presents this conception in concreto； but only to the time…conditions；
which may be found in experience to correspond to the conception。 My
procedure is； therefore； strictly according to conceptions； I cannot
in a case of this kind employ the construction of conceptions； because
the conception is merely a rule for the synthesis of perceptions；
which are not pure intuitions； and which； therefore； cannot be given a
priori。
There is thus a twofold exercise of reason。 Both modes have the
properties of universality and an a priori origin in mon； but
are； in their procedure； of widely different character。 The reason
of this is that in the world of phenomena； in which alone objects
are presented to our minds； there are two main elements… the form of
intuition （space and time）； which can be cognized and determined
pletely a priori； and the matter or content… that which is
presented in space and time； and which； consequently； contains a
something… an existence corresponding to our powers of sensation。 As
regards the latter； which can never be given in a determinate mode
except by experience； there are no a priori notions which relate to
it； except the undetermined conceptions of the synthesis of possible
sensations； in so far as these belong （in a possible experience） to
the unity of consciousness。 As regards the former； we can determine
our conceptions a priori in intuition； inasmuch as we are ourselves
the creators of the objects of the conceptions in space and time…
these objects being regarded simply as quanta。 In the one case； reason
proceeds according to conceptions and can do nothing more than subject
phenomena to these… which can only be determined empirically； that is；
a posteriori… in conformity； however； with those conceptions as the
rules of all empirical synthesis。 In the other case； reason proceeds
by the construction of conceptions； and； as these conceptions relate
to an a priori intuition； they may be given and determined in pure
intuition a priori； and without the aid of empirical data。 The
examination and consideration of everything that exists in space or
time… whether it is a quantum or not； in how far the particular
something （which fills space or time） is a primary substratum； or a
mere determination of some other existence； whether it relates to
anything else… either as cause or effect； whether its existence is
isolated or in reciprocal connection with and dependence upon
others； the possibility of this existence； its reality and necessity
or opposites… all these form part of the cognition of reason on the
ground of conceptions； and this cognition is termed philosophical。 But
to determine a priori an intuition in space （its figure）； to divide
time into periods； or merely to cognize the quantity of an intuition
in space and time； and to determine it by number… all this is an
operation of reason by means of the construction of conceptions； and
is called mathematical。
The success which attends the efforts of reason in the sphere of
mathematics naturally fosters the expectation that the same good
fortune will be its lot； if it applies the mathematical method in
other regions of mental endeavour besides that of quantities。 Its
success is thus great； because it can support all its conceptions by a
priori intuitions and； in this way； make itself a master； as it
were； over nature； while pure philosophy； with its a priori discursive
conceptions； bungles about in the world of nature； and cannot accredit
or show any a priori evidence of the reality of these conceptions。
Masters in the science of mathematics are confident of the success
of this method； indeed； it is a mon persuasion that it is capable
of being applied to any subject of human thought。 They have hardly
ever reflected or philosophized on their favourite science… a task
of great difficulty； and the specific difference between the two modes
of employing the faculty of reason has never entered their thoughts。
Rules current in the field of mon experience； and which mon
sense stamps everywhere with its approval； are regarded by them as
axiomatic。 From what source the conceptions of space and time； with
which （as the only primitive quanta） they have to deal； enter their
minds； is a question which they do not trouble themselves to answer；
and they think it just as unnecessary to examine into the origin of
the pure conceptions of the understanding and the extent of their
validity。 All they have to do with them is to employ them。 In all this
they are perfectly right； if they do not overstep the limits of the
sphere of nature。 But they pass； unconsciously； from the world of
sense to the insecure ground of pure transcendental conceptions
（instabilis tellus； innabilis unda）； where they can neither stand
nor swim； and where the tracks of their footsteps are obliterated by
time； while the march of mathematics is pursued on a broad and
magnificent highway； which the latest posterity shall frequent without
fear of danger or impediment。
As we have taken upon us the task of determining； clearly and
certainly； the limits of pure reason in the sphere of
transcendentalism； and as the efforts of reason in this direction
are persisted in； even after the plainest and most expressive
warnings； hope still beckoning us past the limits of experience into
the splendours of the intellectual world… it bees necessary to
cut away the last anchor of this fallacious and fantastic hope。 We
shall； accordingly； show that the mathematical method is unattended in
the sphere of philosophy by the least advantage… except； perhaps； that
it more plainly exhibits its own inadequacy… that geometry and
philosophy are two quite different things； although they go band in
hand in hand in the field of natural science； and； consequently；
that the procedure of the one can never be imitated by the other。
The evidence of mathematics rests upon definitions； axioms； and
demonstrations。 I shall be satisfied with showing that none of these
forms can be employed or imitated in philosophy in the sense in
which they are understood by mathematicians； and that the
geometrician； if he employs his method in philosophy； will succeed
only in building card…castles； while the employment of the
philosophical method in mathematics can result in nothing but mere
verbiage。 The essential business of philosophy； indeed； is to mark out
the limits of the science； and even the mathematician； unless his
talent is naturally circumscribed and limited to this particular
department of knowledge； cannot turn a deaf ear to the warnings of
philosophy； or set himself above its direction。
I。 Of Definitions。 A definition is； as the term itself indicates；
the representation； upon primary grounds； of the plete conception
of a thing within its own limits。* Accordingly； an empirical
conception cannot be defined； it can only be explained。 For； as
there are in such a conception only a certain number of marks or
signs； which denote a certain class of sensuous objects； we can
never be sure that we do not cogitate under the word which indicates
the same object； at one time a greater； at another a smaller number of
signs。 Thus； one person may cogitate in his conception of gold； in
addition to its properties of weight； colour； malleability； that of
resisting rust； while another person may be ignorant of this
quality。 We employ certain signs only so long as we require them for
the sake of distinction； new observations abstract some and add new
ones； so that an empirical conception never remains within permanent
limits。 It is； in fact； useless to define a conception of this kind。
If； for example； we are speaking of water and its properties； we do
not stop at what we actually think by the word water； but proceed to
observation and experiment； and the word； with the few signs
attached to it； is more properly a designation than a conception of
the thing。 A definition in this case would evidently be nothing more
than a determination of the word。 In the second place； no a priori
conception； such as those of substance； cause； right； fitness； and
so on； can be defined。 For I can never be sure； that the clear
representation of a given conception （which is given in a confused
state） has been fully developed； until I know that the
representation is adequate with its object。 But； inasmuch as the
conception； as it is presented to the mind； may contain a number of
obscure representations； which we do not observe in our analysis；
although we employ them in our application of the conception； I can
never be sure that my analysis is plete； while examples may make
this probable； although they can never demonstrate the fact。 instead
of the word definition； I should rather employ the term exposition…
a more modest expression； which the critic may accept without
surrendering his doubts as to the pleteness of the analysis of
any such conception。 As； therefore； neither empirical nor a priori
conceptions are capable of definition； we have to see whether the only
other kind of conceptions… arbitrary conceptions… can be subjected
to this mental operation。 Such a conception can always be defined； for
I must know thoroughly what I wished to cogitate in i