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construction of conceptions； that is； from intuition； which can be
given a priori in accordance with conceptions。 The method of
algebra； in equations； from which the correct answer is deduced by
reduction； is a kind of construction… not geometrical； but by symbols…
in which all conceptions； especially those of the relations of
quantities； are represented in intuition by signs； and thus the
conclusions in that science are secured from errors by the fact that
every proof is submitted to ocular evidence。 Philosophical cognition
does not possess this advantage； it being required to consider the
general always in abstracto （by means of conceptions）； while
mathematics can always consider it in concreto （in an individual
intuition）； and at the same time by means of a priori
representation； whereby all errors are rendered manifest to the
senses。 The former… discursive proofs… ought to be termed acroamatic
proofs； rather than demonstrations； as only words are employed in
them； while demonstrations proper； as the term itself indicates；
always require a reference to the intuition of the object。
It follows from all these considerations that it is not consonant
with the nature of philosophy； especially in the sphere of pure
reason； to employ the dogmatical method； and to adorn itself with
the titles and insignia of mathematical science。 It does not belong to
that order； and can only hope for a fraternal union with that science。
Its attempts at mathematical evidence are vain pretensions； which
can only keep it back from its true aim； which is to detect the
illusory procedure of reason when transgressing its proper limits； and
by fully explaining and analysing our conceptions； to conduct us
from the dim regions of speculation to the clear region of modest
self…knowledge。 Reason must not； therefore； in its transcendental
endeavours； look forward with such confidence； as if the path it is
pursuing led straight to its aim； nor reckon with such security upon
its premisses； as to consider it unnecessary to take a step back； or
to keep a strict watch for errors； which； overlooked in the
principles； may be detected in the arguments themselves… in which case
it may be requisite either to determine these principles with
greater strictness； or to change them entirely。
I divide all apodeictic propositions； whether demonstrable or
immediately certain； into dogmata and mathemata。 A direct
synthetical proposition； based on conceptions； is a dogma； a
proposition of the same kind； based on the construction of
conceptions； is a mathema。 Analytical judgements do not teach us any
more about an object than what was contained in the conception we
had of it； because they do not extend our cognition beyond our
conception of an object； they merely elucidate the conception。 They
cannot therefore be with propriety termed dogmas。 Of the two kinds
of a priori synthetical propositions above mentioned； only those which
are employed in philosophy can； according to the general mode of
speech； bear this name； those of arithmetic or geometry would not be
rightly so denominated。 Thus the customary mode of speaking confirms
the explanation given above； and the conclusion arrived at； that
only those judgements which are based upon conceptions； not on the
construction of conceptions； can be termed dogmatical。
Thus； pure reason； in the sphere of speculation； does not contain
a single direct synthetical judgement based upon conceptions。 By means
of ideas； it is； as we have shown； incapable of producing
synthetical judgements； which are objectively valid； by means of the
conceptions of the understanding； it establishes certain indubitable
principles； not； however； directly on the basis of conceptions； but
only indirectly by means of the relation of these conceptions to
something of a purely contingent nature； namely； possible
experience。 When experience is presupposed； these principles are
apodeictically certain； but in themselves； and directly； they cannot
even be cognized a priori。 Thus the given conceptions of cause and
event will not be sufficient for the demonstration of the proposition：
Every event has a cause。 For this reason； it is not a dogma；
although from another point of view； that of experience； it is capable
of being proved to demonstration。 The proper term for such a
proposition is principle； and not theorem （although it does require to
be proved）； because it possesses the remarkable peculiarity of being
the condition of the possibility of its own ground of proof； that
is； experience； and of forming a necessary presupposition in all
empirical observation。
If then； in the speculative sphere of pure reason； no dogmata are to
be found； all dogmatical methods； whether borrowed from mathematics；
or invented by philosophical thinkers； are alike inappropriate and
inefficient。 They only serve to conceal errors and fallacies； and to
deceive philosophy； whose duty it is to see that reason pursues a safe
and straight path。 A philosophical method may； however； be
systematical。 For our reason is； subjectively considered； itself a
system； and； in the sphere of mere conceptions； a system of
investigation according to principles of unity； the material being
supplied by experience alone。 But this is not the proper place for
discussing the peculiar method of transcendental philosophy； as our
present task is simply to examine whether our faculties are capable of
erecting an edifice on the basis of pure reason； and how far they
may proceed with the materials at their command。
SECTION II。 The Discipline of Pure Reason in Polemics。
Reason must be subject； in all its operations； to criticism； which
must always be permitted to exercise its functions without
restraint； otherwise its interests are imperilled and its influence
obnoxious to suspicion。 There is nothing； however useful； however
sacred it may be； that can claim exemption from the searching
examination of this supreme tribunal； which has no respect of persons。
The very existence of reason depends upon this freedom； for the
voice of reason is not that of a dictatorial and despotic power； it is
rather like the vote of the citizens of a free state； every member
of which must have the privilege of giving free expression to his
doubts； and possess even the right of veto。
But while reason can never decline to submit itself to the
tribunal of criticism； it has not always cause to dread the
judgement of this court。 Pure reason； however； when engaged in the
sphere of dogmatism； is not so thoroughly conscious of a strict
observance of its highest laws； as to appear before a higher
judicial reason with perfect confidence。 On the contrary； it must
renounce its magnificent dogmatical pretensions in philosophy。
Very different is the case when it has to defend itself； not
before a judge； but against an equal。 If dogmatical assertions are
advanced on the negative side； in opposition to those made by reason
on the positive side； its justification kat authrhopon is complete；
although the proof of its propositions is kat aletheian
unsatisfactory。
By the polemic of pure reason I mean the defence of its propositions
made by reason； in opposition to the dogmatical counter…propositions
advanced by other parties。 The question here is not whether its own
statements may not also be false； it merely regards the fact that
reason proves that the opposite cannot be established with
demonstrative certainty； nor even asserted with a higher degree of
probability。 Reason does not hold her possessions upon sufferance；
for； although she cannot show a perfectly satisfactory title to
them； no one can prove that she is not the rightful possessor。
It is a melancholy reflection that reason； in its highest
exercise； falls into an antithetic； and that the supreme tribunal
for the settlement of differences should not be at union with
itself。 It is true that we had to discuss the question of an
apparent antithetic； but we found that it was based upon a
misconception。 In conformity with the common prejudice； phenomena were
regarded as things in themselves； and thus an absolute completeness in
their synthesis was required in the one mode or in the other （it was
shown to be impossible in both）； a demand entirely out of place in
regard to phenomena。 There was； then； no real self…contradiction of
reason in the propositions： The series of phenomena given in
themselves has an absolutely first beginning； and： This series is
absolutely and in itself without beginning。 The two propositions are
perfectly consistent with each other； because phenomena as phenomena
are in themselves nothing； and consequently the hypothesis that they
are things in themselves must lead to self…contradictory inferences。
But there are cases in which a similar misunderstanding cannot be
provided against； and the dispute must remain unsettled。 Take； for
example； the theistic proposition