true for any determinations of a space originally included in
ourselves, must be true for such determinations for ever, since they
cannot become objects of consciousness to us but in and by that very
mode of conceiving space, that very form of schematism which
originally presented us with these determinations of space, or any
whatever. In the uniformity of our own space-conceiving faculty, we
have a pledge of the absolute and _necessary_ uniformity (or internal
agreement among themselves) of all future or possible determinations
of space; because they could not otherwise become to us conceivable
forms of space, than by adapting themselves to the known conditions of
our conceiving faculty. Here we have the _necessity_ which is
indispensable to all geometrical demonstration: it is a necessity
founded in our human organ, which cannot admit or conceive a space,
unless as preconforming to these original forms or schematisms.
Whereas, on the contrary, if space were something _objective_, and
consequently being a separate existence, independent of a human organ,
then it is altogether impossible to find any intelligible source of
_obligation_ or cogency in the evidence--such as is indispensable to
the very nature of geometrical demonstration. Thus we will suppose
that a regular demonstration has gradually, from step to step
downwards, through a series of propositions--No. 8 resting upon 7,
that upon 5, 5 upon 3--at length reduced you to the elementary axiom,
that Two straight lines cannot enclose a space. Now, if space be
_subjective_ originally--that is to say, founded (as respects us and
our geometry) in ourselves--then it is impossible that two such lines
can enclose a space, because the possibility of anything whatever
relating to the determinations of space is exactly co-extensive with
(and exactly expressed by) our power to conceive it. Being thus able
to affirm its impossibility universally, we can build a demonstration
upon it. But, on the other hypothesis, of space being _objective_, it
is impossible to guess whence we are to draw our proof of the alleged
inaptitude in two straight lines for enclosing a space. The most we
could say is, that hitherto no instance has been found of an enclosed
space circumscribed by two straight lines. It would not do to allege
our human inability to conceive, or in imagination to draw, such a
circumscription. For, besides that such a mode of argument is exactly
the one supposed to have be