the critique of pure reason-第12章

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carry　along　with　them　the　conception　of　necessity；　which　cannot　be

given　by　experience。　If　this　be　demurred　to；　it　matters　not；　I　will

then　limit　my　assertion　to　pure　mathematics；　the　very　conception　of

which　implies　that　it　consists　of　knowledge　altogether　non…empirical

and　a　priori。

　　We　might；　indeed　at　first　suppose　that　the　proposition　7　＋　5　=　12　is

a　merely　analytical　proposition；　following　（according　to　the　principle

of　contradiction）　from　the　conception　of　a　sum　of　seven　and　five。

But　if　we　regard　it　more　narrowly；　we　find　that　our　conception　of

the　sum　of　seven　and　five　contains　nothing　more　than　the　uniting　of

both　sums　into　one；　whereby　it　cannot　at　all　be　cogitated　what　this

single　number　is　which　embraces　both。　The　conception　of　twelve　is　by

no　means　obtained　by　merely　cogitating　the　union　of　seven　and　five；

and　we　may　analyse　our　conception　of　such　a　possible　sum　as　long　as　we

will；　still　we　shall　never　discover　in　it　the　notion　of　twelve。　We

must　go　beyond　these　conceptions；　and　have　recourse　to　an　intuition

which　corresponds　to　one　of　the　two…　our　five　fingers；　for　example；　or

like　Segner　in　his　Arithmetic　five　points；　and　so　by　degrees；　add

the　units　contained　in　the　five　given　in　the　intuition；　to　the

conception　of　seven。　For　I　first　take　the　number　7；　and；　for　the

conception　of　5　calling　in　the　aid　of　the　fingers　of　my　hand　as

objects　of　intuition；　I　add　the　units；　which　I　before　took　together　to

make　up　the　number　5；　gradually　now　by　means　of　the　material　image

my　hand；　to　the　number　7；　and　by　this　process；　I　at　length　see　the

number　12　arise。　That　7　should　be　added　to　5；　I　have　certainly

cogitated　in　my　conception　of　a　sum　=　7　＋　5；　but　not　that　this　sum　was

equal　to　12。　Arithmetical　propositions　are　therefore　always

synthetical；　of　which　we　may　become　more　clearly　convinced　by　trying

large　numbers。　For　it　will　thus　become　quite　evident　that；　turn　and

twist　our　conceptions　as　we　may；　it　is　impossible；　without　having

recourse　to　intuition；　to　arrive　at　the　sum　total　or　product　by

means　of　the　mere　analysis　of　our　conceptions。　just　as　little　is　any

principle　of　pure　geometry　analytical。　〃A　straight　line　between　two

points　is　the　shortest；〃　is　a　synthetical　proposition。　For　my

conception　of　straight　contains　no　notion　of　quantity；　but　is　merely

qualitative。　The　conception　of　the　shortest　is　therefore　fore　wholly

an　addition；　and　by　no　analysis　can　it　be　extracted　from　our

conception　of　a　straight　line。　Intuition　must　therefore　here　lend

its　aid；　by　means　of　which；　and　thus　only；　our　synthesis　is　possible。

　　Some　few　principles　preposited　by　geometricians　are；　indeed；

really　analytical；　and　depend　on　the　principle　of　contradiction。

They　serve；　however；　like　identical　propositions；　as　links　in　the

chain　of　method；　not　as　principles…　for　example；　a　=　a；　the　whole　is

equal　to　itself；　or　（a＋b）　》　a；　the　whole　is　greater　than　its　part。　And

yet　even　these　principles　themselves；　though　they　derive　their

validity　from　pure　conceptions；　are　only　admitted　in　mathematics

because　they　can　be　presented　in　intuition。　What　causes　us　here

commonly　to　believe　that　the　predicate　of　such　apodeictic　judgements

is　already　contained　in　our　conception；　and　that　the　judgement　is

therefore　analytical；　is　merely　the　equivocal　nature　of　the

expression。　We　must　join　in　thought　a　certain　predicate　to　a　given

conception；　and　this　necessity　cleaves　already　to　the　conception。

But　the　question　is；　not　what　we　must　join　in　thought　to　the　given

conception；　but　what　we　really　think　therein；　though　only　obscurely；

and　then　it　becomes　manifest　that　the　predicate　pertains　to　these

conceptions；　necessarily　indeed；　yet　not　as　thought　in　the

conception　itself；　but　by　virtue　of　an　intuition；　which　must　be

added　to　the　conception。

　　2。　The　science　of　natural　philosophy　（physics）　contains　in　itself

synthetical　judgements　a　priori；　as　principles。　I　shall　adduce　two

