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conditions　of　the　possibility　of　things　as　phenomena；　as　also　the
restriction　of　these　principles；　namely；　that　they　cannot　be　applied
to　objects　as　things　in　themselves…　these；　of　course；　do　not　fall
within　the　scope　of　our　present　inquiry。　In　like　manner；　the
principles　of　mathematical　science　form　no　part　of　this　system；
because　they　are　all　drawn　from　intuition；　and　not　from　the　pure
conception　of　the　understanding。　The　possibility　of　these
principles；　however；　will　necessarily　be　considered　here；　inasmuch
as　they　are　synthetical　judgements　a　priori；　not　indeed　for　the
purpose　of　proving　their　accuracy　and　apodeictic　certainty；　which　is
unnecessary；　but　merely　to　render　conceivable　and　deduce　the
possibility　of　such　evident　a　priori　cognitions。
　　But　we　shall　have　also　to　speak　of　the　principle　of　analytical
judgements；　in　opposition　to　synthetical　judgements；　which　is　the
proper　subject　of　our　inquiries；　because　this　very　opposition　will
free　the　theory　of　the　latter　from　all　ambiguity；　and　place　it　clearly
before　our　eyes　in　its　true　nature。

　　　　　　　　SYSTEM　OF　THE　PRINCIPLES　OF　THE　PURE　UNDERSTANDING。

　　SECTION　I。　Of　the　Supreme　Principle　of　all　Analytical　Judgements。

　　Whatever　may　be　the　content　of　our　cognition；　and　in　whatever　manner
our　cognition　may　be　related　to　its　object；　the　universal；　although
only　negative　conditions　of　all　our　judgements　is　that　they　do　not
contradict　themselves；　otherwise　these　judgements　are　in　themselves
（even　without　respect　to　the　object）　nothing。　But　although　there　may
exist　no　contradiction　in　our　judgement；　it　may　nevertheless　connect
conceptions　in　such　a　manner　that　they　do　not　correspond　to　the
object；　or　without　any　grounds　either　a　priori　or　a　posteriori　for
arriving　at　such　a　judgement；　and　thus；　without　being
self…contradictory；　a　judgement　may　nevertheless　be　either　false　or
groundless。
　　Now；　the　proposition：　〃No　subject　can　have　a　predicate　that
contradicts　it；〃　is　called　the　principle　of　contradiction；　and　is　a
universal　but　purely　negative　criterion　of　all　truth。　But　it　belongs
to　logic　alone；　because　it　is　valid　of　cognitions；　merely　as
cognitions　and　without　respect　to　their　content；　and　declares　that　the
contradiction　entirely　nullifies　them。　We　can　also；　however；　make　a
positive　use　of　this　principle；　that　is；　not　merely　to　banish
falsehood　and　error　（in　so　far　as　it　rests　upon　contradiction）；　but
also　for　the　cognition　of　truth。　For　if　the　judgement　is　analytical；
be　it　affirmative　or　negative；　its　truth　must　always　be　recognizable
by　means　of　the　principle　of　contradiction。　For　the　contrary　of　that
which　lies　and　is　cogitated　as　conception　in　the　cognition　of　the
object　will　be　always　properly　negatived；　but　the　conception　itself
must　always　be　affirmed　of　the　object；　inasmuch　as　the　contrary
thereof　would　be　in　contradiction　to　the　object。
　　We　must　therefore　hold　the　principle　of　contradiction　to　be　the
universal　and　fully　sufficient　Principle　of　all　analytical
cognition。　But　as　a　sufficient　criterion　of　truth；　it　has　no　further
utility　or　authority。　For　the　fact　that　no　cognition　can　be　at
variance　with　this　principle　without　nullifying　itself；　constitutes
this　principle　the　sine　qua　non；　but　not　the　determining　ground　of　the
truth　of　our　cognition。　As　our　business　at　present　is　properly　with
the　synthetical　part　of　our　knowledge　only；　we　shall　always　be　on
our　guard　not　to　transgress　this　inviolable　principle；　but　at　the　same
time　not　to　expect　from　it　any　direct　assistance　in　the
establishment　of　the　truth　of　any　synthetical　proposition。
　　There　exists；　however；　a　formula　of　this　celebrated　principle…　a
principle　merely　formal　and　entirely　without　content…　which　contains　a
synthesis　that　has　been　inadvertently　and　quite　unnecessarily　mixed　up
with　it。　It　is　this：　〃It　is　impossible　for　a　thing　to　be　and　not　to　be
at　the　same　time。〃　Not　to　mention　the　superfluousness　of　the
addition　of　the　word　impossible　to　indicate　the　apodeictic
certainty；　which　ought　to　be　self…evident　from　the　proposition　itself；
the　proposition　is　affected　by　the　condition　of　time；　and　as　it　were
says：　〃A　thing　=　A；　which　is　something　=　B；　cannot　at　the　same　time　be
non…B。〃　But　both；　B　as　well　as　non…B；　may　quite　well　exist　in
succession。　For　example；　a　man　who　is　young　cannot　at　the　same　time　be
old；　but　the　same　man　can　very　well　be　at　one　time　young；　and　at
another　not　young；　that　is；　old。　Now　the　principle　of　contradiction　as
a　merely　logical　proposition　must　not　by　any　means　limit　its
application　merely　to　relations　of　time；　and　consequently　a　formula
like　the　preceding　is　quite　foreign　to　its　true　purpose。　The
misunderstanding　arises　in　this　way。　We　first　of　all　separate　a
predicate　of　a　thing　from　the　conception　of　the　thing；　and
afterwards　connect　with　this　predicate　its　opposite；　and　hence　do
not　establish　any　contradiction　with　the　subject；　but　only　with　its
predicate；　which　has　been　conjoined　with　the　subject　synthetically…
a　contradiction；　moreover；　which　obtains　only　when　the　first　and
second　predicate　are　affirmed　in　the　same　time。　If　I　say：　〃A　man　who
is　ignorant　is　not　learned；〃　the　condition　〃at　the　same　time〃　must
be　added；　for　he　who　is　at　one　time　ignorant；　may　at　another　be
learned。　But　if　I　say：　〃No　ignorant　man　is　a　learned　man；〃　the
proposition　is　analytical；　because　the　characteristic　ignorance　is　now
a　constituent　part　of　the　conception　of　the　subject；　and　in　this
case　the　negative　proposition　is　evident　immediately　from　the
proposition　of　contradiction；　without　the　necessity　of　adding　the
condition　〃the　same　time。〃　This　is　the　reason　why　I　have　altered　the
formula　of　this　principle…　an　alteration　which　shows　very　clearly
the　nature　of　an　analytical　proposition。

