the+critique+of+pure+reason_纯粹理性批判-第121部分

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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　pleteness
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　pletely　that　is；
omit　none　of　the　marks　or　signs　of　which　it　posed；　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　mencing　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　inplete
exposition　must　precede　the　plete；　so　that　we　may　be　able　to　draw
certain　inferences　from　the　characteristics　which　an　inplete
analysis　has　enabled　us　to　discover；　before　we　attain　to　the
plete　exposition　or　definition　of　the　conception。　In　one　word；　a
full　and　clear　definition　ought；　in　philosophy；　rather　to　form　the
conclusion　than　the　mencement　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　mencement　of　every　chain　of　mathematical
reasoning。

　　*Philosophy　abounds　in　faulty　definitions；　especially　such　as
contain　some　of　the　elements　requisite　to　form　a　plete
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　inpletely　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　plete　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　mon　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　pleteness　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
pleteness　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　priori　in　accordance　with　conceptions。　The　method　of
algebra；　in　equations；　from　which　the　correct　answer　is　deduced　by
reduction；　is　a　kind　of　construction…　not　geometrical；　but　by　symbols…
in　which　all　conceptions；　especially　those　of　the　relations　of
quantities；　are　represented　in　intuition　by　signs；　and　thus　the
conclusions　in　that　science　are　secured　from　errors　by　the　fact　that
every　proof　is　submitted　to　ocular　evidence。　Philosophical　cognition
does　not　possess　this　advantage；　it　being　required　to　consider　the
general　always　in　abstracto　（by　means　of　conceptions）；　while
mathematics　can　always　consider　it　in　concreto　（in　an　individual
intuition）；　and　at　the　same　time　by　means　of　a　priori
representation；　whereby　all　errors　are　rendered　manifest　to　the
senses。　The　former…　discursive　proofs…　ought　to　be　termed　acroamatic
proofs；　rather　than　demonstrations；　as　only　words　are　employed　in
them；　while　demonstrations　proper；　as　the　term　itself　indicates；
always　require　a　reference　to　the　intuition　of　the　object。
　　It　follows　from　all　these　considerati