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therefore　at　once　proceed　to　examine　the　difference　between　these

two　modes　of　knowledge。



　　IV。　Of　the　Difference　Between　Analytical　and　Synthetical　Judgements。



　　In　all　judgements　wherein　the　relation　of　a　subject　to　the　predicate

is　cogitated　（I　mention　affirmative　judgements　only　here；　the

application　to　negative　will　be　very　easy）；　this　relation　is

possible　in　two　different　ways。　Either　the　predicate　B　belongs　to

the　subject　A；　as　somewhat　which　is　contained　（though　covertly）　in　the

conception　A；　or　the　predicate　B　lies　completely　out　of　the　conception

A；　although　it　stands　in　connection　with　it。　In　the　first　instance；

I　term　the　judgement　analytical；　in　the　second；　synthetical。

Analytical　judgements　（affirmative）　are　therefore　those　in　which　the

connection　of　the　predicate　with　the　subject　is　cogitated　through

identity；　those　in　which　this　connection　is　cogitated　without

identity；　are　called　synthetical　judgements。　The　former　may　be

called　explicative；　the　latter　augmentative　judgements；　because　the

former　add　in　the　predicate　nothing　to　the　conception　of　the

subject；　but　only　analyse　it　into　its　constituent　conceptions；　which

were　thought　already　in　the　subject；　although　in　a　confused　manner；

the　latter　add　to　our　conceptions　of　the　subject　a　predicate　which　was

not　contained　in　it；　and　which　no　analysis　could　ever　have

discovered　therein。　For　example；　when　I　say；　〃All　bodies　are

extended；〃　this　is　an　analytical　judgement。　For　I　need　not　go　beyond

the　conception　of　body　in　order　to　find　extension　connected　with　it；

but　merely　analyse　the　conception；　that　is；　become　conscious　of　the

manifold　properties　which　I　think　in　that　conception；　in　order　to

discover　this　predicate　in　it：　it　is　therefore　an　analytical

judgement。　On　the　other　hand；　when　I　say；　〃All　bodies　are　heavy；〃

the　predicate　is　something　totally　different　from　that　which　I　think

in　the　mere　conception　of　a　body。　By　the　addition　of　such　a　predicate；

therefore；　it　becomes　a　synthetical　judgement。

　　Judgements　of　experience；　as　such；　are　always　synthetical。　For　it

would　be　absurd　to　think　of　grounding　an　analytical　judgement　on

experience；　because　in　forming　such　a　judgement　I　need　not　go　out　of

the　sphere　of　my　conceptions；　and　therefore　recourse　to　the

testimony　of　experience　is　quite　unnecessary。　That　〃bodies　are

extended〃　is　not　an　empirical　judgement；　but　a　proposition　which

stands　firm　a　priori。　For　before　addressing　myself　to　experience；　I

already　have　in　my　conception　all　the　requisite　conditions　for　the

judgement；　and　I　have　only　to　extract　the　predicate　from　the

conception；　according　to　the　principle　of　contradiction；　and　thereby

at　the　same　time　become　conscious　of　the　necessity　of　the　judgement；　a

necessity　which　I　could　never　learn　from　experience。　On　the　other

hand；　though　at　first　I　do　not　at　all　include　the　predicate　of

weight　in　my　conception　of　body　in　general；　that　conception　still

indicates　an　object　of　experience；　a　part　of　the　totality　of

experience；　to　which　I　can　still　add　other　parts；　and　this　I　do　when　I

recognize　by　observation　that　bodies　are　heavy。　I　can　cognize

beforehand　by　analysis　the　conception　of　body　through　the

characteristics　of　extension；　impenetrability；　shape；　etc。；　all

which　are　cogitated　in　this　conception。　But　now　I　extend　my　knowledge；

and　looking　back　on　experience　from　which　I　had　derived　this

conception　of　body；　I　find　weight　at　all　times　connected　with　the

above　characteristics；　and　therefore　I　synthetically　add　to　my

conceptions　this　as　a　predicate；　and　say；　〃All　bodies　are　heavy。〃　Thus

it　is　experience　upon　which　rests　the　possibility　of　the　synthesis

of　the　predicate　of　weight　with　the　conception　of　body；　because　both

conceptions；　although　the　one　is　not　contained　in　the　other；　still

belong　to　one　another　（only　contingently；　however）；　as　parts　of　a

whole；　namely；　of　experience；　which　is　itself　a　synthesis　of

intuitions。

　　But　to　synthetical　judgements　a　priori；　such　aid　is　entirely

wanting。　If　I　go　out　of　and　beyond　the　conception　A；　in　order　to

recognize　another　B　as　connected　with　it；　what　foundation　have　I　to

rest　on；　whereby　to　render　the　synthesis　possible？　I　have　here　no

longer　the　advantage　of　looking　out　in　the　sphere　of　experience　for

what　I　want。　Let　us　take；　for　example；　the　proposition；　〃Everything

that　happens　has　a　cause。〃　In　the　conception　of　〃something　that

happens；〃　I　indeed　think　an　existence　which　a　certain　time

