the critique of pure reason-第102章

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

Masters　in　the　science　of　mathematics　are　confident　of　the　success

of　this　method；　indeed；　it　is　a　common　persuasion　that　it　is　capable

of　being　applied　to　any　subject　of　human　thought。　They　have　hardly

ever　reflected　or　philosophized　on　their　favourite　science…　a　task

of　great　difficulty；　and　the　specific　difference　between　the　two　modes

of　employing　the　faculty　of　reason　has　never　entered　their　thoughts。

Rules　current　in　the　field　of　common　experience；　and　which　common

sense　stamps　everywhere　with　its　approval；　are　regarded　by　them　as

axiomatic。　From　what　source　the　conceptions　of　space　and　time；　with

which　（as　the　only　primitive　quanta）　they　have　to　deal；　enter　their

minds；　is　a　question　which　they　do　not　trouble　themselves　to　answer；

and　they　think　it　just　as　unnecessary　to　examine　into　the　origin　of

the　pure　conceptions　of　the　understanding　and　the　extent　of　their

validity。　All　they　have　to　do　with　them　is　to　employ　them。　In　all　this

they　are　perfectly　right；　if　they　do　not　overstep　the　limits　of　the

sphere　of　nature。　But　they　pass；　unconsciously；　from　the　world　of

sense　to　the　insecure　ground　of　pure　transcendental　conceptions

（instabilis　tellus；　innabilis　unda）；　where　they　can　neither　stand

nor　swim；　and　where　the　tracks　of　their　footsteps　are　obliterated　by

time；　while　the　march　of　mathematics　is　pursued　on　a　broad　and

magnificent　highway；　which　the　latest　posterity　shall　frequent　without

fear　of　danger　or　impediment。

　　As　we　have　taken　upon　us　the　task　of　determining；　clearly　and

certainly；　the　limits　of　pure　reason　in　the　sphere　of

transcendentalism；　and　as　the　efforts　of　reason　in　this　direction

are　persisted　in；　even　after　the　plainest　and　most　expressive

warnings；　hope　still　beckoning　us　past　the　limits　of　experience　into

the　splendours　of　the　intellectual　world…　it　becomes　necessary　to

cut　away　the　last　anchor　of　this　fallacious　and　fantastic　hope。　We

shall；　accordingly；　show　that　the　mathematical　method　is　unattended　in

the　sphere　of　philosophy　by　the　least　advantage…　except；　perhaps；　that

it　more　plainly　exhibits　its　own　inadequacy…　that　geometry　and

philosophy　are　two　quite　different　things；　although　they　go　band　in

hand　in　hand　in　the　field　of　natural　science；　and；　consequently；

that　the　procedure　of　the　one　can　never　be　imitated　by　the　other。

　　The　evidence　of　mathematics　rests　upon　definitions；　axioms；　and

demonstrations。　I　shall　be　satisfied　with　showing　that　none　of　these

forms　can　be　employed　or　imitated　in　philosophy　in　the　sense　in

which　they　are　understood　by　mathematicians；　and　that　the

geometrician；　if　he　employs　his　method　in　philosophy；　will　succeed

only　in　building　card…castles；　while　the　employment　of　the

philosophical　method　in　mathematics　can　result　in　nothing　but　mere

verbiage。　The　essential　business　of　philosophy；　indeed；　is　to　mark　out

the　limits　of　the　science；　and　even　the　mathematician；　unless　his

talent　is　naturally　circumscribed　and　limited　to　this　particular

department　of　knowledge；　cannot　turn　a　deaf　ear　to　the　warnings　of

philosophy；　or　set　himself　above　its　direction。

　　I。　Of　Definitions。　A　definition　is；　as　the　term　itself　indicates；

the　representation；　upon　primary　grounds；　of　the　complete　conception

of　a　thing　within　its　own　limits。*　Accordingly；　an　empirical

conception　cannot　be　defined；　it　can　only　be　explained。　For；　as

there　are　in　such　a　conception　only　a　certain　number　of　marks　or

signs；　which　denote　a　certain　class　of　sensuous　objects；　we　can

never　be　sure　that　we　do　not　cogitate　under　the　word　which　indicates

