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space。 But space and time are in the world of sense。 Consequently
phenomena in the world are conditionally limited； but the world itself
is not limited； either conditionally or unconditionally。
For this reason； and because neither the world nor the cosmical
series of conditions to a given conditioned can be completely given；
our conception of the cosmical quantity is given only in and through
the regress and not prior to it… in a collective intuition。 But the
regress itself is really nothing more than the determining of the
cosmical quantity； and cannot therefore give us any determined
conception of it… still less a conception of a quantity which is； in
relation to a certain standard； infinite。 The regress does not；
therefore； proceed to infinity （an infinity given）； but only to an
indefinite extent； for or the of presenting to us a quantity… realized
only in and through the regress itself。
II。 Solution of the Cosmological Idea of the Totality of
the Division of a Whole given in Intuition。
When I divide a whole which is given in intuition； I proceed from
a conditioned to its conditions。 The division of the parts of the
whole （subdivisio or decompositio） is a regress in the series of these
conditions。 The absolute totality of this series would be actually
attained and given to the mind； if the regress could arrive at
simple parts。 But if all the parts in a continuous decomposition are
themselves divisible； the division； that is to say； the regress；
proceeds from the conditioned to its conditions in infinitum；
because the conditions （the parts） are themselves contained in the
conditioned； and； as the latter is given in a limited intuition； the
former are all given along with it。 This regress cannot； therefore； be
called a regressus in indefinitum； as happened in the case of the
preceding cosmological idea； the regress in which proceeded from the
conditioned to the conditions not given contemporaneously and along
with it； but discoverable only through the empirical regress。 We are
not； however； entitled to affirm of a whole of this kind； which is
divisible in infinitum； that it consists of an infinite number of
parts。 For； although all the parts are contained in the intuition of
the whole； the whole division is not contained therein。 The division
is contained only in the progressing decomposition… in the regress
itself； which is the condition of the possibility and actuality of the
series。 Now； as this regress is infinite； all the members （parts） to
which it attains must be contained in the given whole as an aggregate。
But the complete series of division is not contained therein。 For this
series； being infinite in succession and always incomplete； cannot
represent an infinite number of members； and still less a
composition of these members into a whole。
To apply this remark to space。 Every limited part of space presented
to intuition is a whole； the parts of which are always spaces… to
whatever extent subdivided。 Every limited space is hence divisible
to infinity。
Let us again apply the remark to an external phenomenon enclosed
in limits； that is； a body。 The divisibility of a body rests upon
the divisibility of space； which is the condition of the possibility
of the body as an extended whole。 A body is consequently divisible
to infinity； though it does not； for that reason； consist of an
infinite number of parts。
It certainly seems that； as a body must be cogitated as substance in
space； the law of divisibility would not be applicable to it as
substance。 For we may and ought to grant； in the case of space； that
division or decomposition； to any extent； never can utterly annihilate
composition （that is to say； the smallest part of space must still
consist of spaces）； otherwise space would entirely cease to exist…
which is impossible。 But； the assertion on the other band that when
all composition in matter is annihilated in thought； nothing
remains； does not seem to harmonize with the conception of
substance； which must be properly the subject of all composition and
must remain； even after the conjunction of its attributes in space…
which constituted a body… is annihilated in thought。 But this is not
the case with substance in the phenomenal world； which is not a
thing in itself cogitated by the pure category。 Phenomenal substance
is not an absolute subject； it is merely a permanent sensuous image；
and nothing more than an intuition； in which the unconditioned is
not to be found。
But； although this rule of progress to infinity is legitimate and
applicable to the subdivision of a phenomenon； as a mere occupation or
filling of space； it is not applicable to a whole consisting of a
number of distinct parts and constituting a quantum discretum… that is
to say； an organized body。 It cannot be admitted that every part in an
organized whole is itself organized； and that； in analysing it to
infinity； we must always meet with organized parts； although we may
allow that the parts of the matter which we decompose in infinitum；
may be organized。 For the infinity of the division of a phenomenon
in space rests altogether on the fact that the divisibility of a
phenomenon is given only in and through this infinity； that is； an
undetermined number of parts is given； while the parts themselves
are given and determined only in and through the subdivision； in a
word； the infinity of the division necessarily presupposes that the
whole is not already divided in se。 Hence our division determines a
number of parts in the whole… a number which extends just as far as
the actual regress in the division； while； on the other hand； the very
notion of a body organized to infinity represents the whole as already
and in itself divided。 We expect； therefore； to find in it a
determinate； but at the same time； infinite； number of parts… which is
self…contradictory。 For we should thus have a whole containing a
series of members which could not be completed in any regress… which
is infinite； and at the same time complete in an organized
composite。 Infinite divisibility is applicable only to a quantum
continuum； and is based entirely on the infinite divisibility of
space； But in a quantum discretum the multitude of parts or units is
always determined； and hence always equal to some number。 To what
extent a body may be organized； experience alone can inform us； and
although； so far as our experience of this or that body has
extended； we may not have discovered any inorganic part； such parts
must exist in possible experience。 But how far the transcendental
division of a phenomenon must extend； we cannot know from
experience… it is a question which experience cannot answer； it is
answered only by the principle of reason which forbids us to
consider the empirical regress； in the analysis of extended body； as
ever absolutely complete。
Concluding Remark on the Solution of the Transcendental
Mathematical Ideas… and Introductory to the
Solution of the Dynamical Ideas。
We presented the antinomy of pure reason in a tabular form； and we
endeavoured to show the ground of this self…contradiction on the
part of reason； and the only means of bringing it to a conclusion…
znamely； by declaring both contradictory statements to be false。 We
represented in these antinomies the conditions of phenomena as
belonging to the conditioned according to relations of space and time…
which is the usual supposition of the common understanding。 In this
respect； all dialectical representations of totality； in the series of
conditions to a given conditioned； were perfectly homogeneous。 The
condition was always a member of the series along with the
conditioned； and thus the homogeneity of the whole series was assured。
In this case the regress could never be cogitated as complete； or；
if this was the case； a member really conditioned was falsely regarded
as a primal member； consequently as unconditioned。 In such an
antinomy； therefore； we did not consider the object； that is； the
conditioned； but the series of conditions belonging to the object； and
the magnitude of that series。 And thus arose the difficulty… a
difficulty not to be settled by any decision regarding the claims of
the two parties； but simply by cutting the knot… by declaring the
series proposed by reason to be either too long or too short for the
understanding； which could in neither case make its conceptions
adequate with the ideas。
But we have overlooked； up to this point； an essential difference
existing between the conceptions of the understanding which reason
endeavours to raise to the rank of ideas… two of these indicating a
mathematical； and two a dynamical synthesis of phenomena。 Hitherto； it
was necessary to signalize this distinction； for； just as in our
general representation of all transcendental ideas； we considered them
under phenomenal conditions； so； in the t