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rest of the world in an infinite empty space； or a determination of
the mutual relation of both； cannot possibly be perceived； and is
therefore merely the predicate of a notional entity。
OBSERVATIONS ON THE FIRST ANTINOMY。
ON THE THESIS。
In bringing forward these conflicting arguments； I have not been
on the search for sophisms； for the purpose of availing myself of
special pleading； which takes advantage of the carelessness of the
opposite party； appeals to a misunderstood statute； and erects its
unrighteous claims upon an unfair interpretation。 Both proofs
originate fairly from the nature of the case； and the advantage
presented by the mistakes of the dogmatists of both parties has been
pletely set aside。
The thesis might also have been unfairly demonstrated； by the
introduction of an erroneous conception of the infinity of a given
quantity。 A quantity is infinite； if a greater than itself cannot
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 pleted。* 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 pleted； 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 pleted synthesis of the parts； and this
pletion； 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