the critique of pure reason-第110部分

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suspect　it　to　be　capable　of　substituting　fancies　for　conceptions；

and　words　for　things。

　　Reason；　when　employed　in　the　field　of　experience；　does　not　stand

in　need　of　criticism；　because　its　principles　are　subjected　to　the

continual　test　of　empirical　observations。　Nor　is　criticism　requisite

in　the　sphere　of　mathematics；　where　the　conceptions　of　reason　must

always　be　presented　in　concreto　in　pure　intuition；　and　baseless　or

arbitrary　assertions　are　discovered　without　difficulty。　But　where

reason　is　not　held　in　a　plain　track　by　the　influence　of　empirical　or

of　pure　intuition；　that　is；　when　it　is　employed　in　the

transcendental　sphere　of　pure　conceptions；　it　stands　in　great　need

of　discipline；　to　restrain　its　propensity　to　overstep　the　limits　of

possible　experience　and　to　keep　it　from　wandering　into　error。　In　fact；

the　utility　of　the　philosophy　of　pure　reason　is　entirely　of　this

negative　character。　Particular　errors　may　be　corrected　by　particular

animadversions；　and　the　causes　of　these　errors　may　be　eradicated　by

criticism。　But　where　we　find；　as　in　the　case　of　pure　reason；　a

complete　system　of　illusions　and　fallacies；　closely　connected　with

each　other　and　depending　upon　grand　general　principles；　there　seems　to

be　required　a　peculiar　and　negative　code　of　mental　legislation；　which；

under　the　denomination　of　a　discipline；　and　founded　upon　the　nature　of

reason　and　the　objects　of　its　exercise；　shall　constitute　a　system　of

thorough　examination　and　testing；　which　no　fallacy　will　be　able　to

withstand　or　escape　from；　under　whatever　disguise　or　concealment　it

may　lurk。

　　But　the　reader　must　remark　that；　in　this　the　second　division　of

our　transcendental　Critique　the　discipline　of　pure　reason　is　not

directed　to　the　content；　but　to　the　method　of　the　cognition　of　pure

reason。　The　former　task　has　been　completed　in　the　doctrine　of

elements。　But　there　is　so　much　similarity　in　the　mode　of　employing　the

faculty　of　reason；　whatever　be　the　object　to　which　it　is　applied；

while；　at　the　same　time；　its　employment　in　the　transcendental　sphere

is　so　essentially　different　in　kind　from　every　other；　that；　without

the　warning　negative　influence　of　a　discipline　specially　directed　to

that　end；　the　errors　are　unavoidable　which　spring　from　the

unskillful　employment　of　the　methods　which　are　originated　by　reason

but　which　are　out　of　place　in　this　sphere。



　　　　　SECTION　I。　The　Discipline　of　Pure　Reason　in　the　Sphere

　　　　　　　　　　　　　　　　　　　　　　　of　Dogmatism。



　　The　science　of　mathematics　presents　the　most　brilliant　example　of

the　extension　of　the　sphere　of　pure　reason　without　the　aid　of

experience。　Examples　are　always　contagious；　and　they　exert　an　especial

influence　on　the　same　faculty；　which　naturally　flatters　itself　that　it

will　have　the　same　good　fortune　in　other　case　as　fell　to　its　lot　in

one　fortunate　instance。　Hence　pure　reason　hopes　to　be　able　to　extend

its　empire　in　the　transcendental　sphere　with　equal　success　and

security；　especially　when　it　applies　the　same　method　which　was

attended　with　such　brilliant　results　in　the　science　of　mathematics。　It

is；　therefore；　of　the　highest　importance　for　us　to　know　whether　the

method　of　arriving　at　demonstrative　certainty；　which　is　termed

mathematical；　be　identical　with　that　by　which　we　endeavour　to　attain

the　same　degree　of　certainty　in　philosophy；　and　which　is　termed　in

that　science　dogmatical。

　　Philosophical　cognition　is　the　cognition　of　reason　by　means　of

conceptions；　mathematical　cognition　is　cognition　by　means　of　the

construction　of　conceptions。　The　construction　of　a　conception　is　the

presentation　a　priori　of　the　intuition　which　corresponds　to　the

conception。　For　this　purpose　a　non…empirical　intuition　is　requisite；

which；　as　an　intuition；　is　an　individual　object；　while；　as　the

construction　of　a　conception　（a　general　representation）；　it　must　be

seen　to　be　universally　valid　for　all　the　possible　intuitions　which

rank　under　that　conception。　Thus　I　construct　a　triangle；　by　the

presentation　of　the　object　which　corresponds　to　this　conception；

either　by　mere　imagination；　in　pure　intuition；　or　upon　paper；　in

empirical　intuition；　in　both　cases　completely　a　priori；　without

borrowing　the　type　of　that　figure　from　any　experience。　The

individual　figure　drawn　upon　paper　is　empirical；　but　it　serves；

notwithstanding；　to　indicate　the　conception；　even　in　its　universality；

because　in　this　empirical　intuition　we　keep　our　eye　merely　on　the

act　of　the　construction　of　the　conception；　and　pay　no　attention　to　the

various　modes　of　determining　it；　for　example；　its　size；　the　length

of　its　sides；　the　size　of　its　angles；　these　not　in　the　least　affecting

the　essential　character　of　the　conception。

　　Philosophical　cognition；　accordingly；　regards　the　particular　only　in

the　general；　mathematical　the　general　in　the　particular；　nay；　in　the

individual。　This　is　done；　however；　entirely　a　priori　and　by　means　of

