the critique of pure reason- 第36部分

twelve；　which　results　from　the　synthesis　of　seven　and　five。　Such

propositions；　then；　cannot　be　termed　axioms　（for　in　that　case　we

should　have　an　infinity　of　these）；　but　numerical　formulae。

　　This　transcendental　principle　of　the　mathematics　of　phenomena

greatly　enlarges　our　a　priori　cognition。　For　it　is　by　this　principle

alone　that　pure　mathematics　is　rendered　applicable　in　all　its

precision　to　objects　of　experience；　and　without　it　the　validity　of

this　application　would　not　be　so　self…evident；　on　the　contrary；

contradictions　and　confusions　have　often　arisen　on　this　very　point。

Phenomena　are　not　things　in　themselves。　Empirical　intuition　is

possible　only　through　pure　intuition　（of　space　and　time）；

consequently；　what　geometry　affirms　of　the　latter；　is　indisputably

valid　of　the　former。　All　evasions；　such　as　the　statement　that

objects　of　sense　do　not　conform　to　the　rules　of　construction　in

space　（for　example；　to　the　rule　of　the　infinite　divisibility　of

lines　or　angles）；　must　fall　to　the　ground。　For；　if　these　objections

hold　good；　we　deny　to　space；　and　with　it　to　all　mathematics；　objective

validity；　and　no　longer　know　wherefore；　and　how　far；　mathematics　can

be　applied　to　phenomena。　The　synthesis　of　spaces　and　times　as　the

essential　form　of　all　intuition；　is　that　which　renders　possible　the

apprehension　of　a　phenomenon；　and　therefore　every　external　experience；

consequently　all　cognition　of　the　objects　of　experience；　and

whatever　mathematics　in　its　pure　use　proves　of　the　former；　must

necessarily　hold　good　of　the　latter。　All　objections　are　but　the

chicaneries　of　an　ill…instructed　reason；　which　erroneously　thinks　to

liberate　the　objects　of　sense　from　the　formal　conditions　of　our

sensibility；　and　represents　these；　although　mere　phenomena；　as

things　in　themselves；　presented　as　such　to　our　understanding。　But　in

this　case；　no　a　priori　synthetical　cognition　of　them　could　be

possible；　consequently　not　through　pure　conceptions　of　space　and　the

science　which　determines　these　conceptions；　that　is　to　say；

geometry；　would　itself　be　impossible。



　　　　　　　　　　　　　　　　2。　ANTICIPATIONS　OF　PERCEPTION。



　　　　The　principle　of　these　is：　In　all　phenomena　the　Real；　that

　　　　　　which　is　an　object　of　sensation；　has　Intensive　Quantity；

　　　　　　　　　　　　　　　　　　that　is；　has　a　Degree。



　　　　　　　　　　　　　　　　　　　　　　　　　PROOF。



　　Perception　is　empirical　consciousness；　that　is　to　say；　a

consciousness　which　contains　an　element　of　sensation。　Phenomena　as

objects　of　perception　are　not　pure；　that　is；　merely　formal　intuitions；

like　space　and　time；　for　they　cannot　be　perceived　in　themselves。

They　contain；　then；　over　and　above　the　intuition；　the　materials　for　an

object　（through　which　is　represented　something　existing　in　space　or

time）；　that　is　to　say；　they　contain　the　real　of　sensation；　as　a

representation　merely　subjective；　which　gives　us　merely　the

consciousness　that　the　subject　is　affected；　and　which　we　refer　to　some

external　object。　Now；　a　gradual　transition　from　empirical

consciousness　to　pure　consciousness　is　possible；　inasmuch　as　the

real　in　this　consciousness　entirely　vanishes；　and　there　remains　a

merely　formal　consciousness　（a　priori）　of　the　manifold　in　time　and

space；　consequently　there　is　possible　a　synthesis　also　of　the

production　of　the　quantity　of　a　sensation　from　its　commencement；

that　is；　from　the　pure　intuition　=　0　onwards　up　to　a　certain

quantity　of　the　sensation。　Now　as　sensation　in　itself　is　not　an

objective　representation；　and　in　it　is　to　be　found　neither　the

intuition　of　space　nor　of　time；　it　cannot　possess　any　extensive

quantity；　and　yet　there　does　belong　to　it　a　quantity　（and　that　by

means　of　its　apprehension；　in　which　empirical　consciousness　can　within

a　certain　time　rise　from　nothing　=　0　up　to　its　given　amount）；

consequently　an　intensive　quantity。　And　thus　we　must　ascribe　intensive

quantity；　that　is；　a　degree　of　influence　on　sense　to　all　objects　of

perception；　in　so　far　as　this　perception　contains　sensation。

　　All　cognition；　by　means　of　which　I　am　enabled　to　cognize　and

determine　a　priori　what　belongs　to　empirical　cognition；　may　be

called　an　anticipation；　and　without　doubt　this　is　the　sense　in　which

Epicurus　employed　his　expression　prholepsis。　But　as　there　is　in

phenomena　something　which　is　never　cognized　a　priori；　which　on　this

account　constitutes　the　proper　difference　between　pure　and　empirical

cognition；　that　is　to　say；　sensation　（as　the　matter　of　perception）；　it

follows；　that　sensation　is　just　that　element　in　cognition　which　cannot

be　at　all　anticipated。　On　the　other　hand；　we　might　very　well　term

the　pure　determinations　in　space　and　time；　as　well　in　regard　to　figure

as　to　quantity；　anticipations　of　phenomena；　because　they　represent　a

priori　that　which　may　always　be　given　a　posteriori　in　experience。

But　suppose　that　in　every　sensation；　as　sensation　in　general；

without　any　particular　sensation　being　thought　of；　there　existed

something　which　could　be　cognized　a　priori；　this　would　deserve　to　be