antecedes；　and　from　this　I　can　derive　analytical　judgements。　But　the

conception　of　a　cause　lies　quite　out　of　the　above　conception；　and

indicates　something　entirely　different　from　〃that　which　happens；〃

and　is　consequently　not　contained　in　that　conception。　How　then　am　I

able　to　assert　concerning　the　general　conception…　〃that　which

happens〃…　something　entirely　different　from　that　conception；　and　to

recognize　the　conception　of　cause　although　not　contained　in　it；　yet　as

belonging　to　it；　and　even　necessarily？　what　is　here　the　unknown　=　X；

upon　which　the　understanding　rests　when　it　believes　it　has　found；

out　of　the　conception　A　a　foreign　predicate　B；　which　it　nevertheless

considers　to　be　connected　with　it？　It　cannot　be　experience；　because

the　principle　adduced　annexes　the　two　representations；　cause　and

effect；　to　the　representation　existence；　not　only　with　universality；

which　experience　cannot　give；　but　also　with　the　expression　of

necessity；　therefore　completely　a　priori　and　from　pure　conceptions。

Upon　such　synthetical；　that　is　augmentative　propositions；　depends

the　whole　aim　of　our　speculative　knowledge　a　priori；　for　although

analytical　judgements　are　indeed　highly　important　and　necessary；

they　are　so；　only　to　arrive　at　that　clearness　of　conceptions　which

is　requisite　for　a　sure　and　extended　synthesis；　and　this　alone　is　a

real　acquisition。



　　V。　In　all　Theoretical　Sciences　of　Reason；　Synthetical　Judgements

　　　　　〃a　priori〃　are　contained　as　Principles。



　　1。　Mathematical　judgements　are　always　synthetical。　Hitherto　this

fact；　though　incontestably　true　and　very　important　in　its

consequences；　seems　to　have　escaped　the　analysts　of　the　human　mind；

nay；　to　be　in　complete　opposition　to　all　their　conjectures。　For　as

it　was　found　that　mathematical　conclusions　all　proceed　according　to

the　principle　of　contradiction　（which　the　nature　of　every　apodeictic

certainty　requires）；　people　became　persuaded　that　the　fundamental

principles　of　the　science　also　were　recognized　and　admitted　in　the

same　way。　But　the　notion　is　fallacious；　for　although　a　synthetical

proposition　can　certainly　be　discerned　by　means　of　the　principle　of

contradiction；　this　is　possible　only　when　another　synthetical

proposition　precedes；　from　which　the　latter　is　deduced；　but　never　of

itself　which

　　Before　all；　be　it　observed；　that　proper　mathematical　propositions

are　always　judgements　a　priori；　and　not　empirical；　because　they

carry　along　with　them　the　conception　of　necessity；　which　cannot　be

given　by　experience。　If　this　be　demurred　to；　it　matters　not；　I　will

then　limit　my　assertion　to　pure　mathematics；　the　very　conception　of

which　implies　that　it　consists　of　knowledge　altogether　non…empirical

and　a　priori。

　　We　might；　indeed　at　first　suppose　that　the　proposition　7　＋　5　=　12　is

a　merely　analytical　proposition；　following　（according　to　the　principle

of　contradiction）　from　the　conception　of　a　sum　of　seven　and　five。

But　if　we　regard　it　more　narrowly；　we　find　that　our　conception　of

the　sum　of　seven　and　five　contains　nothing　more　than　the　uniting　of

both　sums　into　one；　whereby　it　cannot　at　all　be　cogitated　what　this

single　number　is　which　embraces　both。　The　conception　of　twelve　is　by

no　means　obtained　by　merely　cogitating　the　union　of　seven　and　five；

and　we　may　analyse　our　conception　of　such　a　possible　sum　as　long　as　we

will；　still　we　shall　never　discover　in　it　the　notion　of　twelve。　We

must　go　beyond　these　conceptions；　and　have　recourse　to　an　intuition

which　corresponds　to　one　of　the　two…　our　five　fingers；　for　example；　or

like　Segner　in　his　Arithmetic　five　points；　and　so　by　degrees；　add

the　units　contained　in　the　five　given　in　the　intuition；　to　the

conception　of　seven。　For　I　first　take　the　number　7；　and；　for　the

conception　of　5　calling　in　the　aid　of　the　fingers　of　my　hand　as

objects　of　intuition；　I　add　the　units；　which　I　before　took　together　to

make　up　the　number　5；　gradually　now　by　means　of　the　material　image

my　hand；　to　the　number　7；　and　by　this　process；　I　at　length　see　the

number　12　arise。　That　7　should　be　added　to　5；　I　have　certainly

cogitated　in　my　conception　of　a　sum　=　7　＋　5；　but　not　that　this　sum　was

equal　to　12。　Arithmetical　propositions　are　therefore　always

synthetical；　of　which　we　may　become　more　clearly　convinced　by　trying

large　numbers。　For　it　will　thus　become　quite　evident　that；　turn　and

twist　our　conceptions　as　we　may；　it　is　impossible；　without　having

recourse　to　intuition；　to　arrive　at　the　sum　total　or　product　by

means　of　the　m