pure　reason；　so　that；　as　this　individual　figure　is　determined　under

certain　universal　conditions　of　construction；　the　object　of　the

conception；　to　which　this　individual　figure　corresponds　as　its　schema；

must　be　cogitated　as　universally　determined。

　　The　essential　difference　of　these　two　modes　of　cognition　consists；

therefore；　in　this　formal　quality；　it　does　not　regard　the　difference

of　the　matter　or　objects　of　both。　Those　thinkers　who　aim　at

distinguishing　philosophy　from　mathematics　by　asserting　that　the

former　has　to　do　with　quality　merely；　and　the　latter　with　quantity；

have　mistaken　the　effect　for　the　cause。　The　reason　why　mathematical

cognition　can　relate　only　to　quantity　is　to　be　found　in　its　form

alone。　For　it　is　the　conception　of　quantities　only　that　is　capable

of　being　constructed；　that　is；　presented　a　priori　in　intuition；

while　qualities　cannot　be　given　in　any　other　than　an　empirical

intuition。　Hence　the　cognition　of　qualities　by　reason　is　possible　only

through　conceptions。　No　one　can　find　an　intuition　which　shall

correspond　to　the　conception　of　reality；　except　in　experience；　it

cannot　be　presented　to　the　mind　a　priori　and　antecedently　to　the

empirical　consciousness　of　a　reality。　We　can　form　an　intuition；　by

means　of　the　mere　conception　of　it；　of　a　cone；　without　the　aid　of

experience；　but　the　colour　of　the　cone　we　cannot　know　except　from

experience。　I　cannot　present　an　intuition　of　a　cause；　except　in　an

example　which　experience　offers　to　me。　Besides；　philosophy；　as　well　as

mathematics；　treats　of　quantities；　as；　for　example；　of　totality；

infinity；　and　so　on。　Mathematics；　too；　treats　of　the　difference　of

lines　and　surfaces…　as　spaces　of　different　quality；　of　the

continuity　of　extension…　as　a　quality　thereof。　But；　although　in　such

cases　they　have　a　common　object；　the　mode　in　which　reason　considers

that　object　is　very　different　in　philosophy　from　what　it　is　in

mathematics。　The　former　confines　itself　to　the　general　conceptions；

the　latter　can　do　nothing　with　a　mere　conception；　it　hastens　to

intuition。　In　this　intuition　it　regards　the　conception　in　concreto；

not　empirically；　but　in　an　a　priori　intuition；　which　it　has

constructed；　and　in　which；　all　the　results　which　follow　from　the

general　conditions　of　the　construction　of　the　conception　are　in　all

cases　valid　for　the　object　of　the　constructed　conception。

　　Suppose　that　the　conception　of　a　triangle　is　given　to　a

philosopher　and　that　he　is　required　to　discover；　by　the

philosophical　method；　what　relation　the　sum　of　its　angles　bears　to　a

right　angle。　He　has　nothing　before　him　but　the　conception　of　a

figure　enclosed　within　three　right　lines；　and；　consequently；　with

the　same　number　of　angles。　He　may　analyse　the　conception　of　a　right

line；　of　an　angle；　or　of　the　number　three　as　long　as　he　pleases；　but

he　will　not　discover　any　properties　not　contained　in　these

conceptions。　But；　if　this　question　is　proposed　to　a　geometrician；　he

at　once　begins　by　constructing　a　triangle。　He　knows　that　two　right

angles　are　equal　to　the　sum　of　all　the　contiguous　angles　which　proceed

from　one　point　in　a　straight　line；　and　he　goes　on　to　produce　one

side　of　his　triangle；　thus　forming　two　adjacent　angles　which　are

together　equal　to　two　right　angles。　He　then　divides　the　exterior　of

these　angles；　by　drawing　a　line　parallel　with　the　opposite　side　of　the

triangle；　and　immediately　perceives　that　be　has　thus　got　an　exterior

adjacent　angle　which　is　equal　to　the　interior。　Proceeding　in　this　way；

through　a　chain　of　inferences；　and　always　on　the　ground　of

intuition；　he　arrives　at　a　clear　and　universally　valid　solution　of　the

question。

　　But　mathematics　does　not　confine　itself　to　the　construction　of

quantities　（quanta）；　as　in　the　case　of　geometry；　it　occupies　itself

with　pure　quantity　also　（quantitas）；　as　in　the　case　of　algebra；

where　complete　abstraction　is　made　of　the　properties　of　the　object

indicated　by　the　conception　of　quantity。　In　algebra；　a　certain

method　of　notation　by　signs　is　adopted；　and　these　indicate　the

different　possible　constructions　of　quantities；　the　extraction　of

roots；　and　so　on。　After　having　thus　denoted　the　general　conception

of　quantities；　according　to　their　different　relations；　the　different

operations　by　which　quantity　or　number　is　increased　or　diminished

are　presented　in　intuition　in　accordance　with　general　rules。　Thus；

when　one　quantity　is　to　be　divided　by　another；　the　signs　which

denote　both　are　placed　in　the　form　peculiar　to　the　operation　of

division；　and　thus　algebra；　by　means　of　a　symbolical　construction　of

quantity；　just　as　geometry；　with　its　ostensive　or　geometrical

construction　（a　construction　of　the　objects　themselves）；　arrives　at

results　which　discursive　cognition　cannot　hope　to　reach　by　the　aid

of　mere　conceptions。

　　Now；　what　is　the　cause　of　this　difference　in　the　fortune　of　the

philosopher　and　the　mathematician；　the　former　of　whom　follows　the　path

of　conceptions；　while　the　latter　pursues　that　of　intuitions；　which

he　represents；　a　priori；　in　correspondence　with　his　concep