propositions。　For　instance；　the　proposition；　〃In　all　changes　of　the

material　world；　the　quantity　of　matter　remains　unchanged〃；　or；　that；

〃In　all　communication　of　motion；　action　and　reaction　must　always　be

equal。〃　In　both　of　these；　not　only　is　the　necessity；　and　therefore

their　origin　a　priori　clear；　but　also　that　they　are　synthetical

propositions。　For　in　the　conception　of　matter；　I　do　not　cogitate　its

permanency；　but　merely　its　presence　in　space；　which　it　fills。　I

therefore　really　go　out　of　and　beyond　the　conception　of　matter；　in

order　to　think　on　to　it　something　a　priori；　which　I　did　not　think　in

it。　The　proposition　is　therefore　not　analytical；　but　synthetical；

and　nevertheless　conceived　a　priori；　and　so　it　is　with　regard　to　the

other　propositions　of　the　pure　part　of　natural　philosophy。

　　3。　As　to　metaphysics；　even　if　we　look　upon　it　merely　as　an　attempted

science；　yet；　from　the　nature　of　human　reason；　an　indispensable　one；

we　find　that　it　must　contain　synthetical　propositions　a　priori。　It

is　not　merely　the　duty　of　metaphysics　to　dissect；　and　thereby

analytically　to　illustrate　the　conceptions　which　we　form　a　priori　of

things；　but　we　seek　to　widen　the　range　of　our　a　priori　knowledge。

For　this　purpose；　we　must　avail　ourselves　of　such　principles　as　add

something　to　the　original　conception…　something　not　identical　with；

nor　contained　in　it；　and　by　means　of　synthetical　judgements　a

priori；　leave　far　behind　us　the　limits　of　experience；　for　example；

in　the　proposition；　〃the　world　must　have　a　beginning；〃　and　such

like。　Thus　metaphysics；　according　to　the　proper　aim　of　the　science；

consists　merely　of　synthetical　propositions　a　priori。



　　VI。　The　Universal　Problem　of　Pure　Reason。



　　It　is　extremely　advantageous　to　be　able　to　bring　a　number　of

investigations　under　the　formula　of　a　single　problem。　For　in　this

manner；　we　not　only　facilitate　our　own　labour；　inasmuch　as　we　define

it　clearly　to　ourselves；　but　also　render　it　more　easy　for　others　to

decide　whether　we　have　done　justice　to　our　undertaking。　The　proper

problem　of　pure　reason；　then；　is　contained　in　the　question：　〃How　are

synthetical　judgements　a　priori　possible？〃

　　That　metaphysical　science　has　hitherto　remained　in　so　vacillating

a　state　of　uncertainty　and　contradiction；　is　only　to　be　attributed

to　the　fact　that　this　great　problem；　and　perhaps　even　the　difference

between　analytical　and　synthetical　judgements；　did　not　sooner

suggest　itself　to　philosophers。　Upon　the　solution　of　this　problem；

or　upon　sufficient　proof　of　the　impossibility　of　synthetical　knowledge

a　priori；　depends　the　existence　or　downfall　of　the　science　of

metaphysics。　Among　philosophers；　David　Hume　came　the　nearest　of　all　to

this　problem；　yet　it　never　acquired　in　his　mind　sufficient

precision；　nor　did　he　regard　the　question　in　its　universality。　On

the　contrary；　he　stopped　short　at　the　synthetical　proposition　of　the

connection　of　an　effect　with　its　cause　（principium　causalitatis）；

insisting　that　such　proposition　a　priori　was　impossible。　According

to　his　conclusions；　then；　all　that　we　term　metaphysical　science　is　a

mere　delusion；　arising　from　the　fancied　insight　of　reason　into　that

which　is　in　truth　borrowed　from　experience；　and　to　which　habit　has

given　the　appearance　of　necessity。　Against　this　assertion；　destructive

to　all　pure　philosophy；　he　would　have　been　guarded；　had　he　had　our

problem　before　his　eyes　in　its　universality。　For　he　would　then　have

perceived　that；　according　to　his　own　argument；　there　likewise　could

not　be　any　pure　mathematical　science；　which　assuredly　cannot　exist

without　synthetical　propositions　a　priori…　an　absurdity　from　which　his

good　understanding　must　have　saved　him。

　　In　the　solution　of　the　above　problem　is　at　the　same　time

comprehended　the　possibility　of　the　use　of　pure　reason　in　the

foundation　and　construction　of　all　sciences　which　contain

theoretical　knowledge　a　priori　of　objects；　that　is　to　say；　the

answer　to　the　following　questions：

　　How　is　pure　mathematical　science　possible？

　　How　is　pure　natural　sc