　　SECTION　II。　Of　the　Supreme　Principle　of　all　Synthetical　Judgements。

　　The　explanation　of　the　possibility　of　synthetical　judgements　is　a
task　with　which　general　logic　has　nothing　to　do；　indeed　she　needs
not　even　be　acquainted　with　its　name。　But　in　transcendental　logic　it
is　the　most　important　matter　to　be　dealt　with…　indeed　the　only　one；　if
the　question　is　of　the　possibility　of　synthetical　judgements　a　priori；
the　conditions　and　extent　of　their　validity。　For　when　this　question　is
fully　decided；　it　can　reach　its　aim　with　perfect　ease；　the
determination；　to　wit；　of　the　extent　and　limits　of　the　pure
understanding。
　　In　an　analytical　judgement　I　do　not　go　beyond　the　given
conception；　in　order　to　arrive　at　some　decision　respecting　it。　If
the　judgement　is　affirmative；　I　predicate　of　the　conception　only
that　which　was　already　cogitated　in　it；　if　negative；　I　merely
exclude　from　the　conception　its　contrary。　But　in　synthetical
judgements；　I　must　go　beyond　the　given　conception；　in　order　to
cogitate；　in　relation　with　it；　something　quite　different　from　that
which　was　cogitated　in　it；　a　relation　which　is　consequently　never
one　either　of　identity　or　contradiction；　and　by　means　of　which　the
truth　or　error　of　the　judgement　cannot　be　discerned　merely　from　the
judgement　itself。
　　Granted；　then；　that　we　must　go　out　beyond　a　given　conception；　in
order　to　pare　it　synthetically　with　another；　a　third　thing　is
necessary；　in　which　alone　the　synthesis　of　two　conceptions　can
originate。　Now　what　is　this　tertium　quid　that　is　to　be　the　medium　of
all　synthetical　judgements？　It　is　only　a　plex　in　which　all　our
representations　are　contained；　the　internal　sense　to　wit；　and　its　form
a　priori；　time。
　　The　synthesis　of　our　representations　rests　upon　the　imagination；
their　synthetical　unity　（which　is　requisite　to　a　judgement）；　upon
the　unity　of　apperception。　In　this；　therefore；　is　to　be　sought　the
possibility　of　synthetical　judgements；　and　as　all　three　contain　the
sources　of　a　priori　representations；　the　possibility　of　pure
synthetical　judgements　also；　nay；　they　are　necessary　upon　these
grounds；　if　we　are　to　possess　a　knowledge　of　objects；　which　rests
solely　upon　the　synthesis　of　representations。
　　If　a　cognition　is　to　have　objective　reality；　that　is；　to　relate　to
an　object；　and　possess　sense　and　meaning　in　respect　to　it；　it　is
necessary　that　the　object　be　given　in　some　way　or　another。　Without
this；　our　conceptions　are　empty；　and　we　may　indeed　have　thought　by
means　of　them；　but　by　such　thinking　we　have　not；　in　fact；　cognized
anything；　we　have　merely　played　with　representation。　To　give　an
object；　if　this　expression　be　understood　in　the　sense　of　〃to
present〃　the　object；　not　mediately　but　immediately　in　intuition；　means
nothing　else　than　to　apply　the　representation　of　it　to　experience；
be　that　experience　real　or　only　possible。　Space　and　time　themselves；
pure　as　these　conceptions　are　from　all　that　is　empirical；　and
certain　as　it　is　that　they　are　represented　fully　a　priori　in　the　mind；
would　be　pletely　without　objective　validity；　and　without　sense
and　significance；　if　their　necessary　use　in　the　objects　of
experience　were　not　shown。　Nay；　the　representation　of　them　is　a　mere
schema；　that　always　relates　to　the　reproductive　imagination；　which
calls　up　the　objects　of　experience；　without　which　they　have　no
meaning。　And　so　it　is　with　all　conceptions　without　distinction。
　　The　possibility　of　experience　is；　then；　that　whi