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ease can it be demonstrated； that the possibility of things as
quantities； and consequently the objective reality of the category
of quantity； can be grounded only in external intuition； and that by
its means alone is the notion of quantity appropriated by the internal
sense。 But I must avoid prolixity； and leave the task of
illustrating this by examples to the reader's own reflection。
The above remarks are of the greatest importance； not only for the
confirmation of our previous confutation of idealism； but still more
when the subject of self…cognition by mere internal consciousness
and the determination of our own nature without the aid of external
empirical intuitions is under discussion； for the indication of the
grounds of the possibility of such a cognition。
The result of the whole of this part of the analytic of principles
is； therefore： 〃All principles of the pure understanding are nothing
more than a priori principles of the possibility of experience； and to
experience alone do all a priori synthetical propositions apply and
relate〃； indeed； their possibility itself rests entirely on this
relation。
CHAPTER III Of the Ground of the Division of all Objects
into Phenomena and Noumena。
We have now not only traversed the region of the pure
understanding and carefully surveyed every part of it； but we have
also measured it； and assigned to everything therein its proper place。
But this land is an island； and enclosed by nature herself within
unchangeable limits。 It is the land of truth （an attractive word）；
surrounded by a wide and stormy ocean； the region of illusion； where
many a fog…bank； many an iceberg； seems to the mariner； on his
voyage of discovery； a new country； and； while constantly deluding him
with vain hopes； engages him in dangerous adventures； from which he
never can desist； and which yet he never can bring to a termination。
But before venturing upon this sea； in order to explore it in its
whole extent； and to arrive at a certainty whether anything is to be
discovered there； it will not be without advantage if we cast our eyes
upon the chart of the land that we are about to leave； and to ask
ourselves； firstly； whether we cannot rest perfectly contented with
what it contains； or whether we must not of necessity be contented
with it； if we can find nowhere else a solid foundation to build upon；
and； secondly； by what title we possess this land itself； and how we
hold it secure against all hostile claims？ Although； in the course
of our analytic； we have already given sufficient answers to these
questions； yet a summary recapitulation of these solutions may be
useful in strengthening our conviction； by uniting in one point the
momenta of the arguments。
We have seen that everything which the understanding draws from
itself； without borrowing from experience； it nevertheless possesses
only for the behoof and use of experience。 The principles of the
pure understanding； whether constitutive a priori （as the mathematical
principles）； or merely regulative （as the dynamical）； contain
nothing but the pure schema； as it were； of possible experience。 For
experience possesses its unity from the synthetical unity which the
understanding； originally and from itself； imparts to the synthesis of
the imagination in relation to apperception； and in a priori
relation to and agreement with which phenomena； as data for a possible
cognition； must stand。 But although these rules of the understanding
are not only a priori true； but the very source of all truth； that is；
of the accordance of our cognition with objects； and on this ground；
that they contain the basis of the possibility of experience； as the
ensemble of all cognition； it seems to us not enough to propound
what is true… we desire also to be told what we want to know。 If；
then； we learn nothing more by this critical examination than what
we should have practised in the merely empirical use of the
understanding； without any such subtle inquiry； the presumption is
that the advantage we reap from it is not worth the labour bestowed
upon it。 It may certainly be answered that no rash curiosity is more
prejudicial to the enlargement of our knowledge than that which must
know beforehand the utility of this or that piece of information which
we seek； before we have entered on the needful investigations； and
before one could form the least conception of its utility； even though
it were placed before our eyes。 But there is one advantage in such
transcendental inquiries which can be made comprehensible to the
dullest and most reluctant learner… this； namely； that the
understanding which is occupied merely with empirical exercise； and
does not reflect on the sources of its own cognition； may exercise its
functions very well and very successfully； but is quite unable to do
one thing； and that of very great importance； to determine； namely；
the bounds that limit its employment； and to know what lies within
or without its own sphere。 This purpose can be obtained only by such
profound investigations as we have instituted。 But if it cannot
distinguish whether certain questions lie within its horizon or not；
it can never be sure either as to its claims or possessions； but
must lay its account with many humiliating corrections； when it
transgresses； as it unavoidably will； the limits of its own territory；
and loses itself in fanciful opinions and blinding illusions。
That the understanding； therefore； cannot make of its a priori
principles； or even of its conceptions； other than an empirical use；
is a proposition which leads to the most important results。 A
transcendental use is made of a conception in a fundamental
proposition or principle； when it is referred to things in general and
considered as things in themselves； an empirical use； when it is
referred merely to phenomena； that is； to objects of a possible
experience。 That the latter use of a conception is the only admissible
one is evident from the reasons following。 For every conception are
requisite； firstly； the logical form of a conception （of thought）
general； and； secondly； the possibility of presenting to this an
object to which it may apply。 Failing this latter； it has no sense；
and utterly void of content； although it may contain the logical
function for constructing a conception from certain data。 Now；
object cannot be given to a conception otherwise than by intuition；
and； even if a pure intuition antecedent to the object is a priori
possible； this pure intuition can itself obtain objective validity
only from empirical intuition； of which it is itself but the form。 All
conceptions； therefore； and with them all principles； however high the
degree of their a priori possibility； relate to empirical
intuitions； that is； to data towards a possible experience。 Without
this they possess no objective validity； but are mere play of
imagination or of understanding with images or notions。 Let us take；
for example； the conceptions of mathematics； and first in its pure
intuitions。 〃Space has three dimensions〃… 〃Between two points there
can be only one straight line；〃 etc。 Although all these principles；
and the representation of the object with which this science
occupies itself； are generated in the mind entirely a priori； they
would nevertheless have no significance if we were not always able
to exhibit their significance in and by means of phenomena
（empirical objects）。 Hence it is requisite that an abstract conception
be made sensuous； that is； that an object corresponding to it in
intuition be forthcoming； otherwise the conception remains； as we say；
without sense； that is； without meaning。 Mathematics fulfils this
requirement by the construction of the figure； which is a phenomenon
evident to the senses。 The same science finds support and significance
in number； this in its turn finds it in the fingers； or in counters；
or in lines and points。 The conception itself is always produced a
priori； together with the synthetical principles or formulas from such
conceptions； but the proper employment of them； and their
application to objects； can exist nowhere but in experience； the
possibility of which； as regards its form； they contain a priori。
That this is also the case with all of the categories and the
principles based upon them is evident from the fact that we cannot
render intelligible the possibility of an object corresponding to them
without having recourse to the conditions of sensibility；
consequently； to the form of phenomena； to which； as their only proper
objects； their use must therefore be confined； inasmuch as； if this
condition is removed； all significance； that is； all relation to an
object； disappears； and no example can be found to make it
comprehensible what sort of things we ought to think under such
conceptions。
The conception of quantity cannot be explained except by saying that
it is t