called　anticipation　in　a　special　sense…　special；　because　it　may　seem

surprising　to　forestall　experience；　in　that　which　concerns　the

matter　of　experience；　and　which　we　can　only　derive　from　itself。　Yet

such　really　is　the　case　here。

　　Apprehension；　by　means　of　sensation　alone；　fills　only　one　moment；

that　is；　if　I　do　not　take　into　consideration　a　succession　of　many

sensations。　As　that　in　the　phenomenon；　the　apprehension　of　which　is

not　a　successive　synthesis　advancing　from　parts　to　an　entire

representation；　sensation　has　therefore　no　extensive　quantity；　the

want　of　sensation　in　a　moment　of　time　would　represent　it　as　empty；

consequently　=　O。　That　which　in　the　empirical　intuition　corresponds　to

sensation　is　reality　（realitas　phaenomenon）；　that　which　corresponds　to

the　absence　of　it；　negation　=　O。　Now　every　sensation　is　capable　of　a

diminution；　so　that　it　can　decrease；　and　thus　gradually　disappear。

Therefore；　between　reality　in　a　phenomenon　and　negation；　there

exists　a　continuous　concatenation　of　many　possible　intermediate

sensations；　the　difference　of　which　from　each　other　is　always

smaller　than　that　between　the　given　sensation　and　zero；　or　complete

negation。　That　is　to　say；　the　real　in　a　phenomenon　has　always　a

quantity；　which　however　is　not　discoverable　in　apprehension；

inasmuch　as　apprehension　take　place　by　means　of　mere　sensation　in

one　instant；　and　not　by　the　successive　synthesis　of　many　sensations；

and　therefore　does　not　progress　from　parts　to　the　whole。　Consequently；

it　has　a　quantity；　but　not　an　extensive　quantity。

　　Now　that　quantity　which　is　apprehended　only　as　unity；　and　in　which

plurality　can　be　represented　only　by　approximation　to　negation　=　O；

I　term　intensive　quantity。　Consequently；　reality　in　a　phenomenon　has

intensive　quantity；　that　is；　a　degree。　if　we　consider　this　reality

as　cause　（be　it　of　sensation　or　of　another　reality　in　the

phenomenon；　for　example；　a　change）；　we　call　the　degree　of　reality　in

its　character　of　cause　a　momentum；　for　example；　the　momentum　of

weight；　and　for　this　reason；　that　the　degree　only　indicates　that

quantity　the　apprehension　of　which　is　not　successive；　but

instantaneous。　This；　however；　I　touch　upon　only　in　passing；　for　with

causality　I　have　at　present　nothing　to　do。

　　Accordingly；　every　sensation；　consequently　every　reality　in

phenomena；　however　small　it　may　be；　has　a　degree；　that　is；　an

intensive　quantity；　which　may　always　be　lessened；　and　between

reality　and　negation　there　exists　a　continuous　connection　of

possible　realities；　and　possible　smaller　perceptions。　Every　colour…

for　example；　red…　has　a　degree；　which；　be　it　ever　so　small；　is　never

the　smallest；　and　so　is　it　always　with　heat；　the　momentum　of　weight；

etc。

　　This　property　of　quantities；　according　to　which　no　part　of　them　is

the　smallest　possible　（no　part　simple）；　is　called　their　continuity。

Space　and　time　are　quanta　continua；　because　no　part　of　them　can　be

given；　without　enclosing　it　within　boundaries　（points　and　moments）；

consequently；　this　given　part　is　itself　a　space　or　a　time。　Space；

therefore；　consists　only　of　spaces；　and　time　of　times。　Points　and

moments　are　only　boundaries；　that　is；　the　mere　places　or　positions

of　their　limitation。　But　places　always　presuppose　intuitions　which　are

to　limit　or　determine　them；　and　we　cannot　conceive　either　space　or

time　composed　of　constituent　parts　which　are　given　before　space　or

time。　Such　quantities　may　also　be　called　flowing；　because　synthesis

（of　the　productive　imagination）　in　the　production　of　these

quantities　is　a　progression　in　time；　the　continuity　of　which　we　are

accustomed　to　indicate　by　the　expression　flowing。

　　All　phenomena；　then；　are　continuous　quantities；　in　respect　both　to

intuition　and　mere　perception　（sensation；　and　with　it　reality）。　In　the

former　case　they　are　extensive　quantities；　in　the　latter；　intensive。

When　the　synthesis　of　the　manifold　of　a　phenomenon　is　interrupted；

there　results　merely　an　aggregate　of　several　phenomena；　and　not

properly　a　phenomenon　as　a　quantity；　which　is　not　produced　by　the　mere

continuation　of　the　productive　synthesis　of　a　certain　kind；　but　by　the

repetition　of　a　synthesis　always　ceasing。　For　example；　if　I　call

thirteen　dollars　a　sum　or　quantity　of　money；　I　employ　the　term　quite

correctly；　inasmuch　as　I　understand　by　thirteen　dollars　the　value　of　a

mark　in　standard　silver；　which　is；　to　be　sure；　a　continuous

quantity；　in　which　no　part　is　the　smallest；　but　every　part　might

constitute　a　piece　of　money；　which　would　contain　material　for　still

smaller　pieces。　If；　however；　by　the　words　thirteen　dollars　I

understand　so　many　coins　（be　their　value　in　silver　what　it　may）；　it

would　be　quite　erroneous　to　use　the　expression　a　quantity　of

dollars；　on　the　contrary；　I　must　call　them　aggregate；　that　is；　a

number　of　coins。　And　as　in　every　number　we　must　have　unity　as　the

foundation；　so　a　phenomenon　taken　as　unity　is　a　quantity；　and　as

such　always　a　continuous　quantity　（q