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possibly exist。 The quantity is measured by the number of given units…
which are taken as a standard… contained in it。 Now no number can be
the greatest； because one or more units can always be added。 It
follows that an infinite given quantity； consequently an infinite
world （both as regards time and extension） is impossible。 It is；
therefore； limited in both respects。 In this manner I might have
conducted my proof； but the conception given in it does not agree with
the true conception of an infinite whole。 In this there is no
representation of its quantity； it is not said how large it is；
consequently its conception is not the conception of a maximum。 We
cogitate in it merely its relation to an arbitrarily assumed unit；
in relation to which it is greater than any number。 Now； just as the
unit which is taken is greater or smaller； the infinite will be
greater or smaller； but the infinity； which consists merely in the
relation to this given unit； must remain always the same； although the
absolute quantity of the whole is not thereby cognized。
The true （transcendental） conception of infinity is： that the
successive synthesis of unity in the measurement of a given quantum
can never be completed。* Hence it follows； without possibility of
mistake； that an eternity of actual successive states up to a given
（the present） moment cannot have elapsed； and that the world must
therefore have a beginning。
*The quantum in this sense contains a congeries of given units；
which is greater than any number… and this is the mathematical
conception of the infinite。
In regard to the second part of the thesis； the difficulty as to
an infinite and yet elapsed series disappears； for the manifold of a
world infinite in extension is contemporaneously given。 But； in
order to cogitate the total of this manifold； as we cannot have the
aid of limits constituting by themselves this total in intuition； we
are obliged to give some account of our conception； which in this case
cannot proceed from the whole to the determined quantity of the parts；
but must demonstrate the possibility of a whole by means of a
successive synthesis of the parts。 But as this synthesis must
constitute a series that cannot be completed； it is impossible for
us to cogitate prior to it； and consequently not by means of it； a
totality。 For the conception of totality itself is in the present case
the representation of a completed synthesis of the parts； and this
completion； and consequently its conception； is impossible。
ON THE ANTITHESIS。
The proof in favour of the infinity of the cosmical succession and
the cosmical content is based upon the consideration that； in the
opposite case； a void time and a void space must constitute the limits
of the world。 Now I am not unaware； that there are some ways of
escaping this conclusion。 It may； for example； be alleged； that a
limit to the world； as regards both space and time； is quite possible；
without at the same time holding the existence of an absolute time
before the beginning of the world； or an absolute space extending
beyond the actual world… which is impossible。 I am quite well
satisfied with the latter part of this opinion of the philosophers
of the Leibnitzian school。 Space is merely the form of external
intuition； but not a real object which can itself be externally
intuited； it is not a correlate of phenomena； it is the form of
phenomena itself。 Space； therefore； cannot be regarded as absolutely
and in itself something determinative of the existence of things；
because it is not itself an object； but only the form of possible
objects。 Consequently； things； as phenomena； determine space； that
is to say； they render it possible that； of all the possible
predicates of space （size and relation）； certain may belong to
reality。 But we cannot affirm the converse； that space； as something
self…subsistent； can determine real things in regard to size or shape；
for it is in itself not a real thing。 Space （filled or void）* may
therefore be limited by phenomena； but phenomena cannot be limited
by an empty space without them。 This is true of time also。 All this
being granted； it is nevertheless indisputable； that we must assume
these two nonentities； void space without and void time before the
world； if we assume the existence of cosmical limits； relatively to
space or time。
*It is evident that what is meant here is； that empty space； in so
far as it is limited by phenomena… space； that is； within the world…
does not at least contradict transcendental principles； and may
therefore； as regards them； be admitted； although its possibility
cannot on that account be affirmed。
For； as regards the subterfuge adopted by those who endeavour to
evade the consequence… that； if the world is limited as to space and
time； the infinite void must determine the existence of actual
things in regard to their dimensions… it arises solely from the fact
that instead of a sensuous world； an intelligible world… of which
nothing is known… is cogitated； instead of a real beginning （an
existence； which is preceded by a period in which nothing exists）；
an existence which presupposes no other condition than that of time；
and； instead of limits of extension； boundaries of the universe。 But
the question relates to the mundus phaenomenon； and its quantity；
and in this case we cannot make abstraction of the conditions of
sensibility； without doing away with the essential reality of this
world itself。 The world of sense； if it is limited； must necessarily
lie in the infinite void。 If this； and with it space as the a priori
condition of the possibility of phenomena； is left out of view； the
whole world of sense disappears。 In our problem is this alone
considered as given。 The mundus intelligibilis is nothing but the
general conception of a world； in which abstraction has been made of
all conditions of intuition； and in relation to which no synthetical
proposition… either affirmative or negative… is possible。
SECOND CONFLICT OF TRANSCENDENTAL IDEAS。
THESIS。
Every composite substance in the world consists of simple parts； and
there exists nothing that is not either itself simple； or composed
of simple parts。
PROOF。
For； grant that composite substances do not consist of simple parts；
in this case； if all combination or composition were annihilated in
thought； no composite part； and （as； by the supposition； there do
not exist simple parts） no simple part would exist。 Consequently； no
substance； consequently； nothing would exist。 Either； then； it is
impossible to annihilate composition in thought； or； after such
annihilation； there must remain something that subsists without
composition； that is； something that is simple。 But in the former case
the composite could not itself consist of substances； because with
substances composition is merely a contingent relation； apart from
which they must still exist as self…subsistent beings。 Now； as this
case contradicts the supposition； the second must contain the truth…
that the substantial composite in the world consists of simple parts。
It follows； as an immediate inference； that the things in the
world are all； without exception； simple beings… that composition is
merely an external condition pertaining to them… and that； although we
never can separate and isolate the elementary substances from the
state of composition； reason must cogitate these as the primary
subjects of all composition； and consequently； as prior thereto… and
as simple substances。
ANTITHESIS。
No composite thing in the world consists of simple parts； and
there does not exist in the world any simple substance。
PROOF。
Let it be supposed that a composite thing （as substance） consists of
simple parts。 Inasmuch as all external relation； consequently all
composition of substances； is possible only in space； the space；
occupied by that which is composite； must consist of the same number
of parts as is contained in the composite。 But space does not
consist of simple parts； but of spaces。 Therefore； every part of the
composite must occupy a space。 But the absolutely primary parts of
what is composite are simple。 It follows that what is simple
occupies a space。 Now； as everything real that occupies a space；
contains a manifold the parts of which are external to each other； and
is consequently composite… and a real composite； not of accidents （for
these cannot exist external to each other apart from substance）； but
of substances… it follows that the simple must be a substantial
composite； which is self…contradictory。
The second proposition of the antithesis… that there exists in the
world nothing that is simple… is here equivalent to the following： The
existence of the absolut