  the  unstable  form 
known  as  electricity,  light,  heat,  etc.15 

4.  Physical  Chemistry. — The  researches  of  physical 


chemistry,  and  more  especially  of  its  most  flourishing 
branch  electro-chemistry,  which  were  inspired  and 
promoted  mainly  by  Wilhelm  Ostwald,16  have  done  much 
to  direct  thought  towards  an  energetic  conception  of 
material  transformations.  If  Dalton's  atomic  theory 
be  rejected  as  a  useless  and  arbitrary  hypothesis,17 
chemistry  enlarges  its  borders  and  looks  to  a  dynamic 
theory  for  a  more  comprehensive  basis ;  chemical 
combination  is  regarded  as  a  special  instance  of 
physical  mixture,  and  a  physical  definition  thereof  is 
accordingly  sought.  It  is  mainly  due  to  the  labours  of 
Van  't  Hoff  that  the  profound  and  accurate  theory  of 
diluted  solutions,  which  institutes  a  comparison  between 
solutions  and  gases  from  the  thermo-dynamic  point  of 
view,  came  into  being  independently  of  any  mechanical 
hypothesis ;  thus  the  fundamental  laws  of  chemical 
transformations,  i.e.  the  laws  of  equilibrium  and  of 
velocity  of  reaction,  are  independent  of  any  mechanical 
presupposition  whatsoever.  The  law  of  mass -action, 
by  which  bodies  are  chemically  efficacious  in  ratio 
of  their  concentration,  can  be  grasped  perfectly  well 
without  the  help  of  hypotheses,  so  much  so  that 
Berthollet,  an  opponent  of  Dalton's  conception,  was 
the  first  to  enunciate  it,  and  the  application  of  it  to 
single  chemical  processes  was  made  by  Guldberg,  Waage, 
and  Wilhelmy  without  having  recourse  to  the  attrac- 
tive forces  of  atoms.  Gibbs'  law  of  phases  18  and  Van  't 
Hoff's  principle  of  mobile  equilibrium  are  infallible 
guides,  enabling  us  to  foresee  and  calculate  many 
chemical  reactions,  when  the  qualitative  difference  of 
bodies  is  disregarded ;  and  the  principles  of  thermo- 
dynamics thus  render  it  possible  to  dispense  with  the  old 
atomic  theory,  which,  however  efficacious  it  may  be 
as  a  representation  of  a  certain  class  of  experimental 
facts,  cannot  afford  a  general  view  of  all  the  phenomena. 
5.  Energetics  in  Rankine  and  Spencer. — Energetics, 
which  has  found  its  staunchest  advocate  in  Wilhelm 
Ostwald,  would  fain  replace  this  narrow  one-sided 
scheme  by  wider  concepts  and  principles,  which  are  not 

cH.m  ENERGETICS  353 

borrowed  from  one  special  branch  of  physics,  regarded 
arbitrarily  as  the  basis  of  all  the  others,  but  com- 
prehend in  one  vast  synthesis  the  characteristics 
common  to  the  different  classes  of  phenomena.  Such 
a  concept  is  nothing  new  either  in  the  realm  of 
science  or  in  that  of  philosophy  19 :  if  we  are  not  pre- 
pared to  return  to  the  dynamism  of  Leibnitz,  which, 
as  opposed  to  the  mechanical  theory  of  Descartes  and 
Gassendi,  regarded  motion  and  extension  as  phenomenal 
manifestations  of  force,  which  last  it  denned  as,  ce  qu'il 
y  a  dans  I'etat  present,  qui  porte  avec  soi  un  changement 
pour  I'avenir,20  we  must  at  all  events  refer  to  two  of 
his  immediate  predecessors,  Rankine  and  Spencer. 
Some  time  before  Ostwald,  Rankine  in  an  article  pub- 
lished in  1846,21  after  distinguishing  the  abstractive 
method,  which  confines  itself  to  the  data  of  experience 
and  does  not  theorise  about  that  which  lies  beyond  those 
data,  but  contents  itself  with  gathering  together  the 
characteristics  common  to  the  various  orders  of  pheno- 
mena in  order  that  it  may  rise  by  induction  to  general 
and  abstract  concepts  and  laws,  from  the  hypothetical 
•method,  which  rather  has  recourse  to  conceptions  of  a 
conjectural  order  with  regard  to  that  intimate  constitu- 
tion of  objects  which  is  not  revealed  to  us  by  the  senses, 
advises  us  to  reject  the  latter  method,  which  is  the  one 
adopted  by  traditional  mechanicism,  in  order  to  raise 
the  new  eclince  of  energetics  with  the  aid  of  the  former.^ 
If  we  would  purge  physics  of  the  arbitrary  hypotheses"? 
of  masses,  movements,  and  imperceptible  forces,  and 
reduce  it  to  the  abstractive  form,  we  must  find  the 
properties  which  are  common  to  the  various  groups  of 
physical  phenomena,  forming  classes  of  a  more  and 
more  extensive  order,  until  we  reach  the  most  general 
concepts  and  principles.  Energy  is  precisely  the  most 
general  property  of  physical  facts,  in  as  much  as  the 
power  of  producing  an  effect  and  of  being  a  potentiality 
of  changes  is  a  characteristic  common  to  them  all ; 
hence  its  laws  must  constitute  the  fundamental  principles 
of  the  new  physical  theory,  from  which  the  special  laws 



