that
can
be approximated
as
closely
as
desired by
the lateral surfaces
by
increasing
the
number of
planes
from which
they
are
formed,
the
same
holds for the surface of the
cylinder.
[Note
in
margin:]
*
The
proof
is
pointless
because
as
well
as we
can assume
that the prismatic
space can
be
unrolled,
the
same
could be
said about the
cylinder!
4.
TWO
PHILOSOPHICAL
COMMENTS
[1891-1895]
Leibnitz
applied
this ad-infinitum
continuing
division of
a
finite quantity
also to
matter,
in order to
arrive
in
this
way
at
its
true
components, and Herbart
rightly
says
about this: "Even
before
one
has done the first cut
through
the clump under
consideration,
there is apparent the
infinite
possibility
that
this
same
cut could be carried out in
an
infinite number of
different
ways.
Herewith, actually,
the whole infinite division
is accomplished all at
once;
and
one
has
arrived at
the
ultimate
elements, to wit in thought,
which has been the
only
thing
that
mattered.
These ultimate
elements
cannot be matter"
(because in
that
case one
would have
to
repeat
anew
these countless divisions
a
countless number of
times,
which is nonsensical). "From
this
one
ought to conclude at
once,
as
Leibnitz has already
done:
It
is not
true
that matter
ultimately
consists of other matter; its
true components
are
simple
(simple
essences,
substances,
monads).
And this is in
conformity
with truth."
(Herbart's
Metaphysik).
It is
wrong
to infer from the imperfection of
our
thinking that
objects
are
imperfect.
[....]
Whether
one,
along with Leibnitz,
Poisson
,
Herbart,
et
al.,
seriously
wants
to
take the
infinitesimally
small for
a
truly
indivisible
element,
or one
wants,
along
with others, to take it
only
for
a
useful
fiction,
so
as
thereby supposedly
to eliminate
all
metaphysical
difficulties, and
conveniently
and
quickly
introduce the calculus, is irrelevant for the calculus, for the
one as
much
as
the other leads
to
the
goal.
[Note in left
margin:]
Sense? [Note in
right margin:]
?!?
5.
ON
THE
INVESTIGATION
OF THE
STATE
OF THE
ETHER IN
A
MAGNETIC FIELD
[Summer? 1895]
On the
Investigation
of the
State
of the Ether
in
a
Magnetic
Field.
The
following
note is the first modest expression of
a
few
simple
thoughts
on
this difficult
topic.
It
is with reluctance that I
am
4