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whole; consequently; not as a contemporaneously given whole。 The world
is consequently; as regards extension in space; not infinite; but
enclosed in limits。 And this was the second thing to be proved。

  *We may consider an undetermined quantity as a whole; when it is
enclosed within limits; although we cannot construct or ascertain
its totality by measurement; that is; by the successive synthesis of
its parts。 For its limits of themselves determine its pleteness
as a whole。

                        ANTITHESIS。

  The world has no beginning; and no limits in space; but is; in
relation both to time and space; infinite。

                          PROOF。

  For let it be granted that it has a beginning。 A beginning is an
existence which is preceded by a time in which the thing does not
exist。 On the above supposition; it follows that there must have
been a time in which the world did not exist; that is; a void time。
But in a void time the origination of a thing is impossible; because
no part of any such time contains a distinctive condition of being; in
preference to that of non…being (whether the supposed thing
originate of itself; or by means of some other cause)。 Consequently;
many series of things may have a beginning in the world; but the world
itself cannot have a beginning; and is; therefore; in relation to past
time; infinite。
  As regards the second statement; let us first take the opposite
for granted… that the world is finite and limited in space; it follows
that it must exist in a void space; which is not limited。 We should
therefore meet not only with a relation of things in space; but also a
relation of things to space。 Now; as the world is an absolute whole;
out of and beyond which no object of intuition; and consequently no
correlate to which can be discovered; this relation of the world to
a void space is merely a relation to no object。 But such a relation;
and consequently the limitation of the world by void space; is
nothing。 Consequently; the world; as regards space; is not limited;
that is; it is infinite in regard to extension。*

  *Space is merely the form of external intuition (formal
intuition); and not a real object which can be externally perceived。
Space; prior to all things which determine it (fill or limit it);
or; rather; which present an empirical intuition conformable to it;
is; under the title of absolute space; nothing but the mere
possibility of external phenomena; in so far as they either exist in
themselves; or can annex themselves to given intuitions。 Empirical
intuition is therefore not a position of phenomena and space (of
perception and empty intuition)。 The one is not the correlate of the
other in a synthesis; but they are vitally connected in the same
empirical intuition; as matter and form。 If we wish to set one of
these two apart from the other… space from phenomena… there arise
all sorts of empty determinations of external intuition; which are
very far from being possible perceptions。 For example; motion or
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 time;
and; 

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