governing  the  different  groups  of  phenomena  are  derived 
f  by  a  process  of  deduction.  Spencer,  too,  as  is  well 
known,  looking  at  the  matter  from  the  philosophical 
and  more  particularly  the  psychological  point  of  view,  in 
his  First  Principles,  after  a  not  very  successful  analysis 
of  the  presentations  of  space,  time,  matter,  and  motion, 
arrives  at  "  force,"  which  he  regards  as  the  ultimate  and 
irreducible  element  in  the  experience  of  the  outer  world. 
6.  Ostwald's  Phenomencdistic  Programme. — Ostwald 
goes  still  farther  than  Spencer :  the  concept  of  energy 
not  only  shows  us  how  to  systematise  the  experience 
of  the  external  world,  but  enables  us  to  penetrate  the 
innermost  recesses  of  human  consciousness,  and  sheds 
its  light  on  the  loftiest  spheres  of  the  mind,  the  noblest 
manifestations  of  art  and  morality.  He  affirms  that 
matter  only  exists  in  thought ;  the  real,  that  which  truly 
acts  upon  us,  is  energy.22  We  must  get  wholly  rid  of 
figurative  hypotheses  and  analogies  with  mechanics,  and 
construct  a  science  devoid  of  hypotheses — eine  hypo- 
thesenfreie  Wissenschaft.*3  Is  such  an  undertaking 
possible  ?  Some  men  of  science  would  absolutely  deny 
such  a  possibility,  maintaining  that  every  mathematical 
formulation  of  phenomena  is  based  upon  some  hypo- 
thesis: thus  in  mechanics  we  speak  of  perfectly  rigid 
bodies  and  of  absolutely  frictionless  fluids,  etc.,  which 
do  not  exist  in  nature  and  are  therefore  only  admitted 
by  hypothesis.  This  argument,  however,  fails  to  dis- 
_tinguish  between  two  different  things.  There  can  be  no  j 
doubt  that  the  relations  expressed  by  natural  laws  are 
never  perfectly  realised  in  experience,  because  they  refer 
to  abstractions,  that  is  to  say  to  real  phenomena,  minus 
certain  aspects  thereof  which  we  voluntarily  leave  out 
of  consideration.  This  holds  good  of  all  the  magnitudes 
which  we  disregard  and  look  upon  as  null,  not  because 
they  are  so  in  reality,  but  because  they  are  too  small 
for  us  to  measure.  We  frequently  disregard  even 
measurable  quantities,  because  we  have  not  yet  found 
out  how  to  calculate  them.  Ostwald  terms  this  general 
procedure  which  is  dependent  upon  the  nature  of  our 

