DOC. 42 SPECIAL AND GENERAL RELATIVITY
251
Physical Meaning of
Geometrical
Propositions
5
made
to
coincide for observation
with
one
eye,
under suitable
choice of
our
place
of observation.
If,
in
pursuance
of
our
habit of
thought,
we now
supple-
ment
the
propositions
of Euclidean
geometry
by
the
single
proposition
that
two
points
on a
practically rigid
body
always
correspond
to
the
same
distance
(line-interval), independently
of
any
changes
in
position to
which
we may
subject
the
body,
the
propositions
of Euclidean
geometry
then resolve them-
selves into
propositions
on
the
possible
relative
position
of
practically
rigid
bodies.1
Geometry
which has
been
supple-
mented in
this
way
is
then
to
be treated
as a
branch of
physics.
We
can
now
legitimately
ask
as
to
the
"truth"
of
geometrical
propositions interpreted
in
this
way,
since
we are
justified
in
asking
whether these
propositions are
satisfied
for
those
real
things
we
have associated with
the
geometrical
ideas. In
less
exact terms
we can
express
this
by saying
that
by
the "truth"
of
a
geometrical proposition
in this
sense we
understand
its
validity
for
a
construction with ruler and
compasses.
Of
course
the conviction of the
"truth"
of
geometrical prop-
ositions in this
sense
is
founded
exclusively
on
rather incom-
plete experience.
For the
present
we
shall
assume
the "truth"
of
the
geometrical propositions,
then
at
a
later
stage
(in
the
general
theory
of
relativity)
we
shall
see
that this
"truth"
is
limited,
and
we
shall
consider the
extent
of
its
limitation.
1
It
follows
that
a
natural
object is
associated
also
with
a
straight line.
Three
points
A,
B
and
C
on a
rigid
body
thus
lie
in
a straight
line
when,
the
points A
and C
being given,
B is
chosen such
that the
sum
of the distances
A
B
and
B
C
is
as
short
as possible.
This
incomplete suggestion
will
suffice for
our present purpose.