THE NEW WINE
231
tion of straight
which
has no
reference
to
size , but
only
to
quality , by defining
“
a straight
line
is
the
shortest
between
two
points ”
(which
is
certainly
untrue :? “ Two straight lines cannot enclose
a space ,'
is
better
; for in
the definition which
he gives , Kant
does
not seem to have grasped the true conception of
“
straight." ] Hume , Kant states , severed
pure mathe
matics from synthetic judgements
à priori , and herein
made a great mistake , as
all
mathematical judgements
he
asserts are synthetic
.
[
But
is
his dogmatism cor
rect
?
Crowley
would disagree
.]
[(a.)
Mathematics
is
analytic
,
because
a
parabola
is
but
a
name
,
and
all
its
qualities are directly deducible
from
its
definitions
,
etc.
,
etc.
,
and therefore contained
therein
,
though
not seen
.
(
6)
Mathematics
is
based
on
racial experience
,
and even
on
individual
learning
;
only
a
few highly developed brains can apprehend
its
propositions
.
It
may
be
doubted whether any synthetic
judgement exists
at
all
;
for the moment
it
is
made
it
becomes
analytic
.
This
is
obvious
of
“
A
”
and
“
E
”
propositions
,
and only not
so
of
“
I”
and
“
0,”
be
cause
the subject
is
impure
.]
Kant then rejecting metaphysics
as
a
true science
(
p.21
),
asserts
,
however with confidence
,
“
that certain
pure
synthetic
cognitions
are
really given
à
priori
,
namely
,
pure mathematics
and pure natural
science
,
...
both
.
.
.
partly
apodictically
certain
through
mere
Reason
.”
[
However
he
fails
to
quote any such
proposition
!
And
his
“
apodictic
certainty
”
only
means
that
the
human mind
is
unable
to
transcend
that limitation
.
Thus metaphysics
is
a
mere branch
of
psychology
,
for one thing
;
for another
,
every result
1
What relation
is
there
between
our conceptions
of
rectitude
and length
?
None
,
till geometry informs
us
.