the critique of pure reason-第101章

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he　represents；　a　priori；　in　correspondence　with　his　conceptions？　The

cause　is　evident　from　what　has　been　already　demonstrated　in　the

introduction　to　this　Critique。　We　do　not；　in　the　present　case；　want　to

discover　analytical　propositions；　which　may　be　produced　merely　by

analysing　our　conceptions…　for　in　this　the　philosopher　would　have

the　advantage　over　his　rival；　we　aim　at　the　discovery　of　synthetical

propositions…　such　synthetical　propositions；　moreover；　as　can　be

cognized　a　priori。　I　must　not　confine　myself　to　that　which　I

actually　cogitate　in　my　conception　of　a　triangle；　for　this　is

nothing　more　than　the　mere　definition；　I　must　try　to　go　beyond　that；

and　to　arrive　at　properties　which　are　not　contained　in；　although

they　belong　to；　the　conception。　Now；　this　is　impossible；　unless　I

determine　the　object　present　to　my　mind　according　to　the　conditions；

either　of　empirical；　or　of　pure；　intuition。　In　the　former　case；　I

should　have　an　empirical　proposition　（arrived　at　by　actual　measurement

of　the　angles　of　the　triangle）；　which　would　possess　neither

universality　nor　necessity；　but　that　would　be　of　no　value。　In　the

latter；　I　proceed　by　geometrical　construction；　by　means　of　which　I

collect；　in　a　pure　intuition；　just　as　I　would　in　an　empirical

intuition；　all　the　various　properties　which　belong　to　the　schema　of

a　triangle　in　general；　and　consequently　to　its　conception；　and　thus

construct　synthetical　propositions　which　possess　the　attribute　of

universality。

　　It　would　be　vain　to　philosophize　upon　the　triangle；　that　is；　to

reflect　on　it　discursively；　I　should　get　no　further　than　the

definition　with　which　I　had　been　obliged　to　set　out。　There　are

certainly　transcendental　synthetical　propositions　which　are　framed

by　means　of　pure　conceptions；　and　which　form　the　peculiar

distinction　of　philosophy；　but　these　do　not　relate　to　any　particular

thing；　but　to　a　thing　in　general；　and　enounce　the　conditions　under

which　the　perception　of　it　may　become　a　part　of　possible　experience。

But　the　science　of　mathematics　has　nothing　to　do　with　such

questions；　nor　with　the　question　of　existence　in　any　fashion；　it　is

concerned　merely　with　the　properties　of　objects　in　themselves；　only　in

so　far　as　these　are　connected　with　the　conception　of　the　objects。

　　In　the　above　example；　we　merely　attempted　to　show　the　great

difference　which　exists　between　the　discursive　employment　of　reason　in

the　sphere　of　conceptions；　and　its　intuitive　exercise　by　means　of

the　construction　of　conceptions。　The　question　naturally　arises：　What

is　the　cause　which　necessitates　this　twofold　exercise　of　reason；　and

how　are　we　to　discover　whether　it　is　the　philosophical　or　the

mathematical　method　which　reason　is　pursuing　in　an　argument？

　　All　our　knowledge　relates；　finally；　to　possible　intuitions；　for　it

is　these　alone　that　present　objects　to　the　mind。　An　a　priori　or

non…empirical　conception　contains　either　a　pure　intuition…　and　in　this

case　it　can　be　constructed；　or　it　contains　nothing　but　the　synthesis

of　possible　intuitions；　which　are　not　given　a　priori。　In　this　latter

case；　it　may　help　us　to　form　synthetical　a　priori　judgements；　but　only

in　the　discursive　method；　by　conceptions；　not　in　the　intuitive；　by

means　of　the　construction　of　conceptions。

　　The　only　a　priori　intuition　is　that　of　the　pure　form　of　phenomena…

space　and　time。　A　conception　of　space　and　time　as　quanta　may　be

presented　a　priori　in　intuition；　that　is；　constructed；　either　alone

with　their　quality　（figure）；　or　as　pure　quantity　（the　mere　synthesis

of　the　homogeneous）；　by　means　of　number。　But　the　matter　of

