This one distinction, as applied to space, for ever secures (what nothing else _can_ secure or explain) the cogency of geometrical evidence. Whatever is 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 no 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 been rejected, it is liable to this unanswerable objection, so long as space is assumed to have an _objective_ existence, viz. that the human inability to conceive such a possibility only argues (what in fact is often found in other cases) that the _objective_ existence of space--_i.e._ the existence of space in itself, and in its absolute