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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

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