the critique of pure reason-第76章

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that　I　am　not　entitled　to　make　any　assertion　at　all　respecting　the

whole　object　of　experience…　the　world　of　sense；　I　must　limit　my

declarations　to　the　rule　according　to　which　experience　or　empirical

knowledge　is　to　be　attained。

　　To　the　question；　therefore；　respecting　the　cosmical　quantity；　the

first　and　negative　answer　is：　〃The　world　has　no　beginning　in　time；　and

no　absolute　limit　in　space。〃

　　For；　in　the　contrary　case；　it　would　be　limited　by　a　void　time　on　the

one　hand；　and　by　a　void　space　on　the　other。　Now；　since　the　world；　as　a

phenomenon；　cannot　be　thus　limited　in　itself　for　a　phenomenon　is　not　a

thing　in　itself；　it　must　be　possible　for　us　to　have　a　perception　of

this　limitation　by　a　void　time　and　a　void　space。　But　such　a

perception…　such　an　experience　is　impossible；　because　it　has　no

content。　Consequently；　an　absolute　cosmical　limit　is　empirically；

and　therefore　absolutely；　impossible。*



　　*The　reader　will　remark　that　the　proof　presented　above　is　very

different　from　the　dogmatical　demonstration　given　in　the　antithesis　of

the　first　antinomy。　In　that　demonstration；　it　was　taken　for　granted

that　the　world　is　a　thing　in　itself…　given　in　its　totality　prior　to

all　regress；　and　a　determined　position　in　space　and　time　was　denied　to

it…　if　it　was　not　considered　as　occupying　all　time　and　all　space。

Hence　our　conclusion　differed　from　that　given　above；　for　we　inferred

in　the　antithesis　the　actual　infinity　of　the　world。



　　From　this　follows　the　affirmative　answer：　〃The　regress　in　the　series

of　phenomena…　as　a　determination　of　the　cosmical　quantity；　proceeds　in

indefinitum。〃　This　is　equivalent　to　saying：　〃The　world　of　sense　has　no

absolute　quantity；　but　the　empirical　regress　（through　which　alone

the　world　of　sense　is　presented　to　us　on　the　side　of　its　conditions）

rests　upon　a　rule；　which　requires　it　to　proceed　from　every　member　of

the　series；　as　conditioned；　to　one　still　more　remote　（whether

through　personal　experience；　or　by　means　of　history；　or　the　chain　of

cause　and　effect）；　and　not　to　cease　at　any　point　in　this　extension

of　the　possible　empirical　employment　of　the　understanding。〃　And　this

is　the　proper　and　only　use　which　reason　can　make　of　its　principles。

　　The　above　rule　does　not　prescribe　an　unceasing　regress　in　one　kind

of　phenomena。　It　does　not；　for　example；　forbid　us；　in　our　ascent

from　an　individual　human　being　through　the　line　of　his　ancestors；　to

expect　that　we　shall　discover　at　some　point　of　the　regress　a

primeval　pair；　or　to　admit；　in　the　series　of　heavenly　bodies；　a　sun　at

the　farthest　possible　distance　from　some　centre。　All　that　it　demands

is　a　perpetual　progress　from　phenomena　to　phenomena；　even　although

an　actual　perception　is　not　presented　by　them　（as　in　the　case　of　our

perceptions　being　so　weak　as　that　we　are　unable　to　become　conscious　of

them）；　since　they；　nevertheless；　belong　to　possible　experience。

　　Every　beginning　is　in　time；　and　all　limits　to　extension　are　in

space。　But　space　and　time　are　in　the　world　of　sense。　Consequently

phenomena　in　the　world　are　conditionally　limited；　but　the　world　itself

is　not　limited；　either　conditionally　or　unconditionally。

　　For　this　reason；　and　because　neither　the　world　nor　the　cosmical

series　of　conditions　to　a　given　conditioned　can　be　completely　given；

our　conception　of　the　cosmical　quantity　is　given　only　in　and　through

the　regress　and　not　prior　to　it…　in　a　collective　intuition。　But　the

regress　itself　is　really　nothing　more　than　the　determining　of　the

cosmical　quantity；　and　cannot　therefore　give　us　any　determined