phenomena；　by　which　things　are　given　in　space　and　time；　can　be

presented　only　in　perception；　a　posteriori。　The　only　conception

which　represents　a　priori　this　empirical　content　of　phenomena　is　the

conception　of　a　thing　in　general；　and　the　a　priori　synthetical

cognition　of　this　conception　can　give　us　nothing　more　than　the　rule

for　the　synthesis　of　that　which　may　be　contained　in　the

corresponding　a　posteriori　perception；　it　is　utterly　inadequate　to

present　an　a　priori　intuition　of　the　real　object；　which　must

necessarily　be　empirical。

　　Synthetical　propositions；　which　relate　to　things　in　general；　an　a

priori　intuition　of　which　is　impossible；　are　transcendental。　For

this　reason　transcendental　propositions　cannot　be　framed　by　means　of

the　construction　of　conceptions；　they　are　a　priori；　and　based　entirely

on　conceptions　themselves。　They　contain　merely　the　rule；　by　which　we

are　to　seek　in　the　world　of　perception　or　experience　the　synthetical

unity　of　that　which　cannot　be　intuited　a　priori。　But　they　are

incompetent　to　present　any　of　the　conceptions　which　appear　in　them

in　an　a　priori　intuition；　these　can　be　given　only　a　posteriori；　in

experience；　which；　however；　is　itself　possible　only　through　these

synthetical　principles。

　　If　we　are　to　form　a　synthetical　judgement　regarding　a　conception；　we

must　go　beyond　it；　to　the　intuition　in　which　it　is　given。　If　we　keep

to　what　is　contained　in　the　conception；　the　judgement　is　merely

analytical…　it　is　merely　an　explanation　of　what　we　have　cogitated　in

the　conception。　But　I　can　pass　from　the　conception　to　the　pure　or

empirical　intuition　which　corresponds　to　it。　I　can　proceed　to

examine　my　conception　in　concreto；　and　to　cognize；　either　a　priori

or　a　posterio；　what　I　find　in　the　object　of　the　conception。　The

former…　a　priori　cognition…　is　rational…mathematical　cognition　by

means　of　the　construction　of　the　conception；　the　latter…　a

posteriori　cognition…　is　purely　empirical　cognition；　which　does　not

possess　the　attributes　of　necessity　and　universality。　Thus　I　may

analyse　the　conception　I　have　of　gold；　but　I　gain　no　new　information

from　this　analysis；　I　merely　enumerate　the　different　properties

which　I　had　connected　with　the　notion　indicated　by　the　word。　My

knowledge　has　gained　in　logical　clearness　and　arrangement；　but　no

addition　has　been　made　to　it。　But　if　I　take　the　matter　which　is

indicated　by　this　name；　and　submit　it　to　the　examination　of　my　senses；

I　am　enabled　to　form　several　synthetical…　although　still　empirical…

propositions。　The　mathematical　conception　of　a　triangle　I　should

construct；　that　is；　present　a　priori　in　intuition；　and　in　this　way

attain　to　rational…synthetical　cognition。　But　when　the

transcendental　conception　of　reality；　or　substance；　or　power　is

presented　to　my　mind；　I　find　that　it　does　not　relate　to　or　indicate

either　an　empirical　or　pure　intuition；　but　that　it　indicates　merely

the　synthesis　of　empirical　intuitions；　which　cannot　of　course　be　given

a　priori。　The　synthesis　in　such　a　conception　cannot　proceed　a

priori…　without　the　aid　of　experience…　to　the　intuition　which

corresponds　to　the　conception；　and；　for　this　reason；　none　of　these

conceptions　can　produce　a　determinative　synthetical　proposition；

they　can　never　present　more　than　a　principle　of　the　synthesis*　of

possible　empirical　intuitions。　A　transcendental　proposition　is；

therefore；　a　synthetical　cognition　of　reason　by　means　of　pure

conceptions　and　the　discursive　method；　and　it　renders　possible　all

synthetical　unity　in　empirical　cognition；　though　it　cannot　present

us　with　any　intuition　a　priori。



　　*In　the　case　of　the　conception　of　cause；　I　do　really　go　beyond　the