the　same　object；　at　one　time　a　greater；　at　another　a　smaller　number　of

signs。　Thus；　one　person　may　cogitate　in　his　conception　of　gold；　in

addition　to　its　properties　of　weight；　colour；　malleability；　that　of

resisting　rust；　while　another　person　may　be　ignorant　of　this

quality。　We　employ　certain　signs　only　so　long　as　we　require　them　for

the　sake　of　distinction；　new　observations　abstract　some　and　add　new

ones；　so　that　an　empirical　conception　never　remains　within　permanent

limits。　It　is；　in　fact；　useless　to　define　a　conception　of　this　kind。

If；　for　example；　we　are　speaking　of　water　and　its　properties；　we　do

not　stop　at　what　we　actually　think　by　the　word　water；　but　proceed　to

observation　and　experiment；　and　the　word；　with　the　few　signs

attached　to　it；　is　more　properly　a　designation　than　a　conception　of

the　thing。　A　definition　in　this　case　would　evidently　be　nothing　more

than　a　determination　of　the　word。　In　the　second　place；　no　a　priori

conception；　such　as　those　of　substance；　cause；　right；　fitness；　and

so　on；　can　be　defined。　For　I　can　never　be　sure；　that　the　clear

representation　of　a　given　conception　（which　is　given　in　a　confused

state）　has　been　fully　developed；　until　I　know　that　the

representation　is　adequate　with　its　object。　But；　inasmuch　as　the

conception；　as　it　is　presented　to　the　mind；　may　contain　a　number　of

obscure　representations；　which　we　do　not　observe　in　our　analysis；

although　we　employ　them　in　our　application　of　the　conception；　I　can

never　be　sure　that　my　analysis　is　complete；　while　examples　may　make

this　probable；　although　they　can　never　demonstrate　the　fact。　instead

of　the　word　definition；　I　should　rather　employ　the　term　exposition…

a　more　modest　expression；　which　the　critic　may　accept　without

surrendering　his　doubts　as　to　the　completeness　of　the　analysis　of

any　such　conception。　As；　therefore；　neither　empirical　nor　a　priori

conceptions　are　capable　of　definition；　we　have　to　see　whether　the　only

other　kind　of　conceptions…　arbitrary　conceptions…　can　be　subjected

to　this　mental　operation。　Such　a　conception　can　always　be　defined；　for

I　must　know　thoroughly　what　I　wished　to　cogitate　in　it；　as　it　was　I

who　created　it；　and　it　was　not　given　to　my　mind　either　by　the　nature

of　my　understanding　or　by　experience。　At　the　same　time；　I　cannot　say

that；　by　such　a　definition；　I　have　defined　a　real　object。　If　the

conception　is　based　upon　empirical　conditions；　if；　for　example；　I　have

a　conception　of　a　clock　for　a　ship；　this　arbitrary　conception　does　not

assure　me　of　the　existence　or　even　of　the　possibility　of　the　object。

My　definition　of　such　a　conception　would　with　more　propriety　be　termed

a　declaration　of　a　project　than　a　definition　of　an　object。　There

are　no　other　conceptions　which　can　bear　definition；　except　those　which

contain　an　arbitrary　synthesis；　which　can　be　constructed　a　priori。

Consequently；　the　science　of　mathematics　alone　possesses

definitions。　For　the　object　here　thought　is　presented　a　priori　in

intuition；　and　thus　it　can　never　contain　more　or　less　than　the

conception；　because　the　conception　of　the　object　has　been　given　by　the

definition…　and　primarily；　that　is；　without　deriving　the　definition

from　any　other　source。　Philosophical　definitions　are；　therefore；

merely　expositions　of　given　conceptions；　while　mathematical

definitions　are　constructions　of　conceptions　originally　formed　by

the　mind　itself；　the　former　are　produced　by　analysis；　the　completeness

of　which　is　never　demonstratively　certain；　the　latter　by　a

synthesis。　In　a　mathematical　definition　the　conception　is　formed；　in　a

philosophical　definition　it　is　only　explained。　From　this　it　follows：



