¡¶the critique of pure reason¡·

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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

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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£º¡¡¡¨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£º¡¡¡¨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¡¡compare¡¡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¡¡complex¡¡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¡¡completely¡¡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¡¡which¡¡gives¡¡objective

reality¡¡to¡¡all¡¡our¡¡a¡¡priori¡¡cognitions¡£¡¡Now¡¡experience¡¡depends¡¡upon

the¡¡synthetical¡¡unity¡¡of¡¡phenomena£»¡¡that¡¡is£»¡¡upon¡¡a¡¡synthesis

according¡¡to¡¡conceptions¡¡of¡¡the¡¡object¡¡of¡¡phenomena¡¡in¡¡general£»¡¡a

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any¡¡connected¡¡text£»¡¡according¡¡to¡¡rules¡¡of¡¡a¡¡thoroughly¡¡united

£¨possible£©¡¡consciousness£»¡¡and¡¡therefore¡¡never¡¡subjected¡¡to¡¡the

transcendental¡¡and¡¡necessary¡¡unity¡¡of¡¡apperception¡£¡¡Experience¡¡has

therefore¡¡for¡¡a¡¡foundation£»¡¡a¡¡priori¡¡principles¡¡of¡¡its¡¡form£»¡¡that¡¡is

to¡¡say£»¡¡general¡¡rules¡¡of¡¡unity¡¡in¡¡the¡¡synthesis¡¡of¡¡phenomena£»¡¡the

objective¡¡reality¡¡of¡¡which¡¡rules£»¡¡as¡¡necessary¡¡conditions¡¡even¡¡of

the¡¡possibility¡¡of¡¡experience¡¡can¡¡which¡¡rules£»¡¡as¡¡necessary

conditions¡­¡¡even¡¡of¡¡the¡¡possibility¡¡of¡¡experience¡­¡¡can¡¡always¡¡be¡¡shown

in¡¡experience¡£¡¡But¡¡apart¡¡from¡¡this¡¡relation£»¡¡a¡¡priori¡¡synthetical

propositions¡¡are¡¡absolutely¡¡impossible£»¡¡because¡¡they¡¡have¡¡no¡¡third

term£»¡¡that¡¡is£»¡¡no¡¡pure¡¡object£»¡¡in¡¡which¡¡the¡¡synthetical¡¡unity¡¡can

exhibit¡¡the¡¡objective¡¡reality¡¡of¡¡its¡¡conceptions¡£

¡¡¡¡Although£»¡¡then£»¡¡respecting¡¡space£»¡¡or¡¡the¡¡forms¡¡which¡¡productive

imagination¡¡describes¡¡therein£»¡¡we¡¡do¡¡cognize¡¡much¡¡a¡¡priori¡¡in

synthetical¡¡judgements£»¡¡and¡¡are¡¡really¡¡in¡¡no¡¡need¡¡of¡¡experience¡¡for

this¡¡purpose£»¡¡such¡¡knowledge¡¡would¡¡nevertheless¡¡amount¡¡to¡¡nothing

but¡¡a¡¡busy¡¡trifling¡¡with¡¡a¡¡mere¡¡chimera£»¡¡were¡¡not¡¡space¡¡to¡¡be

considered¡¡as¡¡the¡¡condition¡¡of¡¡the¡¡phenomena¡¡which¡¡constitute¡¡the

material¡¡of¡¡external¡¡experience¡£¡¡Hence¡¡those¡¡pure¡¡synthetical

judgements¡¡do¡¡relate£»¡¡though¡¡but¡¡mediately£»¡¡to¡¡possible¡¡experience£»¡¡or

rather¡¡to¡¡the¡¡possibility¡¡of¡¡experience£»¡¡and¡¡upon¡¡that¡¡alone¡¡is

founded¡¡the¡¡objective¡¡validity¡¡of¡¡their¡¡synthesis¡£

¡¡¡¡While¡¡then£»¡¡on¡¡the¡¡one¡¡hand£»¡¡experience£»¡¡as¡¡empirical¡¡synthesis£»

is¡¡the¡¡only¡¡possible¡¡mode¡¡of¡¡cognition¡¡which¡¡gives¡¡reality¡¡to¡¡all

other¡¡synthesis£»¡¡on¡¡the¡¡other¡¡hand£»¡¡this¡¡latter¡¡synthesis£»¡¡as

cognition¡¡a¡¡priori£»¡¡possesses¡¡truth£»¡¡that¡¡is£»¡¡accordance¡¡with¡¡its

object£»¡¡only¡¡in¡¡so¡¡far¡¡as¡¡it¡¡contains¡¡nothing¡¡more¡¡than¡¡what¡¡is

necessary¡¡to¡¡the¡¡synthetical¡¡unity¡¡of¡¡experience¡£

¡¡¡¡Accordingly£»¡¡the¡¡supreme¡¡principle¡¡of¡¡all¡¡synthetical¡¡judgements¡¡is£º

