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its principles。
But this sceptical method is essentially peculiar to
transcendental philosophy； and can perhaps be dispensed with in
every other field of investigation。 In mathematics its use would be
absurd； because in it no false assertions can long remain hidden；
inasmuch as its demonstrations must always proceed under the
guidance of pure intuition； and by means of an always evident
synthesis。 In experimental philosophy； doubt and delay may be very
useful； but no misunderstanding is possible； which cannot be easily
removed； and in experience means of solving the difficulty and putting
an end to the dissension must at last be found； whether sooner or
later。 Moral philosophy can always exhibit its principles； with
their practical consequences； in concreto… at least in possible
experiences； and thus escape the mistakes and ambiguities of
abstraction。 But transcendental propositions； which lay claim to
insight beyond the region of possible experience； cannot； on the one
hand； exhibit their abstract synthesis in any a priori intuition； nor；
on the other； expose a lurking error by the help of experience。
Transcendental reason； therefore； presents us with no other
criterion than that of an attempt to reconcile such assertions； and
for this purpose to permit a free and unrestrained conflict between
them。 And this we now proceed to arrange。*
*The antinomies stand in the order of the four transcendental
ideas above detailed。
FIRST CONFLICT OF THE TRANSCENDENTAL IDEAS。
THESIS。
The world has a beginning in time； and is also limited in
regard to space。
PROOF。
Granted that the world has no beginning in time； up to every given
moment of time； an eternity must have elapsed； and therewith passed
away an infinite series of successive conditions or states of things
in the world。 Now the infinity of a series consists in the fact that
it never can be pleted by means of a successive synthesis。 It
follows that an infinite series already elapsed is impossible and
that； consequently； a beginning of the world is a necessary
condition of its existence。 And this was the first thing to be proved。
As regards the second； let us take the opposite for granted。 In this
case； the world must be an infinite given total of coexistent
things。 Now we cannot cogitate the dimensions of a quantity； which
is not given within certain limits of an intuition；* in any other
way than by means of the synthesis of its parts； and the total of such
a quantity only by means of a pleted synthesis； or the repeated
addition of unity to itself。 Accordingly； to cogitate the world； which
fills all spaces； as a whole； the successive synthesis of the parts of
an infinite world must be looked upon as pleted； that is to say； an
infinite time must be regarded as having elapsed in the enumeration of
all co…existing things； which is impossible。 For this reason an
infinite aggregate of actual things cannot be considered as a given
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 u