DOC.
364
JULY
1917 359
You
will
probably
find
it
comprehensible
that
I
hope
to
encounter
more un-
derstanding
for
this
theory
among
mathematicians
and
physicists
with
an
interest
in
philosophy
than
from
philosophers proper.
Certain
obstacles
in
my
theory
are
frequently
particularly
difficult to surmount for
those not versed in
the math-
ematics.
The
set
theorist
is
accustomed to
abstract
from
the
sets of ordered
relations
in
an
analysis
of
cardinal
numbers,
and it
is
thus not difficult for him to
conceive
of
a
set
in which
absolutely
no
ordering
relations exist between
the
ele-
ments.
My
dissolution of
the
temporal
continuum
presents
a
particular
problem
for nonmathematicians,
however.
Philosophers usually are completely unaware
that, for
a
mathematician,
the
linear continuum
is
no more
than
a
set
of separate
individuals, numbers,
or
points,
e.g.,
of
a
specific cardinality
and with
a
specific
order
type, although
the
former also must be familiar with
the
continuum of
real
numbers,
from middleschool. The continuum
appears
to
them
as
something
mysteriously uniform;
and
probably extremely
few
philosophers
would take
the
trouble
to study
Bertrand
Russell’s
Principles of Mathematics,
where
they
could
find clarification of this
point.[13]
Once
the
temporal
continuum
is
conceived
as a
linearly
ordered set
of
elements
of
consciousness,
of
which each
is actually
a
world
of
its
own,
since
they
would notice
nothing
if all
the
rest
of
the world did not
exist,
it
easily
follows
from
this that
this order is not
given
in
the
pure
consciousness
of
the
elements,
rather that
we
merely
consider
it
appropriate
to
imagine
these
elements in
that
order
according
to certain inner
properties
and that,
therefore,
this
order
must be dissolved in
a
consideration of
pure
consciousness.
Philosophers
often
deny
that
a
moment
in
time
or a
state of consciousness
even
exists,
because
they
do
not
know how
a
continuum
can
be
constructed
out
of elements
and
therefore do not consider it
possible;
it
will
seem even
self-evident
to
the modern
mathematician,
and
primarily
to
the
set
theorist,
that
in
a
study of
a
continuum, one
must
proceed
from the
elements.
If
philosophers
say,
however,
that the
individual
state of
consciousness does
not “exist”
but that
only
the
“flow”
of consciousness
does, one
can
reply
that
a momentary
element
of
consciousness
can
perhaps
doubt
whether
anything
beside itself
exists,
but the
existence of
at
least
one
of such closed elements is the
surest thing
that
can
be known.
It
is not certain,
however,
that
what
we
call
a
finite
stretch
of
time
of
a
person’s
consciousness
corresponds
to
a
set
of
consciousness elements
of
the
continuum’s
cardinality
or
even
to
a
countable infinite set.-
Knowledge
of
set
theory
is not
absolutely
necessary
to
understand
my theory, though;
I
myself
had
found
this
theory
6 years ago,
while still in
secondary
school
[Gymnasium],
inspired by
Mach’s
Analysis of Sensations,
and moved
to
criticize it. Even while
writing
the
paper,
I
did not
yet
know
about
set
theory, so
it
contains
the
inaccuracy
that
no
distinction
is
made between
an
uniformly dense,
denumerable order and
a
continuum,
in
that
I call
the
time order continuous
where
what
we
call
time