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first and negative answer is： 〃The world has no beginning in time； and
no absolute limit in space。〃
For； in the contrary case； it would be limited by a void time on the
one hand； and by a void space on the other。 Now； since the world； as a
phenomenon； cannot be thus limited in itself for a phenomenon is not a
thing in itself； it must be possible for us to have a perception of
this limitation by a void time and a void space。 But such a
perception… such an experience is impossible； because it has no
content。 Consequently； an absolute cosmical limit is empirically；
and therefore absolutely； impossible。*
*The reader will remark that the proof presented above is very
different from the dogmatical demonstration given in the antithesis of
the first antinomy。 In that demonstration； it was taken for granted
that the world is a thing in itself… given in its totality prior to
all regress； and a determined position in space and time was denied to
it… if it was not considered as occupying all time and all space。
Hence our conclusion differed from that given above； for we inferred
in the antithesis the actual infinity of the world。
From this follows the affirmative answer： 〃The regress in the series
of phenomena… as a determination of the cosmical quantity； proceeds in
indefinitum。〃 This is equivalent to saying： 〃The world of sense has no
absolute quantity； but the empirical regress （through which alone
the world of sense is presented to us on the side of its conditions）
rests upon a rule； which requires it to proceed from every member of
the series； as conditioned； to one still more remote （whether
through personal experience； or by means of history； or the chain of
cause and effect）； and not to cease at any point in this extension
of the possible empirical employment of the understanding。〃 And this
is the proper and only use which reason can make of its principles。
The above rule does not prescribe an unceasing regress in one kind
of phenomena。 It does not； for example； forbid us； in our ascent
from an individual human being through the line of his ancestors； to
expect that we shall discover at some point of the regress a
primeval pair； or to admit； in the series of heavenly bodies； a sun at
the farthest possible distance from some centre。 All that it demands
is a perpetual progress from phenomena to phenomena； even although
an actual perception is not presented by them （as in the case of our
perceptions being so weak as that we are unable to bee conscious of
them）； since they； nevertheless； belong to possible experience。
Every beginning is in time； and all limits to extension are in
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 pletely 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 depositio） 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 deposition 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 deposition… 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 plete series of division is not contained therein。 For this
series； being infinite in succession and always inplete； cannot
represent an infinite number of members； and still less a
position 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
subst