empirical　conception　of　an　event…　but　not　to　the　intuition　which

presents　this　conception　in　concreto；　but　only　to　the　time…conditions；

which　may　be　found　in　experience　to　correspond　to　the　conception。　My

procedure　is；　therefore；　strictly　according　to　conceptions；　I　cannot

in　a　case　of　this　kind　employ　the　construction　of　conceptions；　because

the　conception　is　merely　a　rule　for　the　synthesis　of　perceptions；

which　are　not　pure　intuitions；　and　which；　therefore；　cannot　be　given　a

priori。



　　There　is　thus　a　twofold　exercise　of　reason。　Both　modes　have　the

properties　of　universality　and　an　a　priori　origin　in　common；　but

are；　in　their　procedure；　of　widely　different　character。　The　reason

of　this　is　that　in　the　world　of　phenomena；　in　which　alone　objects

are　presented　to　our　minds；　there　are　two　main　elements…　the　form　of

intuition　（space　and　time）；　which　can　be　cognized　and　determined

completely　a　priori；　and　the　matter　or　content…　that　which　is

presented　in　space　and　time；　and　which；　consequently；　contains　a

something…　an　existence　corresponding　to　our　powers　of　sensation。　As

regards　the　latter；　which　can　never　be　given　in　a　determinate　mode

except　by　experience；　there　are　no　a　priori　notions　which　relate　to

it；　except　the　undetermined　conceptions　of　the　synthesis　of　possible

sensations；　in　so　far　as　these　belong　（in　a　possible　experience）　to

the　unity　of　consciousness。　As　regards　the　former；　we　can　determine

our　conceptions　a　priori　in　intuition；　inasmuch　as　we　are　ourselves

the　creators　of　the　objects　of　the　conceptions　in　space　and　time…

these　objects　being　regarded　simply　as　quanta。　In　the　one　case；　reason

proceeds　according　to　conceptions　and　can　do　nothing　more　than　subject

phenomena　to　these…　which　can　only　be　determined　empirically；　that　is；

a　posteriori…　in　conformity；　however；　with　those　conceptions　as　the

rules　of　all　empirical　synthesis。　In　the　other　case；　reason　proceeds

by　the　construction　of　conceptions；　and；　as　these　conceptions　relate

to　an　a　priori　intuition；　they　may　be　given　and　determined　in　pure

intuition　a　priori；　and　without　the　aid　of　empirical　data。　The

examination　and　consideration　of　everything　that　exists　in　space　or

time…　whether　it　is　a　quantum　or　not；　in　how　far　the　particular

something　（which　fills　space　or　time）　is　a　primary　substratum；　or　a

mere　determination　of　some　other　existence；　whether　it　relates　to

anything　else…　either　as　cause　or　effect；　whether　its　existence　is

isolated　or　in　reciprocal　connection　with　and　dependence　upon

others；　the　possibility　of　this　existence；　its　reality　and　necessity

or　opposites…　all　these　form　part　of　the　cognition　of　reason　on　the

ground　of　conceptions；　and　this　cognition　is　termed　philosophical。　But

to　determine　a　priori　an　intuition　in　space　（its　figure）；　to　divide

time　into　periods；　or　merely　to　cognize　the　quantity　of　an　intuition

in　space　and　time；　and　to　determine　it　by　number…　all　this　is　an

operation　of　reason　by　means　of　the　construction　of　conceptions；　and

is　called　mathematical。

　　The　success　which　attends　the　efforts　of　reason　in　the　sphere　of

mathematics　naturally　fosters　the　expectation　that　the　same　good

fortune　will　be　its　lot；　if　it　applies　the　mathematical　method　in

other　regions　of　mental　endeavour　besides　that　of　quantities。　Its

success　is　thus　great；　because　it　can　support　all　its　conceptions　by　a

priori　intuitions　and；　in　this　way；　make　itself　a　master；　as　it

were；　over　nature；　while　pure　philosophy；　with　its　a　priori　discursive

conceptions；　bungles　about　in　the　world　of　nature；　and　cannot　accredit

or　show　any　a　priori　evidence　of　the　reality　of　these　conceptions。

Masters　in　the　science　of　mathematics　are　co