the critique of pure reason-第125节

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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　far　as　they　are　immediately　certain；

are　a　priori　synthetical　principles。　Now；　one　conception　cannot　be

connected　synthetically　and　yet　immediately　with　another；　because；

if　we　wish　to　proceed　out　of　and　beyond　a　conception；　a　third

mediating　cognition　is　necessary。　And；　as　philosophy　is　a　cognition　of

reason　by　the　aid　of　conceptions　alone；　there　is　to　be　found　in　it

no　principle　which　deserves　to　be　called　an　axiom。　Mathematics；　on　the

other　hand；　may　possess　axioms；　because　it　can　always　connect　the

predicates　of　an　object　a　priori；　and　without　any　mediating　term；　by

means　of　the　construction　of　conceptions　in　intuition。　Such　is　the

case　with　the　proposition：　Three　points　can　always　lie　in　a　plane。

On　the　other　hand；　no　synthetical　principle　which　is　based　upon

conceptions；　can　ever　be　immediately　certain　（for　example；　the

proposition：　Everything　that　happens　has　a　cause）；　because　I　require　a

mediating　term　to　connect　the　two　conceptions　of　event　and　cause…

namely；　the　condition　of　time…determination　in　an　experience；　and　I

cannot　cognize　any　such　principle　immediately　and　from　conceptions

alone。　Discursive　principles　are；　accordingly；　very　different　from

intuitive　principles　or　axioms。　The　former　always　require　deduction；

which　in　the　case　of　the　latter　may　be　altogether　dispensed　with。

Axioms　are；　for　this　reason；　always　self…evident；　while

philosophical　principles；　whatever　may　be　the　degree　of　certainty　they

possess；　cannot　lay　any　claim　to　such　a　distinction。　No　synthetical

proposition　of　pure　transcendental　reason　can　be　so　evident；　as　is

often　rashly　enough　declared；　as　the　statement；　twice　two　are　four。　It

is　true　that　in　the　Analytic　I　introduced　into　the　list　of

principles　of　the　pure　understanding；　certain　axioms　of　intuition；　but

the　principle　there　discussed　was　not　itself　an　axiom；　but　served

merely　to　present　the　principle　of　the　possibility　of　axioms　in

general；　while　it　was　really　nothing　more　than　a　principle　based

upon　conceptions。　For　it　is　one　part　of　the　duty　of　transcendental

philosophy　to　establish　the　possibility　of　mathematics　itself。

Philosophy　possesses；　then；　no　axioms；　and　has　no　right　to　impose

its　a　priori　principles　upon　thought；　until　it　has　established　their

authority　and　validity　by　a　thoroughgoing　deduction。

　　3。　Of　Demonstrations。　Only　an　apodeictic　proof；　based　upon

intuition；　can　be　termed　a　demonstration。　Experience　teaches　us　what

is；　but　it　cannot　convince　us　that　it　might　not　have　been　otherwise。

Hence　a　proof　upon　empirical　grounds　cannot　be　apodeictic。　A　priori

conceptions；　in　discursive　cognition；　can　never　produce　intuitive

certainty　or　evidence；　however　certain　the　judgement　they　present

may　be。　Mathematics　alone；　therefore；　contains　demonstrations；　because

it　does　not　deduce　its　cognition　from　conceptions；　but　from　the

construction　of　conceptions；　that　is；　from　intuition；　which　can　be

given　a　prio