finite or infinite。 But it is neither finite nor infinite… as has been
shown； on the one side； by the thesis； on the other； by the
antithesis。 Therefore the world… the content of all phenomena… is
not a whole existing in itself。 It follows that phenomena are nothing；
apart from our representations。 And this is what we mean by
transcendental ideality。
This remark is of some importance。 It enables us to see that the
proofs of the fourfold antinomy are not mere sophistries… are not
fallacious； but grounded on the nature of reason； and valid… under the
supposition that phenomena are things in themselves。 The opposition of
the judgements which follow makes it evident that a fallacy lay in the
initial supposition； and thus helps us to discover the true
constitution of objects of sense。 This transcendental dialectic does
not favour scepticism； although it presents us with a triumphant
demonstration of the advantages of the sceptical method； the great
utility of which is apparent in the antinomy； where the arguments of
reason were allowed to confront each other in undiminished force。
And although the result of these conflicts of reason is not what we
expected… although we have obtained no positive dogmatical addition to
metaphysical science… we have still reaped a great advantage in the
correction of our judgements on these subjects of thought。
SECTION VIII。 Regulative Principle of Pure Reason in relation
to the Cosmological Ideas。
The cosmological principle of totality could not give us any certain
knowledge in regard to the maximum in the series of conditions in
the world of sense； considered as a thing in itself。 The actual
regress in the series is the only means of approaching this maximum。
This principle of pure reason； therefore； may still be considered as
valid… not as an axiom enabling us to cogitate totality in the
object as actual； but as a problem for the understanding； which
requires it to institute and to continue； in conformity with the
idea of totality in the mind； the regress in the series of the
conditions of a given conditioned。 For in the world of sense； that is；
in space and time； every condition which we discover in our
investigation of phenomena is itself conditioned； because sensuous
objects are not things in themselves （in which case an absolutely
unconditioned might be reached in the progress of cognition）； but
are merely empirical representations the conditions of which must
always be found in intuition。 The principle of reason is therefore
properly a mere rule… prescribing a regress in the series of
conditions for given phenomena； and prohibiting any pause or rest on
an absolutely unconditioned。 It is； therefore； not a principle of
the possibility of experience or of the empirical cognition of
sensuous objects… consequently not a principle of the understanding；
for every experience is confined within certain proper limits
determined by the given intuition。 Still less is it a constitutive
principle of reason authorizing us to extend our conception of the
sensuous world beyond all possible experience。 It is merely a
principle for the enlargement and extension of experience as far as is
possible for human faculties。 It forbids us to consider any
empirical limits as absolute。 It is； hence； a principle of reason；
which； as a rule； dictates how we ought to proceed in our empirical
regress； but is unable to anticipate or indicate prior to the
empirical regress what is given in the object itself。 I have termed it
for this reason a regulative principle of reason； while the
principle of the absolute totality of the series of conditions； as
existing in itself and given in the object； is a constitutive
cosmological principle。 This distinction will at once demonstrate
the falsehood of the constitutive principle； and prevent us from
attributing （by a transcendental subreptio） objective reality to an
idea； which is valid only as a rule。
In order to understand the proper meaning of this rule of pure
reason； we must notice first that it cannot tell us what the object
is； but only how the empirical regress is to be proceeded with in
order to attain to the plete conception of the object。 If it gave
us any information in respect to the former statement； it would be a
constitutive principle… a principle impossible from the nature of pure
reason。 It will not therefore enable us to establish any such
conclusions as： 〃The series of conditions for a given conditioned is
in itself finite。〃 or； 〃It is infinite。〃 For； in this case； we
should be cogitating in the mere idea of absolute totality； an
object which is not and cannot be given in experience； inasmuch as
we should be attributing a reality objective and independent of the
empirical synthesis； to a series of phenomena。 This idea of reason
cannot then be regarded as valid… except as a rule for the
regressive synthesis in the series of conditions； according to which
we must proceed from the conditioned； through all intermediate and
subordinate conditions； up to the unconditioned； although this goal is