conception　of　it…　still　less　a　conception　of　a　quantity　which　is；　in

relation　to　a　certain　standard；　infinite。　The　regress　does　not；

therefore；　proceed　to　infinity　（an　infinity　given）；　but　only　to　an

indefinite　extent；　for　or　the　of　presenting　to　us　a　quantity…　realized

only　in　and　through　the　regress　itself。



　　　　II。　Solution　of　the　Cosmological　Idea　of　the　Totality　of

　　　　　　　　the　Division　of　a　Whole　given　in　Intuition。



　　When　I　divide　a　whole　which　is　given　in　intuition；　I　proceed　from

a　conditioned　to　its　conditions。　The　division　of　the　parts　of　the

whole　（subdivisio　or　decompositio）　is　a　regress　in　the　series　of　these

conditions。　The　absolute　totality　of　this　series　would　be　actually

attained　and　given　to　the　mind；　if　the　regress　could　arrive　at

simple　parts。　But　if　all　the　parts　in　a　continuous　decomposition　are

themselves　divisible；　the　division；　that　is　to　say；　the　regress；

proceeds　from　the　conditioned　to　its　conditions　in　infinitum；

because　the　conditions　（the　parts）　are　themselves　contained　in　the

conditioned；　and；　as　the　latter　is　given　in　a　limited　intuition；　the

former　are　all　given　along　with　it。　This　regress　cannot；　therefore；　be

called　a　regressus　in　indefinitum；　as　happened　in　the　case　of　the

preceding　cosmological　idea；　the　regress　in　which　proceeded　from　the

conditioned　to　the　conditions　not　given　contemporaneously　and　along

with　it；　but　discoverable　only　through　the　empirical　regress。　We　are

not；　however；　entitled　to　affirm　of　a　whole　of　this　kind；　which　is

divisible　in　infinitum；　that　it　consists　of　an　infinite　number　of

parts。　For；　although　all　the　parts　are　contained　in　the　intuition　of

the　whole；　the　whole　division　is　not　contained　therein。　The　division

is　contained　only　in　the　progressing　decomposition…　in　the　regress

itself；　which　is　the　condition　of　the　possibility　and　actuality　of　the

series。　Now；　as　this　regress　is　infinite；　all　the　members　（parts）　to

which　it　attains　must　be　contained　in　the　given　whole　as　an　aggregate。

But　the　complete　series　of　division　is　not　contained　therein。　For　this

series；　being　infinite　in　succession　and　always　incomplete；　cannot

represent　an　infinite　number　of　members；　and　still　less　a

composition　of　these　members　into　a　whole。

　　To　apply　this　remark　to　space。　Every　limited　part　of　space　presented

to　intuition　is　a　whole；　the　parts　of　which　are　always　spaces…　to

whatever　extent　subdivided。　Every　limited　space　is　hence　divisible

to　infinity。

　　Let　us　again　apply　the　remark　to　an　external　phenomenon　enclosed

in　limits；　that　is；　a　body。　The　divisibility　of　a　body　rests　upon

the　divisibility　of　space；　which　is　the　condition　of　the　possibility

of　the　body　as　an　extended　whole。　A　body　is　consequently　divisible

to　infinity；　though　it　does　not；　for　that　reason；　consist　of　an

infinite　number　of　parts。

　　It　certainly　seems　that；　as　a　body　must　be　cogitated　as　substance　in

space；　the　law　of　divisibility　would　not　be　applicable　to　it　as

substance。　For　we　may　and　ought　to　grant；　in　the　case　of　space；　that

division　or　decomposition；　to　any　extent；　never　can　utterly　annihilate

composition　（that　is　to　say；　the　smallest　part　of　space　must　still

consist　of　spaces）；　otherwise　space　would　entirely　cease　to　exist…

which　is　impossible。　But；　the　assertion　on　the　other　band　that　when

all　composition　in　matter　is　annihilated　in　thought；　nothing

remains；　does　not　seem　to　harmonize　with　the　conception　of

substance；　which　must　be　properly　the　subject　of　all　composition　and

must　remain；　even　after　the　conjunction　of　its　attributes　in　space…

which　constituted　a　body…　is　annihilated　in　thought。　But　this　is　not

the　case　with　substance　in　the　phenomenal　world；　which　is　not　a

