ase with quantities of
every kind, but only with those which are represented and apprehended
by us as _extensive_."[3]

[3] B. 203-4, M. 123.

Kant opposes an extensive quantity to an intensive quantity or a
quantity which has a degree. "That quantity which is apprehended
only as unity and in which plurality can be represented only by
approximation to negation = 0, I call _intensive quantity_."[4] The
aspect of this ultimate distinction which underlies Kant's mode of
stating it is that only an extensive quantity is a whole, i. e.
something made up of parts. Thus a mile can be said to be made up
of two half-miles, but a velocity of one foot per second, though
comparable with a velocity of half a foot per second, cannot be said
to be made up of two such velocities; it is essentially one and
indivisible. Hence, from Kant's point of view, it follows that it is
only an extensive magnitude which can, and indeed must, be apprehended
through a successive synthesis of the parts. The proof of the axiom
seems to be simply this: 'All phenomena as objects of perception are
subject to the forms of perception, space and time. Space and time are
[homogeneous manifolds, and therefore] extensive quantities, only
to be apprehended by a successive synthesis of the parts. Hence
phenomena, or objects of experience, must also be extensive
quantities, to be similarly apprehended.' And Kant goes on to add that
it is for this reason that geometry and pure mathematics generally
apply to objects of experience.

[4] B. 210, M. 127.

We need only draw attention to three points. Firstly, no justification
is given of the term 'axiom'. Secondly, the argument does not really
appeal to the doctrine of the categories, but only to the character
of space and time as forms of perception. Thirdly, it need not appeal
to space and time as forms of perception in the proper sense of ways
in which we apprehend objects, but only in the sense of ways in which
objects are related[5]; in other words, it need not appeal to Kant's
theory of knowledge. The conclusion follows simply from the nature of
objects as spatially and temporally related, whether they are
phenomena or not. It may be objected that Kant's thesis is that _all_
objects of perception are extensive quantities, and that unless space
and time are allowed to be ways in which _we must perceive_ objects,
we cannot say that all objects will be spatially and temporally
related, and so extensive qu