OH.  m  ENERGETICS  355 

mind  the  method  of  abstraction  (Abstractionsverfahren),  in 
order  to  distinguish  it  from  all  other  scientific  methods, 
and  more  particularly  from  hypotheses  properly  so 
called.24  In  hypotheses  the  procedure  is  reversed : 
we  do  not  for  convenience'  sake  disregard  certain  parts 
of  phenomena,  but  add  to  them  characteristics  which 
are  not  given  to  us  by  experience,  and  which  can  never 
admit  of  scientific  proof,  by  forming  images  or  models 
drawn  for  the  most  part  from  the  realm  of  mechanics, 
which  represent  certain  aspects  of  phenomena  in  an 
intuitive  and  communicable  form.  The  images  are  of 
course  chosen  in  such  a  way  as  to  represent  the  properties 
of  the  phenomena  by  means  of  corresponding  properties 
of  the  images.  Can  an  image  be  found  capable  of  afford- 
ing a  complete  presentation  of  all  the  characteristics 
of  phenomena  ?  Ostwald  considers  this  to  be  an 
impossibility,  because  when  using  images  in  the  repre- 
sentation of  phenomena  it  is  impossible  to  avoid 
adding  to  them  certain  essential  parts  which  are  found 
in  the  model,  but  not  seen  in  the  phenomenon ;  now 
between  these  extraneous  parts  and  the  corresponding 
characteristics  of  the  phenomenon  a  contradiction 
will  inevitably  arise  sooner  or  later,  which  will  make 
the  given  model  useless.  Is  it  not  possible,  however, 
to  make  such  a  choice  of  images  that  this  contradiction 
will  not  arise  ?  No,  because,  did  the  image  and  the 
object  coincide  in  all  their  parts,  they  would  be  the  same 
thing.  A  phenomenon  can  only  be  perfectly  represented 
by  means  of  itself :  every  representation  thereof  by  means 
of  other  phenomena  of  a  more  or  less  analogous  order 
must  of  necessity  contain  extraneous  elements.  But,  it 
may  be  objected  by  the  advocates  of  hypotheses,  all 
the  mathematical  formulas,  by  means  of  which  we 
express,  for  example,  the  relation  between  velocity  and 
time  of  descent,  between  tension  and  current,  are 
also  merely  images  of  reality  and  not  reality  itself,  so 
that  science  from  start  to  finish  is  constructed  with  the 
help  of  these  images.  Ostwald  replies  to  this  that  we 
must  draw  a  distinction  between  formulas  and  images  : 


formulas  possess  no  part  which  is  peculiar  to  them,  but 
merely  those  elements  which  we  put  into  them  and  derive 
from  experience.  Every  letter  is  a  symbol,  standing 
for  a  phenomenal  multiplicity  having  the  character  of  a 
magnitude,  and  has  no  further  meaning ;  the  relations 
set  up  by  formulas  between  such  symbols,  corresponding 
to  objective  magnitudes,  can  all  be  verified  by  means 
of  experience.  In  models  or  images,  on  the  contrary, 
properties  are  added  which  are  not  revealed  to  us  by 
phenomena,  and  cannot  therefore  ever  be  verified.  We 
must  for  this  reason  dismiss  these  arbitrary  hypotheses  : 
science  must  set  itself  the  problem  of  representing  pheno- 
mena in  such  a  way  that  those  elements  only  shall  be 
comprised  in  the  representation  which  can  be  observed  in 
experience  and  those  characteristics  which  are  not  capable 
of  verification  put  aside.  This  method  excludes  all 
intuitive  models  or  physical  images  and  leaves  as  means 
of  representation  nothing  but  numbers  and  algebraical 
signs  which  stand  in  their  stead.  We  must,  however,, 
bear  in  mind  that  hypotheses  are  frequently  concealed 
in  formulas.  How  are  we  to  recognise  them  ?  If  every 
magnitude  comprised  in  the  formulas  be  measurable 
in  itself,  we  are  really  dealing  with  a  relation  between 
phenomena,  a  true  natural  law :  if,  on  the  other  hand, 
the  formulas  contain  magnitudes  which  are^not  measur- 
able in  experience,  we  may  rest  assured  that  we  shall 
find  ourselves  confronted  by  hypotheses  in  mathematical 
form.  Let  us  take,  for  instance,  the  formula  of  the 
kinetic  theory  of  gases,  pv  =  %mnc2.  If  we  apply  this 
criterion,  we  see  at  once  that  measurable  magnitudes 
are  symbolised  in  the  first  side  of  the  equation,  namely 
pressure  and  volume,  whereas  the  second  side,  on  the 
contrary,  in  which  m  represents  the  mass  of  a  molecule, 
n  the  number  of  molecules,  and  c  their  velocity,  includes 
/  non-measurable  magnitudes. 

