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 complete 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 complete. There are two terms commonly 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—or 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,
compelled 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 decomposition 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
commenced, and how far ought we to proceed with it?” And here a signal
distinction in the application of this rule becomes 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 series.” In the first case, I am justified in asserting that more
members are empirically given in the object than I attain to in the
regress (of decomposition). In the second case, I am justified only
in saying, that I can always proceed further in the regress, because
no member of the series is given as absolutely conditioned, and thus
a higher member is possible, and an inquiry with regard to it is
necessary. In the one case it is necessary to find other members of the
series, in the other it is necessary to inquire for others, inasmuch as
experience presents no absolute limitation of the regress. For, either
you do not possess a perception which absolutely limits your empirical
regress, and in this case the regress cannot be regarded as complete;
or, you do possess such a limitative perception, in which case it is
not a part of your series (for that which limits must be distinct from
that which is limited by it), and it is incumbent on you to continue
your regress up to this condition, and so on.
These remarks will be placed in their proper light by their application
in the following section.