thing　in　itself　cogitated　by　the　pure　category。　Phenomenal　substance

is　not　an　absolute　subject；　it　is　merely　a　permanent　sensuous　image；

and　nothing　more　than　an　intuition；　in　which　the　unconditioned　is

not　to　be　found。

　　But；　although　this　rule　of　progress　to　infinity　is　legitimate　and

applicable　to　the　subdivision　of　a　phenomenon；　as　a　mere　occupation　or

filling　of　space；　it　is　not　applicable　to　a　whole　consisting　of　a

number　of　distinct　parts　and　constituting　a　quantum　discretum…　that　is

to　say；　an　organized　body。　It　cannot　be　admitted　that　every　part　in　an

organized　whole　is　itself　organized；　and　that；　in　analysing　it　to

infinity；　we　must　always　meet　with　organized　parts；　although　we　may

allow　that　the　parts　of　the　matter　which　we　decompose　in　infinitum；

may　be　organized。　For　the　infinity　of　the　division　of　a　phenomenon

in　space　rests　altogether　on　the　fact　that　the　divisibility　of　a

phenomenon　is　given　only　in　and　through　this　infinity；　that　is；　an

undetermined　number　of　parts　is　given；　while　the　parts　themselves

are　given　and　determined　only　in　and　through　the　subdivision；　in　a

word；　the　infinity　of　the　division　necessarily　presupposes　that　the

whole　is　not　already　divided　in　se。　Hence　our　division　determines　a

number　of　parts　in　the　whole…　a　number　which　extends　just　as　far　as

the　actual　regress　in　the　division；　while；　on　the　other　hand；　the　very

notion　of　a　body　organized　to　infinity　represents　the　whole　as　already

and　in　itself　divided。　We　expect；　therefore；　to　find　in　it　a

determinate；　but　at　the　same　time；　infinite；　number　of　parts…　which　is

self…contradictory。　For　we　should　thus　have　a　whole　containing　a

series　of　members　which　could　not　be　completed　in　any　regress…　which

is　infinite；　and　at　the　same　time　complete　in　an　organized

composite。　Infinite　divisibility　is　applicable　only　to　a　quantum

continuum；　and　is　based　entirely　on　the　infinite　divisibility　of

space；　But　in　a　quantum　discretum　the　multitude　of　parts　or　units　is

always　determined；　and　hence　always　equal　to　some　number。　To　what

extent　a　body　may　be　organized；　experience　alone　can　inform　us；　and

although；　so　far　as　our　experience　of　this　or　that　body　has

extended；　we　may　not　have　discovered　any　inorganic　part；　such　parts

must　exist　in　possible　experience。　But　how　far　the　transcendental

division　of　a　phenomenon　must　extend；　we　cannot　know　from

experience…　it　is　a　question　which　experience　cannot　answer；　it　is

answered　only　by　the　principle　of　reason　which　forbids　us　to

consider　the　empirical　regress；　in　the　analysis　of　extended　body；　as

ever　absolutely　complete。



　　　　　Concluding　Remark　on　the　Solution　of　the　Transcendental

　　　　　　　　　　Mathematical　Ideas…　and　Introductory　to　the

　　　　　　　　　　　　　　　Solution　of　the　Dynamical　Ideas。



　　We　presented　the　antinomy　of　pure　reason　in　a　tabular　form；　and　we

endeavoured　to　show　the　ground　of　this　self…contradiction　on　the

part　of　reason；　and　the　only　means　of　bringing　it　to　a　conclusion…

znamely；　by　declaring　both　contradictory　statements　to　be　false。　We

represented　in　these　antinomies　the　conditions　of　phenomena　as

belonging　to　the　conditioned　according　to　relations　of　space　and　time…

which　is　the　usual　supposition　of　the　common　understanding。　In　this

respect；　all　dialectical　representations　of　totality；　in　the　series　of

conditions　to　a　given　conditioned；　were　perfectly　homogeneous。　The

condition　was　always　a　member　of　the　series　along　with　the

conditioned；　and　thus　the　homogeneity　of　the　whole　series　was　assured。

In　this　case　the　regress　could　never　be　cogitated　as　complete；　or；

if　this　was　the　case；　a　member　really　conditioned　was　falsely　regarded

as　a　primal　member；　conseque