the critique of pure reason-第64章

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that　many　victories　have　been　obtained　on　both　sides；　but　that　the

last　victory；　decisive　of　the　affair　between　the　contending　parties；

was　won　by　him　who　fought　for　the　right；　only　if　his　adversary　was

forbidden　to　continue　the　tourney。　As　impartial　umpires；　we　must　lay

aside　entirely　the　consideration　whether　the　combatants　are　fighting

for　the　right　or　for　the　wrong　side；　for　the　true　or　for　the　false；

and　allow　the　combat　to　be　first　decided。　Perhaps；　after　they　have

wearied　more　than　injured　each　other；　they　will　discover　the

nothingness　of　their　cause　of　quarrel　and　part　good　friends。

　　This　method　of　watching；　or　rather　of　originating；　a　conflict　of

assertions；　not　for　the　purpose　of　finally　deciding　in　favour　of

either　side；　but　to　discover　whether　the　object　of　the　struggle　is　not

a　mere　illusion；　which　each　strives　in　vain　to　reach；　but　which

would　be　no　gain　even　when　reached…　this　procedure；　I　say；　may　be

termed　the　sceptical　method。　It　is　thoroughly　distinct　from

scepticism…　the　principle　of　a　technical　and　scientific　ignorance；

which　undermines　the　foundations　of　all　knowledge；　in　order；　if

possible；　to　destroy　our　belief　and　confidence　therein。　For　the

sceptical　method　aims　at　certainty；　by　endeavouring　to　discover　in　a

conflict　of　this　kind；　conducted　honestly　and　intelligently　on　both

sides；　the　point　of　misunderstanding；　just　as　wise　legislators　derive；

from　the　embarrassment　of　judges　in　lawsuits；　information　in　regard　to

the　defective　and　ill…defined　parts　of　their　statutes。　The　antinomy

which　reveals　itself　in　the　application　of　laws；　is　for　our　limited

wisdom　the　best　criterion　of　legislation。　For　the　attention　of　reason；

which　in　abstract　speculation　does　not　easily　become　conscious　of

its　errors；　is　thus　roused　to　the　momenta　in　the　determination　of

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　completed　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　completed　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　completed；　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　completeness

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　composition　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

completely　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　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