the+critique+of+pure+reason_纯粹理性批判-第76部分

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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；