7.  Criticism  of  the  Traditional  Mechanical  Theory.— 
The  traditional  mechanical  theory,  in  as  much  as  it  is 
wholly  based  upon  the  use  of  hypothetical  images,  fails 
to  answer  to  the  requirements  of  scientific  method : 

CH.  ra  ENERGETICS  357 

its  theories  do  not  give  a  true  reflection  of  the  relations 
of  phenomena ;  it  rather  makes  arbitrary  additions 
thereto,  in  the  mistaken  belief  that  it  is  thus  enabled 
to  penetrate  more  deeply  into  the  nature  of  things.  In 
thermal  phenomena,  for  instance,  no  mechanical  property 
comes  under  immediate  observation,  and,  if  it  be  admitted 
that  these  phenomena  consist  in  movements,  we  go 
beyond  facts  and  construct  an  imaginary  world  of 
invisible  particles,  describing  in  space  trajectories  which 
are  equally  invisible.  Experience  can,  of  course,  neveT 
prove  the  falsity  of  similar  theories,  because  our  imagina- 
tion, being  at  liberty  to  form  any  image  it  likes  of  these 
movements,  can  always  modify  them  in  such  a  way  as  to 
bring  them  into  agreement  with  facts.  But  if  this 
hypothesis  cannot  be  shown  to  be  false  by  experi- 
mental proof,  it  must  be  rejected  from  the  methodo- 
logical point  of  view,  since  it  does  not  simply  tran- 
scribe that  which  is  given  by  experience,  but  contains 
elements  which  can  never  be  verified.  The  upholders 
of  the  mechanical  theory  maintain  that  their  pro- 
cedure is  legitimate,  because  it  endeavours  to  reduce 
the  unknown  to  the  known,  as  is  done  in  every 
explanation ;  but  this  amounts  to  the  postulate  that 
mechanical  phenomena  are  better  known  than  other 
phenomena.  This  is  by  no  means  true  at  the  present 
stage  of  science,  since  the  very  same  functional  relations 
between  magnitudes  to  which  our  knowledge  of  the 
laws  of  motion  and  masses  is  in  the  end  reducible 
have  been  established  between  the  magnitudes  of  the 
other  groups  of  thermal,  electrical,  and  chemical  pheno- 
mena, without  the  help  of  the  mechanical  hypothesis. 
Undoubtedly  there  was  a  time  in  which  mechanical 
phenomena  were  better  known  than  others  ;  it  is,  how- 
ever, owing  to  a  mere  historical  accident  that  the  motions 
of  masses  were  the  first  to  attract  the  attention  of 
students  of  science.25  Had  researches  into  heat  been 
made  first,  there  would  have  been  a  tendency  to  write 
books  entitled :  Motion  considered  as  a  Form  cf  Heat, 
instead  of  those  bearing  titles  such  as  that  of  Tyndall's 


work  :  Heat  considered  as  a  Form  of  Motion.  Hypo- 
theses are  the  perishable  part  of  science,  there  is,  how- 
ever, something  which  lives  on  as  a  lasting  acquisition ; 
namely,  the  laws  which  express  the  relations  between 
the  magnitudes  of  experience.  Naturgesetze  sind 
dauernd,  Hypothesen  sind  vergdnglich.26  The  laws  of 
stoicheiometry  will  endure  when  the  atomic  theory  exists 
only  in  the  pages  of  dusty  forgotten  books  on  our 
library  shelves,  and  Ohm's  laws  will  hold  good  for  ever, 
no  matter  what  representation  of  the  essence  of  electric 
energy  may  be  prevalent  in  the  future.  But  if  Ostwald 
denies  the  usefulness  of  hypotheses  even  as  heuretic 
means,  and  affirms  that  we  have  nothing  to  do  but  keep 
our  eyes  open  in  order  to  make  new  discoveries,  and  that 
working  hypotheses  are  indispensable  only  to  those  who 
are  not  capable  of  advancing  without  them,  just  as 
crutches  are  to  those  who  cannot  walk  without  their  aid, 
he  intends  this  assertion  to  apply  merely  to  conjectures 
as  to  what  lies  beyond  phenomena,  not  to  anticipations 
of  experience,  which  he  terms  prototheses  in  order  to 
distinguish  them  from  hypotheses  properly  so  called,