　　*The　definition　must　describe　the　conception　completely　that　is；

omit　none　of　the　marks　or　signs　of　which　it　composed；　within　its　own

limits；　that　is；　it　must　be　precise；　and　enumerate　no　more　signs

than　belong　to　the　conception；　and　on　primary　grounds；　that　is　to　say；

the　limitations　of　the　bounds　of　the　conception　must　not　be　deduced

from　other　conceptions；　as　in　this　case　a　proof　would　be　necessary；

and　the　so…called　definition　would　be　incapable　of　taking　its　place　at

the　bead　of　all　the　judgements　we　have　to　form　regarding　an　object。



　　（a）　That　we　must　not　imitate；　in　philosophy；　the　mathematical

usage　of　commencing　with　definitions…　except　by　way　of　hypothesis　or

experiment。　For；　as　all　so…called　philosophical　definitions　are　merely

analyses　of　given　conceptions；　these　conceptions；　although　only　in　a

confused　form；　must　precede　the　analysis；　and　the　incomplete

exposition　must　precede　the　complete；　so　that　we　may　be　able　to　draw

certain　inferences　from　the　characteristics　which　an　incomplete

analysis　has　enabled　us　to　discover；　before　we　attain　to　the

complete　exposition　or　definition　of　the　conception。　In　one　word；　a

full　and　clear　definition　ought；　in　philosophy；　rather　to　form　the

conclusion　than　the　commencement　of　our　labours。*　In　mathematics；　on

the　contrary；　we　cannot　have　a　conception　prior　to　the　definition；

it　is　the　definition　which　gives　us　the　conception；　and　it　must　for

this　reason　form　the　commencement　of　every　chain　of　mathematical

reasoning。



　　*Philosophy　abounds　in　faulty　definitions；　especially　such　as

contain　some　of　the　elements　requisite　to　form　a　complete

definition。　If　a　conception　could　not　be　employed　in　reasoning

before　it　had　been　defined；　it　would　fare　ill　with　all　philosophical

thought。　But；　as　incompletely　defined　conceptions　may　always　be

employed　without　detriment　to　truth；　so　far　as　our　analysis　of　the

elements　contained　in　them　proceeds；　imperfect　definitions；　that　is；

propositions　which　are　properly　not　definitions；　but　merely

approximations　thereto；　may　be　used　with　great　advantage。　In

mathematics；　definition　belongs　ad　esse；　in　philosophy　ad　melius　esse。

It　is　a　difficult　task　to　construct　a　proper　definition。　Jurists　are

still　without　a　complete　definition　of　the　idea　of　right。



　　（b）　Mathematical　definitions　cannot　be　erroneous。　For　the　conception

is　given　only　in　and　through　the　definition；　and　thus　it　contains　only

what　has　been　cogitated　in　the　definition。　But　although　a　definition

cannot　be　incorrect；　as　regards　its　content；　an　error　may　sometimes；

although　seldom；　creep　into　the　form。　This　error　consists　in　a　want　of

precision。　Thus　the　common　definition　of　a　circle…　that　it　is　a　curved

line；　every　point　in　which　is　equally　distant　from　another　point

called　the　centre…　is　faulty；　from　the　fact　that　the　determination

indicated　by　the　word　curved　is　superfluous。　For　there　ought　to　be　a

particular　theorem；　which　may　be　easily　proved　from　the　definition；　to

the　effect　that　every　line；　which　has　all　its　points　at　equal

distances　from　another　point；　must　be　a　curved　line…　that　is；　that　not

even　the　smallest　part　of　it　can　be　straight。　Analytical

definitions；　on　the　other　hand；　may　be　erroneous　in　many　respects；

either　by　the　introduction　of　signs　which　do　not　actually　exist　in　the

conception；　or　by　wanting　in　that　completeness　which　forms　the

essential　of　a　definition。　In　the　latter　case；　the　definition　is

necessarily　defective；　because　we　can　never　be　fully　certain　of　the

completeness　of　our　analysis。　For　these　reasons；　the　method　of

definition　employed　in　mathematics　cannot　be　imitated　in　philosophy。

　　2。　Of　Axioms。　These；　in　so　fa