¡¨Every¡¡object¡¡is¡¡subject¡¡to¡¡the¡¡necessary¡¡conditions¡¡of¡¡the

synthetical¡¡unity¡¡of¡¡the¡¡manifold¡¡of¡¡intuition¡¡in¡¡a¡¡possible

experience¡£¡¨

¡¡¡¡A¡¡priori¡¡synthetical¡¡judgements¡¡are¡¡possible¡¡when¡¡we¡¡apply¡¡the

formal¡¡conditions¡¡of¡¡the¡¡a¡¡priori¡¡intuition£»¡¡the¡¡synthesis¡¡of¡¡the

imagination£»¡¡and¡¡the¡¡necessary¡¡unity¡¡of¡¡that¡¡synthesis¡¡in¡¡a

transcendental¡¡apperception£»¡¡to¡¡a¡¡possible¡¡cognition¡¡of¡¡experience£»

and¡¡say£º¡¡¡¨The¡¡conditions¡¡of¡¡the¡¡possibility¡¡of¡¡experience¡¡in¡¡general

are¡¡at¡¡the¡¡same¡¡time¡¡conditions¡¡of¡¡the¡¡possibility¡¡of¡¡the¡¡objects¡¡of

experience£»¡¡and¡¡have£»¡¡for¡¡that¡¡reason£»¡¡objective¡¡validity¡¡in¡¡an¡¡a

priori¡¡synthetical¡¡judgement¡£¡¨



¡¡¡¡¡¡¡¡¡¡SECTION¡¡III¡£¡¡Systematic¡¡Representation¡¡of¡¡all¡¡Synthetical

¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Principles¡¡of¡¡the¡¡Pure¡¡Understanding¡£



¡¡¡¡That¡¡principles¡¡exist¡¡at¡¡all¡¡is¡¡to¡¡be¡¡ascribed¡¡solely¡¡to¡¡the¡¡pure

understanding£»¡¡which¡¡is¡¡not¡¡only¡¡the¡¡faculty¡¡of¡¡rules¡¡in¡¡regard¡¡to

that¡¡which¡¡happens£»¡¡but¡¡is¡¡even¡¡the¡¡source¡¡of¡¡principles¡¡according

to¡¡which¡¡everything¡¡that¡¡can¡¡be¡¡presented¡¡to¡¡us¡¡as¡¡an¡¡object¡¡is

necessarily¡¡subject¡¡to¡¡rules£»¡¡because¡¡without¡¡such¡¡rules¡¡we¡¡never

could¡¡attain¡¡to¡¡cognition¡¡of¡¡an¡¡object¡£¡¡Even¡¡the¡¡laws¡¡of¡¡nature£»¡¡if

they¡¡are¡¡contemplated¡¡as¡¡principles¡¡of¡¡the¡¡empirical¡¡use¡¡of¡¡the

understanding£»¡¡possess¡¡also¡¡a¡¡characteristic¡¡of¡¡necessity£»¡¡and¡¡we

may¡¡therefore¡¡at¡¡least¡¡expect¡¡them¡¡to¡¡be¡¡determined¡¡upon¡¡grounds¡¡which

are¡¡valid¡¡a¡¡priori¡¡and¡¡antecedent¡¡to¡¡all¡¡experience¡£¡¡But¡¡all¡¡laws¡¡of

nature£»¡¡without¡¡distinction£»¡¡are¡¡subject¡¡to¡¡higher¡¡principles¡¡of¡¡the

understanding£»¡¡inasmuch¡¡as¡¡the¡¡former¡¡are¡¡merely¡¡applications¡¡of¡¡the

latter¡¡to¡¡particular¡¡cases¡¡of¡¡experience¡£¡¡These¡¡higher¡¡principles

alone¡¡therefore¡¡give¡¡the¡¡conception£»¡¡which¡¡contains¡¡the¡¡necessary

condition£»¡¡and£»¡¡as¡¡it¡¡were£»¡¡the¡¡exponent¡¡of¡¡a¡¡rule£»¡¡experience£»¡¡on¡¡the

other¡¡hand£»¡¡gives¡¡the¡¡case¡¡which¡¡comes¡¡under¡¡the¡¡rule¡£

¡¡¡¡There¡¡is¡¡no¡¡danger¡¡of¡¡our¡¡mistaking¡¡merely¡¡empirical¡¡principles

for¡¡principles¡¡of¡¡the¡¡pure¡¡understanding£»¡¡or¡¡conversely£»¡¡for¡¡the

character¡¡of¡¡necessity£»¡¡according¡¡to¡¡conceptions¡¡which¡¡distinguish¡¡the

latter£»¡¡and¡¡the¡¡absence¡¡of¡¡this¡¡in¡¡every¡¡empirical¡¡proposition£»¡¡how

extensively¡¡valid¡¡soever¡¡it¡¡may¡¡be£»¡¡is¡¡a¡¡perfect¡¡safeguard¡¡against

confounding¡¡them¡£¡¡There¡¡are£»¡¡however£»¡¡pure¡¡principles¡¡a¡¡priori£»

which¡¡nevertheless¡¡I¡¡should¡¡not¡¡ascribe¡¡to¡¡the¡¡pure¡¡understanding¡­¡¡for

this¡¡reason£»¡¡that¡¡they¡¡are¡¡not¡¡derived¡¡from¡¡pure¡¡conceptions£»¡¡but

£¨although¡¡by¡¡the¡¡mediation¡¡of¡¡the¡¡understanding£©¡¡from¡¡pure¡¡intuitions¡£

But¡¡understanding¡¡is¡¡the¡¡faculty¡¡of¡¡conceptions¡£¡¡Such¡¡principles

mathematical¡¡science¡¡possesses£»¡¡but¡¡their¡¡application¡¡to¡¡experience£»

consequently¡¡their¡¡objective¡¡validity£»¡¡nay¡¡the¡¡possibility¡¡of¡¡such¡¡a

priori¡¡synthetical¡¡cognitions¡¡£¨the¡¡
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