unattained and unattainable。 For the absolutely unconditioned cannot
be discovered in the sphere of experience。
We now proceed to determine clearly our notion of a synthesis
which can never be plete。 There are two terms monly employed for
this purpose。 These terms are regarded as expressions of different and
distinguishable notions； although the ground of the distinction has
never been clearly exposed。 The term employed by the mathematicians is
progressus in infinitum。 The philosophers prefer the expression
progressus in indefinitum。 Without detaining the reader with an
examination of the reasons for such a distinction； or with remarks
on the right or wrong use of the terms； I shall endeavour clearly to
determine these conceptions； so far as is necessary for the purpose in
this Critique。
We may； with propriety； say of a straight line； that it may be
produced to infinity。 In this case the distinction between a
progressus in infinitum and a progressus in indefinitum is a mere
piece of subtlety。 For； although when we say； 〃Produce a straight
line；〃 it is more correct to say in indefinitum than in infinitum；
because the former means； 〃Produce it as far as you please；〃 the
second； 〃You must not cease to produce it〃； the expression in
infinitum is； when we are speaking of the power to do it； perfectly
correct； for we can always make it longer if we please… on to
infinity。 And this remark holds good in all cases； when we speak of
a progressus； that is； an advancement from the condition to the
conditioned； this possible advancement always proceeds to infinity。 We
may proceed from a given pair in the descending line of generation
from father to son； and cogitate a never…ending line of descendants
from it。 For in such a case reason does not demand absolute totality
in the series； because it does not presuppose it as a condition and as
given （datum）； but merely as conditioned； and as capable of being
given （dabile）。
Very different is the case with the problem： 〃How far the regress；
which ascends from the given conditioned to the conditions； must
extend〃； whether I can say： 〃It is a regress in infinitum；〃 or only
〃in indefinitum〃； and whether； for example； setting out from the human
beings at present alive in the world； I may ascend in the series of
their ancestors； in infinitum… mr whether all that can be said is；
that so far as I have proceeded； I have discovered no empirical ground
for considering the series limited； so that I am justified； and
indeed； pelled to search for ancestors still further back； although
I am not obliged by the idea of reason to presuppose them。
My answer to this question is： 〃If the series is given in
empirical intuition as a whole； the regress in the series of its
internal conditions proceeds in infinitum； but； if only one member
of the series is given； from which the regress is to proceed to
absolute totality； the regress is possible only in indefinitum。〃 For
example； the division of a portion of matter given within certain
limits… of a body； that is… proceeds in infinitum。 For； as the
condition of this whole is its part； and the condition of the part a
part of the part； and so on； and as in this regress of deposition
an unconditioned indivisible member of the series of conditions is not
to be found； there are no reasons or grounds in experience for
stopping in the division； but； on the contrary； the more remote
members of the division are actually and empirically given prior to
this division。 That is to say； the division proceeds to infinity。 On
the other hand； the series of ancestors of any given human being is
not given； in its absolute totality； in any experience； and yet the
regress proceeds from every genealogical member of this series to
one still higher； and does not meet with any empirical limit
presenting an absolutely unconditioned member of the series。 But as
the members of such a series are not contained in the empirical
intuition of the whole； prior to the regress； this regress does not
proceed to infinity； but only in indefinitum； that is； we are called
upon to discover other and higher members； which are themselves always
conditioned。
In neither case… the regressus in infinitum； nor the regressus in
indefinitum； is the series of conditions to be considered as
actually infinite in the object itself。 This might be true of things
in themselves； but it cannot be asserted of phenomena； which； as
conditions of each other； are only given in the empirical regress
itself。 Hence； the question no longer is； 〃What is the quantity of
this series of conditions in itself… is it finite or infinite？〃 for it
is nothing in itself； but； 〃How is the empirical regress to be
menced； and how far ought we to proceed with it？〃 And here a signal
distinction in the application of this rule bees apparent。 If the
whole is given empirically； it is possible to recede in the series
of its internal conditions to infinity。 But if the whole is not given；
and can only be given by and through the empirical regress； I can only
say： 〃It is possible to infinity； to proceed to still higher
conditions in the ser