the+critique+of+pure+reason_纯粹理性批判-第119部分

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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　plete　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　conceptions？　The
cause　is　evident　from　what　has　been　already　demonstrated　in　the
introduction　to　this　Critique。　We　do　not；　in　the　present　case；　want　to
discover　analytical　propositions；　which　may　be　produced　merely　by
analysing　our　conceptions…　for　in　this　the　philosopher　would　have
the　advantage　over　his　rival；　we　aim　at　the　discovery　of　synthetical
propositions…　such　synthetical　propositions；　moreover；　as　can　be
cognized　a　priori。　I　must　not　confine　myself　to　that　which　I
actually　cogitate　in　my　conception　of　a　triangle；　for　this　is
nothing　more　than　the　mere　definition；　I　must　try　to　go　beyond　that；
and　to　arrive　at　properties　which　are　not　contained　in；　although
they　belong　to；　the　conception。　Now；　this　is　impossible；　unless　I
determine　the　object　present　to　my　mind　according　to　the　conditions；
either　of　empirical；　or　of　pure；　intuition。　In　the　former　case；　I
should　have　an　empirical　proposition　（arrived　at　by　actual　measurement
of　the　angles　of　the　triangle）；　which　would　possess　neither
universality　nor　necessity；　but　that　would　be　of　no　value。　In　the
latter；　I　proceed　by　geometrical　construction；　by　means　of　which　I
collect；　in　a　pure　intuition；　just　as　I　would　in　an　empirical
intuition；　all　the　various　properties　which　belong　to　the　schema　of
a　triangle　in　general；　and　consequently　to　its　conception；　and　thus
construct　synthetical　propositions　which　possess　the　attribute　of
universality。
　　It　would　be　vain　to　philosophize　upon　the　triangle；　that　is；　to
reflect　on　it　discursively；　I　should　get　no　further　than　the
definition　with　which　I　had　been　obliged　to　set　out。　There　are
certainly　transcendental　synthetical　propositions　which　are　framed
by　means　of　pure　conceptions；　and　which　form　the　peculiar
distinction　of　philosophy；　but　these　do　not　relate　to　any　particular
thing；　but　to　a　thing　in　general；　and　enounce　the　conditions　under
which　the　perception　of　it　may　bee　a　part　of　possible　experience。
But　the　science　of　mathematics　has　nothing　to　do　with　such
questions；　nor　with　the　question　of　existence　in　any　fashion；　it　is
concerned　merely　with　the　properties　of　objects　in　themselves；　only　in
so　far　as　these　are　connected　with　the　conception　of　the　objects。
　　In　the　above　example；　we　merely　attempted　to　show　the　great
difference　which　exists　between　the　discursive　employment　of　reason　in
the　sphere　of　conceptions；　and　its　intuitive　exercise　by　means　of
the　construction　of　conceptions。　The　question　naturally　arises：　What
is　the　cause　which　necessitates　this　twofold　exercise　of　reason；　and
how　are　we　to　discover　whether　it　is　the　philosophical　or　the
mathematical　method　which　reason　is　pursuing　in　an　argument？
　　All　our　knowledge　relates；　finally；　to　possible　intuitions；　for　it
is　these　alone　that　present　objects　to　the　mind。　An　a　priori　or
non…empirical　conception　contains　either　a　pure　intuition…　and　in　this
case　it　can　be　constructed；　or　it　contains　nothing　but　the　synthesis
of　possible　intuitions；　which　are　not　given　a　priori。　In　this　latter
case；　it　may　help　us　to　form　synthetical　a　priori　judgements；　but　only
in　the　discursive　method；　by　conceptions；　not　in　the　intuitive；　by
means　of　the　construction　of　conceptions。
　　The　only　a　priori　intuition　is　that　of　the　pure　form　of　phenomena…
space　and　time。　A　conception　of　space　and　time　as　quanta　may　be
presented　a　priori　in　intuition；　that　is；　constructed；　either　alone
with　their　quality　（figure）；　or　as　pure　quantity　（the　mere　synthesis
of　the　homogeneous）；　by　means　of　number。　But　the　matter　of
phenomena；　by　which　things　are　given　in　space　and　time；　can　be
