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