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there are so many cases in which it is necessary to distinguish the
notion of the former； as a course of corrective training； from that of
the latter； as the communication of knowledge； and the nature of
things itself demands the appropriation of the most suitable
expressions for this distinction； that it is my desire that the former
terms should never be employed in any other than a negative
signification。
That natural dispositions and talents （such as imagination and with；
which ask a free and unlimited development； require in many respects
the corrective influence of discipline； every one will readily
grant。 But it may well appear strange that reason； whose proper duty
it is to prescribe rules of discipline to all the other powers of
the mind； should itself require this corrective。 It has； in fact；
hitherto escaped this humiliation； only because； in presence of its
magnificent pretensions and high position； no one could readily
suspect it to be capable of substituting fancies for conceptions；
and words for things。
Reason； when employed in the field of experience； does not stand
in need of criticism； because its principles are subjected to the
continual test of empirical observations。 Nor is criticism requisite
in the sphere of mathematics； where the conceptions of reason must
always be presented in concreto in pure intuition； and baseless or
arbitrary assertions are discovered without difficulty。 But where
reason is not held in a plain track by the influence of empirical or
of pure intuition； that is； when it is employed in the
transcendental sphere of pure conceptions； it stands in great need
of discipline； to restrain its propensity to overstep the limits of
possible experience and to keep it from wandering into error。 In fact；
the utility of the philosophy of pure reason is entirely of this
negative character。 Particular errors may be corrected by particular
animadversions； and the causes of these errors may be eradicated by
criticism。 But where we find； as in the case of pure reason； a
complete system of illusions and fallacies； closely connected with
each other and depending upon grand general principles； there seems to
be required a peculiar and negative code of mental legislation； which；
under the denomination of a discipline； and founded upon the nature of
reason and the objects of its exercise； shall constitute a system of
thorough examination and testing； which no fallacy will be able to
withstand or escape from； under whatever disguise or concealment it
may lurk。
But the reader must remark that； in this the second division of
our transcendental Critique the discipline of pure reason is not
directed to the content； but to the method of the cognition of pure
reason。 The former task has been completed in the doctrine of
elements。 But there is so much similarity in the mode of employing the
faculty of reason； whatever be the object to which it is applied；
while； at the same time； its employment in the transcendental sphere
is so essentially different in kind from every other； that； without
the warning negative influence of a discipline specially directed to
that end； the errors are unavoidable which spring from the
unskillful employment of the methods which are originated by reason
but which are out of place in this sphere。
SECTION I。 The Discipline of Pure Reason in the Sphere
of Dogmatism。
The science of mathematics presents the most brilliant example of
the extension of the sphere of pure reason without the aid of
experience。 Examples are always contagious； and they exert an especial
influence on the same faculty； which naturally flatters itself that it
will have the same good fortune in other case as fell to its lot in
one fortunate instance。 Hence pure reason hopes to be able to extend
its empire in the transcendental sphere with equal success and
security； especially when it applies the same method which was
attended with such brilliant results in the science of mathematics。 It
is； therefore； of the highest importance for us to know whether the
method of arriving at demonstrative certainty； which is termed
mathematical； be identical with that by which we endeavour to attain
the same degree of certainty in philosophy； and which is termed in
that science dogmatical。
Philosophical cognition is the cognition of reason by means of
conceptions； mathematical cognition is cognition by means of the
construction of conceptions。 The construction of a conception is the
presentation a priori of the intuition which corresponds to the
conception。 For this purpose a non…empirical intuition is requisite；
which； as an intuition； is an individual object； while； as the
construction of a conception （a general representation）； it must be
seen to be universally valid for all the possible intuitions which
rank under that conception。 Thus I construct a triangle； by the
presentation of the object which corresponds to this conception；
either by mere imagination； in pure intuition； or upon paper； in
empirical intuition； in both cases completely a priori； without
borrowing the type of that figure from any experience。 The
individual figure drawn upon paper is empirical； but it serves；
notwithstanding； to indicate the conception； even in its universality；
because in this empirical intuition we keep our eye merely on the
act of the construction of the conception； and pay no attention to the
various modes of determining it； for example； its size； the length
of its sides； the size of its angles； these not in the least affecting
the essential character of the conception。
Philosophical cognition； accordingly； regards the particular only in
the general； mathematical the general in the particular； nay； in the
individual。 This is done； however； entirely a priori and by means of
pure reason； so that； as this individual figure is determined under
certain universal conditions of construction； the object of the
conception； to which this individual figure corresponds as its schema；
must be cogitated as universally determined。
The essential difference of these two modes of cognition consists；
therefore； in this formal quality； it does not regard the difference
of the matter or objects of both。 Those thinkers who aim at
distinguishing philosophy from mathematics by asserting that the
former has to do with quality merely； and the latter with quantity；
have mistaken the effect for the cause。 The reason why mathematical
cognition can relate only to quantity is to be found in its form
alone。 For it is the conception of quantities only that is capable
of being constructed； that is； presented a priori in intuition；
while qualities cannot be given in any other than an empirical
intuition。 Hence the cognition of qualities by reason is possible only
through conceptions。 No one can find an intuition which shall
correspond to the conception of reality； except in experience； it
cannot be presented to the mind a priori and antecedently to the
empirical consciousness of a reality。 We can form an intuition； by
means of the mere conception of it； of a cone； without the aid of
experience； but the colour of the cone we cannot know except from
experience。 I cannot present an intuition of a cause； except in an
example which experience offers to me。 Besides； philosophy； as well as
mathematics； treats of quantities； as； for example； of totality；
infinity； and so on。 Mathematics； too； treats of the difference of
lines and surfaces… as spaces of different quality； of the
continuity of extension… as a quality thereof。 But； although in such
cases they have a common object； the mode in which reason considers
that object is very different in philosophy from what it is in
mathematics。 The former confines itself to the general conceptions；
the latter can do nothing with a mere conception； it hastens to
intuition。 In this intuition it regards the conception in concreto；
not empirically； but in an a priori intuition； which it has
constructed； and in which； all the results which follow from the
general conditions of the construction of the conception are in all
cases valid for the object of the constructed conception。
Suppose that the conception of a triangle is given to a
philosopher and that he is required to discover； by the
philosophical method； what relation the sum of its angles bears to a
right angle。 He has nothing before him but the conception of a
figure enclosed within three right lines； and； consequently； with
the same number of angles。 He may analyse the conception of a right
line； of an angle； or of the number three as long as he pleases； but
he will not discover any properties not contained in these
conceptions。 But； if this question is proposed to a geometrician； he
at once begins by constructing a triangle。 He knows that two right
angles are equal to the sum of all the contiguous angles which proceed
from one point in a