presented　only　in　perception；　a　posteriori。　The　only　conception
which　represents　a　priori　this　empirical　content　of　phenomena　is　the
conception　of　a　thing　in　general；　and　the　a　priori　synthetical
cognition　of　this　conception　can　give　us　nothing　more　than　the　rule
for　the　synthesis　of　that　which　may　be　contained　in　the
corresponding　a　posteriori　perception；　it　is　utterly　inadequate　to
present　an　a　priori　intuition　of　the　real　object；　which　must
necessarily　be　empirical。
　　Synthetical　propositions；　which　relate　to　things　in　general；　an　a
priori　intuition　of　which　is　impossible；　are　transcendental。　For
this　reason　transcendental　propositions　cannot　be　framed　by　means　of
the　construction　of　conceptions；　they　are　a　priori；　and　based　entirely
on　conceptions　themselves。　They　contain　merely　the　rule；　by　which　we
are　to　seek　in　the　world　of　perception　or　experience　the　synthetical
unity　of　that　which　cannot　be　intuited　a　priori。　But　they　are
inpetent　to　present　any　of　the　conceptions　which　appear　in　them
in　an　a　priori　intuition；　these　can　be　given　only　a　posteriori；　in
experience；　which；　however；　is　itself　possible　only　through　these
synthetical　principles。
　　If　we　are　to　form　a　synthetical　judgement　regarding　a　conception；　we
must　go　beyond　it；　to　the　intuition　in　which　it　is　given。　If　we　keep
to　what　is　contained　in　the　conception；　the　judgement　is　merely
analytical…　it　is　merely　an　explanation　of　what　we　have　cogitated　in
the　conception。　But　I　can　pass　from　the　conception　to　the　pure　or
empirical　intuition　which　corresponds　to　it。　I　can　proceed　to
examine　my　conception　in　concreto；　and　to　cognize；　either　a　priori
or　a　posterio；　what　I　find　in　the　object　of　the　conception。　The
former…　a　priori　cognition…　is　rational…mathematical　cognition　by
means　of　the　construction　of　the　conception；　the　latter…　a
posteriori　cognition…　is　purely　empirical　cognition；　which　does　not
possess　the　attributes　of　necessity　and　universality。　Thus　I　may
analyse　the　conception　I　have　of　gold；　but　I　gain　no　new　information
from　this　analysis；　I　merely　enumerate　the　different　properties
which　I　had　connected　with　the　notion　indicated　by　the　word。　My
knowledge　has　gained　in　logical　clearness　and　arrangement；　but　no
addition　has　been　made　to　it。　But　if　I　take　the　matter　which　is
indicated　by　this　name；　and　submit　it　to　the　examination　of　my　senses；
I　am　enabled　to　form　several　synthetical…　although　still　empirical…
propositions。　The　mathematical　conception　of　a　triangle　I　should
construct；　that　is；　present　a　priori　in　intuition；　and　in　this　way
attain　to　rational…synthetical　cognition。　But　when　the
transcendental　conception　of　reality；　or　substance；　or　power　is
presented　to　my　mind；　I　find　that　it　does　not　relate　to　or　indicate
either　an　empirical　or　pure　intuition；　but　that　it　indicates　merely
the　synthesis　of　empirical　intuitions；　which　cannot　of　course　be　given
a　priori。　The　synthesis　in　such　a　conception　cannot　proceed　a
priori…　without　the　aid　of　experience…　to　the　intuition　which
corresponds　to　the　conception；　and；　for　this　reason；　none　of　these
conceptions　can　produce　a　determinative　synthetical　proposition；
they　can　never　present　more　than　a　principle　of　the　synthesis*　of
possible　empirical　intuitions。　A　transcendental　proposition　is；
therefore；　a　synthetical　cognition　of　reason　by　means　of　pure
conceptions　and　the　discursive　method；　and　it　renders　possible　all
synthetical　unity　in　empirical　cognition；　though　it　cannot　present
us　with　any　intuition　a　priori。

　　*In　the　case　of　the　conception　of　cause；　I　do　really　go　beyond　the
empirical　conception　of　an　event…　but　not　to　the　intuition　which
presents　this　conception　in　concreto；　but　only　to　the　time…conditions；
which　may　be　found　in