Pythagoras  saw  that  there  was  an  invariable
existence  lying  beneath  these  varieties ;  but  he
wanted  some  more  definite  expression  for  it,  and  he
called  it  Number.  Thus  each  individual  thing
may  change  its  position,  its  mode  of  existence,  all
its  peculiar  attributes  may  be  destroyed  except  one  ;
and  that  is  its  numerical  attribute.  It  is  always
"  One  "  thing  ;  nothing  can  destroy  that  numerical
existence.  Combine  the  Thing  in  every  possible
variety  of  ways,  and  it  still  remains  "  One  ;"  it
cannot  be  made  less  than  "  one,"  it  cannot  be  made
more  than  "  one."  Resolve  it  into  its  minutest
particles,  and  each  particle  is  "  one."  Having  thus
found  that  numerical  existence  was  the  only  invari
able  existence,  he  was  easily  led  to  proclaim  all
Things  to  be  but  copies  of  Numbers.  "  All
phenomena  must  originate  in  the  simplest  elements,"
jays  Sextus  Empiricus,  "  and  it  would  be  contrary


PHILOSOPHY    OF    PYTHAGORAS.  63

to  reason  to  suppose  the  Principle  of  the  Universe
to  participate  in  the  nature  of  sensible  phenomena.
The  Principia  are  consequently  not  only  invisible
and  intangible,  but  also  incorporeal."

As  the  numerical  existence  is  the  ultimate  state
at  which  analysis  can  arrive  with  respect  to  finite
Things,  so  also  is  it  the  ultimate  state  at  which  we
can  arrive  with  respect  to  the  Infinite,  or  Existence
in  itself.  The  Infinite,  therefore,  must  be  One.
