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 forthing； 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
prehensible what sort of things we ought to think under such
conceptions。
The conception of quantity cannot be explained except by saying that
it is the determination of a thing whereby it can be cogitated how
many times one is placed in it。 But this 〃how many times〃 is based
upon successive repetition； consequently upon time and the synthesis
of the homogeneous therein。 Reality； in contradistinction to negation；
can be explained only by cogitating a time which is either filled
therewith or is void。 If I leave out the notion of permanence （which
is existence in all time）； there remains in the conception of
substance nothing but the logical notion of subject； a notion of which
I endeavour to realize by representing to myself something that can
exist only as a subject。 But not only am I perfectly ignorant of any
conditions under which this logical prerogative can belong to a thing；
I can make nothing out of the notion； and draw no inference from it；
because no object to which to apply the conception is determined；
and we consequently do not know whether it has any meaning at all。
In like manner； if I leave out the notion of time； in which
something follows upon some other thing in conformity with a rule； I
can find nothing in the pure category； except that there is a
something of such a sort that from it a conclusion may be drawn as
to the existence of some other thing。 But in this case it would not
only be impossible to distinguish between a cause and an effect；
but； as this power to draw conclusions requires conditions of which
I am quite ignorant； the conception is not determined as to the mode
in which it ought to apply to an object。 The so…called principle：
〃Everything that is contingent has a cause；〃 es with a gravity
and self…assumed authority that seems to require no support from
without。 But； I ask； what is meant by contingent？ The answer is that
the non…existence of which is possible。 But I should like very well to
know by what means this possibility of non…existence is to be
cognized； if we do not represent to ourselves a succession in the
series of phenomena； and in this succession an existence which follows
a non…existence； or conversely； consequently； change。 For to say； that
the non…existence of a thing is not self…contradictory is a lame
appeal to a logical condition； which is no doubt a necessary condition
of the existence of the conception； but is far from being sufficient
for the real objective possibility of non…existence。 I can
annihilate in thought every existing substance without
self…contradiction； but I cannot infer from this their objective
contingency in existence； that is to say； the possibility of their
non…existence in itself。 As regards the category of munity； it
may easily be inferred that； as the pure categories of substance and
causality are incapable of a definition and explanation sufficient
to determine their object without the aid of intuition； the category
of reciprocal causality in the relation of substances to each other
（mercium） is just as little susceptible thereof。 Possibility；
existence； and necessity nobody has ever yet been able to explain
without being guilty of manifest tautology； when the definition has
been drawn entirely from the pure understanding。 For the
substitution of the logical possibility of the conception… the
condition of which is that it be not self…contradictory； for the
transcendental possibility of things… the condition of which is that
there be an object corresponding to the conception； is a trick which
can only deceive the inexperienced。*
*In one word； to none of these conceptions belongs a corresponding
object； and consequently their real possibility cannot be
demonstrated； if we take away sensuous intuition… the only intuition
which we possess… and there then remains nothing but the logical
possibility； that is； the fact that the conception or thought is
possible… which； however； is not the question； what we want to know
being； whether it relates to an object and thus possesses any meaning。
It follows incontestably； that the pure conceptions of the
understanding are incapable of transcendental； and must always be of
empirical use alone； and that the principles of the pure understanding
relate only to the general conditions of a possible experience； to
objects of the senses； and never to things in general； apart from
the mode in which we intuite them。
Transcendental analytic has accordingly this important result； to
wit； that the understanding is petent' effect nothing a priori；
except the anticipation of the form of a possible experience in
general； and that； as that which is not phenomenon cannot be an object
of experience； it can never overstep the limits of sensibility； within
which alone objects are presented to us。 Its principles are merely
principles of the exposition of phenomena； and the proud name of an
ontology； which professes to present synthetical cognitions a priori
of things in general in a systematic doctrine； must give place to
the modest title of analytic of the pure understanding。
Thought is the act of referring a given intuition to an object。 If
the mode of this intuition is unknown to us； the object is merely
transcendental； and the conception of the understanding is employed
only transcendentally； that is； to produce unity in the thought of a
manifold in general。 Now a pure category； in which all conditions of
sensuous intuition… as the only intuition we possess… are
abstracted； does not determine an object； but merely expresses the
thought of an object in general； according to different modes。 Now； to
employ a conception； the function of judgement is required； by which
an object is subsumed under the conception； consequently the at
least formal condition； under which something can be given in
intuition。 Failing this condition of judgement （schema）； subsumption
is impossible； for there is in such a case nothing given； which may be
subsumed under the conception。 The merely transcendental use of the
categories is therefore； in fact； no use at all and has no determined；
or even； as regards its form； determinable object。 Hence it follows
that the pure category is inpetent to establish a synthetical a
priori principle； and that the principles of the pure understanding
are only of empirical and never of transcendental use； and that beyond
the sphere of possible experience no synthetical a priori principles
are possible。
It may be advisable； therefore； to express ourselves thus。 The
pure categories； apart from the formal conditions of sensibility； have
a merely transcendental meaning； but are nevertheless not of
transcendental use； because this is in itself impossible； inasmuch
as all the conditions of any employment or use of them （in judgements）
are absent； to wit； the formal conditions of the subsumption of an
object under these conceptions。 As； therefore； in the character of
pure categories； they must be employed empirically； and cannot be
employed transcendentally； they are of no use at all； when separated
from sensibility； that is； they cannot be applied to an object。 They
are merely the pur